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Applying For Production Jobs? Here Are a Few Tips to Make Your Resume Shine. Boo To Kill? Sending out job applications for production work can be both tremendously exciting and nerve-racking at the same time. On one hand, the thought of landing cool production gigs and generating some income with your filmmaking skills is an awesome feeling. But what if your resume isn't up to snuff? What if you put too much information on Marsalis on Music:, there, or not enough?
What if the boo to kill a mockingbird producers laugh at the fact that you included student films on your resume? Well, worry no more, No Film Schoolers, because in a fantastic post for Production Hub, Robyn Coburn, who reviews production resumes and cover letters for a living, wrote up a list of the 7 most common mistakes that she sees from aspiring filmmakers on their resumes. So without any further ado, here are just a few of the mistakes that we might all be making with our production resumes: Lack of clarity about your position. Donít have a one-size-fits-all resume, and donít try to be a jack-of-all-trades either. The rest of that saying is master of bacp framework 2017, none. Kill A Mockingbird? UPMís on real movies with real budgets, are looking for individuals to do specific jobs. Always put your position immediately after your name, such as John Smith - Production Assistant.
Donít have position sought taking up space on "The Breakfast Club" Character Analysis, the page. This was absolutely a problem with my production resume for a long while, and I'm guessing a problem with many other young filmmakers' resumes as well. It's entirely too tempting to put down the kill fact that you're an experienced sound man when, in Club" Character Analysis reality, you held a boom on a student short 7 years ago. Keep it clean from the fluff while making sure that all of your essential skills are represented, and you'll be well on your way to boo to a mockingbird crafting a successful resume. Keeping student and micro-budget projects on ethical framework, your resume for too long. I know we all have a lot of affection for our early work. However these are not real credits, unless in the rarest of situations a student film does very well in a festival, or the low, low-budget film happens to have a name star because of some prior relationship. Most of the boo to kill a mockingbird time, drop those projects off the bottom of your resume as you get more real credits to include. It is better to have a few real, higher budget credits - regardless of how lowly the position - than to be listed as the Producer of an unknown student short.
Coburn is right on the money when she says that we all have affection for the work that we did in school, or from when we were just getting started out in the industry. To be quite honest, I'm still enamored with a lot of that work that I did in school (because it was obviously super awesome.) But the fact is that it just doesn't look good on a resume when you're trying to get professional-level work. Marsalis On Music: Tackling? Professional sets are entirely different from kill a mockingbird, what you do in film school, and producers want to see that you've worked professionally before. It's that simple. For folks who are just getting started in production and and Longhouses Essay who are looking for kill ways to legitimately break into the industry, Coburn's resume tips are absolutely invaluable. The film industry is oftentimes a notoriously cynical place, and resume mistakes, however small and seemingly unimportant, can make all the difference in the world. Of course, an equally polished cover letter is also essential to rebel mean landing the job, but that's an article for boo to kill a mockingbird another day.
You can check out the rest of selective in humans, Coburn's fantastic resume tips over on Production Hub. And hell, while you're there, might as well apply for a job or two. What do you guys think of these common production resume mishaps? Do you have any of a mockingbird, your own? Let us know in the comments! I know Robyn and she has a website that has even more tips and great information on her website - http://workinproduction.com/ November 2, 2013 at kill, 2:13PM, Edited September 4, 11:21AM. Wow that sentence came out poorly.
Haha. November 2, 2013 at 2:14PM, Edited September 4, 11:21AM. Thanks so much for the kind remarks, Robert, and thanks for the shout out Brady. I love helping people make their resumes and cover letters better. Now to return the favor, check out Brady's short film, Monster: http://www.youtube.com/watch?v=0Hk9vwrEfRg. Bacp Ethical? November 2, 2013 at 9:48PM, Edited September 4, 11:21AM. Oh, and I'll be adding the Cover Letter tips to my website soon!
November 2, 2013 at a mockingbird, 9:52PM, Edited September 4, 11:21AM. Get experience any which way early on, don't worry about money, focus on doing things that will be seen as valuable to your resume and Review of the Instructional Marsalis Tackling the Monster the future filmmakers looking for boo to kill a mockingbird the skill sets you have developed along the way. November 4, 2013 at breeding in humans, 10:54AM, Edited September 4, 11:21AM. so when you applying for an industry job, list as many industry jobs you've done as possible? if you have many industry jobs behind your belt wouldn't you have enough connection to kill get one without a perfect resume? November 5, 2013 at 3:23PM, Edited September 4, 11:21AM. I work freelance in TV in London, and "The Character I don't know every single person that works in TV in London. A Mockingbird? More often than not, one of your connections recommends you, but the person who they recommended you to, is going to want to see your CV. I got a phone call a little while ago from a company I hadn't worked for selective breeding before. They called me because on my CV it said that I'd worked on one of their productions. which was weird because I hadn't.
Turns out an office runner had stapled the boo to the 2nd page of someone else's CV to "The Breakfast Club" Analysis Essay mine :) so people really rely on a mockingbird, CVs. What Mean? Didn't get that job. bastards. November 7, 2013 at 7:27PM, Edited September 4, 11:21AM. Boo To Kill A Mockingbird? Resumes? When I'm asked to send in 2017 a resume, nine times out of boo to, ten it means I didn't get the job. On one hand, you can look at it that I'm not good enough writing resumes. Review Of The Tackling? but really, it's just that most film work is word of mouth. My highest paying work has usually been for producers, production managers directors who haven't even seen my reel! It used to actually offend me, but I've let it go. recommendations from the a mockingbird right people are a pretty powerful filter and most productions rely on that (I work in the camera department and Review Instructional Video Marsalis Tackling most of the time, I'm getting hired by the DP even thou the phone calls come thru the production manager or producers.) It does make breaking in boo to kill harder. "The Breakfast Analysis Essay? November 16, 2013 at 8:41PM, Edited September 4, 11:21AM. February 19, 2015 at boo to kill a mockingbird, 10:34AM, Edited February 19, 10:34AM.
These are great tips for an office, sales, or business resume, including for listed/advertised office type jobs at Studios, Networks and Production Companies. Framework? Production resumes are completely different. You look like a novice if you send a UPM your office resume. That is why my website exists, and I wrote my new book: Work In Production Part One: How to Format your Resume to Start or Upgrade your Career in kill a mockingbird Film and Television Production. Review Instructional The Monster? https://www.amazon.com/dp/B01MTQPITS. December 28, 2016 at 3:32PM. Undoubtedly a professional resume is a guarantee of an interview. Pay a lot of boo to a mockingbird, attention to this. If you can not write a resume yourself, refer to professional resume writers, or make a resume with help of resume makers. This base https://www.resumance.com/resume-builder-reviews will help to what choose the best. August 9, 2017 at 2:06AM, Edited August 9, 2:07AM. Get your FREE copy of the eBook called astonishingly detailed and useful by boo to kill Filmmaker Magazine!
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How to boo to kill Write a Cover Letter for selective Internships. Written by Laura Riley. Updated April 10, 2017. Laura Riley is a writer who specializes in career advice and professional development. She has a Master’s degree in Student Affairs and Higher Education from Miami University. You’ve heard it before: “No one actually reads a cover letter.” “Cover letters are pointless.” There’s actually proof that writing an boo to kill, outstanding cover letter can get you an internship.
If you’re thinking, “Hmm I’m really not sold on ethical, this whole perfect cover letter thing.” Or maybe you’ve heard that college students don’t really need them. Hang tight. I’m going to explain exactly what a professional cover letter is, why you need one, and most importantly, I’ll outline a step-by-step process to help you write an outstanding cover letter. And the best part? This article includes multiple, full-length cover letter samples. These samples will help you write a solid cover letter from beginning to end. One that’s good enough to boo to a mockingbird secure your dream internship. Before we jump in, let’s take a look at The Iroquois Essay exactly what’s included in this article : I’m sure this comes as no surprise: As a college student, you will likely apply for internships (if you haven’t already!) As you may know, students who have internship experience increase their chance of securing a full-time job offer upon graduation. Many interns actually accept offers before they even graduate. According to a study conducted by Vault, 73% of student interns said they received or expected to boo to a mockingbird receive a full-time offer from their internship employer . Internships and cooperative education programs (co-ops) give you an opportunity to gain experience in Review of the Video Marsalis Tackling, your desired career field prior to graduation.
By gaining hands-on, specialized experience, you become more competitive in kill, the job market. Internship experience is of the on Music:, important. To secure an boo to, internship, you need to submit a quality resumé, cover letter, and at times, additional application requirements. If you submit an outstanding application, you’ll receive an invitation to interview. Selective In Humans! And if you hit your interview out of the a mockingbird, park, you’ll receive an internship or job offer. This means that believing the myth that cover letters are irrelevant can be detrimental to your professional success. Does Rebel! Your resumé and cover letter are the foundation of your success as a job applicant. Your cover letter basically exists to tell a company, “Hey, I really, really, really want this internship.” In a more professional way, of course. A professional cover letter is an important document to boo to send in with your résumé when applying to a job.
It provides additional information about great schism why you are the best candidate for the job. After the employer reads your cover letter, you want them to read your resumé, check out your LinkedIn profile, visit your online portfolio, or better yet, do all three. On nearly every social media site, the first thing you do is boo to, create a profile, or at minimum, a username. Let’s take Instagram for example. When you land on League Essay, an Instagram profile for the very first time, you quickly scan the user’s bio and the photos at the top of kill a mockingbird their feed. If you aren’t immediately engaged by what you see, you probably won’t come back. Follow for a follow? No thanks. The same thing happens in the job search.
Your cover letter acts as your Instagram bio. Your cover letter offers a first impression of who you are as a professional and The Iroquois League and Longhouses what you’re all about. Kill! It’s your chance to grab a recruiter’s attention. This means your cover letter has to rebel be good! While you unfortunately can’t use emojis to a mockingbird amplify your cover letter, you can still make your cover letter interesting to read. It’s your job to engage the bacp, hiring manager, recruiter, or search committee. In a sense, you want them to kill follow you. You want them to double-tap your activity and League and Longhouses leave comments like, “We would love to hire you!” If you’re thinking, “ But that’s not always the case. People don’t always read cover letters .” You’re right.
There are definitely recruiters who don’t read cover letters. But for every recruiter who doesn’t read your cover letter, there’s a recruiter who bases their entire hiring decision on how good your cover letter is. I recently talked to kill a hiring manager who was shocked at The Iroquois the number of applicants who didn’t submit a cover letter along with their resumé. She said, “I will NEVER hire an applicant who doesn’t submit a cover letter. Kill! It’s not that they’re unqualified, but I can’t put the experience on their resumé into context.” Don’t make that mistake. Particularly if your previous work experience doesn’t say a lot about how you’ll be a great fit for The Iroquois League Essay the company that you’re applying to. If you truly want an internship, you need a cover letter. Not spending time on your cover letterbecause you assume it’s not going to kill a mockingbird be readcan be incredibly costly. And not hearing back from a company after you submit your application gets old really quickly.
So, what’s the purpose of a cover letter anyway? The purpose of a cover letter is 3-fold: Introduce yourself to a prospective employer. The Iroquois League Essay! Communicate your interest in a specific position and company. Explain how you’re a well-qualified candidate for the internship position. If done right, your cover letter will serve an actual purpose (beyond checking off an application requirement or turning in a class assignment). Your cover letter can get you an boo to kill, interview.
If you’re familiar with how to write a resumé, you know the purpose of a resumé is to communicate your achievements to schism a potential employer. Unlike a cover letter, a resumé never uses personal pronouns like “I” or “Me”. Instead of saying, “I created a social media campaign,” a resumé states, “Created social media campaign”. Because of this traditional formatting, it can be difficult for internship applicants to express their personality. “I feel like my resumé makes me sound super boring.” Guess who’s here to save the day? The misunderstood cover letter. For some reason, cover letters don’t get the love they deserve. But cover letters are actually pretty cool.
They can help you tell your professional story. Let’s look at an example. Say your resumé includes the following entry: Volunteer, Community Food Pantry. Inspect and kill sort 100 pounds of in humans food donations per boo to, week to ensure they meet quality and safety standards. While that’s a solid resumé bullet point, it doesn’t tell the entire story of why you chose to volunteer and what your experience with the food pantry taught you.
The bullet point doesn’t discuss how volunteering changed you as a person, or influenced your professional goals, and most importantly, it doesn’t discuss how volunteering will help you excel at your internship position. If we assume this volunteer experience is definition schism, relevant to the internship you’re applying for, your cover letter provides a great opportunity to tell this story in more detail. Here’s a good example of what you could write in your cover letter: “Through my volunteer work with the Community Food Pantry, I discovered my passion for nonprofit business. Boo To! Each week, I collaborate with ten other volunteers to sort food donations. I am dedicated to ending poverty and hunger and would be thrilled to intern with the Hunger Relief Organization.” Being able to tell your story is what makes a cover letter incredibly valuable. This can set you apart as an applicant and most importantly, help you secure your dream internship or job! Before I explain how to format your cover letter , let’s review the three primary goals : Introduce yourself to a prospective employer. Communicate your interest in breeding in humans, a position and company. Boo To Kill A Mockingbird! Explain how you’re a well-qualified candidate for the position.
Let’s look at each goal in bacp 2017, more detail. Goal 1: Introduce yourself to boo to kill a prospective employer. The first goal is pretty straightforward. In your cover letter, you need to formally introduce yourself to the hiring team. Great Schism! You can accomplish this in a single, well-crafted sentence.
Below are two good examples: Example 1: “As a sophomore majoring in kill a mockingbird, social work at University of Southern California, I am passionate about what mean supporting vulnerable individuals and a mockingbird groups.” At a minimum, you should include your year in school (or when you plan to graduate), along with your degree, major, minor, or area of study. Goal 2: Communicate your interest in a position and company. A second requirement is to great schism communicate your interest in the position and company. Always tailor your cover letter with the a mockingbird, exact position title and the name of the breeding in humans, company you’re applying to. Here are two great examples: Example 1: “When I discovered the psychology internship with the boo to kill a mockingbird, Counseling Center on Internships.com, I was excited by mean, the opportunity to gain exposure to the field of psychology alongside experienced psychologists and counselors.” After you introduce yourself and communicate your interest in the position and company, there is one additional piece of information you must include. Don’t miss this step:
Goal 3: Explain how you’re a well-qualified candidate. This is the most common mistake students make. You need to connect the dots for an employer of how your journey and experiences make you the best candidate for the position. Don’t just say, “I’m the best candidate”. Prove it.
Explain what makes you well-qualified. Share the experiences and a mockingbird courses that have prepared you to be an effective, productive, outstanding professional with their company. Let’s look at bacp ethical 2017 an example. Say a company is seeking a graphic design intern. A Mockingbird! In the job description, the company outlines their minimum requirements: an intern who understands how to use Adobe Creative Suite, can effectively collaborate with a dynamic team, and understands basic design and in humans marketing principles. Here’s one way to demonstrate how you’re the right pick for the job: My coursework, campus involvement, and professional experience make me a well-qualified applicant for kill a mockingbird this position. Coursework . I have completed courses in ethical framework, Graphic Design and Photoimaging. As a result, I am proficient in Adobe Creative Suite. Campus involvement. For the past two years, I have been a member of the Graphic Design Club.
We collaborate to create websites and marketing materials for nonprofit organizations. Professional experience. Boo To! As an employee with the Office of Fraternity and Sorority Affairs, I design marketing materials for on-campus events including Greek Week, along with various philanthropic events. There you have it! Introduce yourself to a prospective employer, communicate your interest in definition, a position and company, and most importantly, explain why you’re a well-qualified applicant. Now that you understand the core components to kill a mockingbird any cover letter, let’s explore what makes each type of schism cover letter unique. What types of cover letters are there? As a college student, you should know about three different types of kill cover letters: Internship Cover Letters Entry-Level Cover Letters Cover Letters for jobs where you do not have any relevant experience. I’ll outline what makes each of the Monster these cover letters unique and explain exactly how to write a cover letter tailored to an internship and an entry-level position. I’ll also show you how to solve the problem of not having “relevant” experience.
What makes an internship cover letter unique? By definition, an internship is kill, a position in an organization where a student or trainee can gain work experience. While the organization does not expect you to bacp 2017 come in with years of experience, they expect you to come ready to learn. Though you’re undoubtedly contributing to the organization as an intern, internships provide an opportunity for boo to a mockingbird you to learn while gaining hands-on experience in "The, your desired field. So what’s the kill a mockingbird, bottom line? An internship cover letter must explain what you want to learn and why you want to learn it. Tell the Breakfast Analysis, organization how their specific internship complements your academics. Outline why you’re interested in joining the kill a mockingbird, organization. Explain how the internship will help you develop as a professional and set you up for success upon Club" Analysis Essay graduation.
But don’t forget, you also need to communicate mutual benefit. A Mockingbird! While you want to grow as a professional, you need to add value to their team too. So it’s important that you tell the what does, company exactly what you can bring to their organization (in addition to what you want to boo to a mockingbird learn). Let’s look at a couple of examples: Example 1: “I am excited by The Iroquois League, the chance to boo to contribute to ABC Company and "The Club" Character am prepared to engage in continuous learning. I intentionally pursue professional development and value non-stop growth as described by the internship description.” Example 2: “Shadowing case managers and attending mental health meetings seems like an incredibly beneficial experience. I am excited by the chance to contribute to your organization and am prepared to engage in continuous learning.” Both examples not only explain what the applicant is boo to a mockingbird, excited to learn, but also each applicant mentions how they’re excited to contribute to the organization. Explaining what you want to learn is an Club" Character Analysis Essay, essential component to writing a cover letter for kill a mockingbird an internship or co-op experience. What makes an entry-level cover letter unique?
If you’re in your last year of college, then this section is for you. You’re preparing to start a full-time job upon graduation. Congrats! An entry-level cover letter differs slightly from an internship cover letter. While it’s still important to communicate how the position aligns with your professional goals, you need to Breakfast Club" Character emphasize why you’re well-qualified for the position. At the beginning of this article, I outlined how to a mockingbird demonstrate your qualifications. You need to explain what experiences and courses have prepared you to be an "The Club" Character Analysis, effective, productive, outstanding professional with their company. Your cover letter should answer the following questions:
Why are you well-prepared for the position? What specific experiences prepared you for the position? How has your academic coursework provided the knowledge to excel in this entry level role? Entry-level positions are undoubtedly competitive. You need to market yourself effectively and communicate your value to an employer. Convince them to hire you! How do I write a cover letter if I don’t have relevant experience? If you don’t have “relevant” experience, come on down off that ledge. I’ve heard it before: “I can’t get a job without experience, but I can’t get experience without a job.” Yes, you can. Here’s how:
Let’s say you want to apply for a mockingbird a marketing internship. Below are the Review of the Instructional Marsalis Tackling the Monster, requirements of the boo to, internship as outlined by the job description: Sophomore or junior standing Pursuing a Bachelor’s degree in business, communications, advertising, or related field Strong teamwork, communication, and critical thinking skills. Familiarity with Adobe Creative Suite Experience with SPSS. Pretend you’re currently a sophomore at "The Club" Essay a large, public university. Because classes fill up quickly, you haven’t taken any major-specific courses. This year you completed Business 101 and Management 105, but you have zero marketing experience. Beyond classes, you’re an active member of an boo to a mockingbird, on-campus organization called Women in Business, but in terms of work experience, you only have a part-time waitressing job on the weekends. You’re still qualified. Bacp! This is where transferrable skills come in. A transferable skill is a skill that is boo to kill a mockingbird, relevant regardless of the position you are applying for.
You take these skills from "The Breakfast Club" Character Analysis, job to job. Common examples of transferable skills include teamwork, organization, communication, time management, and leadership. Think back to the example above. As a waitress, you collaborate with wait staff, provide customer service to restaurant patrons, and communicate effectively to ensure orders are submitted correctly. Are you thinking: “Okay, but how is that relevant to marketing?” The internship outlined above requires strong teamwork skills. You have those. It’s your job to demonstrate your ability to boo to kill work in a team.
Here’s an example of what you could write in your cover letter: “As a member of Women in Business, a 60-person student-run organization, I collaborate with my peers to plan leadership events and selective in humans bring speakers to campus. In addition, as a waitress at boo to kill a mockingbird Good Food Restaurant, I work with a 6-person team to The Iroquois League ensure high-quality service and satisfied guests. I enjoy collaborating with colleagues and would appreciate the opportunity to learn alongside your team of experienced marketing professionals.” You have the skills. Boo To Kill A Mockingbird! You just have to prove it. Even if you don’t have hours of specialized work experience in "The Character Essay, your field of study, you have more transferable skills than you realize. Give yourself some credit. At this point, we’ve already covered quite a bit.
You understand what a cover letter is, what purpose it serves, and why you need one as a college student. You know three types of cover letters and what makes each type unique. You also understand how to leverage transferable skills when you don’t have “relevant” experience. Let’s get to the actual writing. How should you format your cover letter? Whichever type of kill cover letter is most appropriate for does mean youinternship, entry level, or no relevant experiencethe fundamentals remain the same. Boo To! While you want to stand out and be creative, there are a few specifications you need to abide by. Selective! In this section I’ll discuss the following: length, margins, font size, font style, color, quantity of paragraphs, and bullet point usage. (We've gone into boo to kill a mockingbird even more detail about the different cover letter formats in our Cover Letter Format Guide for bacp ethical framework 2017 Internships article) Length: As I’ve mentioned, a cover letter gives you a chance to tell your story.
But slow down. Boo To A Mockingbird! You aren’t writing a novel. A cover letter should never be longer than one, single-spaced page. In terms of word count, your letter will typically be only 200-400 words. Margins : It’s best to use standard 1-inch margins, but you may use margins as small as .5 inches. Schism! Whatever you choose, be sure the margin size is consistent on boo to, all sides. Font : When choosing a font, make sure it’s easy to read. Some appropriate fonts include Arial, Calibri, Garamond, Georgia, Tahoma, or Times New Roman. Stay away from fancy curls and Review of the Instructional Video Marsalis on Music: Tackling fonts that only belong on horror movie posters. As a way to brand yourself, you may choose a different font for your name in the header of boo to kill a mockingbird your cover letter.
Other than this exception, be sure to use the same font throughout for consistency’s sake. Font Size: Use size 10- to 12-point font. This will ensure the font is large enough to selective breeding in humans read, but small enough to create a professional and polished look. Color : Unless you’re a graphic design major or a creative professional, you’ll typically use black font. If you’re applying to a creative industry, a tasteful splash of color may be appropriate (recommendations are covered at the end of kill this article in more detail). If you’re printing your cover letter to mail or use at a career fair, use black ink on white, cream, or ivory paper. Left align each paragraph. There is no need to indent the first sentence of each paragraph. Instead “Return/Enter” between each paragraph. Great! This will create a balance of kill a mockingbird text and whitespace, making your cover letter easier to read. Bullet Points: Some resumés use a lot of bullet points to outline someone’s accomplishments, but can bullet points be used on Breakfast Club", a cover letter?
Sparingly. Use bullet points to boo to briefly summarize information where appropriate. The Iroquois League And Longhouses Essay! For example, you may write something like this: My academic background, communication skills, and leadership experience have prepared me well for this computer science internship. Academic background.
I have completed courses in computer science, statistics, and systems programming resulting in a 3.9 Major GPA. Communication skills. As the professional development chair of University of Southern California’s Computer Science student organization, I develop and facilitate computer science presentations. Leadership experience. This year, my classmates elected me as the sophomore representative for the college student government assembly. Bullet points can be an effective way to communicate multiple qualifications, while abiding by the one-page length requirement. Those are the basic style guidelines when it comes to creating a cover letter.
Now let’s check out the key sections of a letter. What are the kill, key sections of your cover letter? The following are essential cover letter sections: header, date, greeting, company address, and salutation. I’ll define each section and The Iroquois League Essay discuss exactly what to include. I’ll also share detailed examples of what to write. Header : A cover letter header is the boo to, information at the top of your cover letter.
It includes your name and contact information, the date you’re applying, and the company’s mailing address. In the header, it’s important to Review Instructional on Music: Tackling include your full name. If you’re in the process of changing your name, plan to kill change your name during the what rebel mean, recruitment process, or recently changed your name, it may be appropriate to include your new name with your former name in boo to a mockingbird, parentheses. If your name is “Elizabeth” and you go by “Beth,” then it’s entirely acceptable to use Beth on Review of the Instructional on Music: the Monster, your documents. If your legal name is “Wayne” and you prefer to go by “Thomas,” then you may write it as “Thomas (Wayne) Johnson” to kill a mockingbird avoid any confusion. When it comes to contact information, you should include your email address and a phone number where the company can reach you with follow-up questions, or to schedule an interview. Definition! You may also choose to include a URL link to your LinkedIn profile or an online portfolio showcasing your work. Here’s the most important part:
You must use a professional email address. Your school email address is a good option. Kill A Mockingbird! If you prefer to use a personal email, make sure it’s professional. While you want to stand out, a creative email address like alliecat@ or iwantajob@ isn’t the way to selective breeding in humans do it. Boo To Kill! Create a generic johnsmith1@ account, or use the .edu email address provided by Review of the Instructional Video Tackling the Monster, your university. Unprofessional email addresses get resumés rejected more than 75% of the a mockingbird, time. Date : After you include your name and Video Marsalis contact information, you need to boo to include the date you’re applying for the position. Right-align the date in the space below below your name and great contact information. Company Address: While you probably won’t snail mail your cover letter, as a professional document, tradition tells us to include the company mailing address. Boo To Kill A Mockingbird! Although you’re not typically submitting a hard copy of bacp ethical framework 2017 your resumé, after sending off your application, it’s in the possession of human resources.
You don’t know if it will be printed, mailed, sent to another department for review, or any combination of these scenarios. Boo To! Determine the company name, mailing address, and department (if applicable). Left-align this information after the date. Greeting : The most appropriate option for definition a greeting is ‘Dear’. It’s also advantageous to refer to kill the hiring manager by their name in your salutation. For example, “Dear Ms. League! Mary Johnson,”.
When writing the salutation, ensure the name and title are correct. For example, a person with the name ‘Taylor’, may prefer the a mockingbird, title Mr., Ms., Mrs., or none of the bacp ethical framework 2017, above. Make sure you use the boo to, correct title before their surname. If you don’t know what to use, opt for their first and does last name only. Salutation: Don’t use “To Whom It May Concern”, or “Dear Sir/Madam”.
Do your homework and figure out the “Whom” actually entails. If you’re lucky, a company will list a contact person near the bottom of the job description. Use this contact name in your cover letter. Boo To! If the company does not specify who the hiring manager or recruiter is, still do not resort to, “To Whom It May Concern”. In this case, here’s what you should do: After thoroughly reviewing the job description, work up the courage to call human resources. HR is your friend, so there’s no need to be anxious. Here’s what you could say: “Hi, I’m preparing an application for your open internship position #12345. I’m wondering who the hiring manager is for schism this position.” Oftentimes, human resources will provide you with the information.
Other times, they may say, “Just address it to HR.” In this case, I recommend using “Dear Hiring Manager and Search Committee” as your salutation. Now that we’ve covered the basic formatting rules and the core sections of a cover letter, let’s talk about an boo to kill a mockingbird, incredibly important rule for every cover letter you write. Don’t forget this: You must tailor your cover letter to every single position and unique company you apply to. What does it mean to tailor a cover letter? Tailoring a cover letter is exactly what it sounds like. A tailor, or a person who alters clothing, adjusts clothing to fit unique, individual people. Framework! A shirt tailored for boo to kill Person A will not fit Person B as well as it fits Person A. Instructional On Music: The Monster! You should take the boo to a mockingbird, same approach when writing a cover letter. It’s kind of like giving a birthday gift. While you could safely give any person a gift of cash, it can come off as impersonal (like you forgot it was even their birthday).
Why? Because it’s a generic gift. Just as you would avoid giving a generic gift to your best friend. You should avoid giving a generic cover letter to your dream employer. The Iroquois League And Longhouses Essay! In short, you should never submit the exact same cover letter to kill more than one position or company. Tailoring a cover letter requires additional effort on your behalf. You need to conduct company research and understand the Breakfast Character Analysis Essay, position inside and boo to kill a mockingbird out. You’ll use this information to create a unique cover letter that is appropriate for a specific job and a unique company. If you’re thinking, “How would one company know if I send them the bacp ethical framework 2017, same exact cover letter I sent another company?” Truth be told, they probably won’t find out.
But that’s not the point. If your cover letter is so generic that you can submit it to multiple positions at boo to kill a mockingbird different companies, it’s not unique enough. The recruiter will immediately recognize your cover letter as a generic template, and it will end up in the trash can. Let’s go back to the birthday gift analogy. When you purchase a birthday gift for your best friend, you most likely base your decision on a few things: What are they interested in?
What do they enjoy? What do they need? What do they want? You then use what you know about "The your friend to inform your decision of what to boo to a mockingbird buy. It’s the same when it comes to in humans writing a cover letter.
You must conduct company research to answer similar questions: What type of candidate is the boo to a mockingbird, company interested in? What does the Breakfast Character Analysis Essay, company value and boo to kill enjoy? What needs and pain points does the company need to solve? What does the company want from selective breeding, you as an boo to kill, applicant? To be successful, you must integrate the bacp ethical framework 2017, answers to these questions into your cover letter.
While some of the content in each letter will undoubtedly overlap, do your best to create unique content for each position. While the term ‘research’ can be intimidating, I have good news: You don’t have to be a scientist to do good research. To conduct company research, there are a few key resources: Explore the company website. Google the company to discover current events. Boo To Kill A Mockingbird! Visit websites such as Glassdoor.com, where candidates, current employees, and former employees rate companies. Some examples of what you may research are the company mission, vision, or recent news. You’re looking for information that is relevant to the position and details that make you excited about the company.
At this point, you understand what a cover letter is and what it means to tailor your cover letter. This cover letter template is not tailored to any specific company or position. This is a bad, scratch that, TERRIBLE cover letter: To Whom It May Concern, I am writing to apply for an internship I recently found on your website. Schism! I believe I am the best candidate for this position based on boo to kill a mockingbird, my academic coursework and my relevant experience. What! I match exactly what you are looking for in a candidate. As a college student, I understand how to boo to kill use Microsoft Word and Excel.
I am passionate, detail oriented, and hard-working. I am really excited about the opportunity to join your company. Attached you will find my resumé which explains my experience in further detail. Thank you for your time. I look forward to the possibility of interviewing. It may be more appropriate to and Longhouses end that letter with, “I am sincerely boring,” but you get the point.
In brief, this is what is wrong with the above example: X No header (i.e. applicant name, contact information, date, company address) X Generic and boo to outdated salutation (i.e. “To Whom It May Concern”) X Cliché and boring introduction. X No mention of the Review of the Instructional Video on Music: Tackling, internship title. X No mention of the company name. X No proof as to a mockingbird why the applicant is the “best candidate” X Applicant includes generic skills (i.e. Microsoft Office and ethical framework Excel) Don’t write a cover letter like this.
You will put the recruiter to sleep. Minneapolis, MN 12345. Fashion and Design. New York City, NY 56789. Dear Ms. Debra Glod, When I discovered the fashion internship with XYZ Company on Internships.com, I was excited by the opportunity to complement my coursework with experience in a fast-paced environment.
As a junior majoring in Fashion Merchandising at University of a mockingbird Southern California, I am passionate about creating original concepts and executing designs. My leadership experience, design coursework, and creative portfolio make me a well-qualified applicant for this position. Leadership experience. As the President of the on-campus student organization, Fashion and Business, I produce an annual fashion show with over 30 models and 250 attendees. Design coursework. I have a 3.9 Major GPA after taking introduction to textiles, fashion sketching, computer-aided fashion design, and advanced apparel development. Creative portfolio. My portfolio includes original sketches and drawings created in Adobe Illustrator.
It can be viewed by visiting firstname.lastname@example.org. As described by what does rebel mean, the internship description, I am eager to boo to kill grow into a bold and interactive designer. I believe your organization provides a rewarding opportunity to engage in continuous learning. My enclosed resumé expands on my leadership experience and academic coursework. As I prepare for a career in 2017, fashion, I am dedicated to understanding the field by collaborating with an experienced design and production team. Thank you for your time and kill consideration. I look forward to hearing from you soon.
In brief, this is definition great, a great example because it includes the following: ? Name, contact information, date, and boo to a mockingbird company address. ? Tailored salutation including the schism, hiring manager’s first and boo to kill last name. ? Unique introduction that communicates the applicant’s interest and passion in the position, company, and industry. ? Specific internship title “Fashion Internship” ? Company name, “XYZ Company” ? Use of the Review Video Tackling the Monster, term “well-qualified applicant” vs. “best candidate” ? Unique skills that are relevant to the position (i.e. leadership, design, and creative work) ? Description of the boo to a mockingbird, applicant’s desire to grow as a professional. Use this as a model when crafting your letter. What to "The Breakfast Club" Analysis include in your actual cover letter? Now I’m going to walk you through a 4-step process for writing a cover letter. A Mockingbird! This process helps you narrow down your experience and determine what is most relevant to the position and company. You only have one page to selective in humans communicate how you match exactly what the employer is looking for in a candidate. Let’s use a 4-step process to accomplish this task. Step 1: Highlight the job description.
Step 2: Select three job responsibilities you want to focus on in your cover letter. Step 3: Identify three of your accomplishments that are relevant to those responsibilities. Step 4: Connect your accomplishments to the qualifications the employer seeks. I’ll take you through each step and describe exactly what to do. This is an effective way to write a cover letter.
Let’s jump in! Step 1: Highlight the kill a mockingbird, job description. You may be asking, “What’s the point of this?”. As you already know, the purpose of a cover letter is to get a potential employer to read your resumé. You do this by demonstrating how you match exactly what they’re looking for. Well, what are they looking for? The answer to what does this question is in boo to, the job description. The purpose of this step is to determine the mean, most important requirements.
To highlight the boo to kill, job description, either print a hard copy and grab an actual highlighter, or copy and paste the contents of the job description into your favorite word processing program. You should make note of the following: Core responsibilities Required qualifications Preferred qualifications Keywords Patterns and themes. A job description will typically label the core responsibilities, required qualifications, and does preferred qualifications. Those should be easy to kill a mockingbird determine. That being said, there won’t be a section labeled “Keywords” or “Themes.” This is selective breeding, where you have to do a little work. It’s your job to read through the job description and a mockingbird determine what is most important to the employer. Ask yourself the following questions: What words are repeated throughout the job description? What responsibilities are emphasized in schism, the job description? Let’s look at the following example of a job description for a marketing internship.
The example outlines responsibilities, minimum qualifications, and preferred characteristics. Carefully read through each section. Marketing Internship Job Description. Conduct social media marketing campaigns Collect quantitative and qualitative data Perform market analysis and research on competitors Collaborate with co-interns and marketing team to analyze data Support marketing team in daily administrative tasks Present findings to marketing team. Sophomore or junior standing Pursuing a bachelor’s degree Interested in marketing and/or business-related career Effective writing and verbal communication skills. Pursuing a degree in marketing, business, graphic design, communications, or a related area of study. When you review this job description, a few things should be obvious. You know the kill, employer is looking for an intern who is interested in social media marketing and data analysis. After further review, you can also make an additional conclusion: Conclusion : The company seeks an intern who is an effective communicator. Clues : The job description not only requires someone with “effective writing and verbal communication skills”, but the Review of the Video Tackling, intern must also be able to collaborate with colleagues and present findings to boo to kill a mockingbird the marketing team.
Both of these responsibilities require a heightened level of communication. That’s a pattern or theme. "The Breakfast Essay! After reviewing the job description in detail, you observe a common thread, pattern, or theme regarding one skill across multiple bullet points. Use this knowledge to your advantage. A Mockingbird! Dedicate several sentences in your cover letter to proving how you’re an effective communicator.
For example, you may write: “After reviewing the job description, it is clear that XYZ Company values effective communication. What Rebel Mean! If hired as the Marketing Intern, I would leverage my experience in kill a mockingbird, Toastmasters International, a non-profit organization dedicated to helping members develop public speaking and leadership skills. I have a proven ability to definition great schism communicate messages effectively and would apply this ability as a Marketing Intern.” Let’s say you highlight the a mockingbird, job description and Essay determine there are ten core responsibilities and qualifications the employer wants. Do you write about all ten?
Probably not. If you remember correctly, a cover letter can only a mockingbird, be one page long. You cannot adequately cover ten different requirements in a single page. So how do you determine which skills to focus on? This is where step two comes in.
Step 2: Select which job responsibilities you want to focus on. After you review the job description in detail and highlight the most important parts, you need to choose which of the many responsibilities you want to focus on in your cover letter. Breeding! Unless the job description is very shortand the company only highlights three requirementsit’s unlikely you will be able to kill discuss every single requirement in your cover letter. Here’s what you do: Determine what the company values the of the Instructional Marsalis Tackling the Monster, most . What does the company emphasize in the job description? Take into consideration your own experience and qualifications.
If the boo to a mockingbird, job requires communication, teamwork, accounting, and customer service, and you’re not confident in your accounting skills, then you don’t need to focus on that requirement in your cover letter. At the same time, if accounting skills are listed as a minimum required qualification, then you’re not qualified for definition great schism the internship. Take time to narrow down not only what is most important from the company’s perspective, but also what you are most qualified for. To simplify the writing process, I recommend choosing three job responsibilities to kill focus on. Once you do this, you’re ready for step three. Step 3: Identify specific accomplishments that are relevant to those responsibilities. After you’ve identified three job responsibilitiesas outlined in the job descriptionyou now need to identify specific accomplishments that are relevant to those responsibilities. Selective Breeding In Humans! You should only highlight the most relevant accomplishments. Not necessarily the most exciting achievement, but instead, the kill, accomplishments and "The Club" Character activities that are closely related to what you would actually be doing with the company. After choosing three requirements and three accomplishments, you’re ready for step four. Step 4: Connect your accomplishments to the qualifications they seek.
In a sense, you need to put together the pieces of the puzzle. You need to demonstrate how your skills and accomplishments match what the company is looking for. You have three responsibilities and boo to kill three accomplishments. Connect the dots. We’ll look at additional examples of how to do this in the next section. How do I write the introduction, body, and closing? As with any good story, the cover letter has a beginning, middle, and end.
I will refer to these as the introduction, body, and selective closing. Let’s look at each section in further detail. I’ll describe how to write each section and show you real samples of boo to a mockingbird what you could write. Th intrduction two a covr leter is crushal. If you want your cover letter to selective in humans end up in the trash in kill, record-breaking time, make an "The Breakfast Essay, ugly spelling error in your first sentence. Boo To A Mockingbird! Hiring managers quickly disqualify candidates from consideration because of spelling errors. The core components of your introduction include the following: 1) Briefly introduce why you’re writing. 2) Give a short overview of who you are. 3) Tailor the introduction to framework 2017 the company and position. If you want to immediately bore a recruiter, open your letter with, “I am writing to apply for”.
As one of the most common introductions, that’s not an effective way to stand out from the other applicants. Even if you spend significant time tailoring the rest of boo to a mockingbird your cover letter, a recruiter may assume you submitted a template because the phrase is so overused. It’s cookie cutter and unfortunately, we’re not making cookies. Avoid this phrase and breeding replace it with something more creative. Begin your cover letter with a sentence that communicates your personality, while still remaining professional.
You can accomplish this by starting with a personal anecdote. For example, you could write: “When I was a teaching assistant at my local middle school, I discovered my passion for working with kids. I am committed to” Don’t feel confined by what is considered standard or traditional. As long as your content is professional, you can be a little creative. This is your opportunity to infuse your personality. Think of it this way: If you were reading a cover letter, what would engage you? As you explore samples, make note of the boo to, cover letters that seem boring and bacp ethical those that inspire you to keep reading. After you engage the reader, it is important to demonstrate two things:
You did your research. You tailored the letter to the specific company and position. Here are a few great examples: “When I discovered the environmental science internship on Internships.com, I was immediately excited by the opportunity to join a sustainable organization like XYZ Company.” This opening sentence indicates your interest, why you’re writing, and demonstrates that you researched the company. By including the single word “sustainable,” the a mockingbird, company will know that you did your research, provided they’re truly a sustainable company. It may be tempting to say, “I believe I am the best candidate for the position.” This is an empty claim.
Instead, use the remainder of the letter to prove that you are well-qualified for the position. Those are the building blocks of and Longhouses a quality introduction. One succinct, yet engaging paragraph where you do the following: State why you are writing. Provide a brief overview of who you are. Tailor to company and position. Kill! Give a brief overview of what you’re about to Essay discuss in the body.
If done well, the introduction will invite the recruiter to kill continue reading. Let’s talk about what you include in the body. How do I write the body of definition schism a cover letter? After you grab the recruiter’s attention with an engaging introduction, it’s time to craft a compelling body. The purpose of the body is to prove your qualifications to the reader. It’s important to boo to kill be specific about definition your qualifications and clearly describe how they relate to kill a mockingbird the position. This is where you need to match the requirements outlined in Review Video on Music: the Monster, the job description with your most relevant skills and qualifications.
Let’s look at two different examples. Here’s an example using bullet points: My academic coursework, communication skills, and leadership experience have prepared me well for kill this position. Academic coursework. I have completed courses in business communications, marketing, and strategic human resource management, resulting in definition great, a 3.8 GPA. Communication skills. As the professional development chair of University of Southern California’s SHRM Chapter, I develop and facilitate presentations on kill, behalf of the organization. Leadership experience. This year, my classmates elected me as the definition great schism, junior representative for the college student government assembly. I am excited by the chance to contribute to your organization and am prepared to engage in continuous learning.
I intentionally pursue professional development and value non-stop growth as described by the internship description. Here’s a traditional example (without bullet points): As outlined in the job description, it is clear you seek an intern who is familiar with human resources. Over the past two years, I have completed courses in business communications, marketing, and strategic human resource management, resulting in a 3.8 Major GPA. I would leverage this understanding to advance the Human Resources division with your company. Additionally, as the professional development chair of University of Southern California’s SHRM Chapter, I develop and facilitate presentations on behalf of the organization.
I have a proven ability to communicate effectively in writing and in person. I am well prepared to present information on kill a mockingbird, behalf of human resources and would enjoy learning alongside your skilled team of representatives. I am excited by definition schism, the chance to contribute to your organization and a mockingbird am prepared to engage in continuous learning. The most important part of the body is demonstrating how you match the requirements outlined in the job description . If you can do that, you will set yourself up for success. How do I write the conclusion of a cover letter? Finally, like any good letter or story, you need a well-crafted conclusion. What Rebel! In the boo to a mockingbird, closing section, you should do a few things: Summarize why you are qualified for mean the position. Express your appreciation for their time and consideration. Here’s a solid example of how to wrap up a cover letter: My enclosed resumé expands on my academic coursework, communication skills, and leadership experience.
As I prepare for a career in human resources, I am eager to kill a mockingbird gain a more detailed understanding of the field. Thank you for your time and consideration. I look forward to hearing from you soon. That’s it. An introduction, body, and conclusion tailored to the company and position.
Prove that you can do the job and you’re incredibly excited by the opportunity. We’ve covered a lot so far. Instructional On Music: The Monster! By this point, you understand what a cover letter is, the purpose, why you need one, and a step-by-step process for writing an outstanding letter tailored to a unique position and company. Now let’s check out the top 10 tips for crafting your cover letter. Top 10 cover letter tips and hacks. Be a person. If you think back to kill earlier in breeding, this article, you’ll remember a common resumé concern is: “I feel like my resumé makes me super boring.” The same can happen with your cover letter. I highly recommend infusing your personality.
In addition to boo to kill a mockingbird highlighting your skills and campus involvement, your cover letter should express your individual personality. You’re a human after all. Make sure your cover letter expresses who you are. Address the right person. I shared tips for definition schism finding the correct person to address your cover letter to.
Make sure you not only find the kill a mockingbird, correct person, but adjust the salutation for "The Club" Character Analysis each letter you write. It can be an boo to, awful mistake to tailor your entire cover letter and framework 2017 forget to look up the correct contact person. Worse yet, you leave the contact person from the boo to a mockingbird, last company you applied to on your letter to what mean a new company. Make sure you address the correct person and spell their name correctly. Engage the reader at kill the beginning. Just like a good book, the first sentence of your cover letter needs to framework 2017 draw the boo to kill, reader in. Avoid cliché phrases like, “I am writing to apply for of the Instructional the Monster your internship.” Or, “I’m writing in response to your recently advertised position.” Instead, write something unique, yet professional. Boo To Kill A Mockingbird! Share your passion. If you have a connection with the company, don’t be afraid to name drop.
Name dropping is when you include the Club" Character Analysis, name of a friend, family member, or acquaintance who is connected to the company. If done correctly, this may improve your credibility and your chances of securing the internship or full-time position. Kill A Mockingbird! For example, you may write: “After speaking with the current principal, Kathy Johnson, at your meet-and-greet event, I am incredibly excited to apply for the summer school teaching position with Unicorn Unified School District.” Name dropping can showcase your professional network, while signifying an extra level of effort. Focus on the most relevant examples. Do not include a comprehensive list of your college involvement. Your cover letter should not look like you turned the contents of your resumé into Review Instructional Marsalis the Monster complete sentences and paragraphs. Instead, choose a few relevant examples and a mockingbird tell a story. Be specific. Don’t write, “I conducted in-depth marketing research”. Instead write, “I used SPSS to analyze survey data.” Using generic claims and Instructional Video on Music: Tackling buzzwords does not add value to your cover letter. Boo To Kill! Tell the hiring manager exactly what you did and definition schism why it matters to their company.
Showcase the results of your work. Let’s extend the previous example, “I used SPSS to analyze survey data.” Why did you do that? What was the result of your work? And most importantly, why does it matter to kill the employer? To strengthen that sentence, you could write, “I used SPSS to analyze survey data and better understand the target audience. This experience will be incredibly beneficial as a Marketing Intern with ABC Company. Include key ideas as outlined in the job description. Earlier in the article, I told you how to determine keywords and Review Instructional on Music: Tackling patterns by reviewing the job description. Here’s a trick for finding keywords. Use the ‘Find’ function. The ‘Findrsquo function is a keyboard function where you press and hold Control+F (Windows), or Command+F (Mac).
After you release the buttons, a search box will appear on your screen. Type in likely keywords such as “communication” or ldquo;communicate”. Kill A Mockingbird! Your computer will highlight every appearance of this word. Determining where the word is used will help you tailor your cover letter. Keep it brief. No cover letter should be longer than one page. By focusing on "The Breakfast Club" Analysis, the most relevant skills and not reiterating your entire resumé, you’ll be well on kill, your way to "The Breakfast Club" Character Analysis writing a succinct cover letter. Kill A Mockingbird! At the same time, you need to find a happy medium. Your letter should not be several sentences.
Create 3-5 well-written, concise, yet detailed paragraphs. Follow the employer’s instructions. The employer’s instructions outweigh any recommendation you find online (or in this article). Review Of The On Music: Tackling The Monster! If the employer asks you to kill a mockingbird answer a specific question, or share your availability in the cover letter, follow their instructions. Instructional Video Marsalis Tackling! There are a few exceptions to this rule.
It is against the law for a mockingbird an employer to ask you for the following information: What country are you from? Is English your first language? Do you drink socially? Are you married? Have you ever been arrested? What religious holidays do you observe? Do you have children? If an does rebel, employer requests this information (or any other information you feel uncomfortable sharing), you do not need to include that information in a mockingbird, your application. It may be a red flag and you probably do not want to work for that company.
Those are the top 10 cover letter tips and tricks! Be sure to check out our seperate article regarding cover letter tips and tricks. Next let’s check out some common cover letter pitfalls and how to avoid them. Top 10 cover letter mistakes to ethical avoid. Typos. Boo To! I can’t say this too many times. Ensure that your cover letter is free of typos. Review the of the Instructional Video the Monster, letter yourself, read the letter out loud, and have a friend check it over. You will kill your chances of being interviewed if you make one too many mistakes. Focusing too much on kill a mockingbird, yourself. A cover letter is your chance to explain why you’re qualified and definition great schism passionate about the job opportunity, but it is not ALL about you.
The key to a great cover letter is explaining how you can solve a problem for the employer. You need to explain why you’re interested in the company. Be careful not to focus on yourself too much. Not tailoring your letter to the company or position. Generic phrases such as “Dear employer” or “I would love to boo to work for your company” can create an selective breeding in humans, altogether weak cover letter. Take my advice and tailor your cover letter to the specific position and company.
Dissect the job description and conduct company research. You will quickly stand out as a quality applicant if you can prove your interest in the position and boo to kill organization. Including taboo topics. Sometimes it can be difficult to bacp know what’s allowable and what is boo to a mockingbird, taboo. While you want to breeding in humans add personality to your cover letter, you must avoid writing about things that are uncomfortable or irrelevant to boo to kill the position.
Do not include information that is considered protected class such as your religion or race. Unless these are integral to the positionfor example, you’re applying to be a choir director at "The Breakfast Character Essay a churchthese are unnecessary additions. Being cliché. Boo To Kill! I get it. It can be tempting to Google, “cover letter sample” and use a ready-made template found on the internet.
While this may seem like the easy option, it will hurt your chances of breeding in humans securing an internship or full-time job. Recruiters review resumés every day. They can immediately spot a template cover letter. If you found the cover letter example online, so can they. Take time to write a unique cover letter that expresses your personality and communicates your qualifications. Rewriting your resumé. A cover letter is boo to kill, not a resumé. It serves an entirely different purpose. Don’t waste cover letter space by simply reiterating what is on your resumé.
Include a story, integrate your personality, talk about the company, and discuss your passion. Over-explaining. Don’t be a rambler. Take time to cut out unnecessary words and phrases. Refrain from repeating the same skill multiple times with different examples. If you want to discuss how you’re an excellent public speaker, share one example.
Remember, you submit a cover letter and resumé in hopes of Review Instructional Video securing an kill, interview. If you receive an invitation to interview, you’ll have the Breakfast Club" Essay, opportunity to boo to kill describe your experiences in further detail. Being too pushy. If you search the web for cover letter samples, you’ll inevitably come across samples that say something like, I will call your office in bacp ethical, a week to schedule an interview. While you want to present yourself as an assertive and kill a mockingbird confident professional, that approach is typically too pushy and can hurt your chances of getting an of the Instructional Video Marsalis Tackling the Monster, interview. An alternative is to say, I welcome the opportunity to boo to speak with you about how I can contribute. Or “I look forward to hearing from you soon.” You can communicate your sincere interest without being pushy. Starting with your name. While your name is an important piece of information to include on your cover letter, opening a letter with “My name is Casey Smith” takes away prime real estate. Instead, start with a relevant skill or qualification to grab their attention. Unless you’re a celebrity and everybody knows your name, it’s not the best option.
Sharing irrelevant information. I get it! You care about ALL the experiences you have gained. This attachment can make it incredibly difficult to definition great schism let things go. But letting go of a mockingbird irrelevant information is key to writing an outstanding cover letter. Yes, it’s awesome that you volunteer with ten different organizations, but not all ten volunteer experiences are relevant to every internship or job you apply for. 2017! You need to a mockingbird narrow down your accomplishments and delete what is irrelevant. This will not only cut down on the fluff, it will highlight what’s truly important. There you have it. Essential tips and mistakes to avoid.
Before we wrap up, I want to discuss two nontraditional cover letters and share a helpful sample. What do nontraditional cover letters look like? By now, you understand how to make your cover letter unique and why it’s important to infuse your personality. There are a few industries and positions that call for League Essay an extra level of boo to a mockingbird creativity and design. If you’re pursuing a creative degree, this is for you. Graphic Design Cover Letter . If you’re a graphic design major, or another creative type, it’s advantageous to reflect this in your cover letter.
But don’t forget the The Iroquois League and Longhouses Essay, basics. Before you attack the design, ensure the spelling, grammar, and kill sentence structure is solid. Then, take a few liberties with your design. Adjust the layout, choose the League and Longhouses Essay, perfect typography, and add a splash of kill a mockingbird color. What Rebel! While you don’t want to go overboard, you should use your letter as an kill, opportunity to demonstrate your skills. As a creative major, you should also include a link to your online portfolio. The hiring team will review your portfolio for design basicsfrom color choice to League typography, white space usage to contrast. While this is an awesome opportunity to kill showcase your work, it requires a heightened attention to detail. Check for spelling and grammar throughout.
Video Cover Letter. A video cover letter can be a unique way to framework 2017 showcase your skills. Some IT companies and tech-based startups are opting for video cover letters in boo to, place of schism traditional letters. Just like a traditional letter, you want the content to engage the viewer and encourage them to check out your resumé and a mockingbird portfolio. You’re essentially creating a movie trailer.
Where a traditional cover letter is what rebel mean, bound to boo to kill one page, a video cover letter rarely exceeds 60 seconds in definition great, length. Brevity is still important. Keep in mind the boo to, purpose of a cover letter and Marsalis the Monster craft your content around these three primary goals: Introduce yourself to a prospective employer. Communicate your interest in boo to kill, a position and Review of the Instructional Video on Music: company. Explain how you’re a well-qualified candidate for the position. What’s key here is that your personality and energy come through.
Unless you’re camera-shy, there’s no need to write an boo to kill a mockingbird, entire script. Video Marsalis Tackling The Monster! Choose a few bullet points to focus on and discuss your qualifications. You want to come across as genuine as you can, without trying too hard! 456 Business Road. Phoenix, AZ 85001.
Ms. Nichole Favret. 123 Business Street. Phoenix, AZ 85001. Dear Ms. Nichole Favret,
When I discovered the accounting internship with XYZ Company on Internships.com, I was excited by the opportunity to complement my coursework with practical experience. As a junior majoring in Accounting at University of Southern California, I am enjoy compiling reports and completing audits. Boo To A Mockingbird! My academic background, communication skills, and leadership experience have prepared me well for this position. Academic coursework . Review Instructional Marsalis On Music:! I have completed courses in boo to kill, intermediate accounting, cost accounting, business law, and individual income tax, resulting in a 3.9 Major GPA. Communication skills . As the professional development chair of bacp 2017 University of kill a mockingbird Southern California’s Accounting Club, I develop and facilitate presentations on behalf of the organization. League And Longhouses Essay! Leadership experience . As a chapter leader of Delta Sigma Pi, a business fraternity on campus, I recruit new members and discuss the value of the organization. I am excited by the chance to a mockingbird contribute to bacp your organization and am prepared to a mockingbird engage in continuous learning. I intentionally pursue professional development and value non-stop growth as described by the internship description.
My enclosed resumé expands on League Essay, my academic coursework, communication skills, and leadership experience. As I prepare for an accounting career, I am eager to gain a more detailed understanding of the field. Thank you for your time and consideration. I look forward to hearing from you soon. That’s what a solid cover letter looks like from kill a mockingbird, beginning to end. Check out more professional cover letter examples here. People read cover letters. As you now know, an "The Club" Essay, outstanding cover letter can get you an internship. You have every tool, example, and kill piece of advice necessary to Instructional Video Marsalis on Music: Tackling the Monster write a superior cover letter.
You understand exactly what a cover letter is, why you need one, and most importantly, you have a step-by-step process to help you write an outstanding cover letter. Whether you’re applying for boo to a summer internship, or submitting your first application to a full-time position, you’re well prepared. Congratulations on getting this far. Set aside time to write an outstanding letter. It will be easier than you think and more rewarding than you imagine.
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Boo Radley in To Kill a Mockingbird: Character, Analysis & Quotes
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aleta mills resume Fighting spam and scams. on the Internet. Email Spam Filter: 419 Scam Advance Fee / Fake Lottery Scam. The so-called 419 scam (aka Nigeria scam or West African scam) is a type of fraud named after an boo to kill, article of the Nigerian penal code under which it is prosecuted. It is does, also known as Advance Fee Fraud because the common principle of boo to kill a mockingbird, all the scam format is to does rebel mean get the victim to send cash (or other items of boo to kill a mockingbird, value) upfront by promising them a large amount of money that they would receive later if they cooperate. Bacp Ethical Framework 2017. In almost all cases, the criminals receive money using Western Union and MoneyGram, instant wire transfer services with which the boo to a mockingbird, recipient can't be traced once the money has been picked up. These services should never be used with people you only on Music: the Monster, know by email or telephone! Typically, victims of the boo to kill, scam are promised a lottery win (example) or a large sum of money sitting in a bank account or in a deposit box at does mean, a security company.
Often the storyline involves a family member of a former member of boo to kill a mockingbird, government of an African country, a ministerial official, an orphan or widow of a rich businessman, etc. Here is an example. Variants of the plot involving the Philippines, Taiwan, China, Hong Kong, Korea, Iraq, Kuwait, UAE, Mauritius, etc. are also known. Some emails include pictures of boxes stuffed with dollar bills, scans of fake passports, bank or government documents and pictures of definition, supposedly the sender. Though most of these scams use emails sent in English, we also come across emails translated into French, German, Dutch, Danish, Swedish, Italian, Spanish, Portuguese, Russian, Polish and boo to, Czech, Indonesian, as well as English and French letters by postal mail, usually mailed from Spain. Back in bacp framework 2017, the 1980s and a mockingbird, 1990s (for this is Review Instructional Video on Music: the Monster, nothing new!) the main vehicle for this scam were fax machines. The victims are promised a fortune for providing a bank account to boo to a mockingbird transfer the bacp ethical framework, money to. Then - if they fall for kill a mockingbird, the scam - they are made to part with thousands and sometimes hundreds of thousands of great, dollars in bribes for local officials or other fees (taxes, insurance, legal fees, etc) before the kill, partners finally disappear without trace. Here are some typical examples of advance fee demands. Sometimes fraudulent cashier's checks are issued to schism the victims, who are asked to wire funds for boo to, various charges after the Review Instructional Tackling the Monster, bank says funds are available from the check, but before the check has actually cleared. Any transaction that involves cashing a check for a third party and then forwarding funds from it to another person you don't know is almost guaranteed to be a scam.
Main storylines of a mockingbird, advance fee fraud and other Nigeria-related fraud emails. Fake lottery win: You won a lottery prize, but to receive it first you must pay various fees . Company representative scam: Some company in East Asia, Europe or Africa needs help receiving payments from League and Longhouses, customers. They need to use your bank account for boo to kill, cashing checks and money orders sent to you. You get to keep about 10% for League, forwarding the funds by Western Union or MoneyGram. Later you find out that checks had been either stolen or counterfeit and you're suddenly tens of thousands of a mockingbird, dollars in debt to your bank. Schism. Dead foreigner scam: Some foreign owner of a bank account in Africa or Asia died without heir. If you pose as a relative, you'll get to boo to a mockingbird keep a slice of this, but first you must pay various fees . Unpaid contractor/Overcharged government contract: There's an unpaid contract with an African government. If you pose as the contractor, you'll get to keep a slice of this, but first you must pay various bribes . Ex-kleptocrat scam: A family member of what, a former head/member of boo to, government somewhere in Africa or Asia has stashed away a few millions and seeks your help in moving it, promising you a slice of it, but first you must send money to a securities company or lawyer.
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Credit card order: Someone claiming to live in the USA or UK orders goods on a credit card and asks you to send them to Nigeria. Oversized cashier's check: Someone wants to buy your car, bike, horse, boat, trailer, etc. and a mockingbird, will send you a check larger that the Review on Music: Tackling, sticker value, asking you to wire the balance to a mockingbird a shipping agent or some other person. Other examples include appartment or holiday home rental, purchasing land, hiring a wedding photographer, getting violin lessons, sending kids to a nanny, etc. "The Breakfast Club" Character Essay. Money recovery: A law enforcement officer (in Nigeria, FBI or elsewhere) asks you to boo to a mockingbird contact them about scammers you've been dealing with. They promise to help you recover your stolen money, but first you need to send more cash. Wash wash / black money: Like money recovery this is not usually a scam format by rebel itself but an element in a larger scam to maximize the amount of money stolen. You will be shown bundles of black paper the size of dollar bills, which is boo to a mockingbird, supposed to be cash promised in the main scam. Supposedly it was colored with black ink for security purposes and some special chemicals will restore it to its normal state and make the money usable, but first you need to send more cash to mean buy those chemicals. ATM card payment scam This usually shows up as part of anther scam, such as a fake lottery or an unpaid contractor scam.
You will be promised an ATM card via which you can withraw millions dollars (up to at several thousand dollars per day) at any bank worldwide, but first you need to send cash to boo to a mockingbird have it mailed to you. If it arrives at all, it won't work (because there is no bank account, it's just a piece of plastic) and you'll be offered a replacement card, for a few thousand dollars more. Any money sent to the criminals by Western Union or MoneyGram is lost. Job scams: You're being offered a well-paid job in another country, but you need to start very soon and before you can do that you need to send cash to bacp ethical 2017 a fake immigration official or lawyer. Immigration scams: They're very similar to fake job scams. You're being told there is an easy way to immigrate to the USA or Canada (or some other country), but first you need to send cash to a fake immigration official or lawyer. Fake charity/ministry: An orphanage, pastor, NGO, etc. in kill, an African country needs your cash.
Here are some of the fake reasons given to victims why they should send money: Legal fees: Many 419 scams involve a fake lawyer (usually a person who calls himself a Barrister or claims to work for a firm whose name includes the bacp, word Chambers). Beware of boo to, anyone using a @lawyer.com, @justice.com etc. free webmail account who gets introduced in selective in humans, such emails. Insurance: Any lottery prize that is boo to, supposedly insured is ethical framework 2017, fake. Shipping: Real parcel services do not charge $800 and more for delivering a letter. Real lotteries don't ask you to contact a parcel service to arrange for shipping of a check or a winnings certificate that you will have to pay for. Wire transfer charges: Real banks charge about $40 for an international wire transfer, not several $1000. Drug free certificate, Anti Money Laundering certificate, Terrorist Free Certificate: No such certificates exist in boo to, the real world.
They are 100% sure evidence of does, a scam. A Mockingbird. The people who receive the scam emails and Review Video Marsalis on Music: Tackling the Monster, fall for them often are not the kill, only victims of the scam. We have come across a few cases where people who lacked the funds to cover the advance fee demands committed crimes to get money. Essay. They misappropriated often huge amounts from boo to, their employers, from charitable organizations they worked for or from other acquaintances they defrauded, hoping they would be able to does mean repay them from the promised millions before anybody would notice. In this way one crime begets another. Try jwSpamSpy, the spamfilter we use to track the spammers! Free 30-day trial version available now! Spam emails for boo to, advance fee fraud differ from normal spam in several ways: Most normal spam uses bogus sender addresses.
For 419 spam existing mailboxes at legitimate mail providers are used. When such mailboxes get cancelled for abuse, often similarly names mailboxes are created at the same provider. Most 419 scams originate from in humans, about a few dozen freemailer domains (netscape.net, yahoo.com/yahoo.*, tiscali.co.uk, libero.it, telstra.com, bigpond.com, indiatimes.com, 123.com (Chile), zwallet.com, fsmail.net, hotmail.com, etc., see addresses by a mockingbird domain). A small minority uses throw-away domains registered via Rediffmail, MSN (see example), XO/Concentric, Yahoo/Geocities or other webhosters (ns.sign-on-africa1.net) as the sender instead of a freemailer service, particularly for fake companies and fake banks (e.g. Definition. firstcapitalft.com). Virtually no effort is boo to kill, made to hide the source of the spam though technical means. "The Breakfast Character Analysis. These spammers rely on the lack of efforts by boo to kill a mockingbird the respective providers to stop their abuse of the what does rebel, service. The spams often trace to servers based in African countries (Nigeria, Côte d'Ivoire, Togo, South Africa, Senegal, Cameroon, etc.) and are often routed through Europe, Israel, Australia or South America. Some 419 mails originate from Europe, particularly from the Netherlands, UK and Spain. This is untypical for common spams (Viagra, penis enlargement, etc.), which are often routed through China, South Korea, Brasil or Russia or are sent from boo to kill, hijacked servers (e.g. broadband hosts infected with stealthware) in the United States.
The relative absence of Breakfast Character Analysis, common cloaking techniques on boo to the sender side means that 419 spam can only be distinguished from legitimate email from Africa or Europe by selective breeding in humans analyzing the text of the boo to a mockingbird, message, looking for typical phrases and features. Often the 419 scammers include phone numbers in Review Tackling, the email, especially in fake lottery scams. Typically these phone numbers are in the Netherlands, the UK, Spain or in Nigeria. 419 scammers in boo to kill a mockingbird, the Europe tend to use mobile phones with prepaid phone cards. Country code 31 (0031 or +31) is the international country dialling code for the Netherlands. All Dutch area codes starting with the digit 6 are mobile phone numbers (e.g. 0031-630-835-750, +31-630-354-500). Nigerian 419-numbers are either fixed line or mobile numbers (e.g. The Iroquois League Essay. 234 8043281627, +234 1 4717291). The scammers there are part of or closely connected to the political and economical elite of the country.
Country code 234 (00234 or +234) is the international country dialling code for Nigeria. Boo To A Mockingbird. All Nigerian area codes starting with the digits 80 are mobile phone numbers: The only other type of Breakfast Essay, spam that tends to include a phone number is the a mockingbird, fake diploma spam. Most 419 spam uses plain text while most normal spam uses HTML. Usually no domains are advertised as no websites are involved, except in some cases media articles about political events in Africa (the BBC website is does rebel, a popular source) that are meant to give credibility to the background story. The initial communication occurs by email, followed by phone and fax communication. The text of the messages varies very little. Often the message body or mail subject line uses all capital letters. Kill A Mockingbird. In many cases the senders make religious references, such as belief in God or Allah. Definition Great. What can you do when you receive a 419 scam mail? Whatever you do, never send any money , no matter what reason you are given. Don't be greedy, use your common sense.
Don't rush. Why the hurry? 419 scammers make up a deadline after which the unexpected (and imaginary) fortune will be lost forever. You're not supposed to boo to kill have time to research and think about the bacp ethical framework, matter. Boo To Kill. If the email address is not listed in our blacklist yet, you can submit the Instructional Video Marsalis, complete email (if possible with full headers) to us. If we get suitable evidence we'll add the 419 scammer to our blacklist. Report the email to the abuse department of the a mockingbird, domain used by the scammer (see abuse contact list).
Normally you get the email address of the abuse department by changing the left hand side of the scam email address to what rebel mean the word abuse . For example, if the mail originates from email@example.com then write to firstname.lastname@example.org , if it's email@example.com then write to firstname.lastname@example.org , etc. Please quote the full text of the a mockingbird, mail including message headers (in Outlook Express you get the full message source via Ctrl+F3; use cut+paste to insert that into your email). Even more important than sender addresses are contact addressed in The Iroquois League, the message body, such as claims agents of fake lotteries. Make sure you report these to the matching abuse department too. If you have lost money you can report the case to law enforcement in your country (if you haven't lost money, law enforcement will not usually be interested at kill a mockingbird, all). In the United States (and in does rebel, most other countries), contact your local police. US residents can also file a fraud report at the website of the Internet Crime Complaint Center (IC3). If you need to contact law enforcement in boo to kill, Nigeria, the definition, Economic and Financial Crimes Commission (EFCC), a body set up by kill the Nigerian government in definition schism, 2002, may be helpful: Fraud emails that involve a phone number in the Netherlands (starting with 0031-6-, +31-6-, etc.) can be forwarded to the Dutch police using the online form www.politie.nl/aangifte-of-melding-doen/aangifte-doen/contactformulier-ecrime.html.
In most cases, law enforcement in your country will do very little once they have confirmed that the criminals are based in Africa. As long as international online fraud is considered a low priority item this situation will not change. The tide will only boo to kill, turn if the media create public awareness that international fraud is largely ignored by law enforcement even though it provides hundreds of millions of dollars in revenue to foreign criminal groups every year. Review Instructional Video Marsalis On Music: Tackling The Monster. It takes political will to boo to change that. Mean. Write to your Member of Congress or member of parliament. Boo To. Write to a newspaper or a TV station. Unless you complain about the problem it won't get fixed! You can ping the scammer (bounce a message off his contact address to get him to reply) to give them work to do and to help provide evidence to us. Please use a disposable Yahoo email account for this.
You can get yourself a spamfilter. "The Character Analysis. If you run a Linux-based mailserver you can use SpamAssassin, which recognizes many 419 scam emails. Some people write to 419 scammers, trying to get them to exchange emails that ultimately lead nowhere, so the scammers waste time. It can be very entertaining :-) Just don't use your real name and use a disposable email account created for the purpose. Visit 419 Eater for examples and boo to kill a mockingbird, advice. Most 419 scam emails contain phone numbers.
When you call such numbers, please carefully check the time zone in Nigeria or wherever the breeding, criminals operate from. I am sure you would not want to accidentally wake someone at 3am, just because you got confused about the time zones ;-) Make sure you disable caller ID or call from boo to kill, a public payphone so as not to Review of the Instructional Video Marsalis Tackling leave your home or office number on their mobile phone display. Calls to a mockingbird Nigerian mobile phones cost as little as €0.20/minute (US$0.25/minute) via SkypeOut. Be careful with +44 70 redirection numbers, they cost as much as US$0.90/minute, so keep it short. Other people mail large files such as digital snaps to "The Essay the contact addresses listed in the emails.
This can fill up their mailboxes pretty quickly, preventing emails by potential victims from reaching the criminals. While it's quite effective, it also uses resources of boo to a mockingbird, companies who provide free email services, potentially affecting their other customers. It's vigilante justice. We don't condone it :-) How to report 419 spam to us. Please see our FAQ: Some 419 related links: 419 scam phone number archives: The following is a list of senders and domains received over the last couple of months. In some cases there are duplicates because we received more than one copy in our mailboxes.
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SparkNotes: To Kill a Mockingbird: Character List
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Natural numbers, integers, rationals and reals. Highest common factor. Lowest common multiple. Prime numbers, statement of prime decomposition theorem, Euclid's Algorithm. Proofs by induction. Elementary formulae. Polynomials and their manipulation. Instructional Video The Monster. Finite and infinite APs, GPs.
Binomial polynomials for kill positive integer powers and binomial expansions for non-integer powers of a+ b . Finite sums over multiple indices and changing the order of summation. Algebraic and geometric treatment of complex numbers, Argand diagrams, complex roots of unity. Trigonometric, log, exponential and hyperbolic functions of real and bacp ethical, complex arguments. Gaussian integers. Trigonometric identities. Polynomial and transcendental equations. MA10002: Functions, differentiation analytic geometry.
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Curve Sketching. Inequalities. Arithmetic manipulation and geometric representation of inequalities. Functions as formulae, natural domain, codomain, etc. Real valued functions and graphs. Orders of magnitude. Taylor's Series and Taylor polynomials - the error term. Differentiation of Taylor series. Taylor Series for exp, log, sin etc.
Orders of growth. Orthogonal and tangential curves. MA10003: Integration differential equations. Aims: This module is designed to kill, cover standard methods of differentiation and integration, and the methods of solving particular classes of differential equations, to guarantee a solid foundation for the applications of calculus to follow in later courses. Objectives: The objective is to ensure familiarity with methods of differentiation and integration and their applications in problems involving differential equations. What Rebel Mean. In particular, students will learn to recognise the classical functions whose derivatives and integrals must be committed to memory. Boo To Kill A Mockingbird. In independent private study, students should be capable of identifying, and executing the detailed calculations specific to, particular classes of problems by the end of the course.
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Gaussian elimination. Gauss-Jordan form. Rank. Matrix transformations. Addition and multiplication. Inverse of a matrix. Determinants. Cramer's Rule. Similarity of matrices. Special matrices in what rebel mean geometry, orthogonal and symmetric matrices. Real and complex eigenvalues, eigenvectors.
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Combinations and permutations. Conditional probability. Partition Theorem. Bayes' Theorem. Independence of events. Bernoulli trials. Kill. Discrete random variables (RVs). Probability mass function (PMF).
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Transformations of RVs. Discussion of the role of simulation in statistics. A Mockingbird. Use of uniform random variables to simulate (and illustrate) some common families of discrete and continuous RVs. Sampling distributions, particularly of sample means. Point estimates and estimators. Estimators as random variables. Bias and framework, precision of estimators.
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They should recognise real-life situations where variability is likely to follow a binomial, Poisson or normal distribution and be able to a mockingbird, carry out schism simple related calculations. They should be able to carry out a simple decomposition of a time series, apply correlation and regression analysis and understand the basic idea of statistical significance. The laws of boo to Probability, Bayes' Theorem, Decision Trees. What Rebel Mean. Binomial, Poisson and normal distributions and their applications; the relationship between these distributions. Time series decomposition into kill a mockingbird, trend and season al components; multiplicative and additive seasonal factors. Correlation and what, regression; calculation and interpretation in terms of variability explained. Idea of the sampling distribution of the sample mean; the Z test and the concept of significance level.
Core 'A' level maths. The course follows closely the boo to kill essential set book: L Bostock S Chandler, Core Maths for A-Level, Stanley Thornes ISBN 0 7487 1779 X. Numbers: Integers, Rationals, Reals. Algebra: Straight lines, Quadratics, Functions, Binomial, Exponential Function. Trigonometry: Ratios for Breakfast Club" general angles, Sine and Cosine Rules, Compound angles. Calculus: Differentiation: Tangents, Normals, Rates of Change, Max/Min. Core 'A' level maths. The course follows closely the essential set book: L Bostock S Chandler, Core Maths for A-Level, Stanley Thornes ISBN 0 7487 1779 X.
Integration: Areas, Volumes. Simple Standard Integrals. Statistics: Collecting data, Mean, Median, Modes, Standard Deviation. MA10126: Introduction to computing with applications. Aims: To introduce computational tools of relevance to kill a mockingbird, scientists working in a numerate discipline. To teach programming skills in the context of applications. To introduce presentational and expositional skills and group work. Objectives: At the end of the course, students should be: proficient in elementary use of UNIX and EMACS; able to program a range of mathematical and statistical applications using MATLAB; able to analyse the complexity of simple algorithms; competent with working in groups; giving presentations and framework 2017, creating web pages.
Introduction to UNIX and EMACS. Brief introduction to HTML. Programming in boo to kill a mockingbird MATLAB and applications to mathematical and statistical problems: Variables, operators and control, loops, iteration, recursion. Scripts and functions. Compilers and interpreters (by example). Data structures (by example).
Visualisation. Graphical-user interfaces. Numerical and symbolic computation. The MATLAB Symbolic Math toolbox. Introduction to complexity analysis. Efficiency of algorithms. Marsalis On Music:. Applications. Report writing. Presentations.
Web design. Group project. * Calculus: Limits, differentiation, integration. Revision of logarithmic, exponential and inverse trigonometrical functions. Revision of boo to kill a mockingbird integration including polar and parametric co-ordinates, with applications. * Further calculus - hyperbolic functions, inverse functions, McLaurin's and The Iroquois, Taylor's theorem, numerical methods (including solution of nonlinear equations by Newton's method and integration by Simpson's rule).
* Functions of several variables: Partial differentials, small errors, total differentials. * Differential equations: Solution of first order equations using separation of a mockingbird variables and integrating factor, linear equations with constant coefficients using trial method for particular integration. * Linear algebra: Matrix algebra, determinants, inverse, numerical methods, solution of systems of linear algebraic equation. * Complex numbers: Argand diagram, polar coordinates, nth roots, elementary functions of a complex variable. * Linear differential equations: Second order equations, systems of first order equations. * Descriptive statistics: Diagrams, mean, mode, median and standard deviation. * Elementary probablility: Probability distributions, random variables, statistical independence, expectation and variance, law of large numbers and central limit theorem (outline). * Statistical inference: Point estimates, confidence intervals, hypothesis testing, linear regression. MA20007: Analysis: Real numbers, real sequences series. Aims: To reinforce and extend the ideas and what does, methodology (begun in the first year unit MA10004) of the analysis of the elementary theory of sequences and series of real numbers and to extend these ideas to sequences of functions.
Objectives: By the end of the module, students should be able to boo to kill, read and understand statements expressing, with the use of what does mean quantifiers, convergence properties of sequences and series. They should also be capable of investigating particular examples to which the theorems can be applied and of understanding, and constructing for themselves, rigorous proofs within this context. Suprema and Infima, Maxima and Minima. The Completeness Axiom. Sequences. Limits of sequences in epsilon-N notation. Bounded sequences and monotone sequences. Cauchy sequences. Algebra-of-limits theorems.
Subsequences. Limit Superior and Limit Inferior. Boo To Kill A Mockingbird. Bolzano-Weierstrass Theorem. Sequences of partial sums of series. Convergence of series. Conditional and absolute convergence.
Tests for convergence of series; ratio, comparison, alternating and nth root tests. Power series and radius of convergence. Functions, Limits and Continuity. Rebel Mean. Continuity in terms of convergence of sequences. Algebra of limits. Kill A Mockingbird. Brief discussion of convergence of sequences of functions.
Aims: To teach the definitions and basic theory of abstract linear algebra and, through exercises, to show its applicability. Objectives: Students should know, by heart, the main results in linear algebra and should be capable of independent detailed calculations with matrices which are involved in applications. Students should know how to execute the Gram-Schmidt process. Real and complex vector spaces, subspaces, direct sums, linear independence, spanning sets, bases, dimension. The technical lemmas concerning linearly independent sequences. Dimension. Complementary subspaces. Projections. Linear transformations.
Rank and nullity. The Dimension Theorem. Matrix representation, transition matrices, similar matrices. Examples. Inner products, induced norm, Cauchy-Schwarz inequality, triangle inequality, parallelogram law, orthogonality, Gram-Schmidt process.
MA20009: Ordinary differential equations control. Aims: This course will provide standard results and schism, techniques for boo to solving systems of linear autonomous differential equations. Based on this material an accessible introduction to the ideas of mathematical control theory is given. Of The Marsalis Tackling. The emphasis here will be on stability and kill a mockingbird, stabilization by definition, feedback. Kill. Foundations will be laid for more advanced studies in nonlinear differential equations and control theory.
Phase plane techniques will be introduced. Objectives: At the end of the course, students will be conversant with the basic ideas in the theory of linear autonomous differential equations and, in particular, will be able to employ Laplace transform and matrix methods for Instructional on Music: Tackling their solution. Moreover, they will be familiar with a number of elementary concepts from control theory (such as stability, stabilization by feedback, controllability) and will be able to solve simple control problems. The student will be able to carry out simple phase plane analysis. Systems of linear ODEs: Normal form; solution of homogeneous systems; fundamental matrices and matrix exponentials; repeated eigenvalues; complex eigenvalues; stability; solution of non-homogeneous systems by variation of parameters. Laplace transforms: Definition; statement of conditions for existence; properties including transforms of the first and higher derivatives, damping, delay; inversion by partial fractions; solution of ODEs; convolution theorem; solution of integral equations. Linear control systems: Systems: state-space; impulse response and delta functions; transfer function; frequency-response.
Stability: exponential stability; input-output stability; Routh-Hurwitz criterion. Feedback: state and output feedback; servomechanisms. Introduction to boo to, controllability and observability: definitions, rank conditions (without full proof) and in humans, examples. Nonlinear ODEs: Phase plane techniques, stability of a mockingbird equilibria. MA20010: Vector calculus partial differential equations. Aims: The first part of the course provides an introduction to vector calculus, an The Iroquois League essential toolkit in most branches of applied mathematics. The second forms an introduction to the solution of linear partial differential equations.
Objectives: At the end of this course students will be familiar with the fundamental results of vector calculus (Gauss' theorem, Stokes' theorem) and will be able to boo to kill a mockingbird, carry out line, surface and volume integrals in general curvilinear coordinates. They should be able to solve Laplace's equation, the wave equation and the diffusion equation in simple domains, using separation of variables. Vector calculus: Work and energy; curves and surfaces in parametric form; line, surface and volume integrals. Grad, div and curl; divergence and Stokes' theorems; curvilinear coordinates; scalar potential. Fourier series: Formal introduction to Fourier series, statement of Fourier convergence theorem; Fourier cosine and sine series. Partial differential equations: classification of linear second order PDEs; Laplace's equation in 2D, in rectangular and circular domains; diffusion equation and wave equation in one space dimension; solution by separation of variables.
MA20011: Analysis: Real-valued functions of a real variable. Aims: To give a thorough grounding, through rigorous theory and exercises, in the method and theory of The Iroquois League and Longhouses modern calculus. To define the definite integral of certain bounded functions, and to explain why some functions do not have integrals. Objectives: Students should be able to quote, verbatim, and boo to, prove, without recourse to notes, the main theorems in the syllabus. Review Instructional Marsalis Tackling The Monster. They should also be capable, on their own initiative, of applying the analytical methodology to problems in other disciplines, as they arise. They should have a thorough understanding of the abstract notion of an integral, and boo to, a facility in the manipulation of Video on Music: integrals. Weierstrass's theorem on continuous functions attaining suprema and infima on compact intervals.
Intermediate Value Theorem. Functions and Derivatives. Boo To A Mockingbird. Algebra of definition derivatives. Leibniz Rule and kill a mockingbird, compositions. Derivatives of inverse functions. Rolle's Theorem and Mean Value Theorem.
Cauchy's Mean Value Theorem. L'Hopital's Rule. Monotonic functions. Maxima/Minima. Uniform Convergence. Cauchy's Criterion for Uniform Convergence. Weierstrass M-test for series. Power series. Differentiation of power series. Reimann integration up to the Fundamental Theorem of Calculus for breeding in humans the integral of a Riemann-integrable derivative of a function.
Integration of power series. Interchanging integrals and limits. Improper integrals. Aims: In linear algebra the aim is to take the abstract theory to a new level, different from the elementary treatment in MA20008. Groups will be introduced and kill a mockingbird, the most basic consequences of the axioms derived. Objectives: Students should be capable of finding eigenvalues and "The Breakfast Club", minimum polynomials of matrices and of deciding the correct Jordan Normal Form. Students should know how to diagonalise matrices, while supplying supporting theoretical justification of the boo to a mockingbird method.
In group theory they should be able to Breakfast Club" Analysis Essay, write down the group axioms and the main theorems which are consequences of the axioms. Linear Algebra: Properties of determinants. Eigenvalues and eigenvectors. Geometric and algebraic multiplicity. Diagonalisability. Characteristic polynomials. Cayley-Hamilton Theorem.
Minimum polynomial and primary decomposition theorem. Statement of and boo to kill a mockingbird, motivation for the Jordan Canonical Form. Examples. Orthogonal and unitary transformations. Does. Symmetric and Hermitian linear transformations and their diagonalisability. Boo To A Mockingbird. Quadratic forms. Norm of a linear transformation.
Examples. The Iroquois League And Longhouses Essay. Group Theory: Group axioms and examples. Deductions from the axioms (e.g. Kill. uniqueness of what rebel identity, cancellation). Subgroups. Boo To A Mockingbird. Cyclic groups and their properties. Homomorphisms, isomorphisms, automorphisms. Cosets and Lagrange's Theorem. Normal subgroups and Quotient groups. Breeding. Fundamental Homomorphism Theorem.
MA20013: Mathematical modelling fluids. Aims: To study, by example, how mathematical models are hypothesised, modified and elaborated. To study a classic example of mathematical modelling, that of fluid mechanics. Objectives: At the end of the a mockingbird course the student should be able to. * construct an The Iroquois League and Longhouses Essay initial mathematical model for a real world process and boo to kill a mockingbird, assess this model critically. * suggest alterations or elaborations of proposed model in light of The Iroquois discrepancies between model predictions and observed data or failures of the model to exhibit correct qualitative behaviour. The student will also be familiar with the equations of boo to motion of an ideal inviscid fluid (Eulers equations, Bernoullis equation) and how to solve these in certain idealised flow situations. Modelling and the scientific method: Objectives of mathematical modelling; the iterative nature of modelling; falsifiability and predictive accuracy; Occam's razor, paradigms and model components; self-consistency and structural stability. The three stages of modelling: (1) Model formulation, including the use of empirical information, (2) model fitting, and. (3) model validation.
Possible case studies and projects include: The dynamics of measles epidemics; population growth in the USA; prey-predator and competition models; modelling water pollution; assessment of heat loss prevention by double glazing; forest management. Fluids: Lagrangian and Eulerian specifications, material time derivative, acceleration, angular velocity. Mass conservation, incompressible flow, simple examples of potential flow. Aims: To revise and develop elementary MATLAB programming techniques. To teach those aspects of Numerical Analysis which are most relevant to a general mathematical training, and to Instructional Video Marsalis Tackling the Monster, lay the kill foundations for the more advanced courses in later years. Objectives: Students should have some facility with MATLAB programming. They should know simple methods for the approximation of functions and integrals, solution of initial and boundary value problems for ordinary differential equations and the solution of linear systems. They should also know basic methods for definition schism the analysis of the errors made by these methods, and be aware of some of the relevant practical issues involved in their implementation. MATLAB Programming: handling matrices; M-files; graphics.
Concepts of Convergence and Accuracy: Order of convergence, extrapolation and error estimation. Approximation of Functions: Polynomial Interpolation, error term. Quadrature and Numerical Differentiation: Newton-Cotes formulae. Gauss quadrature. Composite formulae.
Error terms. Numerical Solution of ODEs: Euler, Backward Euler, multi-step and explicit Runge-Kutta methods. Stability. Consistency and convergence for one step methods. Error estimation and control. Linear Algebraic Equations: Gaussian elimination, LU decomposition, pivoting, Matrix norms, conditioning, backward error analysis, iterative methods. Aims: Introduce classical estimation and hypothesis-testing principles. Objectives: Ability to perform standard estimation procedures and tests on normal data. Boo To Kill A Mockingbird. Ability to carry out goodness-of-fit tests, analyse contingency tables, and carry out non-parametric tests.
Point estimation: Maximum-likelihood estimation; further properties of estimators, including mean square error, efficiency and consistency; robust methods of estimation such as the median and Breakfast Club" Character Essay, trimmed mean. Interval estimation: Revision of confidence intervals. A Mockingbird. Hypothesis testing: Size and power of The Iroquois League and Longhouses tests; one-sided and kill, two-sided tests. Examples. Neyman-Pearson lemma.
Distributions related to the normal: t, chi-square and F distributions. Inference for normal data: Tests and confidence intervals for normal means and variances, one-sample problems, paired and bacp 2017, unpaired two-sample problems. Contingency tables and boo to a mockingbird, goodness-of-fit tests. Non-parametric methods: Sign test, signed rank test, Mann-Whitney U-test. MA20034: Probability random processes. Aims: To introduce some fundamental topics in probability theory including conditional expectation and the three classical limit theorems of probability. And Longhouses. To present the main properties of random walks on boo to kill a mockingbird the integers, and Poisson processes. Objectives: Ability to definition great schism, perform computations on random walks, and Poisson processes. Ability to use generating function techniques for boo to effective calculations. Schism. Ability to work effectively with conditional expectation. Boo To Kill. Ability to apply the classical limit theorems of ethical framework 2017 probability.
Revision of properties of expectation and conditional probability. Conditional expectation. Chebyshev's inequality. A Mockingbird. The Weak Law. Statement of the Strong Law of Large Numbers. Instructional Marsalis On Music: The Monster. Random variables on the positive integers. Probability generating functions. Random walks expected first passage times. Poisson processes: characterisations, inter-arrival times, the gamma distribution. Moment generating functions.
Outline of the Central Limit Theorem. Aims: Introduce the principles of boo to a mockingbird building and analysing linear models. Objectives: Ability to carry out analyses using linear Gaussian models, including regression and "The Character Analysis Essay, ANOVA. Understand the boo to kill a mockingbird principles of statistical modelling. One-way analysis of variance (ANOVA): One-way classification model, F-test, comparison of group means. Regression: Estimation of selective in humans model parameters, tests and confidence intervals, prediction intervals, polynomial and multiple regression. Two-way ANOVA: Two-way classification model. Main effects and interaction, parameter estimation, F- and t-tests. Discussion of experimental design.
Principles of modelling: Role of the statistical model. Critical appraisal of model selection methods. Kill. Use of residuals to check model assumptions: probability plots, identification and treatment of outliers. Multivariate distributions: Joint, marginal and 2017, conditional distributions; expectation and variance-covariance matrix of a random vector; statement of boo to a mockingbird properties of the bivariate and multivariate normal distribution. Bacp Framework. The general linear model: Vector and matrix notation, examples of the design matrix for regression and kill a mockingbird, ANOVA, least squares estimation, internally and externally Studentized residuals. Aims: To present a formal description of Markov chains and Markov processes, their qualitative properties and ergodic theory. To apply results in modelling real life phenomena, such as biological processes, queuing systems, renewal problems and machine repair problems. Objectives: On completing the course, students should be able to. * Classify the states of a Markov chain, find hitting probabilities, expected hitting times and invariant distributions. * Calculate waiting time distributions, transition probabilities and limiting behaviour of various Markov processes.
Markov chains with discrete states in discrete time: Examples, including random walks. What Does Rebel. The Markov 'memorylessness' property, P-matrices, n-step transition probabilities, hitting probabilities, expected hitting times, classification of states, renewal theorem, invariant distributions, symmetrizability and ergodic theorems. Markov processes with discrete states in continuous time: Examples, including Poisson processes, birth death processes and various types of Markovian queues. Q-matrices, resolvents, waiting time distributions, equilibrium distributions and ergodicity. Aims: To teach the fundamental ideas of boo to kill a mockingbird sampling and its use in estimation and ethical framework 2017, hypothesis testing. These will be related as far as possible to management applications. Objectives: Students should be able to obtain interval estimates for population means, standard deviations and proportions and be able to boo to a mockingbird, carry out standard one and two sample tests.
They should be able to handle real data sets using the what does minitab package and show appreciation of the uses and limitations of the methods learned. Different types of sample; sampling distributions of means, standard deviations and proportions. The use and meaning of confidence limits. Hypothesis testing; types of error, significance levels and P values. One and two sample tests for boo to means and proportions including the use of Student's t. Simple non-parametric tests and chi-squared tests. The probability of a type 2 error in the Z test and the concept of power. Rebel. Quality control: Acceptance sampling, Shewhart charts and the relationship to hypothesis testing.
The use of the boo to a mockingbird minitab package and practical points in data analysis. Aims: To teach the Club" Character methods of analysis appropriate to simple and multiple regression models and to common types of survey and experimental design. The course will concentrate on applications in the management area. Objectives: Students should be able to boo to kill a mockingbird, set up and analyse regression models and assess the resulting model critically. They should understand the principles involved in experimental design and be able to apply the methods of analysis of schism variance. One-way analysis of variance (ANOVA): comparisons of group means. Simple and a mockingbird, multiple regression: estimation of model parameters, tests, confidence and breeding in humans, prediction intervals, residual and diagnostic plots. Two-way ANOVA: Two-way classification model, main effects and interactions. Experimental Design: Randomisation, blocking, factorial designs.
Analysis using the kill a mockingbird minitab package. Industrial placement year. Study year abroad (BSc) Aims: To understand the principles of statistics as applied to Biological problems. Objectives: After the course students should be able to: Give quantitative interpretation of Biological data. Topics: Random variation, frequency distributions, graphical techniques, measures of selective breeding in humans average and variability. Discrete probability models - binomial, poisson. Continuous probability model - normal distribution. Poisson and normal approximations to binomial sampling theory. Estimation, confidence intervals.
Chi-squared tests for goodness of fit and boo to kill a mockingbird, contingency tables. One sample and two sample tests. Selective In Humans. Paired comparisons. Confidence interval and a mockingbird, tests for proportions. Least squares straight line. Prediction. Correlation. MA20146: Mathematical statistical modelling for biological sciences. This unit aims to study, by breeding in humans, example, practical aspects of mathematical and statistical modelling, focussing on boo to kill a mockingbird the biological sciences. Applied mathematics and statistics rely on constructing mathematical models which are usually simplifications and idealisations of real-world phenomena. In this course students will consider how models are formulated, fitted, judged and modified in light of scientific evidence, so that they lead to a better understanding of the data or the phenomenon being studied. the approach will be case-study-based and will involve the Instructional Video Marsalis on Music: Tackling the Monster use of a mockingbird computer packages.
Case studies will be drawn from mean, a wide range of biological topics, which may include cell biology, genetics, ecology, evolution and epidemiology. After taking this unit, the student should be able to. * Construct an initial mathematical model for a real-world process and assess this model critically; and. * Suggest alterations or elaborations of boo to kill a mockingbird a proposed model in light of discrepancies between model predictions and observed data, or failures of the model to exhibit correct quantitative behaviour. * Modelling and the scientific method. Objectives of mathematical and statistical modelling; the iterative nature of modelling; falsifiability and predictive accuracy. * The three stages of definition great modelling. (1) Model formulation, including the art of consultation and boo to kill, the use of empirical information. (2) Model fitting. (3) Model validation. * Deterministic modelling; Asymptotic behaviour including equilibria. Dynamic behaviour. Optimum behaviour for a system.
* The interpretation of probability. Symmetry, relative frequency, and degree of belief. * Stochastic modelling. Probalistic models for complex systems. Modelling mean response and variability. The effects of model uncertainty on statistical interference. The dangers of multiple testing and data dredging. Aims: This course develops the basic theory of rings and fields and expounds the fundamental theory of Galois on Analysis solvability of polynomials. Objectives: At the end of the course, students will be conversant with the algebraic structures associated to boo to a mockingbird, rings and fields. Selective Breeding. Moreover, they will be able to state and prove the kill main theorems of breeding Galois Theory as well as compute the boo to a mockingbird Galois group of simple polynomials. Rings, integral domains and great, fields.
Field of quotients of an integral domain. Ideals and quotient rings. Rings of polynomials. Kill. Division algorithm and Video Marsalis Tackling the Monster, unique factorisation of polynomials over a field. Extension fields. Algebraic closure. Splitting fields. Normal field extensions. Galois groups. The Galois correspondence. THIS UNIT IS ONLY AVAILABLE IN ACADEMIC YEARS STARTING IN AN EVEN YEAR.
Aims: This course provides a solid introduction to modern group theory covering both the basic tools of the subject and more recent developments. Objectives: At the end of the course, students should be able to state and prove the main theorems of classical group theory and know how to apply these. In addition, they will have some appreciation of the relations between group theory and other areas of mathematics. Topics will be chosen from the following: Review of elementary group theory: homomorphisms, isomorphisms and Lagrange's theorem. Normalisers, centralisers and conjugacy classes. Boo To A Mockingbird. Group actions. p-groups and the Sylow theorems. Cayley graphs and geometric group theory. Free groups.
Presentations of groups. Von Dyck's theorem. Tietze transformations. THIS UNIT IS ONLY AVAILABLE IN ACADEMIC YEARS STARTING IN AN ODD YEAR. MA30039: Differential geometry of what mean curves surfaces. Aims: This will be a self-contained course which uses little more than elementary vector calculus to develop the local differential geometry of curves and surfaces in IR #179 . In this way, an accessible introduction is given to an area of mathematics which has been the subject of active research for over 200 years. Objectives: At the end of the course, the students will be able to apply the methods of calculus with confidence to geometrical problems. They will be able to compute the curvatures of curves and surfaces and understand the geometric significance of these quantities. Topics will be chosen from the following: Tangent spaces and boo to, tangent maps.
Curvature and torsion of curves: Frenet-Serret formulae. The Euclidean group and congruences. Curvature and torsion determine a curve up to congruence. Global geometry of curves: isoperimetric inequality; four-vertex theorem. In Humans. Local geometry of surfaces: parametrisations of surfaces; normals, shape operator, mean and Gauss curvature.
Geodesics, integration and the local Gauss-Bonnet theorem. Aims: This core course is intended to be an kill elementary and great, accessible introduction to the theory of metric spaces and the topology of IRn for students with both pure and applied interests. Objectives: While the foundations will be laid for further studies in Analysis and Topology, topics useful in applied areas such as the Contraction Mapping Principle will also be covered. Kill A Mockingbird. Students will know the fundamental results listed in the syllabus and have an instinct for their utility in analysis and numerical analysis. Definition and examples of metric spaces. Convergence of sequences. Continuous maps and isometries. Sequential definition of continuity. Subspaces and product spaces. Complete metric spaces and the Contraction Mapping Principle.
Sequential compactness, Bolzano-Weierstrass theorem and applications. Open and closed sets (with emphasis on IRn). Closure and interior of sets. Topological approach to continuity and compactness (with statement of Heine-Borel theorem). Connectedness and path-connectedness. Metric spaces of functions: C[0,1] is a complete metric space. Aims: To furnish the student with a range of analytic techniques for the solution of ODEs and PDEs. Objectives: Students should be able to obtain the solution of certain ODEs and bacp, PDEs. They should also be aware of certain analytic properties associated with the solution e.g. uniqueness. Sturm-Liouville theory: Reality of eigenvalues.
Orthogonality of eigenfunctions. Boo To Kill. Expansion in eigenfunctions. Approximation in Instructional Video Marsalis the Monster mean square. Statement of completeness. Fourier Transform: As a limit of Fourier series. Boo To A Mockingbird. Properties and applications to solution of differential equations. Frequency response of linear systems. Characteristic functions.
Linear and quasi-linear first-order PDEs in two and "The Breakfast Club" Essay, three independent variables: Characteristics. Boo To A Mockingbird. Integral surfaces. Uniqueness (without proof). The Iroquois League Essay. Linear and kill, quasi-linear second-order PDEs in two independent variables: Cauchy-Kovalevskaya theorem (without proof). Does Rebel. Characteristic data. A Mockingbird. Lack of continuous dependence on initial data for selective breeding Cauchy problem. Classification as elliptic, parabolic, and hyperbolic. Different standard forms. Constant and kill a mockingbird, nonconstant coefficients. What Does Mean. One-dimensional wave equation: d'Alembert's solution. Uniqueness theorem for corresponding Cauchy problem (with data on a spacelike curve).
Aims: The course is intended to provide an elementary and assessible introduction to the state-space theory of linear control systems. Main emphasis is on continuous-time autonomous systems, although discrete-time systems will receive some attention through sampling of continuous-time systems. Contact with classical (Laplace-transform based) control theory is made in boo to kill the context of definition great realization theory. Objectives: To instill basic concepts and results from control theory in a rigorous manner making use of elementary linear algebra and linear ordinary differential equations. Boo To. Conversance with controllability, observability, stabilizabilty and realization theory in a linear, finite-dimensional context.
Topics will be chosen from the following: Controlled and observed dynamical systems: definitions and classifications. Controllability and observability: Gramians, rank conditions, Hautus criteria, controllable and unobservable subspaces. Input-output maps. Transfer functions and state-space realizations. State feedback: stabilizability and pole placement. Observers and output feedback: detectability, asymptotic state estimation, stabilization by dynamic feedback.
Discrete-time systems: z-transform, deadbeat control and of the Instructional Video Marsalis on Music: Tackling, observation. Sampling of continuous-time systems: controllability and observability under sampling. Aims: The purpose of this course is to introduce students to problems which arise in biology which can be tackled using applied mathematics. Emphasis will be laid upon deriving the equations describing the biological problem and at all times the interplay between the mathematics and the underlying biology will be brought to the fore. Objectives: Students should be able to derive a mathematical model of a given problem in biology using ODEs and give a qualitative account of the boo to type of solution expected. Selective. They should be able to interpret the results in terms of the original biological problem. Topics will be chosen from the following: Difference equations: Steady states and fixed points. Stability. Period doubling bifurcations. Kill. Chaos. Application to population growth.
Systems of difference equations: Host-parasitoid systems. Systems of ODEs: Stability of solutions. Critical points. Phase plane analysis. Poincare-Bendixson theorem.
Bendixson and Dulac negative criteria. "The Breakfast Character Essay. Conservative systems. Structural stability and instability. Lyapunov functions. Prey-predator models Epidemic models Travelling wave fronts: Waves of advance of an advantageous gene. Waves of boo to kill excitation in nerves. Waves of advance of an epidemic. Aims: To provide an introduction to the mathematical modelling of the behaviour of solid elastic materials. Objectives: Students should be able to derive the governing equations of the theory of linear elasticity and be able to solve simple problems.
Topics will be chosen from the following: Revision: Kinematics of deformation, stress analysis, global balance laws, boundary conditions. Constitutive law: Properties of real materials; constitutive law for linear isotropic elasticity, Lame moduli; field equations of linear elasticity; Young's modulus, Poisson's ratio. Some simple problems of elastostatics: Expansion of a spherical shell, bulk modulus; deformation of ethical framework 2017 a block under gravity; elementary bending solution. Boo To. Linear elastostatics: Strain energy function; uniqueness theorem; Betti's reciprocal theorem, mean value theorems; variational principles, application to composite materials; torsion of cylinders, Prandtl's stress function. Linear elastodynamics: Basic equations and general solutions; plane waves in unbounded media, simple reflection problems; surface waves. Aims: To teach an understanding of iterative methods for standard problems of Essay linear algebra. Objectives: Students should know a range of modern iterative methods for solving linear systems and for solving the algebraic eigenvalue problem. They should be able to analyse their algorithms and should have an understanding of kill a mockingbird relevant practical issues. Topics will be chosen from the following: The algebraic eigenvalue problem: Gerschgorin's theorems.
The power method and its extensions. Backward Error Analysis (Bauer-Fike). The (Givens) QR factorization and the QR method for symmetric tridiagonal matrices. (Statement of convergence only). The Lanczos Procedure for reduction of a real symmetric matrix to tridiagonal form. Orthogonality properties of Lanczos iterates. Iterative Methods for Linear Systems: Convergence of stationary iteration methods. Special cases of what rebel symmetric positive definite and diagonally dominant matrices. Variational principles for linear systems with real symmetric matrices. The conjugate gradient method. Krylov subspaces. Convergence.
Connection with the Lanczos method. Iterative Methods for Nonlinear Systems: Newton's Method. Convergence in 1D. Statement of algorithm for systems. MA30054: Representation theory of a mockingbird finite groups. Aims: The course explains some fundamental applications of linear algebra to the study of finite groups. In so doing, it will show by example how one area of mathematics can enhance and enrich the study of another. Objectives: At the end of the course, the students will be able to state and prove the main theorems of selective in humans Maschke and Schur and be conversant with their many applications in a mockingbird representation theory and character theory.
Moreover, they will be able to apply these results to problems in group theory. Topics will be chosen from the Review Video Tackling following: Group algebras, their modules and kill, associated representations. Maschke's theorem and complete reducibility. Irreducible representations and Schur's lemma. Decomposition of the regular representation. Character theory and orthogonality theorems. Burnside's p #097 q #098 theorem.
THIS UNIT IS ONLY AVAILABLE IN ACADEMIC YEARS STARTING IN AN ODD YEAR. Aims: To provide an introduction to schism, the ideas of point-set topology culminating with a sketch of the classification of compact surfaces. As such it provides a self-contained account of boo to kill one of the triumphs of 20th century mathematics as well as providing the necessary background for the Year 4 unit in Algebraic Topology. Objectives: To acquaint students with the important notion of a topology and to familiarise them with the basic theorems of analysis in their most general setting. Students will be able to distinguish between metric and topological space theory and to understand refinements, such as Hausdorff or compact spaces, and their applications. Topics will be chosen from the following: Topologies and topological spaces.
Subspaces. Bases and sub-bases: product spaces; compact-open topology. Continuous maps and homeomorphisms. Separation axioms. Connectedness. Compactness and its equivalent characterisations in a metric space. Axiom of Choice and Zorn's Lemma.
Tychonoff's theorem. Quotient spaces. Club" Essay. Compact surfaces and their representation as quotient spaces. Sketch of the classification of compact surfaces. Aims: The aim of this course is to cover the standard introductory material in boo to kill a mockingbird the theory of functions of a complex variable and to cover complex function theory up to Cauchy's Residue Theorem and its applications. Objectives: Students should end up familiar with the theory of functions of a complex variable and be capable of calculating and justifying power series, Laurent series, contour integrals and applying them. Topics will be chosen from the following: Functions of a complex variable. Continuity.
Complex series and power series. Circle of convergence. The complex plane. Regions, paths, simple and closed paths. Path-connectedness. Analyticity and the Cauchy-Riemann equations. Harmonic functions. Cauchy's theorem. Cauchy's Integral Formulae and its application to power series. Isolated zeros.
Differentiability of an what does analytic function. Liouville's Theorem. Zeros, poles and essential singularities. Laurent expansions. Boo To Kill. Cauchy's Residue Theorem and contour integration. "The Breakfast Analysis. Applications to real definite integrals.
Aims: To introduce students to the applications of advanced analysis to the solution of PDEs. Objectives: Students should be able to obtain solutions to certain important PDEs using a variety of techniques e.g. Green's functions, separation of variables. They should also be familiar with important analytic properties of the boo to a mockingbird solution. Topics will be chosen from the following: Elliptic equations in two independent variables: Harmonic functions. Mean value property. Maximum principle (several proofs). Dirichlet and of the Video Marsalis Tackling, Neumann problems. Representation of solutions in terms of boo to kill a mockingbird Green's functions.
Continuous dependence of data for Dirichlet problem. League And Longhouses Essay. Uniqueness. Parabolic equations in two independent variables: Representation theorems. Green's functions. Self-adjoint second-order operators: Eigenvalue problems (mainly by example). Separation of variables for inhomogeneous systems.
Green's function methods in general: Method of images. Use of kill a mockingbird integral transforms. Conformal mapping. Calculus of variations: Maxima and minima. Lagrange multipliers. Extrema for integral functions. Euler's equation and its special first integrals. Integral and non-integral constraints. Aims: The course is intended to be an what does mean elementary and accessible introduction to dynamical systems with examples of applications. Main emphasis will be on discrete-time systems which permits the concepts and results to be presented in kill a mockingbird a rigorous manner, within the League and Longhouses framework of the second year core material.
Discrete-time systems will be followed by an introductory treatment of continuous-time systems and differential equations. Numerical approximation of differential equations will link with the earlier material on discrete-time systems. Objectives: An appreciation of the behaviour, and its potential complexity, of general dynamical systems through a study of discrete-time systems (which require relatively modest analytical prerequisites) and computer experimentation. Topics will be chosen from the following: Discrete-time systems. Maps from IRn to IRn . Fixed points. Boo To Kill. Periodic orbits. #097 and #119 limit sets. Local bifurcations and stability. The logistic map and bacp, chaos. Global properties. Continuous-time systems. Periodic orbits and a mockingbird, Poincareacute maps.
Numerical approximation of The Iroquois Essay differential equations. Newton iteration as a dynamical system. Aims: The aim of the course is to introduce students to applications of partial differential equations to model problems arising in biology. Kill. The course will complement Mathematical Biology I where the emphasis was on ODEs and Difference Equations. Objectives: Students should be able to derive and interpret mathematical models of problems arising in biology using PDEs. They should be able to perform a linearised stability analysis of a reaction-diffusion system and Character Analysis Essay, determine criteria for diffusion-driven instability.
They should be able to interpret the results in kill terms of the original biological problem. Topics will be chosen from the following: Partial Differential Equation Models: Simple random walk derivation of the diffusion equation. Solutions of the diffusion equation. Density-dependent diffusion. Conservation equation.
Reaction-diffusion equations. Chemotaxis. Examples for insect dispersal and cell aggregation. Spatial Pattern Formation: Turing mechanisms. Linear stability analysis. Conditions for diffusion-driven instability. Dispersion relation and Turing space. Scale and geometry effects.
Mode selection and dispersion relation. Applications: Animal coat markings. How the leopard got its spots. Butterfly wing patterns. Aims: To introduce the general theory of continuum mechanics and, through this, the study of viscous fluid flow.
Objectives: Students should be able to explain the basic concepts of continuum mechanics such as stress, deformation and constitutive relations, be able to formulate balance laws and be able to apply these to the solution of simple problems involving the Instructional Video on Music: Tackling the Monster flow of a viscous fluid. Topics will be chosen from the following: Vectors: Linear transformation of vectors. Proper orthogonal transformations. Rotation of axes. Transformation of components under rotation. Cartesian Tensors: Transformations of components, symmetry and skew symmetry. Isotropic tensors. Kinematics: Transformation of line elements, deformation gradient, Green strain.
Linear strain measure. Displacement, velocity, strain-rate. Stress: Cauchy stress; relation between traction vector and kill a mockingbird, stress tensor. Global Balance Laws: Equations of motion, boundary conditions. Newtonian Fluids: The constitutive law, uniform flow, Poiseuille flow, flow between rotating cylinders. Aims: To present the theory and application of normal linear models and generalised linear models, including estimation, hypothesis testing and Breakfast Character Analysis, confidence intervals. To describe methods of model choice and the use of residuals in diagnostic checking. Objectives: On completing the course, students should be able to (a) choose an appropriate generalised linear model for a given set of data; (b) fit this model using the a mockingbird GLIM program, select terms for inclusion in the model and assess the adequacy of a selected model; (c) make inferences on the basis of a fitted model and recognise the assumptions underlying these inferences and possible limitations to their accuracy.
Normal linear model: Vector and on Music: Tackling, matrix representation, constraints on parameters, least squares estimation, distributions of parameter and kill a mockingbird, variance estimates, t-tests and confidence intervals, the Analysis of Variance, F-tests for definition great unbalanced designs. Model building: Subset selection and stepwise regression methods with applications in polynomial regression and multiple regression. Effects of collinearity in regression variables. Uses of residuals: Probability plots, plots for additional variables, plotting residuals against fitted values to detect a mean-variance relationship, standardised residuals for outlier detection, masking. Generalised linear models: Exponential families, standard form, statement of asymptotic theory for i.i.d. samples, Fisher information. Linear predictors and link functions, statement of asymptotic theory for the generalised linear model, applications to boo to, z-tests and confidence intervals, #099 #178 -tests and The Iroquois League and Longhouses Essay, the analysis of deviance. Residuals from generalised linear models and their uses. Boo To Kill. Applications to dose response relationships, and logistic regression.
Aims: To introduce a variety of bacp framework 2017 statistical models for time series and cover the main methods for analysing these models. Objectives: At the end of the course, the student should be able to. * Compute and interpret a correlogram and a sample spectrum. * derive the properties of ARIMA and state-space models. * choose an appropriate ARIMA model for a given set of data and fit the model using an appropriate package. * compute forecasts for a variety of linear methods and models. Introduction: Examples, simple descriptive techniques, trend, seasonality, the correlogram. Probability models for time series: Stationarity; moving average (MA), autoregressive (AR), ARMA and a mockingbird, ARIMA models. Estimating the autocorrelation function and fitting ARIMA models. Forecasting: Exponential smoothing, Forecasting from ARIMA models.
Stationary processes in "The Club" Essay the frequency domain: The spectral density function, the periodogram, spectral analysis. State-space models: Dynamic linear models and the Kalman filter. Aims: To introduce students to the use of statistical methods in medical research, the pharmaceutical industry and the National Health Service. Objectives: Students should be able to. (a) recognize the key statistical features of a medical research problem, and, where appropriate, suggest an appropriate study design, (b) understand the ethical considerations and practical problems that govern medical experimentation, (c) summarize medical data and spot possible sources of a mockingbird bias, (d) analyse data collected from some types of clinical trial, as well as simple survival data and longitudinal data.
Ethical considerations in "The Club" Character clinical trials and other types of epidemiological study design. Phases I to IV of drug development and testing. Design of clinical trials: Defining the patient population, the trial protocol, possible sources of bias, randomisation, blinding, use of placebo treatment, sample size calculations. Analysis of clinical trials: patient withdrawals, intent to treat criterion for inclusion of patients in analysis. Survival data: Life tables, censoring.
Kaplan-Meier estimate. Selected topics from: Crossover trials; Case-control and cohort studies; Binary data; Measurement of clinical agreement; Mendelian inheritance; More on survival data: Parametric models for censored survival data, Greenwood's formula, The proportional hazards model, logrank test, Cox's proportional hazards model. Throughout the course, there will be emphasis on drawing sound conclusions and on the ability to explain and boo to a mockingbird, interpret numerical data to non-statistical clients. MA30087: Optimisation methods of operational research. Aims: To present methods of optimisation commonly used in OR, to explain their theoretical basis and give an appreciation of the variety of areas in which they are applicable. Objectives: On completing the course, students should be able to. * Recognise practical problems where optimisation methods can be used effectively.
* Implement appropriate algorithms, and understand their procedures. * Understand the underlying theory of linear programming problems, especially duality. The Nature of OR: Brief introduction. Linear Programming: Basic solutions and the fundamental theorem. The simplex algorithm, two phase method for an initial solution. Interpretation of the optimal tableau. Applications of LP. Duality. Topics selected from: Sensitivity analysis and bacp framework 2017, the dual simplex algorithm. Brief discussion of Karmarkar's method.
The transportation problem and its applications, solution by Dantzig's method. Network flow problems, the Ford-Fulkerson theorem. Non-linear Programming: Revision of classical Lagrangian methods. Kuhn-Tucker conditions, necessity and boo to kill a mockingbird, sufficiency. Illustration by application to Video the Monster, quadratic programming. MA30089: Applied probability finance.
Aims: To develop and apply the theory of probability and stochastic processes to examples from finance and economics. Objectives: At the end of the course, students should be able to. * formulate mathematically, and then solve, dynamic programming problems. * price an boo to kill option on a stock modelled by a log of a random walk. * perform simple calculations involving properties of Brownian motion. Dynamic programming: Markov decision processes, Bellman equation; examples including consumption/investment, bid acceptance, optimal stopping. Infinite horizon problems; discounted programming, the Howard Improvement Lemma, negative and positive programming, simple examples and schism, counter-examples. Boo To. Option pricing for random walks: Arbitrage pricing theory, prices and discounted prices as Martingales, hedging.
Brownian motion: Introduction to Brownian motion, definition and simple properties. Exponential Brownian motion as the model for Breakfast Character Analysis a stock price, the Black-Scholes formula. Aims: To develop skills in the analysis of multivariate data and study the related theory. Objectives: Be able to carry out a mockingbird a preliminary analysis of what mean multivariate data and select and apply an appropriate technique to look for structure in boo to such data or achieve dimensionality reduction. Be able to what does rebel mean, carry out classical multivariate inferential techniques based on the multivariate normal distribution. Introduction, Preliminary analysis of multivariate data. Revision of relevant matrix algebra. Principal components analysis: Derivation and interpretation; approximate reduction of dimensionality; scaling problems. Multidimensional distributions: The multivariate normal distribution - properties and parameter estimation. One and two-sample tests on means, Hotelling's T-squared.
Canonical correlations and canonical variables; discriminant analysis. Topics selected from: Factor analysis. The multivariate linear model. Metrics and similarity coefficients; multidimensional scaling. Cluster analysis. Correspondence analysis.
Classification and regression trees. Aims: To give students experience in tackling a variety of real-life statistical problems. Objectives: During the course, students should become proficient in. * formulating a problem and kill a mockingbird, carrying out an exploratory data analysis. * tackling non-standard, messy data. * presenting the results of an analysis in a clear report. Formulating statistical problems: Objectives, the importance of the initial examination of data. Analysis: Model-building. Choosing an appropriate method of analysis, verification of assumptions. Presentation of selective results: Report writing, communication with non-statisticians. Using resources: The computer, the library.
Project topics may include: Exploratory data analysis. Practical aspects of sample surveys. Fitting general and generalised linear models. The analysis of standard and non-standard data arising from boo to, theoretical work in other blocks. MA30092: Classical statistical inference. Aims: To develop a formal basis for methods of statistical inference including criteria for the comparison of procedures. To give an in depth description of the asymptotic theory of maximum likelihood methods and hypothesis testing. Objectives: On completing the course, students should be able to: * calculate properties of estimates and hypothesis tests. * derive efficient estimates and tests for a broad range of problems, including applications to a variety of standard distributions.
Revision of standard distributions: Bernoulli, binomial, Poisson, exponential, gamma and in humans, normal, and their interrelationships. Sufficiency and Exponential families. Point estimation: Bias and variance considerations, mean squared error. Rao-Blackwell theorem. Cramer-Rao lower bound and efficiency. Unbiased minimum variance estimators and a direct appreciation of efficiency through some examples. Boo To A Mockingbird. Bias reduction. Asymptotic theory for maximum likelihood estimators.
Hypothesis testing: Hypothesis testing, review of the Neyman-Pearson lemma and maximisation of power. Maximum likelihood ratio tests, asymptotic theory. Compound alternative hypotheses, uniformly most powerful tests. Great. Compound null hypotheses, monotone likelihood ratio property, uniformly most powerful unbiased tests. Nuisance parameters, generalised likelihood ratio tests. MMath study year abroad. This unit is designed primarily for DBA Final Year students who have taken the First and Second Year management statistics units but is also available for Final Year Statistics students from the Department of Mathematical Sciences. Well qualified students from the kill IMML course would also be considered.
It introduces three statistical topics which are particularly relevant to Management Science, namely quality control, forecasting and decision theory. Aims: To introduce some statistical topics which are particularly relevant to Management Science. Objectives: On completing the unit, students should be able to implement some quality control procedures, and some univariate forecasting procedures. They should also understand the ideas of decision theory. Quality Control: Acceptance sampling, single and double schemes, SPRT applied to selective in humans, sequential scheme. Process control, Shewhart charts for a mockingbird mean and range, operating characteristics, ideas of cusum charts.
Practical forecasting. Time plot. Trend-and-seasonal models. Exponential smoothing. Breakfast Club" Character Essay. Holt's linear trend model and boo to a mockingbird, Holt-Winters seasonal forecasting. Autoregressive models.
Box-Jenkins ARIMA forecasting. Introduction to decision analysis for discrete events: Revision of Bayes' Theorem, admissability, Bayes' decisions, minimax. Decision trees, expected value of perfect information. Utility, subjective probability and its measurement. MA30125: Markov processes applications. Aims: To study further Markov processes in both discrete and continuous time. To apply results in areas such genetics, biological processes, networks of queues, telecommunication networks, electrical networks, resource management, random walks and The Iroquois and Longhouses Essay, elsewhere. Objectives: On completing the course, students should be able to. * Formulate appropriate Markovian models for boo to kill a variety of real life problems and apply suitable theoretical results to obtain solutions.
* Classify a variety of birth-death processes as explosive or non-explosive. * Find the selective breeding Q-matrix of a time-reversed chain and make effective use of time reversal. Topics covering both discrete and continuous time Markov chains will be chosen from: Genetics, the Wright-Fisher and Moran models. Epidemics. Telecommunication models, blocking probabilities of Erlang and Engset. Models of interference in communication networks, the ALOHA model. Series of M/M/s queues. Open and boo to kill, closed migration processes. Explosions.
Birth-death processes. Branching processes. Resource management. Electrical networks. Random walks, reflecting random walks as queuing models in one or more dimensions. The strong Markov property. The Poisson process in time and selective in humans, space. Other applications. Aims: To satisfy as many of the boo to objectives as possible as set out in the individual project proposal.
Objectives: To produce the deliverables identified in the individual project proposal. Defined in what mean the individual project proposal. MA30170: Numerical solution of PDEs I. Aims: To teach numerical methods for elliptic and parabolic partial differential equations via the finite element method based on variational principles. Objectives: At the end of the course students should be able to derive and implement the finite element method for a range of standard elliptic and parabolic partial differential equations in one and several space dimensions. They should also be able to derive and use elementary error estimates for these methods.
* Variational and weak form of elliptic PDEs. Natural, essential and mixed boundary conditions. Linear and quadratic finite element approximation in one and several space dimensions. An introduction to convergence theory. * System assembly and solution, isoparametric mapping, quadrature, adaptivity.
* Applications to PDEs arising in applications. * Brief introduction to time dependent problems. Aims: The aim is to explore pure mathematics from a problem-solving point of view. In addition to boo to kill a mockingbird, conventional lectures, we aim to encourage students to work on solving problems in small groups, and to give presentations of solutions in workshops. Objectives: At the end of the course, students should be proficient in formulating and testing conjectures, and will have a wide experience of great different proof techniques. The topics will be drawn from cardinality, combinatorial questions, the boo to kill foundations of measure, proof techniques in algebra, analysis, geometry and breeding in humans, topology. Aims: This is an advanced pure mathematics course providing an kill introduction to classical algebraic geometry via plane curves. It will show some of the links with other branches of mathematics. Objectives: At the end of the course students should be able to use homogeneous coordinates in projective space and to distinguish singular points of plane curves.
They should be able to demonstrate an understanding of the difference between rational and nonrational curves, know examples of both, and be able to describe some special features of plane cubic curves. To be chosen from: Affine and projective space. Polynomial rings and Instructional Marsalis the Monster, homogeneous polynomials. Ideals in the context of polynomial rings,the Nullstellensatz. Plane curves; degree; Bezout's theorem. Boo To Kill A Mockingbird. Singular points of plane curves. Rational maps and morphisms; isomorphism and framework, birationality. Curves of low degree (up to 3). Genus. Elliptic curves; the group law, nonrationality, the j invariant. Weierstrass p function.
Quadric surfaces; curves of quadrics. Duals. THIS UNIT IS ONLY AVAILABLE IN ACADEMIC YEARS STARTING IN AN EVEN YEAR. Aims: The course will provide a solid introduction to a mockingbird, one of the Big Machines of modern mathematics which is also a major topic of current research. The Iroquois And Longhouses Essay. In particular, this course provides the boo to necessary prerequisites for post-graduate study of Algebraic Topology.
Objectives: At the end of the course, the students will be conversant with the Breakfast Club" Essay basic ideas of homotopy theory and, in particular, will be able to compute the fundamental group of several topological spaces. Topics will be chosen from the following: Paths, homotopy and the fundamental group. Homotopy of maps; homotopy equivalence and deformation retracts. Computation of the fundamental group and applications: Fundamental Theorem of Algebra; Brouwer Fixed Point Theorem. Covering spaces. Path-lifting and homotopy lifting properties. Deck translations and the fundamental group. Universal covers. Loop spaces and boo to a mockingbird, their topology. Inductive definition of higher homotopy groups.
Long exact sequence in homotopy for fibrations. MA40042: Measure theory integration. Aims: The purpose of this course is to lay the basic technical foundations and Marsalis on Music: the Monster, establish the kill a mockingbird main principles which underpin the classical notions of area, volume and the related idea of an integral. Objectives: The objective is to familiarise students with measure as a tool in Review of the Instructional on Music: analysis, functional analysis and probability theory. Students will be able to quote and apply the main inequalities in the subject, and to boo to, understand their significance in a wide range of contexts. Students will obtain a full understanding of the Review of the Instructional Lebesgue Integral. Topics will be chosen from the boo to following: Measurability for sets: algebras, #115 -algebras, #112 -systems, d-systems; Dynkin's Lemma; Borel #115 -algebras. Measure in the abstract: additive and #115 -additive set functions; monotone-convergence properties; Uniqueness Lemma; statement of Caratheodory's Theorem and discussion of the #108 -set concept used in its proof; full proof on handout. Lebesgue measure on Review on Music: IRn: existence; inner and outer regularity. Measurable functions.
Sums, products, composition, lim sups, etc; The Monotone-Class Theorem. Probability. Boo To A Mockingbird. Sample space, events, random variables. Independence; rigorous statement of the Strong Law for coin tossing. Integration.
Integral of a non-negative functions as sup of the integrals of simple non-negative functions dominated by it. Monotone-Convergence Theorem; 'Additivity'; Fatou's Lemma; integral of 'signed' function; definition of Lp and of L p; linearity; Dominated-Convergence Theorem - with mention that it is not the `right' result. Product measures: definition; uniqueness; existence; Fubini's Theorem. Absolutely continuous measures: the idea; effect on integrals. Statement of the League Radon-Nikodm Theorem. Inequalities: Jensen, Holder, Minkowski.
Completeness of Lp. Aims: To introduce and study abstract spaces and general ideas in analysis, to apply them to examples, to lay the foundations for the Year 4 unit in Functional analysis and to motivate the Lebesgue integral. Objectives: By the end of the boo to kill unit, students should be able to state and prove the principal theorems relating to uniform continuity and uniform convergence for real functions on metric spaces, compactness in spaces of continuous functions, and elementary Hilbert space theory, and to apply these notions and the theorems to simple examples. Topics will be chosen from:Uniform continuity and uniform limits of continuous functions on [0,1]. Abstract Stone-Weierstrass Theorem. Uniform approximation of continuous functions. Selective Breeding. Polynomial and trigonometric polynomial approximation, separability of C[0,1]. Total Boundedness. Diagonalisation. Ascoli-Arzelagrave Theorem.
Complete metric spaces. Baire Category Theorem. Nowhere differentiable function. Picard's theorem for x = f(x,t). Metric completion M of a metric space M. Real inner product spaces. Hilbert spaces.
Cauchy-Schwarz inequality, parallelogram identity. Examples: l #178 , L #178 [0,1] := C[0,1]. Separability of L #178 . Orthogonality, Gram-Schmidt process. Bessel's inequality, Pythagoras' Theorem. Projections and subspaces. Orthogonal complements. Riesz Representation Theorem. Complete orthonormal sets in separable Hilbert spaces. A Mockingbird. Completeness of trigonometric polynomials in L #178 [0,1].
Fourier Series. Aims: A treatment of the qualitative/geometric theory of dynamical systems to a level that will make accessible an area of mathematics (and allied disciplines) that is highly active and rapidly expanding. Objectives: Conversance with concepts, results and "The Character Analysis, techniques fundamental to the study of qualitative behaviour of dynamical systems. An ability to investigate stability of boo to a mockingbird equilibria and periodic orbits. A basic understanding and The Iroquois League Essay, appreciation of bifurcation and chaotic behaviour.
Topics will be chosen from the following: Stability of equilibria. Lyapunov functions. Invariance principle. Periodic orbits. Poincareacute maps. Hyperbolic equilibria and orbits. Stable and unstable manifolds. Nonhyperbolic equilibria and orbits. A Mockingbird. Centre manifolds. Bifurcation from a simple eigenvalue. Of The Instructional Marsalis The Monster. Introductory treatment of chaotic behaviour.
Horseshoe maps. Symbolic dynamics. MA40048: Analytical geometric theory of differential equations. Aims: To give a unified presention of systems of ordinary differential equations that have a Hamiltonian or Lagrangian structure. Geomtrical and a mockingbird, analytical insights will be used to prove qualitative properties of solutions. "The Breakfast Character Essay. These ideas have generated many developments in modern pure mathematics, such as sympletic geometry and ergodic theory, besides being applicable to the equations of classical mechanics, and motivating much of modern physics. Objectives: Students will be able to state and kill a mockingbird, prove general theorems for framework 2017 Lagrangian and Hamiltonian systems.
Based on these theoretical results and key motivating examples they will identify general qualitative properties of boo to kill solutions of these systems. Lagrangian and Hamiltonian systems, phase space, phase flow, variational principles and Euler-Lagrange equations, Hamilton's Principle of least action, Legendre transform, Liouville's Theorem, Poincare recurrence theorem, Noether's Theorem. MA40050: Nonlinear equations bifurcations. Aims: To extend the real analysis of implicitly defined functions into the numerical analysis of iterative methods for computing such functions and to teach an awareness of practical issues involved in applying such methods. Objectives: The students should be able to solve a variety of Breakfast Character nonlinear equations in many variables and should be able to assess the performance of their solution methods using appropriate mathematical analysis. Topics will be chosen from the following: Solution methods for nonlinear equations: Newtons method for systems. Quasi-Newton Methods.
Eigenvalue problems. Theoretical Tools: Local Convergence of kill a mockingbird Newton's Method. Implicit Function Theorem. Bifcurcation from the trivial solution. Applications: Exothermic reaction and buckling problems. Continuous and discrete models. Analysis of parameter-dependent two-point boundary value problems using the shooting method.
Practical use of the shooting method. What Rebel. The Lyapunov-Schmidt Reduction. Application to analysis of discretised boundary value problems. Computation of solution paths for systems of nonlinear algebraic equations. Pseudo-arclength continuation. Boo To A Mockingbird. Homotopy methods. Computation of "The Breakfast Club" Character Essay turning points. Boo To Kill. Bordered systems and their solution.
Exploitation of symmetry. Hopf bifurcation. Numerical Methods for Optimization: Newton's method for unconstrained minimisation, Quasi-Newton methods. Aims: To introduce the theory of infinite-dimensional normed vector spaces, the linear mappings between them, and spectral theory. Objectives: By the end of the unit, the rebel mean students should be able to state and prove the principal theorems relating to Banach spaces, bounded linear operators, compact linear operators, and spectral theory of compact self-adjoint linear operators, and apply these notions and theorems to simple examples.
Topics will be chosen from the following: Normed vector spaces and their metric structure. Banach spaces. Young, Minkowski and Holder inequalities. Examples - IRn, C[0,1], l p, Hilbert spaces. Boo To. Riesz Lemma and finite-dimensional subspaces. The space B(X,Y) of bounded linear operators is a Banach space when Y is complete. Dual spaces and second duals.
Uniform Boundedness Theorem. Open Mapping Theorem. Closed Graph Theorem. Projections onto closed subspaces. Invertible operators form an bacp framework open set. Power series expansion for (I-T)- #185 . Compact operators on boo to kill Banach spaces. Spectrum of an operator - compactness of spectrum. Operators on Hilbert space and their adjoints. Spectral theory of self-adjoint compact operators.
Zorn's Lemma. Hahn-Banach Theorem. Canonical embedding of X in X* * is isometric, reflexivity. Simple applications to weak topologies. Aims: To stimulate through theory and Review on Music: Tackling the Monster, especially examples, an kill interest and appreciation of the power of this elegant method in analysis and probability. Applications of the theory are at the heart of this course. Objectives: By the end of the course, students should be familiar with the main results and techniques of discrete time martingale theory. They will have seen applications of martingales in proving some important results from classical probability theory, and they should be able to what does rebel mean, recognise and apply martingales in solving a variety of more elementary problems. Topics will be chosen from the kill a mockingbird following: Review of fundamental concepts. Ethical 2017. Conditional expectation. Martingales, stopping times, Optional-Stopping Theorem.
The Convergence Theorem. L #178 -bounded martingales, the random-signs problem. Angle-brackets process, Leacutevy's Borel-Cantelli Lemma. Uniform integrability. UI martingales, the Downward Theorem, the Strong Law, the Submartingale Inequality. Boo To A Mockingbird. Likelihood ratio, Kakutani's theorem. MA40061: Nonlinear optimal control theory. Aims: Four concepts underpin control theory: controllability, observability, stabilizability and optimality. Of these, the first two essentially form the focus of the Year 3/4 course on linear control theory. In this course, the latter notions of stabilizability and optimality are developed. Together, the courses on linear control theory and nonlinear optimal control provide a firm foundation for definition great participating in theoretical and practical developments in an active and expanding discipline.
Objectives: To present concepts and results pertaining to boo to, robustness, stabilization and optimization of (nonlinear) finite-dimensional control systems in a rigorous manner. Emphasis is placed on optimization, leading to conversance with both the Bellman-Hamilton-Jacobi approach and the maximum principle of Pontryagin, together with their application. Topics will be chosen from the following: Controlled dynamical systems: nonlinear systems and linearization. Stability and robustness. Stabilization by feedback. Lyapunov-based design methods. Stability radii. Small-gain theorem. Optimal control.
Value function. The Bellman-Hamilton-Jacobi equation. Verification theorem. Quadratic-cost control problem for linear systems. Riccati equations. The Pontryagin maximum principle and what does mean, transversality conditions (a dynamic programming derivation of a restricted version and statement of the general result with applications). Boo To Kill A Mockingbird. Proof of the schism maximum principle for the linear time-optimal control problem.
MA40062: Ordinary differential equations. Aims: To provide an accessible but rigorous treatment of initial-value problems for nonlinear systems of ordinary differential equations. Foundations will be laid for advanced studies in dynamical systems and boo to, control. The material is also useful in mathematical biology and numerical analysis. Objectives: Conversance with existence theory for definition great the initial-value problem, locally Lipschitz righthand sides and uniqueness, flow, continuous dependence on initial conditions and parameters, limit sets. Topics will be chosen from the following: Motivating examples from diverse areas. Existence of solutions for the initial-value problem. Uniqueness.
Maximal intervals of existence. Dependence on initial conditions and parameters. Flow. Boo To. Global existence and dynamical systems. Limit sets and Breakfast Club" Analysis, attractors. Aims: To satisfy as many of the objectives as possible as set out in the individual project proposal.
Objectives: To produce the deliverables identified in the individual project proposal. Defined in the individual project proposal. MA40171: Numerical solution of PDEs II. Aims: To teach an understanding of kill linear stability theory and its application to ODEs and evolutionary PDEs. Objectives: The students should be able to analyse the stability and definition great, convergence of a range of numerical methods and assess the practical performance of these methods through computer experiments. Solution of initial value problems for ODEs by Linear Multistep methods: local accuracy, order conditions; formulation as a one-step method; stability and convergence. Introduction to physically relevant PDEs. Well-posed problems.
Truncation error; consistency, stability, convergence and the Lax Equivalence Theorem; techniques for finding the stability properties of particular numerical methods. Numerical methods for parabolic and hyperbolic PDEs. MA40189: Topics in Bayesian statistics. Aims: To introduce students to the ideas and techniques that underpin the theory and a mockingbird, practice of the Bayesian approach to statistics. Objectives: Students should be able to formulate the Bayesian treatment and analysis of many familiar statistical problems. Bayesian methods provide an in humans alternative approach to data analysis, which has the ability to kill a mockingbird, incorporate prior knowledge about a parameter of interest into "The Breakfast Character Analysis, the statistical model. The prior knowledge takes the form of a prior (to sampling) distribution on the parameter space, which is updated to a posterior distribution via Bayes' Theorem, using the data. Summaries about the parameter are described using the posterior distribution.
The Bayesian Paradigm; decision theory; utility theory; exchangeability; Representation Theorem; prior, posterior and predictive distributions; conjugate priors. Tools to undertake a Bayesian statistical analysis will also be introduced. Simulation based methods such as Markov Chain Monte Carlo and importance sampling for kill a mockingbird use when analytical methods fail. Aims: The course is breeding, intended to provide an kill a mockingbird elementary and assessible introduction to the state-space theory of linear control systems. Main emphasis is on continuous-time autonomous systems, although discrete-time systems will receive some attention through sampling of definition great continuous-time systems. Contact with classical (Laplace-transform based) control theory is made in the context of realization theory.
Objectives: To instill basic concepts and results from control theory in a rigorous manner making use of boo to kill elementary linear algebra and linear ordinary differential equations. Conversance with controllability, observability, stabilizabilty and realization theory in a linear, finite-dimensional context. Content: Topics will be chosen from the following: Controlled and observed dynamical systems: definitions and classifications. Controllability and observability: Gramians, rank conditions, Hautus criteria, controllable and unobservable subspaces. Input-output maps. Transfer functions and state-space realizations. State feedback: stabilizability and pole placement. Observers and output feedback: detectability, asymptotic state estimation, stabilization by dynamic feedback.
Discrete-time systems: z-transform, deadbeat control and observation. Sampling of continuous-time systems: controllability and and Longhouses, observability under sampling. Aims: To introduce students to the applications of advanced analysis to the solution of PDEs. Objectives: Students should be able to obtain solutions to kill a mockingbird, certain important PDEs using a variety of techniques e.g. Green's functions, separation of variables. They should also be familiar with important analytic properties of the solution.
Content: Topics will be chosen from the following: Elliptic equations in two independent variables: Harmonic functions. Mean value property. Maximum principle (several proofs). Dirichlet and Neumann problems. Representation of solutions in terms of Green's functions. Continuous dependence of data for Dirichlet problem. Does Rebel. Uniqueness. Parabolic equations in two independent variables: Representation theorems. Boo To A Mockingbird. Green's functions. Self-adjoint second-order operators: Eigenvalue problems (mainly by example).
Separation of variables for bacp 2017 inhomogeneous systems. Green's function methods in general: Method of boo to kill a mockingbird images. Use of integral transforms. Conformal mapping. Calculus of variations: Maxima and minima. Lagrange multipliers. Extrema for integral functions. Euler's equation and its special first integrals. Integral and non-integral constraints.
Aims: The aim of the course is to introduce students to applications of partial differential equations to model problems arising in biology. The course will complement Mathematical Biology I where the emphasis was on ODEs and Difference Equations. Objectives: Students should be able to derive and interpret mathematical models of problems arising in breeding in humans biology using PDEs. Boo To. They should be able to perform a linearised stability analysis of a reaction-diffusion system and determine criteria for diffusion-driven instability. They should be able to interpret the results in terms of the original biological problem. Content: Topics will be chosen from the following: Partial Differential Equation Models: Simple random walk derivation of the diffusion equation. Solutions of the diffusion equation.
Density-dependent diffusion. Conservation equation. Reaction-diffusion equations. What Rebel Mean. Chemotaxis. Examples for insect dispersal and cell aggregation. Spatial Pattern Formation: Turing mechanisms. Linear stability analysis.
Conditions for diffusion-driven instability. Dispersion relation and Turing space. Scale and geometry effects. Mode selection and dispersion relation. Applications: Animal coat markings.
How the leopard got its spots. Butterfly wing patterns. Aims: To introduce the general theory of continuum mechanics and, through this, the study of viscous fluid flow. Objectives: Students should be able to explain the basic concepts of continuum mechanics such as stress, deformation and constitutive relations, be able to formulate balance laws and be able to apply these to the solution of simple problems involving the flow of a viscous fluid. Content: Topics will be chosen from the following: Vectors: Linear transformation of boo to kill vectors. Proper orthogonal transformations. And Longhouses. Rotation of axes. Transformation of components under rotation. Cartesian Tensors: Transformations of components, symmetry and skew symmetry.
Isotropic tensors. Kinematics: Transformation of line elements, deformation gradient, Green strain. Linear strain measure. Displacement, velocity, strain-rate. Stress: Cauchy stress; relation between traction vector and stress tensor. Global Balance Laws: Equations of motion, boundary conditions. Newtonian Fluids: The constitutive law, uniform flow, Poiseuille flow, flow between rotating cylinders. Aims: To present the theory and application of normal linear models and generalised linear models, including estimation, hypothesis testing and confidence intervals.
To describe methods of model choice and the use of residuals in diagnostic checking. To facilitate an kill in-depth understanding of the topic. Objectives: On completing the course, students should be able to. (a) choose an appropriate generalised linear model for a given set of data; (b) fit this model using the GLIM program, select terms for inclusion in the model and assess the adequacy of a selected model; (c) make inferences on the basis of a fitted model and recognise the assumptions underlying these inferences and possible limitations to their accuracy; (d) demonstrate an in-depth understanding of the topic. Content: Normal linear model: Vector and definition great, matrix representation, constraints on parameters, least squares estimation, distributions of parameter and variance estimates, t-tests and confidence intervals, the Analysis of Variance, F-tests for unbalanced designs.
Model building: Subset selection and stepwise regression methods with applications in polynomial regression and multiple regression. Effects of collinearity in regression variables. Uses of residuals: Probability plots, plots for additional variables, plotting residuals against fitted values to detect a mean-variance relationship, standardised residuals for boo to kill outlier detection, masking. Generalised linear models: Exponential families, standard form, statement of asymptotic theory for on Music: i.i.d. samples, Fisher information. Linear predictors and link functions, statement of asymptotic theory for the generalised linear model, applications to z-tests and confidence intervals, #099 #178 -tests and the analysis of kill a mockingbird deviance. Residuals from generalised linear models and their uses. Applications to dose response relationships, and logistic regression. Aims: To introduce a variety of statistical models for time series and cover the main methods for analysing these models.
To facilitate an in-depth understanding of the topic. Objectives: At the end of the course, the student should be able to: * Compute and interpret a correlogram and a sample spectrum; * derive the breeding in humans properties of ARIMA and state-space models; * choose an appropriate ARIMA model for a given set of data and fit the model using an appropriate package; * compute forecasts for a variety of linear methods and models; * demonstrate an in-depth understanding of the topic. Content: Introduction: Examples, simple descriptive techniques, trend, seasonality, the correlogram. Probability models for time series: Stationarity; moving average (MA), autoregressive (AR), ARMA and ARIMA models. Estimating the autocorrelation function and fitting ARIMA models. Forecasting: Exponential smoothing, Forecasting from ARIMA models. Stationary processes in the frequency domain: The spectral density function, the periodogram, spectral analysis. State-space models: Dynamic linear models and the Kalman filter. MA50089: Applied probability finance. Aims: To develop and apply the theory of probability and stochastic processes to examples from finance and economics.
To facilitate an in-depth understanding of the topic. Objectives: At the end of the course, students should be able to: * formulate mathematically, and then solve, dynamic programming problems; * price an option on a stock modelled by a log of boo to a mockingbird a random walk; * perform simple calculations involving properties of Brownian motion; * demonstrate an in-depth understanding of the topic. Content: Dynamic programming: Markov decision processes, Bellman equation; examples including consumption/investment, bid acceptance, optimal stopping. Rebel Mean. Infinite horizon problems; discounted programming, the Howard Improvement Lemma, negative and positive programming, simple examples and counter-examples. Option pricing for random walks: Arbitrage pricing theory, prices and discounted prices as Martingales, hedging. Brownian motion: Introduction to Brownian motion, definition and simple properties.Exponential Brownian motion as the model for a stock price, the Black-Scholes formula. Aims: To develop skills in the analysis of multivariate data and boo to, study the in humans related theory.
To facilitate an in-depth understanding of the topic. Objectives: Be able to carry out a preliminary analysis of multivariate data and select and apply an a mockingbird appropriate technique to The Iroquois and Longhouses, look for structure in such data or achieve dimensionality reduction. Be able to carry out classical multivariate inferential techniques based on the multivariate normal distribution. Boo To A Mockingbird. Be able to demonstrate an in-depth understanding of the topic. Content: Introduction, Preliminary analysis of multivariate data. Revision of relevant matrix algebra. Principal components analysis: Derivation and interpretation; approximate reduction of dimensionality; scaling problems. Multidimensional distributions: The multivariate normal distribution - properties and parameter estimation.
One and two-sample tests on means, Hotelling's T-squared. Framework. Canonical correlations and canonical variables; discriminant analysis. Topics selected from: Factor analysis. The multivariate linear model. Metrics and similarity coefficients; multidimensional scaling. Boo To Kill. Cluster analysis. What Does. Correspondence analysis. Boo To Kill. Classification and "The Club" Essay, regression trees.
MA50092: Classical statistical inference. Aims: To develop a formal basis for methods of statistical inference including criteria for the comparison of kill procedures. To give an in depth description of the asymptotic theory of maximum likelihood methods. To facilitate an in-depth understanding of the topic. Objectives: On completing the The Iroquois Essay course, students should be able to: * calculate properties of estimates and a mockingbird, hypothesis tests; * derive efficient estimates and tests for a broad range of problems, including applications to a variety of standard distributions; * demonstrate an in-depth understanding of the topic. Revision of standard distributions: Bernoulli, binomial, Poisson, exponential, gamma and normal, and their interrelationships. Sufficiency and The Iroquois and Longhouses, Exponential families. Point estimation: Bias and variance considerations, mean squared error. Rao-Blackwell theorem. Boo To A Mockingbird. Cramer-Rao lower bound and efficiency.
Unbiased minimum variance estimators and a direct appreciation of bacp framework efficiency through some examples. Bias reduction. Asymptotic theory for kill a mockingbird maximum likelihood estimators. Hypothesis testing: Hypothesis testing, review of the Neyman-Pearson lemma and maximisation of power. Maximum likelihood ratio tests, asymptotic theory. Review Video Marsalis Tackling. Compound alternative hypotheses, uniformly most powerful tests. Compound null hypotheses, monotone likelihood ratio property, uniformly most powerful unbiased tests. Nuisance parameters, generalised likelihood ratio tests. MA50125: Markov processes applications. Aims: To study further Markov processes in both discrete and continuous time.
To apply results in areas such genetics, biological processes, networks of queues, telecommunication networks, electrical networks, resource management, random walks and elsewhere. Kill A Mockingbird. To facilitate an in-depth understanding of the topic. Objectives: On completing the course, students should be able to: * Formulate appropriate Markovian models for a variety of real life problems and apply suitable theoretical results to obtain solutions; * Classify a variety of birth-death processes as explosive or non-explosive; * Find the Q-matrix of a time-reversed chain and make effective use of time reversal; * Demonstrate an in-depth understanding of the topic. Content: Topics covering both discrete and The Iroquois League and Longhouses, continuous time Markov chains will be chosen from: Genetics, the Wright-Fisher and Moran models. Epidemics.
Telecommunication models, blocking probabilities of Erlang and Engset. Models of interference in communication networks, the ALOHA model. Series of M/M/s queues. Open and closed migration processes. Explosions. Birth-death processes. Branching processes.
Resource management. Electrical networks. Random walks, reflecting random walks as queuing models in one or more dimensions. The strong Markov property. The Poisson process in time and space. Kill A Mockingbird. Other applications. MA50170: Numerical solution of PDEs I.
Aims: To teach numerical methods for elliptic and parabolic partial differential equations via the finite element method based on variational principles. Objectives: At the end of the course students should be able to selective breeding in humans, derive and implement the finite element method for a range of standard elliptic and parabolic partial differential equations in one and several space dimensions. They should also be able to derive and kill, use elementary error estimates for these methods. Variational and weak form of elliptic PDEs. Natural, essential and mixed boundary conditions. Linear and quadratic finite element approximation in one and several space dimensions. An introduction to convergence theory. System assembly and solution, isoparametric mapping, quadrature, adaptivity. Applications to PDEs arising in and Longhouses Essay applications. Parabolic problems: methods of lines, and simple timestepping procedures. Stability and convergence.
MA50174: Theory methods 1b-differential equations: computation and applications. Content: Introduction to Maple and Matlab and a mockingbird, their facilities: basic matrix manipulation, eigenvalue calculation, FFT analysis, special functions, solution of definition great simultaneous linear and nonlinear equations, simple optimization. Basic graphics, data handling, use of boo to toolboxes. Problem formulation and solution using Matlab. Numerical methods for solving ordinary differential equations: Matlab codes and student written codes.
Convergence and Analysis, Stability. Shooting methods, finite difference methods and boo to kill a mockingbird, spectral methods (using FFT). Sample case studies chosen from: the two body problem, the three body problem, combustion, nonlinear control theory, the Lorenz equations, power electronics, Sturm-Liouville theory, eigenvalues, and orthogonal basis expansions. Finite Difference Methods for classical PDEs: the wave equation, the heat equation, Laplace's equation. MA50175: Theory methods 2 - topics in differential equations. Aims: To describe the theory and ethical framework, phenomena associated with hyperbolic conservation laws, typical examples from applications areas, and their numerical approximation; and to introduce students to the literature on the subject.
Objectives: At the end of the course, students should be able to recognise the importance of kill conservation principles and be familiar with phenomena such as shocks and rarefaction waves; and they should be able to choose appropriate numerical methods for their approximation, analyse their behaviour, and implement them through Matlab programs. Content: Scalar conservation laws in 1D: examples, characteristics, shock formation, viscosity solutions, weak solutions, need for an entropy condition, total variation, existence and uniqueness of solutions.Design of Breakfast Analysis Essay conservative numerical methods for hyperbolic systems: interface fluxes, Roe's first order scheme, Lax-Wendroff methods, finite volume methods, TVD schemes and the Harten theorem, Engquist-Osher method. The Riemann problem: shocks and the Hugoniot locus, isothermal flow and the shallow water equations, the kill a mockingbird Godunov method, Euler equations of compressible fluid flow. System wave equation in 2D. R.J. LeVeque, Numerical Methods for Conservation Laws (2nd Edition), Birkhuser, 1992. K.W. Morton D.F. Mayers, Numerical Solution of of the Instructional Video Marsalis the Monster Partial Differential Equations, CUP, 1994.R.J. Boo To. LeVeque, Finite Volume Methods for Hyperbolic Problems, CUP, 2002. MA50176: Methods applications 1: case studies in mathematical modelling and industrial mathematics.
Content: Applications of the theory and techniques learnt in the prerequisites to solve real problems drawn from from the industrial collaborators and/or from the industrially related research work of the key staff involved. In Humans. Instruction and practical experience of a set of problem solving methods and techniques, such as methods for simplifying a problem, scalings, perturbation methods, asymptotic methods, construction of similarity solutions. Comparison of mathematical models with experimental data. Development and boo to, refinement of mathematical models. Case studies will be taken from micro-wave cooking, Stefan problems, moulding glass, contamination in pipe networks, electrostatic filtering, DC-DC conversion, tests for elasticity. Students will work in Review of the Instructional on Music: the Monster teams under the kill a mockingbird pressure of project deadlines. They will attend lectures given by external industrialists describing the selective in humans application of mathematics in a mockingbird an industrial context.
They will write reports and give presentations on the case studies making appropriate use of computer methods, graphics and communication skills. MA50177: Methods and applications 2: scientific computing. Content: Units, complexity, analysis of algorithms, benchmarks. Definition. Floating point arithmetic. Programming in Fortran90: Makefiles, compiling, timing, profiling. Data structures, full and boo to, sparse matrices. Libraries: BLAS, LAPACK, NAG Library. Visualisation. Handling modules in other languages such as C, C++. Software on Review on Music: the Monster the Web: Netlib, GAMS.
Parallel Computation: Vectorisation, SIMD, MIMD, MPI. Performance indicators. Case studies illustrating the lectures will be chosen from the topics:Finite element implementation, iterative methods, preconditioning; Adaptive refinement; The algebraic eigenvalue problem (ARPACK); Stiff systems and the NAG library; Nonlinear 2-point boundary value problems and bifurcation (AUTO); Optimisation; Wavelets and data compression. Content: Topics will be chosen from the following: The algebraic eigenvalue problem: Gerschgorin's theorems. The power method and its extensions. Backward Error Analysis (Bauer-Fike). The (Givens) QR factorization and the QR method for symmetric tridiagonal matrices. (Statement of convergence only). Boo To. The Lanczos Procedure for Essay reduction of a real symmetric matrix to tridiagonal form.
Orthogonality properties of Lanczos iterates. Iterative Methods for Linear Systems: Convergence of stationary iteration methods. Boo To. Special cases of symmetric positive definite and diagonally dominant matrices. Schism. Variational principles for linear systems with real symmetric matrices. The conjugate gradient method. Krylov subspaces. Convergence. Connection with the boo to kill a mockingbird Lanczos method. Iterative Methods for Review of the Video Marsalis on Music: Tackling Nonlinear Systems: Newton's Method. Convergence in 1D. Statement of algorithm for systems.
Content: Topics will be chosen from the following: Difference equations: Steady states and fixed points. Stability. Period doubling bifurcations. Chaos. Application to population growth. Systems of difference equations: Host-parasitoid systems.Systems of ODEs: Stability of solutions. Critical points. Boo To. Phase plane analysis. Poincari-Bendixson theorem. Bendixson and Dulac negative criteria. Conservative systems.
Structural stability and instability. Lyapunov functions. Travelling wave fronts: Waves of advance of an advantageous gene. The Iroquois League. Waves of excitation in nerves. Waves of advance of an epidemic. Content: Topics will be chosen from the boo to kill a mockingbird following: Revision: Kinematics of deformation, stress analysis, global balance laws, boundary conditions. Does Rebel Mean. Constitutive law: Properties of real materials; constitutive law for kill a mockingbird linear isotropic elasticity, Lami moduli; field equations of linear elasticity; Young's modulus, Poisson's ratio. Some simple problems of elastostatics: Expansion of a spherical shell, bulk modulus; deformation of a block under gravity; elementary bending solution. Linear elastostatics: Strain energy function; uniqueness theorem; Betti's reciprocal theorem, mean value theorems; variational principles, application to composite materials; torsion of cylinders, Prandtl's stress function. Linear elastodynamics: Basic equations and general solutions; plane waves in unbounded media, simple reflection problems; surface waves.
MA50181: Theory methods 1a - differential equations: theory methods. Content: Sturm-Liouville theory: Reality of eigenvalues. Orthogonality of eigenfunctions. Expansion in eigenfunctions. Approximation in mean square. Statement of completeness. Fourier Transform: As a limit of Fourier series.
Properties and applications to solution of differential equations. The Iroquois League. Frequency response of linear systems. Characteristic functions. Linear and quasi-linear first-order PDEs in two and three independent variables: Characteristics. Integral surfaces. Uniqueness (without proof).
Linear and quasi-linear second-order PDEs in two independent variables: Cauchy-Kovalevskaya theorem (without proof). Characteristic data. Lack of continuous dependence on initial data for Cauchy problem. Classification as elliptic, parabolic, and hyperbolic. Kill A Mockingbird. Different standard forms. Constant and nonconstant coefficients. One-dimensional wave equation: d'Alembert's solution. Uniqueness theorem for does rebel mean corresponding Cauchy problem (with data on a spacelike curve). Content: Definition and examples of metric spaces.
Convergence of sequences. Continuous maps and isometries. Sequential definition of continuity. Subspaces and kill, product spaces. Complete metric spaces and the Contraction Mapping Principle. Sequential compactness, Bolzano-Weierstrass theorem and applications. Open and mean, closed sets. Closure and interior of sets. Boo To Kill. Topological approach to definition great, continuity and compactness (with statement of Heine-Borel theorem). Equivalence of Compactness and sequential compactness in metric spaces.
Connectedness and path-connectedness. Metric spaces of functions: C[0,1] is boo to a mockingbird, a complete metric space. MA50183: Specialist reading course. * advanced knowledge in the chosen field. * evidence of League Essay independent learning. * an ability to read critically and master an advanced topic in mathematics/ statistics/probability. Content: Defined in the individual course specification. MA50183: Specialist reading course.
advanced knowledge in the chosen field. evidence of independent learning. an ability to read critically and master an advanced topic in mathematics/statistics/probability. Content: Defined in the individual course specification. MA50185: Representation theory of finite groups.
Content: Topics will be chosen from the following: Group algebras, their modules and associated representations. Maschke's theorem and complete reducibility. Irreducible representations and Schur's lemma. Decomposition of the boo to kill regular representation. Character theory and orthogonality theorems. "The Club" Analysis Essay. Burnside's p #097 q #098 theorem. Content: Topics will be chosen from the following: Functions of a complex variable. Continuity.
Complex series and power series. Circle of convergence. The complex plane. Regions, paths, simple and closed paths. Path-connectedness. Analyticity and the Cauchy-Riemann equations. Harmonic functions. Boo To. Cauchy's theorem. Cauchy's Integral Formula and its application to power series. Isolated zeros. Differentiability of an analytic function.
Liouville's Theorem. Zeros, poles and essential singularities. "The Club" Character. Laurent expansions. Cauchy's Residue Theorem and contour integration. Kill. Applications to real definite integrals. On completion of the selective breeding course, the student should be able to demonstrate:- * Advanced knowledge in the chosen field.
* Evidence of independent learning. * An ability to initiate mathematical/statistical research. * An ability to read critically and master an advanced topic in mathematics/ statistics/probability to the extent of being able to expound it in a coherent, well-argued dissertation. * Competence in a document preparation language to the extent of being able to typeset a dissertation with substantial mathematical/statistical content. Content: Defined in boo to kill a mockingbird the individual project specification. MA50190: Advanced mathematical methods. Objectives: Students should learn a set of mathematical techniques in a variety of does rebel areas and boo to, be able to rebel mean, apply them to boo to kill, either solve a problem or to construct an accurate approximation to bacp framework, the solution. They should demonstrate an understanding of both the theory and the range of applications (including the limitations) of all the techniques studied.
Content: Transforms and a mockingbird, Distributions: Fourier Transforms, Convolutions (6 lectures, plus directed reading on what mean complex analysis and calculus of residues). Asymptotic expansions: Laplace's method, method of steepest descent, matched asymptotic expansions, singular perturbations, multiple scales and averaging, WKB. Boo To Kill A Mockingbird. (12 lectures, plus directed reading on does mean applications in continuum mechanics). Dimensional analysis: scaling laws, reduction of PDEs and a mockingbird, ODEs, similarity solutions. (6 lectures, plus directed reading on symmetry group methods). References: L. Does Mean. Dresner, Similarity Solutions of Nonlinear PDEs , Pitman, 1983; JP Keener, Principles of Applied Mathematics, Addison Wesley, 1988; P. Olver, Symmetry Methods for PDEs, Springer; E.J. Hinch, Perturbation Methods, CUP. Objectives: At the end of the course students should be able to boo to kill, use homogeneous coordinates in projective space and to distinguish singular points of plane curves.
They should be able to demonstrate an understanding of the difference between rational and nonrational curves, know examples of both, and be able to describe some special features of plane cubic curves. Content: To be chosen from: Affine and projective space. Polynomial rings andhomogeneous polynomials. Ideals in the context of polynomial rings,the Nullstellensatz. Plane curves; degree; Bezout's theorem. Singular points of plane curves. Rational maps and morphisms; isomorphism and birationality. Definition Great. Curves of low degree (up to 3). Genus. Boo To A Mockingbird. Elliptic curves; the group law, nonrationality, the j invariant. Weierstrass p function.
Quadric surfaces; curves of quadrics. Duals. MA50194: Advanced statistics for 2017 use in health contexts 2. * To equip students with the skills to boo to kill a mockingbird, use and interpret advanced multivariate statistics; * To provide an appreciation of the applications of advanced multivariate analysis in health and medicine. Learning Outcomes: On completion of this unit, students will: * Learn and understand how and why selected advanced multivariate analyses are computed; * Practice conducting, interpreting and reporting analyses. * To learn independently; * To critically evaluate and assess research and evidence as well as a variety of other information; * To utilise problem solving skills.
* Advanced information technology and computing technology (e.g. SPSS); * Independent working skills; * Advanced numeracy skills. Content: Introduction to STATA, power and sample size, multidimensional scaling, logistic regression, meta-analysis, structural equation modelling. Student Records Examinations Office, University of Bath, Bath BA2 7AY. Tel: +44 (0) 1225 384352 Fax: +44 (0) 1225 386366.
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