best way to write a math essay

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How to write a good mathematical paper?

I hesitate to ask this question. However I read many advices from math.stackexchange, and I couldn't find anything similar.

A good time always goes too fast! Two years are fled. In the third year of PHD, my major is general topology and I'm facing with graduation from PHD. I do enjoy research, however the pressure to publish makes me be agitated and not quite, for I haven't publish any paper. I find, sometimes, doing research and to publish are contradictory.

Here is my question: How to write a good mathematical paper? Could anybody give me some suggestions?

Thanks ahead.

• soft-question
• article-writing

• 10 $\begingroup$ It appears that you have done research and produced some results. Writing a paper should be easy once you have something to write about. You should write done your results and proofs as clearly as possible. Try not to get bogged down by details, and consult your advisor to determine what details an expert should be able fill in themselves. Check your spelling and grammar. Talk to advisor about the known journals of your area and those likely to accept your paper. The important thing is to consult your advisor, but since you have results, I think the hardest part is already done. $\endgroup$ –  William Commented Aug 11, 2012 at 1:38
• 4 $\begingroup$ Don't do the classic textbook approach of having your main statement and the preceeding lemmas be a total secret until the reader get to the specific page. The most negative comment I recieved on the only thing I have ever written close to a mathematical paper was that I started out too "heavy". I was told it was better to have an abstract (which should only be a sentence or two) and then a relatively short section explaining basic ideas in a way that wouldn't be considered a wall of text or an overload of definitions and constructions. $\endgroup$ –  Arthur Commented Aug 11, 2012 at 1:48
• 12 $\begingroup$ You have to have a result first. $\endgroup$ –  user2468 Commented Aug 11, 2012 at 3:44
• 3 $\begingroup$ @Paul Unfortunately I cannot edit it, although it does work for me. Here is the direct link: terrytao.wordpress.com/advice-on-writing-papers $\endgroup$ –  Sniper Clown Commented Aug 11, 2012 at 6:58
• 9 $\begingroup$ Having just refereed my first paper, I'll try to say a few of meaningful things. (1) Don't obfuscate with formally correct notation where a general idea -- simply expressible in English with perhaps a few mathematical symbols -- will suffice. (2) Be consistent with notations/conventions. (3) If your proof involves a long, tedious, technical component, break it up into segments and explain what it is you are attempting to do in each segment. (4) Remember that while after two years of intense study everything seems natural and clear, it might not be for someone seeing it for the first time. $\endgroup$ –  user642796 Commented Aug 11, 2012 at 7:07

5 Answers 5

As someone who is currently working on my first mathematical paper, I've found this guide from MIT to be very helpful. It covers both writing a clear and precise paper in general as well as the specific challenges presented by a mathematical paper. It's also fun to read! For example, the author likes to illustrate common mistakes within the text. One of my favorites is:

Don’t string adjectives together, especially if they are really nouns. Many high quality pure mathematics original research journal article sentences illustrate this problem.

• 1 $\begingroup$ Thanks for your answer and your paper. The paper seems very helpful for me. I'v downloaded it:) $\endgroup$ –  Paul Commented Aug 11, 2012 at 1:58
• 8 $\begingroup$ +1 for the intelligent sentence. Made me laugh this morning! $\endgroup$ –  Gottfried Helms Commented Aug 12, 2012 at 8:34
• 1 $\begingroup$ it is funny)))) $\endgroup$ –  Seyhmus Güngören Commented Aug 23, 2012 at 8:54

There are some notes on Mathematical Writing from a course taught by Knuth. They are quite extensive; I've only read the first few pages and those were already quite helpful to me, but there are also notes from guest lectures by various people, e.g. Wilf and Halmos.

You say you haven't published a paper yet. Then perhaps this would be useful to you: How to Write Your First Paper by Steven G. Krantz (Notices of the AMS, December 2007, pp. 1507-1511).

I would like to add the above mentioned Paul Halmos work on How to Write Mathematics .

In too short (taken from the MAA ):

Say something. To have something to say is by far the most important ingredient of good exposition. Speak to someone. Ask yourself who it is that you want to reach. Organize. Arrange the material so as to minimize the resistance and maximize the insight of the reader. Use consistent notation. The letters (or symbols) that you use to denote the concepts that you’ll discuss are worthy of thought and careful design. Write in spirals. Write the first section, write the second section, rewrite the first section, rewrite the second section, write the third section, rewrite the first section, rewrite the second section, rewrite the third section, write the fourth section, and so on. ( Annotation : 1,2,1,2,3,1,2,3,4,...) Watch your language. Good English style implies correct grammar, correct choice of words, correct punctuation, and common sense. Be honest. Smooth the reader’s way, anticipating difficulties and forestalling them. Aim for clarity, not pedantry; understanding, not fuss. Remove the irrelevant. Irrelevant assumptions, incorrect emphasis, or even the absence of correct emphasis can wreak havoc. Use words correctly. Think about and use with care the small words of common sense and intuitive logic, and the specifically mathematical words (technical terms) that can have a profound effect on mathematical meaning. Resist symbols. The best notation is no notation; whenever it is possible to avoid the use of a complicated alphabetic apparatus, avoid it.

I would like to add

"If you work eight hours to save five minutes of the reader's time, you have saved over 80 man-hours for each 1000 readers, and your name will be deservedly blessed down the corridors of many mathematics buildings." p. 134

and emphasize that at least the former holds for every scientific writing.

http://padic.mathstat.uottawa.ca/~mnevins/latex/sample.pdf , here is a good short and simple guide. other is the following: www2.kenyon.edu/Depts/Math/Aydin/.../Report.doc, which goes to the main aspects of the body of a math report.

Hope to be useful. Greetings.

• $\begingroup$ www2.kenyon.edu/Depts/Math/Aydin/Teach/Spring03/112/Report.doc $\endgroup$ –  erder Commented Jul 21, 2014 at 2:40

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How mathematical practices can improve your writing

Writing is similar to three specific mathematical practices: modelling, problem-solving and proving, writes Caroline Yoon. Here, she gives some tips on how to use these to improve academic writing

Caroline Yoon

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I feel for my students when I hand them their first essay assignment. Many are mathematicians, students and teachers who chose to study mathematics partly to avoid writing. But in my mathematics education courses, and in the discipline more generally, academic writing is part of our routine practice.

Mathematicians face some challenging stereotypes when it comes to writing. Writing is seen as ephemeral, subjective and context-dependent, whereas mathematics is seen as enduring, universal and context-free. Writing reflects self, but mathematics transcends it: they are distinct from each other.

This is a false dichotomy that can discourage mathematicians from writing. It suggests writing is outside the natural skill set of the mathematician, and that one’s mathematics training not only neglects one’s development as a writer but actively prevents it. Rather than capitulate to this false dichotomy, I propose we turn it around to examine how writing is similar to three specific mathematical practices: modelling, problem-solving and proving.

Three mathematical practices that can improve your writing

Mathematical modelling.

Let us consider a hypothetical mathematics education student who has spent weeks thinking, reading and talking about her essay topic, but only starts writing it the night before it is due. She writes one draft only – the one she hands in – and is disappointed with the low grade her essay receives.

She wishes she had started earlier but she was still trying to figure out what she wanted to say up until the moment she started writing. It was only the pressure of the deadline that forced her to start; without it, she would have spent even more time thinking and reading to develop her ideas. After all, she reasons, there is no point writing when you do not know what to write about!

This “think first, write after” approach, sometimes known as the “writing up” model is a dangerous trap many students fall into, and is at odds with the way writing works. The approach allows no room for imperfect drafts that are a necessary part of the writing process . Writing experts trade on the generative power of imperfect writing; they encourage writers to turn off their internal critics and allow themselves to write badly as a way of overcoming writing inertia and discovering new ideas. The “shitty first draft” is an ideal (and achievable) first goal in the writing process. Anyone can produce a sketchy first draft that generates material that can be worked on, improved and eventually rewritten into a more sharable form.

Mathematical modelling offers a compelling metaphor for the generative power of imperfect writing. Like polished writing, polished mathematical models are seldom produced in the first attempt. A modeller typically begins with some understanding of the real situation to be modelled. The modeller considers variables and relationships from his or her understanding of the real situation and writes them into an initial mathematical model.

The model is his or her mathematical description of the situation, written in mathematical notation, and the modeller who publishes a mathematical model has typically created and discarded multiple drafts along the way, just as the writer who publishes a piece of writing has typically written and discarded multiple drafts along the way.

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Problem-solving

Writing an original essay is like trying to solve a mathematics problem. There is no script to follow; it must be created by simultaneously determining one’s goals and figuring out how to achieve them. In both essay writing and mathematical problem-solving, getting stuck is natural and expected. It is even a special kind of thrill.

This observation might come as a surprise to mathematicians who do not think of their problem-solving activity as writing. But doing mathematics, the ordinary everyday act of manipulating mathematical relationships and objects to notice new levels of structure and pattern, involves scratching out symbols and marks, and moving ideas around the page or board.

Why do I care that mathematicians acknowledge their natural language of symbols and signs as writing? Quite frankly because they are good at it. They have spent years honing their ability to use writing to restructure their thoughts, to dissect their ideas, identify new arguments. They possess an analytic discipline that most writers struggle with.

Yet few of my mathematics education students take advantage of this in their academic writing. They want their writing to come out in consecutive, polished sentences and become discouraged when it does not. They do not use their writing to analyse and probe their arguments as they do when they are stuck on mathematical problems. By viewing writing only as a medium for communicating perfectly formed thoughts, they deny themselves their own laboratories, their own thinking tools.

I am not suggesting that one’s success in solving mathematical problems automatically translates into successful essay writing. But the metaphor of writing as problem-solving might encourage a mathematics education student not to give up too easily when she finds herself stuck in her writing.

Our hypothetical student now has a good draft that she is happy with. She is satisfied it represents her knowledge of the subject matter and has read extensively to check the accuracy of its content. A friend reads the draft and remarks that it is difficult to understand. Our student is unperturbed. She puts it down to her friend’s limited knowledge of the subject and is confident her more knowledgeable teacher will understand her essay.

But the essay is not an inert record judged on the number of correct facts it contains. It is also a rhetorical act that seeks to engage the public. It addresses an audience, it tries to persuade, to inspire some response or action.

Mathematical proofs are like expository essays in this regard; they must convince an audience. When undergraduate mathematics students learn to construct proofs of their own, a common piece of advice is to test them on different audiences. The phrase “Convince yourself, convince a friend, convince an enemy” becomes relevant in this respect.

Mathematicians do not have to see themselves as starting from nothing when they engage in academic writing. Rather, they can use mathematical principles they have already honed in their training, but which they might not have formerly recognised as tools for improving their academic writing.

Practical tips for productive writing beliefs and behaviours

• Writing can generate ideas. Free writing is a good way to start. Set a timer and write continuously for 10 minutes without editing. These early drafts will be clumsy, but there will also be some gold that can be mined and developed.
• Writing can be used to analyse and organise ideas. When stuck, try to restructure your ideas. Identify the main point in each paragraph and play around with organising their flow. 
• Writing is a dialogue with the public. Seek out readers’ interpretations of your writing and listen to their impressions. Read your writing out loud to yourself: you will hear it differently!

Caroline Yoon is an associate professor of mathematics at the University of Auckland.

This is an edited version of the journal article “The writing mathematician” by Caroline Yoon, published in For the Learning of Mathematics  and collected in The Best Writing on Mathematics , edited by  Mircea Pitici  (Princeton University Press).

If you would like advice and insight from academics and university staff delivered direct to your inbox each week,  sign up for the Campus newsletter .

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How to Apply a Mathematical Approach to Essay Writing

The use of mathematical strategies has long gone beyond solving complex levels and problems, making it easier and faster to complete tasks from other disciplines. One example of an academic task where the math approach will come into handy is writing an essay. With various techniques, your academic grades will increase, and your writing style will prosper.

Beneficial Impact on Your Writing

As a queen of science, mathematics promotes the development of various skills applicable to solving diverse problems and the formation of true-and-tried strategies for completing multiple academic assignments. With accuracy, objectivity, and logical rigor as a few fundamental principles, it provides students with a powerful tool to optimize many learning processes.

Not the least of them is writing essays that combine diverse techniques and approaches, the alternation of which will allow students to pump a range of skills from different angles. Using various mathematical models contributes to a more in-depth understanding of multiple cases and concepts while delegating tasks to professionals will save time to develop extra skills, requiring to visit ScamFighter for honest reviews preliminarily to avoid making a mistake in the choice.

Regular application of mathematical techniques, accompanied by developing strategies based on your experience and specific secrets, helps significantly expand the list of abilities and enhance those you already have. Among them are:

• logical reasoning;
• analytical abilities;
• mathematical literacy;
• visualization skills;
• critical thinking;

Many of the above may be helpful to you outside of academics, boosting personal and professional growth. These include activities such as communication strengthened through developed argumentation skills, deep understanding of concepts, etc.

Subsequently, you will quickly and qualitatively analyze large volumes of complex materials, making informed conclusions. It will help you figure out is MyAssignmentHelp.com safe and answer similar issues to see through suspicious companies in the shortest possible time, eliminating the risk of twisting you around someone’s finger by contacting only trusted services.

Where It Will Come in Very Handy

The mathematical approach can become the core of many strategies for writing academic papers in multiple fields of knowledge. Narrowing the latter’s focus, we can highlight economics in studying complex processes and concepts that mathematical methods can help with. In addition to in-depth analysis of large volumes of data, they will help you predict the further development of economic processes and identify key trends.

It also applies to essays studying scientific and high-tech phenomena where math strategies will cost modeling and interpretation. In addition, the use of mathematical approaches when writing essays on philosophy strengthens the argumentation and evidence provided. The well-known approaches of deduction and induction will allow you to shape the paper’s logical sequence while maintaining the structure’s integrity.

Specialists with many years of experience are always ready to help you with any topic, regardless of academic discipline, while the paperhelp.org promo codes on reddit and other available gifts enhance your experience.

Math Techniques to Apply in Writing Papers

Many ways to make your academic paper better and more detailed while at the same time infusing your writing style with new skills are based on multiple math approaches. Among them is a statistical method that strengthens your arguments and thoughts by involving various facts, surveys, and analyses. Another way to improve your paper would be to conduct a unique survey and then implement the results and processed information.

The use of math models, which facilitate the study of complex concepts and phenomena, will be no less valuable. Its beneficial effect lies in predicting trends, making effective comparisons, and identifying correlations between several concepts. Boosting visualization with graphs, figures, and diagrams will help achieve the latter. Probability theory can help analyze and assess the probability of a particular event. It will be especially effective if your essay topic explores random phenomena and considers potential risks.

Beyond academic writing, climate change approaches help develop valuable skills for solving various problems. You will not notice how you start reading your favorite book, article, or EssayBot review with increased attention to detail and in-depth analysis of multiple statements.

A Few More Things to Consider

Writing an essay using mathematical approaches can make your paper richer, making it easier to complete various tasks at specific workflow stages and presenting the materials you have mastered in the best light. However, it is necessary to remember some nuances to avoid the opposite effect, which manifests in various shortcomings that worsen the quality of the essay and confuse readers.

One of the primary reasons for the latter is an overabundance of formal vocabulary, turning your paper into a treasure trove of mathematical concepts. It makes it necessary to maintain maximum clarity, providing all relevant information where required. The same goes for introducing a variety of visual components, moving the tracking of their relevance to the top of your to-do list.

It is also necessary to familiarize yourself with the central requirements and extra recommendations to find a mathematical approach to develop your topic quickly. At the same time, answers to questions like is EssayBot legit will bring you closer to successfully writing a paper without unnecessary investments. Another mandatory task is carefully proofreading and checking the essay after finishing writing, eliminating all the shortcomings and unnecessary things.

Final Thoughts

Using mathematical approaches to write essays can be advantageous from different angles, contributing to the development of a wide range of skills. However, adhering to a few points is essential to achieve maximum effect and avoid obstacles.

by: Effortless Math Team about 4 months ago (category: Blog )

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A Comprehensive Guide to Math Writing Strategies

Math writing? Is that even possible? Perhaps, this topic currently raises some eyebrows. It’s even possible that you are hearing this term for the first time. So, to get this question out of the way, math writing is real. But what does it mean? Personally, math writing isn’t about making math; it is about making mathematical reasoning. Some mathematicians are said to be “mathematicians of the hands” because of their ability to apply mathematical reasoning to different objects.

Mathematical reasoning is an area that requires not only mathematical knowledge but also the application of that knowledge. Without mathematical reasoning then maths, itself, is worthless. But how do we note that reasoning that encapsulates our intelligence and capabilities? This is where math writing comes into play. Math writing helps us to record ideas, thoughts, and observations to gain insights and develop conjectures.

Why Isn’t Math Writing Common In Schools?

Teaching math writing in schools is difficult for a variety of reasons, including the fact that students have varied ways of processing and articulating information. Some of them go to great lengths to find the best website to get essay written in a bid to aid study. Even at that, they receive minimal guidance from their educators on what type of mathematical writing to incorporate.

Part of the issue originates from tutors’ lack of knowledge about the best methods for teaching math writing to their students. As a result, they completely disregard it, confining these students to standard instructional techniques that focus on computation and procedural competence. For example, there is a difference between knowing that 2 plus 2 is 4, and understanding why it is 4.

Most students are confined to knowing, but not understanding - these are two different concepts. Hence, they work out mathematical calculations effortlessly but can’t understand or communicate mathematically. Unfortunately, some tutors are helpless in bridging this gap as they were once students who weren’t privileged to learn math writing. This situation makes it difficult for them to teach this topic to their students. Besides, you cannot give what you don’t have.

Math writing obstacles come with feasible practical solutions that benefit both teachers and students.

Strategies that Promote Math Writing

Students who incorporate “cramming” into mathematical problems may have a hard time understanding the underlying factors that make maths relevant. Even though they know that 12 divided by 3 is 4, they don’t understand what makes it so. In such situations, learning becomes more of “what I was told,” rather than “what I understood.” However, the following strategies can improve mathematical learning and understanding when applied by tutors.

Modelling Writing Technique

This math writing technique focuses on constructing grammatical structures, sequencing ideas logically, justifying mathematical thoughts, using simple to complex vocabularies, among other strategies. With this process, tutors communicate their mathematical thoughts aloud while putting them into writing. Not only do the students grasp the teacher’s modelled writing style, but they connect with the tutor’s thoughts as well. Learning becomes visual and mental.

How can this technique work effectively? The modelling writing technique, also known as the think-aloud technique, comprises three segments: the writing process and the revision process.

Writing Process

This writing process helps students to understand how to put their mathematical thoughts on paper. The ideal timeframe for this phase should be between 5 to 10 minutes, and here is how it works:

• Find a learning need in the students concerning a maths topic and create a think-aloud lesson

• Explain to the students the purpose of this technique, targeted audience, benefits, and resources to be used

• Record your writing using an interactive board or paper chart, communicating your thoughts aloud as you proceed

• Be concise in writing these thoughts to prevent boredom and distraction

• Once done, communicate conclusive thoughts on the technique

• Ask the students to share their experience, questions, and lessons learnt during the process

Revision Process

Tutors and students should revise previous documentation to improve learning. But in what way? Revision inculcates the habit of rereading previously written documents. So, here is how it works:

• Dedicate time with the students to revise previous modelling-based documentations

• Explain to them the benefits of revision, including ways to improve on previous works

• Display the document and encourage group reading

• Put revisions into writing to aid learning

Mathematical Writing Conference

This math writing technique involves one-on-one learning communication between a tutor and a student. This time around, the students share their thoughts and ideas on their mathematical documentation with their tutors. With the information gathered, the teacher can provide the students with more insights on how to make their works better. This technique comprises four working parts:

• Researching the students’ mathematical thought and writing process

• Identifying the students’ actual instructional and learning needs

• Delivering a teaching point that addresses mathematical learning and writing needs

• Linking current learning process to the students’ future writing skills

The mathematical writing conference technique pushes the student to do better as there is a feedback mechanism on the teacher’s part. Students use highly focused teaching guidelines from their tutors to improve their math writing skills. Ideally, this technique should not last beyond five minutes. Conferences should be conversational, but brief as well.

Feedback should be concise, brief, and within the students’ capabilities. It should also come after a genuine compliment, celebrating their works.

Minilessons

Minilessons can focus on a smaller group or the entire class. Such learning sessions are concise and intensely focused, as students are assigned independent writing strategies to improve their math writing skills. These lessons span a maximum of 10 minutes. During this period, the tutor delivers a teaching point, after which the student put the lesson into practice, mostly in the class. By doing so, the teacher can engage them actively.

In summary, the teacher makes a connection, deliver a teaching point, engage the students, and link the lesson taught to future math writing works.

In Conclusion

Math writing is designed to help students test their abilities to observe and write down math problems in English. Students who need help with complex math problems can undertake math writing . By using this technique, tutors can also provide individual instructional learning that enhances the students’ level of understanding. As such, schools should promote this technique more.

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Expository Papers in Mathematics

Introduction.

It is very helpful to have an introduction (and, depending on how long your paper is, an abstract) to contextualize your paper. Introductions should not yet bombard the reader with heavy mathematics. Keep it light. It is often interesting to frame the paper in some interesting question that can only be answered by understanding the material in your paper. Or, if your topic is not something you can tie into a real-world problem, use your introduction to convince the reader of the relevance of the topic. Why is it interesting? What subfields of math is it pertinent to? Historical background, if you choose to use any, finds a great home in the introduction.

As with any paper, it is important to know your audience. If your professor doesn’t specify, ask. Can you assume that the reader has taken your course? Or should your paper be accessible to the general public? With math being in essence its own language, it is important to know how much hand-holding and defining your paper should do. Regardless of your audience, though, you must give concrete examples of the often abstract ideas being discussed.

When in doubt, use examples! Examples are the best way to ground your reader and ensure they understand your complex material. Particularly when your definitions or theorems are in general form, pick a basic yet illustrative example with which to couple it. It is often helpful to give an example before stating the general definition or theorem. That way, the example eases your reader into the general form, as opposed to serving as damage control after having scared them with abstraction.

Let your voice come through! Just because it’s a math paper doesn’t mean it has to uphold the field’s stigma of being dry and clinical-sounding. Your reader should want to read your paper. So, don’t shy away from being punny, taking on a tone, or varying your syntax. And have fun—just as you would in any piece of writing. What is unique about a math paper, though, is that actual definitions, theorems, conjectures, proofs etc. must retain their formalities.

As such, it is helpful to keep your informal prose visually separate from the more precise and technical components of the paper. Paragraphs and punctuation are still crucial in math papers (and the same rules of grammar apply), but the prose certainly can and should be spliced by definitions, examples, theorems, proofs, etc. It would be helpful for the mind and easier on the eye to use boldface and italicized language where appropriate, for distinction and consistency. Additionally, papers are often divided into sections and subsections, in order to make structural sense of the material.

LaTeX is a typesetting language that does much of this formatting for you and is particularly helpful in typing out equations. It is the most commonly used language for writing technical math papers. Some professors may even require you to use LaTeX. If so, Claremont Center for the Mathematical Sciences (CCMS) Software Lab is a helpful resource for learning. They offer tutorials at the library.

Make sure that you understand the conventions of the subfield you’re discussing. Subfields of mathematics have specific ways of expressing things, and the same symbol may mean something totally different in two different subfields. In that vein, clarify what your symbols mean. Now, mathematical shorthand is prevalent in class lectures, but it should not make an appearance in your paper. Just as academic papers refrain from using contractions and abbreviations, your math paper’s prose should use words.

You don’t necessarily need a conclusion, but it is a nice way to wrap up. Many math papers end abruptly, so you really shouldn’t feel obligated to write a conclusion. If you choose to write one, you can bookend it with some of the information relayed in your introduction. It can include more math within it than did the introduction, but it should not leave your reader with the sensation of being overwhelmed. It can also include the limitations or extending applications of the topic/results, and it can highlight open problems and suggest areas for future research.

Bibliography

Lastly, make sure to cite your sources! It is convention to use endnotes to cite information throughout the paper, so it does not interrupted the flow of the sentence. If you are using LaTeX, it compiles a bibliography for you, as you write and cite. Make sure your sources are reliable and valid. Peer reviewed sources are ideal.

For more information on mathematical writing (including tips for writing proofs, posters, and research papers) reference Handbook of Writing for the Mathematical Sciences by Nicholas J. Higham (1998).

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25 Interesting Math Topics: How to Write a Good Math Essay

writing good math essay

Mathematics is a fascinating world of numbers, shapes, and patterns. 

Whether you are a student looking to grasp math concepts or someone who finds math intriguing, these topics will spark your curiosity and help you discover the beauty of mathematics straightforwardly and engagingly.

In this article, I will explore interesting math topics that make this subject not only understandable but also enjoyable.

Why Write About Mathematics

First, it helps demystify a subject that many find intimidating. By breaking down complex mathematical concepts into simple, understandable language, we can make math accessible to a wider audience, fostering greater understanding and appreciation.

Second, writing about mathematics allows us to showcase the practical applications of math in everyday life, from managing personal finances to solving real-world problems.

This helps readers recognize the relevance of math and its role in various fields and industries.

Additionally, writing about mathematics can inspire curiosity and a love for learning.

It encourages critical thinking and problem-solving skills, promoting intellectual growth and academic success.

Finally, mathematics is a universal language that transcends cultural and linguistic barriers.

After discussing math topics, we can connect with a global audience, fostering a sense of unity and collaboration in the pursuit of knowledge

 25 Interesting Math Topics to Write On

 Mathematics is a vast and intriguing field, offering a multitude of interesting topics to explore and write about.

Here are 25 such topics that promise to engage both math enthusiasts and those seeking a deeper understanding of this fascinating subject.

1. Fibonacci Sequence: Delve into the mesmerizing world of numbers with this sequence, where each number is the sum of the two preceding ones.

2. Golden Ratio: Explore the ubiquity of the golden ratio in art, architecture, and nature.

3. Prime Numbers: Investigate the mysterious properties of prime numbers and their role in cryptography.

4. Chaos Theory: Understand the unpredictability of chaotic systems and how small changes can lead to drastically different outcomes.

5. Game Theory: Examine the strategies and decision-making processes behind games and real-world situations.

6. Cryptography: Uncover the mathematical principles behind secure communication and encryption.

7. Fractals: Discover the self-replicating geometric patterns that occur in nature and mathematics.

8. Probability Theory: Dive into the world of uncertainty and randomness, where math helps us make informed predictions.

9. Number Theory: Explore the properties and relationships of integers, including divisibility and congruence.

10. Geometry of Art: Analyze how geometry and math principles influence art and design.

11. Topology: Study the properties of space that remain unchanged under continuous transformations, leading to the concept of “rubber-sheet geometry.”

12. Knot Theory: Investigate the mathematical study of knots and their applications in various fields.

13. Number Systems: Learn about different number bases, such as binary and hexadecimal, and their significance in computer science.

14. Graph Theory: Explore networks, relationships, and the mathematics of connections.

15. The Monty Hall Problem: Delight in this famous probability puzzle based on a game show scenario.

16. Calculus: Examine the principles of differentiation and integration that underlie a wide range of scientific and engineering applications.

17. The Riemann Hypothesis: Consider one of the most famous unsolved problems in mathematics involving the distribution of prime numbers.

18. Euler’s Identity: Marvel at the beauty of Euler’s equation, often described as the most elegant mathematical formula.

19. The Four-Color Theorem: Uncover the fascinating problem of coloring maps with only four colors without adjacent regions sharing the same color.

20. P vs. NP Problem: Delve into one of the most critical unsolved problems in computer science, addressing the efficiency of algorithms.

21. The Bridges of Konigsberg: Explore a classic problem in graph theory that inspired the development of topology.

22. The Birthday Paradox: Understand the surprising likelihood of shared birthdays in a group.

23. Non-Euclidean Geometry: Step into the world of geometries where Euclid’s parallel postulate doesn’t hold, leading to intriguing alternatives like hyperbolic and elliptic geometry.

24. Perfect Numbers: Learn about the properties of numbers that are the sum of their proper divisors.

25. Zero: The History of Nothing: Trace the historical and mathematical significance of the number zero and its role in the development of mathematics.

How to Write a Good Math Essay

Mathematics essays , though often perceived as daunting, can be a rewarding way to delve into the world of mathematical concepts, problem-solving, and critical thinking.

Whether you are a student assigned to write a math essay or someone who wants to explore math topics in-depth, this guide will provide you with the key steps to write a good math essay that is clear, concise, and engaging.

1. Understanding the Essay Prompt

Before you begin writing, it’s crucial to understand the essay prompt or question.

Analyze the specific topic, the scope of the essay, and any guidelines or requirements provided by your instructor.

Mostly, this initial step sets the direction for your essay and ensures you stay on topic.

2. Research and Gather Information

You need to gather relevant information and resources to write a strong math essay. This includes textbooks, academic papers, and reputable websites.

Make sure to cite your sources properly using a recognized citation style such as APA, MLA, or Chicago.

3. Structuring Your Math Essay

Start with a clear introduction that provides an overview of the topic and the main thesis or argument of your essay. This section should capture the reader’s attention and present a roadmap for what to expect.

The body of your essay is where you present your arguments, explanations, and evidence. Use clear subheadings to organize your ideas. Ensure that your arguments are logical and well-structured.

Begin by defining any important mathematical concepts or terms necessary to understand your topic.

Clearly state your main arguments or theorems. Please support them with evidence, equations, diagrams, or examples.

Explain the logical steps or mathematical reasoning behind your arguments. This can include proofs, derivations, or calculations.

Ensure your writing is clear and free from jargon that might confuse the reader. Explain complex ideas in a way that’s accessible to a broader audience.

Whenever applicable, include diagrams, graphs, or visual aids to illustrate your points. Visual representations can enhance the clarity of your essay.

Summarize your main arguments, restate your thesis, and offer a concise conclusion. Address the significance of your findings and the implications of your research or discussion.

4. Proofreading and Editing

Once you’ve written your math essay, take the time to proofread and edit it. Pay attention to grammar, spelling, punctuation, and the overall flow of your writing.

Ensure that your essay is well-organized and free from errors.

Consider seeking feedback from peers or an instructor to gain a fresh perspective.

5. Presentation and Formatting

A well-presented essay is more likely to engage the reader. Follow these formatting guidelines:

• Use a legible font (e.g., Times New Roman or Arial) in a standard size (12-point).
• Double-space your essay and include page numbers if required.
• Create a title page with your name, essay title, course information, and date.
• Use section headings and subheadings for clarity.
• Include a reference page to cite your sources appropriately.

6. Mathematical Notation and Symbols

Mathematics relies heavily on notation and symbols. Ensure that you use mathematical notation correctly and consistently.

If you introduce new symbols or terminology, define them clearly for the reader’s understanding.

7. Seek Clarification

If you encounter difficulties or ambiguities in your math essay, don’t hesitate to seek clarification from your instructor or peers.

Discussing complex mathematical concepts with others can help you refine your understanding and improve your essay.

8. Practice and Feedback

Writing math essays, like any skill, improves with practice. The more you write and receive feedback, the better you’ll become.

Take your time with initial challenges. Instead, view them as opportunities for growth and learning.

With dedication and attention to detail, you can craft a math essay that not only conveys your mathematical knowledge but also engages and informs your readers.

Josh Jasen or JJ as we fondly call him, is a senior academic editor at Grade Bees in charge of the writing department. When not managing complex essays and academic writing tasks, Josh is busy advising students on how to pass assignments. In his spare time, he loves playing football or walking with his dog around the park.

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How to Effectively Write a Mathematics Research Paper

Mathematics research papers are different from standard academic research papers in important ways, but not so different that they require an entirely separate set of guidelines. Mathematical papers rely heavily on logic and a specific type of language, including symbols and regimented notation. There are two basic structures of mathematical research papers: formal and informal exposition .

Structure and Style

Formal Exposition

The author must start with an outline that develops the logical structure of the paper. Each hypothesis and deduction should flow in an orderly and linear fashion using formal definitions and notation. The author should not repeat a proof or substitute words or phrases that differ from the definitions already established within the paper. The theorem-proof format, definitions, and logic fall under this style.

Informal Exposition

Informal exposition complements the formal exposition by providing the reasoning behind the theorems and proofs. Figures, proofs, equations, and mathematical sentences do not necessarily speak for themselves within a mathematics research paper . Authors will need to demonstrate why their hypotheses and deductions are valid and how they came to prove this. Analogies and examples fall under this style.

Conventions of Mathematics

Clarity is essential for writing an effective mathematics research paper. This means adhering to strong rules of logic, clear definitions, theorems and equations that are physically set apart from the surrounding text, and using math symbols and notation following the conventions of mathematical language. Each area incorporates detailed guidelines to assist the authors.

Related: Do you have questions on language, grammar, or manuscript drafting? Get personalized answers on the FREE Q&A Forum!

Logic is the framework upon which every good mathematics research paper is built. Each theorem or equation must flow logically.

Definitions

In order for the reader to understand the author’s work, definitions for terms and notations used throughout the paper must be set at the beginning of the paper. It is more effective to include this within the Introduction section of the paper rather than having a stand-alone section of definitions.

Theorems and Equations

Theorems and equations should be physically separated from the surrounding text. They will be used as reference points throughout, so they should have a well-defined beginning and end.

Math Symbols and Notations

Math symbols and notations are standardized within the mathematics literature. Deviation from these standards will cause confusion amongst readers. Therefore, the author should adhere to the guidelines for equations, units, and mathematical notation, available from various resources .

Protocols for mathematics writing get very specific – fonts, punctuation, examples, footnotes, sentences, paragraphs, and the title, all have detailed constraints and conventions applied to their usage. The American Mathematical Society is a good resource for additional guidelines.

LaTeX and Wolfram

Mathematical sentences contain equations, figures, and notations that are difficult to typeset using a typical word-processing program. Both LaTeX and Wolfram have expert typesetting capabilities to assist authors in writing.

LaTeX is highly recommended for researchers whose papers constitute mathematical figures and notation. It produces professional-looking documents and authentically represents mathematical language.

Wolfram Language & System Documentation Center’s Mathematica has sophisticated and convenient mathematical typesetting technology that produces professional-looking documents.

The main differences between the two systems are due to cost and accessibility. LaTeX is freely available, whereas Wolfram is not. In addition, any updates in Mathematica will come with an additional charge. LaTeX is an open-source system, but Mathematica is closed-source.

Good Writing and Logical Constructions

Regardless of the document preparation system selected, publication of a mathematics paper is similar to the publication of any academic research in that it requires good writing. Authors must apply a strict, logical construct when writing a mathematics research paper.

There are resources that provide very specific guidelines related to following sections to write and publish a mathematics research paper.

• Concept of a math paper
• Title, acknowledgment, and list of authors
• Introduction
• Body of the work
• Conclusion, appendix, and references
• Publication of a math paper
• Preprint archive
• Choice of the journal, submission
• Publication

The critical elements of a mathematics research paper are good writing and a logical construct that allows the reader to follow a clear path to the author’s conclusions.

Good advice. For me, writing an essay on mathematics was very difficult. I did not have enough time and knowledge to write a quality essay. I worked a lot in the library and read many articles on the Internet. I studied information about essay writing. But I couldn’t finish the essay in full. I had to look for professional writers on the subject of mathematics. He helped me finish a few paragraphs. The work was delivered on time and on an excellent assessment.

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• June 2, 2022

• What is an essay? 

What makes a good essay?

Typical essay structure, 7 steps to writing a good essay, a step-by-step guide to writing a good essay.

Whether you are gearing up for your GCSE coursework submissions or looking to brush up on your A-level writing skills, we have the perfect essay-writing guide for you. 💯

Staring at a blank page before writing an essay can feel a little daunting . Where do you start? What should your introduction say? And how should you structure your arguments? They are all fair questions and we have the answers! Take the stress out of essay writing with this step-by-step guide – you’ll be typing away in no time. 👩‍💻

What is an essay?

Generally speaking, an essay designates a literary work in which the author defends a point of view or a personal conviction, using logical arguments and literary devices in order to inform and convince the reader.

So – although essays can be broadly split into four categories: argumentative, expository, narrative, and descriptive – an essay can simply be described as a focused piece of writing designed to inform or persuade. 🤔

The purpose of an essay is to present a coherent argument in response to a stimulus or question and to persuade the reader that your position is credible, believable and reasonable. 👌

So, a ‘good’ essay relies on a confident writing style – it’s clear, well-substantiated, focussed, explanatory and descriptive . The structure follows a logical progression and above all, the body of the essay clearly correlates to the tile – answering the question where one has been posed. 

But, how do you go about making sure that you tick all these boxes and keep within a specified word count? Read on for the answer as well as an example essay structure to follow and a handy step-by-step guide to writing the perfect essay – hooray. 🙌

Sometimes, it is helpful to think about your essay like it is a well-balanced argument or a speech – it needs to have a logical structure, with all your points coming together to answer the question in a coherent manner. ⚖️

Of course, essays can vary significantly in length but besides that, they all follow a fairly strict pattern or structure made up of three sections. Lean into this predictability because it will keep you on track and help you make your point clearly. Let’s take a look at the typical essay structure:  

#1 Introduction

Start your introduction with the central claim of your essay. Let the reader know exactly what you intend to say with this essay. Communicate what you’re going to argue, and in what order. The final part of your introduction should also say what conclusions you’re going to draw – it sounds counter-intuitive but it’s not – more on that below. 1️⃣

Make your point, evidence it and explain it. This part of the essay – generally made up of three or more paragraphs depending on the length of your essay – is where you present your argument. The first sentence of each paragraph – much like an introduction to an essay – should summarise what your paragraph intends to explain in more detail. 2️⃣

#3 Conclusion

This is where you affirm your argument – remind the reader what you just proved in your essay and how you did it. This section will sound quite similar to your introduction but – having written the essay – you’ll be summarising rather than setting out your stall. 3️⃣

No essay is the same but your approach to writing them can be. As well as some best practice tips, we have gathered our favourite advice from expert essay-writers and compiled the following 7-step guide to writing a good essay every time. 👍

#1 Make sure you understand the question

#2 complete background reading.

#3 Make a detailed plan 

#4 Write your opening sentences 

#5 flesh out your essay in a rough draft, #6 evidence your opinion, #7 final proofread and edit.

Now that you have familiarised yourself with the 7 steps standing between you and the perfect essay, let’s take a closer look at each of those stages so that you can get on with crafting your written arguments with confidence . 

This is the most crucial stage in essay writing – r ead the essay prompt carefully and understand the question. Highlight the keywords – like ‘compare,’ ‘contrast’ ‘discuss,’ ‘explain’ or ‘evaluate’ – and let it sink in before your mind starts racing . There is nothing worse than writing 500 words before realising you have entirely missed the brief . 🧐

Unless you are writing under exam conditions , you will most likely have been working towards this essay for some time, by doing thorough background reading. Re-read relevant chapters and sections, highlight pertinent material and maybe even stray outside the designated reading list, this shows genuine interest and extended knowledge. 📚

#3 Make a detailed plan

Following the handy structure we shared with you above, now is the time to create the ‘skeleton structure’ or essay plan. Working from your essay title, plot out what you want your paragraphs to cover and how that information is going to flow. You don’t need to start writing any full sentences yet but it might be useful to think about the various quotes you plan to use to substantiate each section. 📝

Having mapped out the overall trajectory of your essay, you can start to drill down into the detail. First, write the opening sentence for each of the paragraphs in the body section of your essay. Remember – each paragraph is like a mini-essay – the opening sentence should summarise what the paragraph will then go on to explain in more detail. 🖊️

Next, it's time to write the bulk of your words and flesh out your arguments. Follow the ‘point, evidence, explain’ method. The opening sentences – already written – should introduce your ‘points’, so now you need to ‘evidence’ them with corroborating research and ‘explain’ how the evidence you’ve presented proves the point you’re trying to make. ✍️

With a rough draft in front of you, you can take a moment to read what you have written so far. Are there any sections that require further substantiation? Have you managed to include the most relevant material you originally highlighted in your background reading? Now is the time to make sure you have evidenced all your opinions and claims with the strongest quotes, citations and material. 📗

This is your final chance to re-read your essay and go over it with a fine-toothed comb before pressing ‘submit’. We highly recommend leaving a day or two between finishing your essay and the final proofread if possible – you’ll be amazed at the difference this makes, allowing you to return with a fresh pair of eyes and a more discerning judgment. 🤓

If you are looking for advice and support with your own essay-writing adventures, why not t ry a free trial lesson with GoStudent? Our tutors are experts at boosting academic success and having fun along the way. Get in touch and see how it can work for you today. 🎒

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How to Write the Perfect Essay

06 Feb, 2024 | Blog Articles , English Language Articles , Get the Edge , Humanities Articles , Writing Articles

You can keep adding to this plan, crossing bits out and linking the different bubbles when you spot connections between them. Even though you won’t have time to make a detailed plan under exam conditions, it can be helpful to draft a brief one, including a few key words, so that you don’t panic and go off topic when writing your essay.

If you don’t like the mind map format, there are plenty of others to choose from: you could make a table, a flowchart, or simply a list of bullet points.

Discover More

Thanks for signing up, step 2: have a clear structure.

Think about this while you’re planning: your essay is like an argument or a speech. It needs to have a logical structure, with all your points coming together to answer the question.

Start with the basics! It’s best to choose a few major points which will become your main paragraphs. Three main paragraphs is a good number for an exam essay, since you’ll be under time pressure. 

If you agree with the question overall, it can be helpful to organise your points in the following pattern:

• YES (agreement with the question)
• AND (another YES point)
• BUT (disagreement or complication)

If you disagree with the question overall, try:

• AND (another BUT point)

For example, you could structure the Of Mice and Men sample question, “To what extent is Curley’s wife portrayed as a victim in Of Mice and Men ?”, as follows:

• YES (descriptions of her appearance)
• AND (other people’s attitudes towards her)
• BUT (her position as the only woman on the ranch gives her power as she uses her femininity to her advantage)

If you wanted to write a longer essay, you could include additional paragraphs under the YES/AND categories, perhaps discussing the ways in which Curley’s wife reveals her vulnerability and insecurities, and shares her dreams with the other characters. Alternatively, you could also lengthen your essay by including another BUT paragraph about her cruel and manipulative streak.

Of course, this is not necessarily the only right way to answer this essay question – as long as you back up your points with evidence from the text, you can take any standpoint that makes sense.

Step 3: Back up your points with well-analysed quotations

You wouldn’t write a scientific report without including evidence to support your findings, so why should it be any different with an essay? Even though you aren’t strictly required to substantiate every single point you make with a quotation, there’s no harm in trying.

A close reading of your quotations can enrich your appreciation of the question and will be sure to impress examiners. When selecting the best quotations to use in your essay, keep an eye out for specific literary techniques. For example, you could highlight Curley’s wife’s use of a rhetorical question when she says, a”n’ what am I doin’? Standin’ here talking to a bunch of bindle stiffs.” This might look like:

The rhetorical question “an’ what am I doin’?” signifies that Curley’s wife is very insecure; she seems to be questioning her own life choices. Moreover, she does not expect anyone to respond to her question, highlighting her loneliness and isolation on the ranch.

Other literary techniques to look out for include:

• Tricolon – a group of three words or phrases placed close together for emphasis
• Tautology – using different words that mean the same thing: e.g. “frightening” and “terrifying”
• Parallelism – ABAB structure, often signifying movement from one concept to another
• Chiasmus – ABBA structure, drawing attention to a phrase
• Polysyndeton – many conjunctions in a sentence
• Asyndeton – lack of conjunctions, which can speed up the pace of a sentence
• Polyptoton – using the same word in different forms for emphasis: e.g. “done” and “doing”
• Alliteration – repetition of the same sound, including assonance (similar vowel sounds), plosive alliteration (“b”, “d” and “p” sounds) and sibilance (“s” sounds)
• Anaphora – repetition of words, often used to emphasise a particular point

Don’t worry if you can’t locate all of these literary devices in the work you’re analysing. You can also discuss more obvious techniques, like metaphor, simile and onomatopoeia. It’s not a problem if you can’t remember all the long names; it’s far more important to be able to confidently explain the effects of each technique and highlight its relevance to the question.

Step 4: Be creative and original throughout

Anyone can write an essay using the tips above, but the thing that really makes it “perfect” is your own unique take on the topic. If you’ve noticed something intriguing or unusual in your reading, point it out – if you find it interesting, chances are the examiner will too!

Creative writing and essay writing are more closely linked than you might imagine. Keep the idea that you’re writing a speech or argument in mind, and you’re guaranteed to grab your reader’s attention.

It’s important to set out your line of argument in your introduction, introducing your main points and the general direction your essay will take, but don’t forget to keep something back for the conclusion, too. Yes, you need to summarise your main points, but if you’re just repeating the things you said in your introduction, the body of the essay is rendered pointless.

Think of your conclusion as the climax of your speech, the bit everything else has been leading up to, rather than the boring plenary at the end of the interesting stuff.

To return to Of Mice and Men once more, here’s an example of the ideal difference between an introduction and a conclusion:

Introduction

In John Steinbeck’s Of Mice and Men , Curley’s wife is portrayed as an ambiguous character. She could be viewed either as a cruel, seductive temptress or a lonely woman who is a victim of her society’s attitudes. Though she does seem to wield a form of sexual power, it is clear that Curley’s wife is largely a victim. This interpretation is supported by Steinbeck’s description of her appearance, other people’s attitudes, her dreams, and her evident loneliness and insecurity.

Overall, it is clear that Curley’s wife is a victim and is portrayed as such throughout the novel in the descriptions of her appearance, her dreams, other people’s judgemental attitudes, and her loneliness and insecurities. However, a character who was a victim and nothing else would be one-dimensional and Curley’s wife is not. Although she suffers in many ways, she is shown to assert herself through the manipulation of her femininity – a small rebellion against the victimisation she experiences.

Both refer back consistently to the question and summarise the essay’s main points. However, the conclusion adds something new which has been established in the main body of the essay and complicates the simple summary which is found in the introduction.

Hannah is an undergraduate English student at Somerville College, University of Oxford, and has a particular interest in postcolonial literature and the Gothic. She thinks literature is a crucial way of developing empathy and learning about the wider world. When she isn’t writing about 17th-century court masques, she enjoys acting, travelling and creative writing. 

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Intellectual Mathematics

How to write a history of mathematics essay

This is a guide for students writing a substantial course essay or bachelors thesis in the history of mathematics.

The essence of a good essay is that it shows independent and critical thought. You do not want to write yet another account of some topic that has already been covered many times before. Your goal should not be to write an encyclopaedia-style article that strings together various facts that one can find in standard sources. Your goal should not be to simply retell in your own words a story that has already been told many times before in various books. Such essays do not demonstrate thought, and therefore it is impossible to earn a good grade this way.

So you want to look for ways of framing your essay that give you opportunity for thought. The following is a basic taxonomy of some typical ways in which this can be done.

Critique. A good rule of thumb is: if you want a good grade you should, in your essay, disagree with and argue against at least one statement in the secondary literature. This is probably easier than you might think; errors and inaccuracies are very common, especially in general and popular books on the history of mathematics. When doing research for your essay, it is a good idea to focus on a small question and try to find out what many different secondary sources say about it. Once you have understood the topic well, you will most likely find that some of the weaker secondary sources are very superficial and quite possibly downright wrong. You want to make note of such shortcomings in the literature and cite and explain what is wrong about them in your essay, and why their errors are significant in terms of a proper understanding of the matter.

The point, of course, is not that finding errors in other people’s work is an end in itself. The point, rather, is that if you want to get anywhere in history it is essential to read all texts with a critical eye. It is therefore a good exercise to train yourself to look for errors in the literature, not because collecting errors is interesting in itself but because if you believe everything you read you will never get anywhere in this world, especially as far as history is concerned.

Maybe what you really wanted to do was simply to learn some nice things about the topic and write them up in your essay as a way of organising what you learned when reading about it. That is a fine goal, and certainly history is largely about satisfying our curiosities in this way. However, when it comes to grading it is difficult to tell whether you have truly thought something through and understood it, or whether you are simply paraphrasing someone else who has done so. Therefore such essays cannot generally earn a very good grade. But if you do this kind of work it will not be difficult for you to use the understanding you develop to find flaws in the secondary literature, and this will give a much more concrete demonstration of your understanding. So while developing your understanding was the true goal, critiquing other works will often be the best way to make your understanding evident to the person grading your essay.

For many examples of how one might write a critique, see my book reviews categorised as “critical.”

Debate. A simple way of putting yourself in a critical mindset is to engage with an existing debate in the secondary literature. There are many instances where historians disagree and offer competing interpretations, often in quite heated debates. Picking such a topic will steer you away from the temptation to simply accumulate information and facts. Instead you will be forced to critically weigh the evidence and the arguments on both sides. Probably you will find yourself on one side or the other, and it will hopefully come quite naturally to you to contribute your own argument for your favoured side and your own replies to the arguments of the opposing side.

Some sample “debate” topics are: Did Euclid know “algebra”? Did Copernicus secretly borrow from Islamic predecessors? “Myths” in the historiography of Egyptian mathematics? Was Galileo a product of his social context? How did Leibniz view the foundations of infinitesimals?

Compare & contrast. The compare & contrast essay is a less confrontational sibling of the debate essay. It too deals with divergent interpretations in the secondary literature, but instead of trying to “pick the winner” it celebrates the diversity of approaches. By thoughtfully comparing different points of view, it raises new questions and illuminates new angles that were not evident when each standpoint was considered in isolation. In this way, it brings out more clearly the strengths and weaknesses, and the assumptions and implications, of each point of view.

When you are writing a compare & contrast essay you are wearing two (or more) “hats.” One moment you empathise with one viewpoint, the next moment with the other. You play out a dialog in your mind: How would one side reply to the arguments and evidence that are key from the other point of view, and vice versa? What can the two learn from each other? In what ways, if any, are they irreconcilable? Can their differences be accounted for in terms of the authors’ motivations and goals, their social context, or some other way?

Following the compare & contrast model is a relatively straightforward recipe for generating reflections of your own. It is almost always applicable: all you need is two alternate accounts of the same historical development. It could be for instance two different mathematical interpretations, two perspectives emphasising different contexts, or two biographies of the same person.

The compare & contrast approach is therefore a great choice if you want to spend most of your research time reading and learning fairly broadly about a particular topic. Unlike the critique or debate approaches, which requires you to survey the literature for weak spots and zero in for pinpoint attacks, it allows you to take in and engage with the latest and best works of scholarship in a big-picture way. The potential danger, on the other hand, is that it may come dangerously close to merely survey or summarise the works of others. They way to avoid this danger is to always emphasise the dialog between the different points of view, rather than the views themselves. Nevertheless, if you are very ambitious you may want to complement a compare & contrast essay with elements of critique or debate.

Verify or disprove. People often appeal to history to justify certain conclusions. They give arguments of the form: “History works like this, so therefore [important conclusions].” Often such accounts allude briefly to specific historical examples without discussing them in any detail. Do the historical facts of the matter bear out the author’s point, or did he distort and misrepresent history to serve his own ends? Such a question is a good starting point for an essay. It leads you to focus your essay on a specific question and to structure your essay as an analytical argument. It also affords you ample opportunity for independent thought without unreasonable demands on originality: your own contribution lies not in new discoveries but in comparing established scholarly works from a new point of view. Thus it is similar to a compare & contrast essay, with the two works being compared being on the one hand the theoretical work making general claims about history, and on the other hand detailed studies of the historical episodes in question.

Sample topics of this type are: Are there revolutions in mathematics in the sense of Kuhn ? Or does mathematics work according to the model of Kitcher ? Or that of Lakatos or Crowe ? Does the historical development of mathematical concepts mirror the stages of the learning process of students learning the subject today, in the manner suggested by Sfard or Sierpinska ? Was Kant’s account of the nature of geometrical knowledge discredited by the discovery of non-Euclidean geometry?

Cross-section. Another way of combining existing scholarship in such a way as to afford scope for independent thought is to ask “cross-sectional” questions, such as comparing different approaches to a particular mathematical idea in different cultures or different time periods. Again, a compare & contrast type of analysis gives you the opportunity to show that you have engaged with the material at a deeper and more reflective level than merely recounting existing scholarship.

Dig. There are still many sources and issues in the history of mathematics that have yet to be investigated thoroughly by anyone. In such cases you can make valuable and original contributions without any of the above bells and whistles by simply being the first to really study something in depth. It is of course splendid if you can do this, but there are a number of downsides: (1) you will be studying something small and obscure, while the above approaches allow you to tackle any big and fascinating question you are interested in; (2) it often requires foreign language skills; (3) finding a suitable topic is hard, since you must locate an obscure work and master all the related secondary literature so that you can make a case that it has been insufficiently studied.

In practice you may need someone to do (3) for you. I have some suggestions which go with the themes of 17th-century mathematics covered in my history of mathematics book . It would be interesting to study for instance 18th-century calculus textbooks (see e.g. the bibliography in this paper ) in light of these issues, especially the conflict between geometric and analytic approaches. If you know Latin there are many more neglected works, such as the first book on integral calculus, Gabriele Manfredi’s De constructione aequationum differentialium primi gradus (1707), or Henry Savile’s Praelectiones tresdecim in principium Elementorum Euclidis , 1621, or many other works listed in a bibliography by Schüling .

Expose. A variant of the dig essay is to look into certain mathematical details and write a clear exposition of them. Since historical mathematics is often hard to read, being able to explain its essence in a clear and insightful way is often an accomplishment in itself that shows considerable independent thought. This shares some of the drawbacks of the dig essay, except it is much easier to find a topic, even an important one. History is full of important mathematics in need of clear exposition. But the reason for this points to another drawback of this essay type: it’s hard. You need to know your mathematics very well to pull this off, but the rewards are great if you do.

Whichever of the above approaches you take you want to make it very clear and explicit in your essay what parts of it reflect your own thinking and how your discussion goes beyond existing literature. If this is not completely clear from the essay itself, consider adding a note to the grader detailing these things. If you do not make it clear when something is your own contribution the grader will have to assume that it is not, which will not be good for your grade.

Here’s another way of looking at it. This table is a schematic overview of different ways in which your essay can add something to the literature:

The table shows the state of the literature before and after your research project has been carried out.

A Describe project starts from a chaos of isolated bits of information and analyses it so as to impose order and organisation on it. You are like an explorer going into unknown jungles. You find exotic, unknown things. You record the riches of this strange new world and start organise it into a systematic taxonomy.

You need an exotic “jungle” for this project to work. In the history of mathematics, this could mean obscure works or sources that have virtually never been studied, or mathematical arguments that have never been elucidated or explained in accessible form.

An Explain project is suitable when others have done the exploration and descriptions of fact, but left why-questions unanswered. First Darwin and other naturalists went to all the corners of the world and gathered and recorded all the exotic species they could find. That was the Describe phase. Darwin then used that mass of information to formulate and test his hypothesis of the origin of species. That was the Explain phase.

Many areas of the history of mathematics have been thoroughly Described but never Explained.

What if you find that someone has done the Explain already? If you think the Explain is incomplete, you can Critique it. If you think the Explain is great you can Extend it: do the same thing but to a different but similar body of data. That way you get to work with the stimulating work that appealed to you, but you also add something of your own.

Likewise if you find two or more Explains that are all above Critique in your opinion. Then you can do a Compare & Contrast, or a Synthesise. This way you get to work with the interesting works but also show your independent contribution by drawing out aspects and connections that were not prominent in the originals.

See also History of mathematics literature guide .

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How to Write a Stellar “Why This College?” Essay + Examples

What’s covered:, sample “why this college” prompts, faqs about the “why this college” essay.

• Common Mistakes to Avoid

Good “Why This College?” Essay Examples

• Brainstorming for this Essay
• Outlining Your Essay
• Where to Get Your Essay Edited

One of the most common college essay supplements will ask you to answer the question: “Why This College?” These essays are looking to see whether you’re a good fit for the campus community, and whether the college is a good fit for you and your goals. 

In this post, we’ll show you a couple examples of these prompts, go over good and bad sample responses, and break down how to ensure yours is one of the good ones. 

Let’s start by taking a look at real prompts that fit under the “Why This College?” archetype: 

Tufts: Which aspects of the Tufts undergraduate experience prompt your application? In short, ‘Why Tufts?’ (150 words)

Northwestern: Other parts of your application give us a sense for how you might contribute to Northwestern. But we also want to consider how Northwestern will contribute to your interests and goals. Help us understand what aspects of Northwestern appeal most to you, and how you’ll make use of specific resources and opportunities here. (300 words)

As you can see, these prompts are basically asking why you want to attend the school in question. Northwestern spells it out even further, and specifically asks how you’ll use their resources to achieve your goals.

Both prompts have word counts that are much shorter than that of the Common App, which is typical of supplemental essays. These two word counts are pretty representative, and you can expect the “Why This College?” essay length to be 100-400 words on average. That’s not a lot of space for a pretty important question, so it’s especially vital to use the word count wisely.

What are colleges looking for in the “Why Us” essay?

Colleges want to admit students who will not only enroll (to protect their yield), but also thrive on their campus. They ask this question to see whether you’re truly interested in the school and whether it’s the right place for you. You can write a strong response by citing specific ways the college can support your goals, as well as demonstrating your enthusiasm.

Which colleges have a “Why This College?” essay?

This is one of the most popular supplements among colleges. Here is a selection of top schools that ask this question:

• Northwestern
• Boston University
• University of Michigan

Check out our essay guides for these schools for more in-depth advice on how to write these essays.

What kind of writing style should I use?

This is a straightforward question that generally has a short word count, so you don’t need to use a narrative form at all. You can simply explain what you like about the school and why, but try to use varied sentence structure and organize the essay around your major goals. 

You can start your essay with a story if you want, however. For example, if you visited campus and experienced a really interesting course, or sat in on a meeting of a club you liked, this can make for a strong anecdote to begin your essay. Just make sure that whatever story you tell has some substance, and isn’t just a narration of how nice it was to walk around campus.

Can I copy and paste my essay for other schools?

Absolutely not. If your essay is general enough to apply to other schools, you know you need to rewrite it. The resources you mention should be highly specific to the college you’re writing about.

Common Mistakes When Writing the “Why This College?” Essay

The most common mistake students make is listing generic characteristics that could apply to any school. This negatively impacts your application, since it sends the message that you didn’t do your research, and aren’t truly interested in the school.

Here’s an example of something NOT to list in your “Why this college essay.” We’ll take the example of Tufts since we shared the prompt in the beginning.

What NOT to write: I’m applying to Tufts because of its low student to faculty ratio, the strong math department, and its prime location in Medford, just a hop away from Boston. When I visited campus, the school already felt like home.

This example is bad because many schools have low student to faculty ratios and strong math departments. There are also a ton of schools in or near Boston, many of which have low student to faculty ratios and great math departments too, such as Boston College, Harvard, Northeastern, Boston University, etc. If your statements can apply to other schools, that’s definitely not a good sign (avoid things like location, weather, size, and ranking).

The student also uses an emotional appeal with the line “it felt like home,” which might sound nice, but it has no substance and can be written for any school. You should definitely avoid making any statements like these.

This example shows that the student really hasn’t thought much about their fit with Tufts, and that it probably isn’t their top choice. This will impact your application negatively, especially since Tufts is known for taking applicants’ demonstrated interest more seriously than other schools . So, if you show that you show little interest through your essay, you may end up waitlisted or rejected, even if your stats are excellent.

Another thing that this example gets wrong is that it doesn’t describe the student’s goals or interests at all. It’s important to not only talk about why you picked the school, but also how exactly those aspects will help you grow. Remember, this kind of prompt is two-fold: in addition to explaining why the school is a good fit for you, you want to show why you, out of the many thousands of applicants they get each year, are a good fit for them.

To summarize, the main mistakes to avoid are:

• Citing generic aspects of the school (location, weather, size, and ranking)
• Using empty emotional appeals
• Not describing your goals and interests

Now that we know what a bad example might look like, here’s an example of a rewrite to part of the Tufts essay:

What TO write: As a potential Applied Mathematics major, I hope to gain the tools to model political behavior. I’m especially interested in elections, and am looking forward to taking the course “Mathematics of Social Choice,” as the centerpiece of Social Choice Theory is voting. I would also love to take “Nonlinear Dynamics and Chaos,” because it will teach me to use differential equations to predict chaotic behavior. 

This is a good example, as the courses listed are highly-specific to Tufts, as well as the student’s professional goals. We not only learned something about Tufts, but also the student. Keep in mind that this wouldn’t be a complete essay⁠—it’s just an example of good, specific resources to list, and how to connect them to your own interests. 

If you want an example of a complete essay, here’s this real student response for Boston University’s “Why This College?” prompt.

Prompt: In no more than 250 words, please tell us why BU is a good fit for you and what

specifically has led you to apply for admission.

Boston University’s College of Arts and Sciences (CAS) attracts me because of its support of interdisciplinary study among its wide array of majors. In fact, the CAS now offers a course that combines biology, chemistry, and neuroscience. As I hope to conduct medical research into brain disorders, I plan to pursue all three areas of study. These cross-disciplinary connections at BU will prepare me to do so.

CAS’s undergraduate research program would allow me to work with a mentor, such as Dr. Alice Cronin-Golomb or Dr. Robert M.G. Reinhart related to their research on neurological disorders. With them, I can advance the work I have already completed related to Dissociative Identity Disorder (DID). In a summer class at our local university, my partner and I extracted data from fMRI and PET studies and inputted them into a coding program. We then created an indicator map, which we imported into another software program, AFNI, to display significant activity in the brain regions affected by DID. Seeing the representation of our data thrilled me because I knew it could eventually help people who live with DID. I want to experience that feeling again. Successfully analyzing these fMRI and PET studies and learning to code drives me to pursue more research opportunities, and this desire motivates me to study at a university that offers research opportunities to undergraduates. BU’s interdisciplinary approach to psychology and support for independent undergraduate undergraduate research will optimally prepare me for a career as a neurological researcher.

This student clearly outlines BU-specific resources (the interdisciplinary course and undergrad research program), plus how these resources align with their professional goals (to become a neurological researcher). They do “name-drop” professors, but since their work clearly relates to the student’s interests, it doesn’t look disingenuous, and shows that the student has done research on their fit with BU. The student also provides background on why they want to pursue research, and shows that they already have experience, which makes their interest in the undergrad research program more concrete.

The only thing missing from this essay is the student’s fit with BU in terms of extracurriculars and social life. “Why This College?” essays should also cover extracurriculars, as the residential college experience is about more than just class and homework. Admissions officers are also interested in how you’ll contribute to their broader campus community.

In general, these essays should be academic-leaning (especially if they’re under 250 words), but you should still address some social aspects of the college that appeal to you (we recommend about 70% academics, 30% social, with more or less focus on social aspects depending on the word count). Since the student probably already detailed their previous research in their Common App activities section, they could’ve just summarized their research background in one sentence, and used the space saved to talk about a specific social aspect of BU that interests them.

Here’s another sample essay, but for UPenn. This essay’s word count was much longer, so the student was able to really hone in on several specific aspects of UPenn.

Prompt: How will you explore your intellectual and academic interests at the University of Pennsylvania? Please answer this question given the specific undergraduate school to which you are applying (650 words).

Sister Simone Roach, a theorist of nursing ethics, said, “caring is the human mode of being.” I have long been inspired by Sister Roach’s Five C’s of Caring: commitment, conscience, competence, compassion, and confidence. Penn both embraces and fosters these values through a rigorous, interdisciplinary curriculum and unmatched access to service and volunteer opportunities.

COMMITMENT. Reading through the activities that Penn Quakers devote their time to (in addition to academics!) felt like drinking from a firehose in the best possible way. As a prospective nursing student with interests outside of my major, I value this level of flexibility. I plan to leverage Penn’s liberal arts curriculum to gain an in-depth understanding of the challenges LGBT people face, especially regarding healthcare access. Through courses like “Interactional Processes with LGBT Individuals” and volunteering at the Mazzoni Center for outreach, I hope to learn how to better support the Penn LGBT community as well as my family and friends, including my cousin, who came out as trans last year.

CONSCIENCE. As one of the first people in my family to attend a four-year university, I wanted a school that promoted a sense of moral responsibility among its students. At Penn, professors challenge their students to question and recreate their own set of morals by sparking thought- provoking, open-minded discussions. I can imagine myself advocating for universal healthcare in courses such as “Health Care Reform & Future of American Health System” and debating its merits with my peers. Studying in an environment where students confidently voice their opinions – conservative or liberal – will push me to question and strengthen my value system.

COMPETENCE. Two aspects that drew my attention to Penn’s BSN program were its high-quality research opportunities and hands-on nursing projects. Through its Office of Nursing Research, Penn connects students to faculty members who share similar research interests. As I volunteered at a nursing home in high school, I hope to work with Dr. Carthon to improve the quality of care for senior citizens. Seniors, especially minorities, face serious barriers to healthcare that I want to resolve. Additionally, Penn’s unique use of simulations to bridge the gap between classroom learning and real-world application impressed me. Using computerized manikins that mimic human responses, classes in Penn’s nursing program allow students to apply their emergency medical skills in a mass casualty simulation and monitor their actions afterward through a video system. Participating in this activity will help me identify my strengths and areas for improvement regarding crisis management and medical care in a controlled yet realistic setting. Research opportunities and simulations will develop my skills even before I interact with patients.

COMPASSION. I value giving back through community service, and I have a particular interest in Penn’s Community Champions and Nursing Students For Sexual & Reproductive Health (NSRH). As a four-year volunteer health educator, I hope to continue this work as a Community Champions member. I am excited to collaborate with medical students to teach fourth and fifth graders in the city about cardiology or lead a chair dance class for the elders at the LIFE Center. Furthermore, as a feminist who firmly believes in women’s abortion rights, I’d like to join NSRH in order to advocate for women’s health on campus. At Penn, I can work with like-minded people to make a meaningful difference.

CONFIDENCE. All of the Quakers that I have met possess one defining trait: confidence. Each student summarized their experiences at Penn as challenging but fulfilling. Although I expect my coursework to push me, from my conversations with current Quakers I know it will help me to be far more effective in my career.

The Five C’s of Caring are important heuristics for nursing, but they also provide insight into how I want to approach my time in college. I am eager to engage with these principles both as a nurse and as a Penn Quaker, and I can’t wait to start.

This student takes a creative approach to the essay, by using the Five C’s of Caring as a framework. This technique works especially well since these qualities relate to the student’s future career in nursing. In addition to emphasizing the student’s creativity and passion for nursing, having the Five C’s in all caps at the start of each paragraph gives this long essay a clear, easy-to-read format.

What really makes the essay stand out is the depth of the student’s fit with UPenn, and how they’re able to also share more about who they are. The student lists specific courses, research opportunities, technology, and student groups. We also learn that they are a first-generation student, are passionate about increasing access to healthcare (particularly for LGBTQ+ people, minorities, and the elderly), care about health education, and are a feminist who staunchly defends abortion rights (this controversial topic could be risky, but since UPenn is a very liberal school, this should be fine).

Overall, this essay paints a vivid picture of how the student would engage academically at Penn, and we also see clearly how the student would pursue their intellectual passions outside the classroom. Since this essay prompt focused on “intellectual and academic interests,” there was no need to address other aspects of UPenn beyond those supporting their various interests in healthcare.

See more “ Why This College?” essay examples to understand what makes a strong response.

Brainstorming for the “Why This College?” Essay

Now that we’ve gone through a couple examples, you might be wondering how to get started yourself. 

Here are three steps we recommend to get your essay underway:

• Reflect on your academic and career goals
• Research unique opportunities related to your academic and extracurricular interests
• Pick your top academic reasons for applying, and your top extracurricular/social reasons

1. Reflect on your academic and career goals.

The driver behind this essay needs to be you , and not the school itself. Anyone can write nice things about the college, but only you can explain why you would be a good fit for it.

Ask yourself:

• What do you want to major in, if you know? If you’re undecided, what are the subjects you’re interested in?
• Which career do you want to pursue, or what are the potential options?
• What do you want to get out of college? Any particular skills or experiences?

Once you have a clear idea of your college plan, then you can dig into how the college can support your plan.

2. Research unique opportunities related to your academic, career, and extracurricular interests.

You might be wondering where you can find all these specific courses, clubs, and other resources. The school’s website is a good place to start, or if you have a general idea of what you’re looking for, you can even use Google with the school name in your search, such as “Tufts orchestra.” 

Take a look at the website of your department/major and dig into the courses, fellowships, internships, and other resources. For course syllabi, you can visit the website of the professor who’s teaching the course; they’ll often post more detailed information than the online course catalog, including readings and concepts to be covered.

Clubs may have their own websites, but you can also try to find their Facebook groups or Instagram pages, which might be more current and even show events they’re hosting⁠.

If you can, try to speak with a current student. Your school counselor may be able to connect you with one, or you can also reach out to the admissions office to see if they can connect you. If not, speaking with an admissions officer is also great, or you can try to find day-in-the-life videos on YouTube.

3. Pick your top academic reasons for applying, and your top extracurricular/social reasons.

Once you’ve done your research and found specific opportunities to cite in your essay, pick your top 1-3 academic reasons and top 1-3 extracurricular ones, depending on the word count. Going back to the Tufts essay, the good example we gave actually was already 65 words, and it was only able to mention two courses. 

Keep in mind that you not only have to describe resources specific to the school, but also how they’ll contribute to your goals. This personal aspect is just as important as the actual opportunities, so be sure to allot space to describe why exactly these resources make the school a good fit for you.

When it comes to academic reasons, you are free to list anything from special programs to unique majors to specific courses and professors. We want to caution you against “name-dropping” professors, however⁠—unless their work actually fits with your established interests and professional goals. Otherwise, it might seem like you’re being disingenuous.

We also want to reiterate that you should be sure to not only talk about academics in your essay, but also extracurriculars (unless the prompt asks you to focus only on academics, or if the word count is unusually short, i.e. 150 words or fewer). Again, college isn’t just about what you do in the classroom. Admissions committees want to be sure that accepted students will also contribute to the college community. 

Outlining Your “Why This College?” Essay

Once you’ve identified your goals and the resources to support them, it’s time to start writing. An easy format/outline for your essay would be:

• Introduction to your main goals and the why behind them (great spot for an anecdote). 
• Your first goal and how the school can support it.
• Your second goal and how the school can support it.
• Conclusion where you look towards the future and reaffirm how the college can get you there.

You can adjust the length of the essay by adding or subtracting the number of goals you write about. As noted above, r emember to include extracurriculars when sharing how the college can support your goals. You should plan to spend about 70% of your space on academic reasons, and 30% on extracurricular reasons.

Some students choose to use a more unconventional format, like the Five C’s of Caring essay above, and that works too if you want to show off your creative writing skills. Some examples include a letter to the school or a schedule of your day as a student at the college. These unconventional formats can be harder to pull off though, so only go that route if you’re confident in your writing. The letter format can be especially tricky since it’s easy to sound cheesy and overenthusiastic.

Regardless of the format you choose, remember these two things that your essay should do. It should:

• Reveal more about your goals and interests.
• D escribe how the school can help you develop your interests and reach your goals, by naming highly-specific and unique campus resources, both academic and extracurricular.

If your essay checks both of those boxes, you’re well on your way to making your candidacy more compelling to admissions officers!

Where to Get Your “Why This College?” Essay Edited

Do you want feedback on your “Why This College?” essays? After rereading your essays countless times, it can be difficult to evaluate your writing objectively. That’s why we created our free Peer Essay Review tool , where you can get a free review of your essay from another student. You can also improve your own writing skills by reviewing other students’ essays. 

If you want a college admissions expert to review your essay, advisors on CollegeVine have helped students refine their writing and submit successful applications to top schools. Find the right advisor for you to improve your chances of getting into your dream school!

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The grades you have earned while in high school or secondary school play the most important role in determining your competitiveness for admission to the University of Colorado Boulder.

Since there are many different grading scales and weighting methods, we use the total weighted GPA provided by your graduating high school, using a standard 4.00 scale. GPAs that are not on a 4.00 scale are converted accordingly.

If your high school does not provide a weighted GPA but provides a total unweighted GPA, we will use your total unweighted GPA on a standard 4.00 scale. If your high school does not provide a GPA or the GPA provided does not include all completed high school courses, we will recalculate the GPA according to the grading scale in use at your high school at the time the course was completed. When recalculating a GPA, we will not add weight for honors, AP and/or IB curricula because there is not a standard format for the designation or grading scale for these courses. However, we do consider the number of honors, AP and/or IB courses a student takes when determining the rigor of their overall curriculum.

Class Selection

Academic rigor in your course selection is also a primary factor that we consider. To be competitive, challenge yourself by pursuing the most rigorous courses available that are appropriate to your level of ability.

The number of courses taken beyond the minimum recommendation of 17—as well as those designated as advanced, honors, gifted, concurrent enrollment, dual-enrollment, AP or IB —will be considered in the admission process.

First-year students applying to undergraduate programs are strongly encouraged to meet the following Higher Education Admission Recommendations (HEAR) . Students may be admitted to CU Boulder even though they have not completed all of the HEAR courses. There are no consequences if HEAR is not met. However, not completing HEAR might result in taking additional courses to meet the CU Boulder graduation requirements of individual majors. International students with four or less semesters of U.S. schooling should refer to their country's specific requirements .

Please note: a challenging schedule will not outweigh a non-competitive GPA, as your grades ultimately remain the single most important factor in your admission decision. Additionally, any grades of D or F on your transcript—especially in your junior or senior year—would be cause for concern and should be addressed in your application.

Standardized Tests

ACT or SAT scores are not required for first-year students, but you may provide self-reported scores if you would like us to take your scores into consideration when reviewing your application. You will indicate on the Common App whether you plan to submit standardized test scores. If you choose to submit scores, please ensure that we have received them by the relevant application deadline so that your application will not be considered late.

First-Year Applicant FAQs

English Proficiency Requirements for International Students

In addition to our general admission requirements, all international applicants are also required to meet a minimum standard of English proficiency. International students who do not meet this requirement may still be eligible for conditional admission.

Review English Proficiency Requirements

Beyond Academics

While academics and test scores play a large role in your admission decision, we want students who are actively involved in their schools and communities. We place importance on secondary factors beyond academic achievement to assess the overall qualities of an applicant. 

What makes you stand out? Be thoughtful and use your required essays and your letter of recommendation to highlight your school and community activities, leadership positions and awards, participation in athletics or music, work experience, summer activities and special circumstances. Please note: we do not accept or use portfolio or audio/video submissions in our admission process.

Personal Essays

Your personal essays give you the opportunity to tell us more about yourself. They provide insight into your challenges and triumphs in a way that transcripts and test scores simply cannot.

When reading your essays, we are looking for sincerity and authenticity. It’s easy to tell when a student’s essay is something they care deeply about, compared to a student who writes what they think we want to hear. A funny or interesting story doesn’t hurt, either!

There is one essay and one short answer required for first year applicants. As you write your essay and short answer, consider reflecting on challenges that you've overcome, your family or cultural heritage, your academic or co-curricular achievements or specific moments that have defined your character. There are no 'correct' answers to these questions; your responses should reflect the unique aspects and experiences of your life.

What we are looking for:

• Be yourself. Open up to us and write about something that is meaningful to you.
• Be specific. Give examples and tell stories to make your points.
• Be honest. We are interested in your journey—even if it hasn’t always been perfect.
• Be clear. Effective writing and communication skills are expected.

Letter of Recommendation

Just like your essays give you the chance to tell us more about you, a letter of recommendation gives someone else the opportunity to speak to your academic strengths and co-curricular involvement.

This is the one chance in your application where we get to learn about you from someone other than you, so choose someone who knows you well. Many students ask a teacher or school counselor to write their letter of recommendation.

Suggested topics:

• Student’s academic ability and college readiness
• Student’s overall performance in class and attitude
• Why the student would be a good fit for CU Boulder

Admitted Student Averages

Credentials based on the middle 50% of 2024 admitted first-year students. High School GPAs are weighted and may represent self-reported GPAs. SAT/ACT scores reflect the middle 50% score range for students who requested test scores be considered in their application review. For the 2024 first-year application, SAT/ACT scores are not required and we take a holistic approach when reviewing your application.  

Weighted High School GPA: 3.74 - 4.23

SAT Total: 1290 - 1460 Math and Evidence-Based Reading & Writing

ACT Composite: 29 - 34

College of Arts & Sciences

Weighted High School GPA: 3.70 - 4.20

SAT Total: 1270 - 1440 Math and Evidence-Based Reading & Writing

ACT Composite: 29 - 33

College of Engineering & Applied Science

Weighted High School GPA: 3.97 - 4.42

SAT Total: 1360 - 1500 Math and Evidence-Based Reading & Writing

ACT Composite: 31 - 34

College of Media, Communication & Information

Weighted High School GPA: 3.54 - 4.06

SAT Total: 1220 - 1380 Math and Evidence-Based Reading & Writing

ACT Composite: 28 - 32

College of Music

Weighted High School GPA: 3.71 - 4.20

SAT Total: 1290 - 1470 Math and Evidence-Based Reading & Writing

ACT Composite: 30 - 33

Leeds School of Business

Weighted High School GPA: 4.0 - 4.36

SAT Total: 1360 - 1450 Math and Evidence-Based Reading & Writing

ACT Composite: 30 - 34

Program in Environmental Design

Weighted High School GPA: 3.62 - 4.17

SAT Total: 1270 - 1410 Math and Evidence-Based Reading & Writing

ACT Composite: 29 - 32

School of Education

Weighted High School GPA: 3.40 - 3.99

SAT Total: 1160 - 1330 Math and Evidence-Based Reading & Writing

ACT Composite: 26 - 31

Credit for Course work or Exams

Students applying to CU Boulder have the opportunity to earn college credit before enrollment. CU Boulder accepts credit from AP/IB exams, A-Level exams, college course work taken concurrently while in high school and limited CLEP credit. Earning college credit while in high school is a great way to help offset some of your estimated cost of attendance. Students are highly encouraged to explore credit for course work options while in high school. For more information on how credit is transferred to CU Boulder and what credit can be accepted please see the links below.

Official Advanced Placement (AP) scores must be sent to the admissions office directly from the College Board. CU Boulder's CEEB/ETS code is 004841.

Review the Advanced Placement Chart

For A-level examinations from an international examining board to be considered for transfer credit, the student must submit an official copy of the examination result, either by submitting the original certificate upon arrival on campus (University of Colorado Boulder will make and keep a copy as official, returning the original to the student), or through verification of results between the Office of Admissions and the examinations board. Methods of approved verification are below.

• AQA : Student must request verification by emailing [email protected] (add 'Verification' in the subject box) and have it sent to [email protected] . 
• CIE:   The University of Colorado Boulder can use CIE Direct after requesting the following information from the student: Cambridge Center and candidate numbers, student’s date of birth and the relevant examination series (month and year, e.g. June 2014). 
• OCR : Student must request that OCR send a fax confirming student’s results to the University of Colorado Boulder. Fax number: +1-303-735-2501, ATTN: International Admissions.
• Pearson/Edexcel : Student must apply for a copy of the certificate  to be sent directly to the University of Colorado Boulder.
• WJEC/CBAC : Student must submit original Certificate or Certifying Statement of Results only (confirmation of grades via email/telephone/fax not available). 

If you took college-level courses while enrolled in high school, you may be able to transfer the credit to CU Boulder. Only courses taken at a college or university of recognized standing with grades of C- or better are accepted for transfer. All college-level work will be evaluated in accordance with CU Boulder transfer credit guidelines. You must have an official college transcript sent directly to the Office of Admissions in order for transfer credit to be evaluated.

Review the Transfer Credit Policy

The International Baccalaureate (IB) diploma programs provide pre-university study. IB examinations, whether leading to a full IB diploma or to an IB certificate, often qualify students for advanced standing at CU Boulder. In general, credit is granted for approved IB examinations at the higher level with a score of 4 or better. Students admitted to the University of Colorado Boulder who have graduated from high school with an International Baccalaureate Diploma shall be granted 24 semester hours of college credit. This credit will be applied toward degree requirements only if approved by the college or school. Depending on the student’s degree program, some of the 24 credits may not be applicable towards degree requirements. No CU Boulder tuition will be charged for these credits and the 24 credits will only be granted if the student receives a score of 4 or better on an examination administered as part of the IB Diploma program. If the student scores less than 4 on each IB subject test, the credit hours granted will be reduced accordingly. Official scores must be sent to the Admissions Office directly from the IB organization.

Review the International Baccalaureate Chart

Ready to apply?

Learn how to apply

Undergraduate Admission Information For:

First-Year Applicants

First-year applicants are in high school, or have graduated from high school but have not taken any college courses after graduating or earning a GED.

Transfer Applicants

Transfer applicants have attended another college or university since earning their high school diploma or GED. Transfer applicants are looking to complete a bachelor’s degree at CU Boulder.

International Applicants

Undergraduate international applicants are students who need a visa to be in the U.S. Apply as a domestic student if you have a U.S. passport or green card.

Readmit Applicants

Veteran Applicants

Undocumented Applicants

CU Boulder counselors are here to help you through the application and answer any questions that may arise during the admission process.

Find Your Counselor

• Join Our Communication List
• Contact Admissions

The University of Colorado does not discriminate on the basis of race, color, national origin, sex, age, pregnancy, disability, creed, religion, sexual orientation, gender identity, gender expression, veteran status, political affiliation, or political philosophy. All qualified individuals are encouraged to apply. You may  view the list of ADA and Title IX coordinators  and  review the Regent policy .

As a student or prospective student at CU Boulder, you have a right to certain information pertaining to financial aid programs, the Clery Act, crime and safety, graduation rates, athletics and other general information such as the costs associated with attending CU Boulder. To view this information visit  colorado.edu/your-right-know .

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15 Things You Can Do With ChatGPT

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Quick Links

What is chatgpt.

• Quickly Write a Customized Resume and Cover Letter
• Create Original Jokes and Memes
• Explain Complex Topics
• Solve Tricky Math Problems Step-by-Step
• Write Music In Almost Any Genre
• Write, Debug, and Explain Code
• Create, Edit, and Modify Media Files
• Decide What to Watch Next
• Get Cooking Help
• Improve Your Health
• Translate and Learn In Multiple Languages
• Prepare for a Job Interview
• Write Essays on Almost Any Topic
• A Chat Companion

Key Takeaways

• ChatGPT is a versatile tool that can help with tasks like writing customized resumes & cover letters.
• The AI can generate original jokes and memes, as well as explain complex topics in an easy-to-understand manner.
• ChatGPT can assist with mathematics, music composition, coding, media file manipulation, and health improvement.

Artificial intelligence tools have seen a meteoric rise within the last few years. We've been wowed by AI writing tools, AI image generators, and even AI self-portraits. Since its launch in November 2022, ChatGPT has gotten a lot of attention for its numerous uses. To help you leverage this tool, here are 15 ways you can also use ChatGPT.

If you've somehow missed the whole ChatGPT buzz, or you're not exactly sure what it's all about, let's help you get up to speed. ChatGPT is a conversational artificial intelligence chatbot that can answer just about any question you throw at it.

You can think of it as a supercharged Google Search. Rather than just providing links or snippets, ChatGPT generates thoughtful, conversational responses to queries. It synthesizes information from diverse sources into cohesive answers on nearly any topic, similar to how a knowledgeable human would respond.

While not infallible, ChatGPT demonstrates an impressive ability to understand natural language questions and offers nuanced explanations in a lot of fields.

ChatGPT is more than just hype—it has practical uses. Here are some cool day-to-day uses for ChatGPT you can try right now.

1. Quickly Write a Customized Resume and Cover Letter

If you're currently job-hunting, one of the most tiring parts of the job application process is writing a personalized resume and cover letter for every job you apply for. You need custom-made copies for each job to increase your chances of getting hired. ChatGPT can help you create a customized resume or craft professional cover letters in minutes.

We asked ChatGPT to write a resume for a content marketing role at a fictional SaaS company, and it was near perfect.

We also prompted it to prepare a cover letter for the same role, and the first result wasn't bad.

Notice how detail-rich and well-formatted the resume and cover letter are? How did I do it? I pasted my LinkedIn profile details, and then asked ChatGPT to write a resume for the target role "using LaTex." I copied the result, pasted it in a free latex editor like Overleaf , and compiled it.

2. Create Original Jokes and Memes

What's life without a bit of fun? Whether you're looking for a good laugh or to create some hilarious jokes to impress your friends, ChatGPT can come in handy. Sure, AI chatbots aren't exactly known to be great comedians, but ChatGPT shows some potential. We asked ChatGPT to tell us a joke about Apple and foldable smartphones; we'll let you judge the results:

ChatGPT can also create images, so you can also play around with meme ideas. Here's one to try: Ask ChatGPT to create a meme about the grind of 9-to-5 jobs.

3. Explain Complex Topics

Sometimes, simply Googling a topic doesn't give you a clear understanding. Think of topics like wormholes, dark matter, and all those head-spinning theories. Or maybe it's a weird sport you don't understand.

ChatGPT could be useful in explaining them in layperson terms. We prompted ChatGPT to "Explain wormholes like I'm 5," and here's the result:

We also prompted it to explain the internet similarly. It wasn't too bad, either.

4. Solve Tricky Math Problems Step-by-Step

Whether you're looking to tackle complex algebra problems or simple math problems that are too tricky to piece together, ChatGPT is particularly strong at handling math. You'll need to present your problems clearly and concisely for the best results. We prompted ChatGPT to answer a tricky math problem, and here's the result:

5. Write Music In Almost Any Genre

One of the most exciting things you can do with ChatGPT is writing a song. It might sound like a bad idea at first, but it's really a fun thing to try. The results can be amazing when you get the prompts right. The key to getting the best result is to provide as many details as possible about how you want the song to be. Need a mix of English and some Spanish with a touch of Afrobeat style? Just say it.

If you really want to find out how good your lyrics would sound in an actual song, you'll need to head over to a tool like Suno.ai to turn the lyrics into music. Just paste the lyrics into the tool, make some tweaks and listen to what ChatGPT could make.

6. Write, Debug, and Explain Code

Whether you're an experienced programmer or a newbie, you're bound to run into a few bugs in your code from time to time. ChatGPT can help you narrow down the problem within your code, saving you hours looking for a misplaced comma. You can also write entire blocks of functional code snippets from scratch or analyze existing code bases to figure out the best ways to use them. There are endless ways you can use ChatGPT in programming .

We prompted ChatGPT to write a simple to-do list app using HTML, CSS, and JavaScript, and here's the result:

We also got the AI chatbot to write us a simple Tetris game, snake game, pong game, and even code a complete chat web app from scratch . ChatGPT is a very useful programming tool.

7. Create, Edit, and Modify Media Files

With ChatGPT, you can create, edit, modify, and read from a wide range of media files. The feature which is available on the ChatGPT Plus plan provides an interface to programmatically create images, modify videos, adjust audio tracks, and retrieve crucial metadata from media files with ease and precision.

To learn more about manipulating media files with ChatGPT, read our guide on how to use the ChatGPT Code Interpreter feature .

8. Decide What to Watch Next

ChatGPT is one of the most powerful movie recommendation tools on the internet if you know how to use it. While there are dozens of powerful movie recommendation tools you can get your hands on, ChatGPT stands out because of the accuracy and precision you get from simply describing the kind of movies you want using simple natural language prompts.

We asked ChatGPT to give us some movies that are similar to "The Walking Dead" and here's the result:

Not sure how to use ChatGPT as a movie recommendation tool? We've previously put together a detailed guide on how to use ChatGPT to decide what to watch next .

9. Play Games

Looking for a fun activity? ChatGPT has some creative game ideas to try with friends or by yourself. You could play classic games like tic-tac-toe or trivia with new twists that ChatGPT can suggest to make it more engaging. Whether you want a competitive game against ChatGPT or a cooperative game you can all play together, ChatGPT can provide unique game suggestions tailored to what you're looking for.

So if you're bored and want to try something new, ask ChatGPT to invent a fun, customized game—it's a great way to liven up your day! Not sure which games you can play with ChatGPT? Here are some interesting games you can play with ChatGPT right now .

10. Get Cooking Help

A robot help in the kitchen? ChatGPT and cooking seem like a weird combination, but it works excellently if you know the right prompts to use. You can use ChatGPT to explore new recipes, prepare shopping lists, brainstorm new flavor combinations, learn new cooking tips, or explore healthier ways to cook popular meals .

Fancy testing ChatGPT's culinary skills? Here are some interesting ways you can use ChatGPT as a cooking assistant .

11. Improve Your Health

With its vast wealth of health information, you can leverage ChatGPT to improve your health in several ways. It can help you create personalized workout and meal plans tailored to your unique needs.

You can also use it to develop healthy habits like sleep routines and mindfulness practices or even use it as a medical symptom checker. Although ChatGPT has its limitations in the field of health, it is still an immensely useful tool you can utilize to improve your health. We've put together a guide on how to use ChatGPT to improve your health .

12. Translate and Learn In Multiple Languages

ChatGPT is a great tool to have around if you need to work in multiple languages. It is fluent in dozens of languages. If you're a content creator who would love to reach a wider audience, ChatGPT could be incredibly useful for creating content in multiple languages.

Sure, there's Google Translate, but writing in one language and translating to the other means context and language-specific tones could be lost. When we compared ChatGPT to Google Translate in translation tasks, ChatGPT was noticeably better in several metrics.

With ChatGPT's latest voice mode, the tool has become even significantly more powerful for those trying to learn a new language or communicate with someone that speaks a different one.

13. Prepare for a Job Interview

With its wealth of knowledge across several fields, ChatGPT is one of the best AI tools to help you prepare for a job interview. With a few intelligent prompts, ChatGPT can help you get your dream job . You can use it to generate hypothetical scenarios in a job interview, possible questions, intelligent replies to possible questions, and many other useful interview prep tips.

We created a hypothetical situation during an interview and asked ChatGPT for help. Here's the result:

14. Write Essays on Almost Any Topic

While we strongly advise you to write your essays yourself, ChatGPT can compose amazing essays on a wide range of topics, even the most complex. If the tone of the resulting write-up doesn't suit your test, you can teach ChatGPT how to write like you so you can get the chatbot to replicate your writing style.

15. A Chat Companion

When all is said and done, ChatGPT is an AI chatbot. Despite its almost endless use cases, ChatGPT is a very accommodating companion when you need someone (or a robot) to talk to.

Despite ChatGPT's impressive capabilities, the AI chatbot is not infallible. Consequently, exercising caution with ChatGPT's information is highly advised. Always strive to verify any critical data from ChatGPT before applying it, especially for important health or financial choices. While ChatGPT is a game-changing tool, it is still a work in progress, and human oversight remains essential.

• Technology Explained

DNC Night 2

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Live fact check: Night 2 of the Democratic National Convention

By PolitiFact staff

Live updates: The Obamas and Doug Emhoff are set to speak on Day 2 of the DNC

By Associated Press

A look at James Baldwin’s enduring influence on art and activism

Jeffrey Brown Jeffrey Brown

Lena I. Jackson Lena I. Jackson

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• Copy URL https://www.pbs.org/newshour/show/a-look-at-james-baldwins-enduring-influence-on-art-and-activism

The legendary writer and activist James Baldwin would have turned 100 this month. He is best known for his novels and essays and as a moral voice addressing race, sexuality and the very fabric of American democracy. Jeffrey Brown looks at Baldwin's enduring legacy for our series, Art in Action, exploring the intersection of art and democracy and for our arts and culture coverage, CANVAS.

Read the Full Transcript

Notice: Transcripts are machine and human generated and lightly edited for accuracy. They may contain errors.

Amna Nawaz:

This month, the legendary writer and activist James Baldwin would have turned 100 years old.

Baldwin is best known for his novels and essays and as a moral voice addressing race, sexuality and the very fabric of American democracy. Nearly 40 years after his death, his words are more relevant than ever.

Jeffrey Brown looks at his enduring legacy for our series Art in Action, exploring the intersection of art and democracy, and our ongoing Canvas coverage.

James Baldwin, Writer:

The inequality suffered by the American Negro population of the United States has hindered the American dream.

Jeffrey Brown:

James Baldwin, novelist, essayist, civil rights activist, public intellectual, here debating William F. Buckley Jr. at the University of Cambridge in 1965.

Eddie Glaude Jr., Princeton University:

He's engaged in this ongoing work of self-creation, in this sustained reflection on the power of the American idea. He's bringing the full weight of his intellect to bear on this project.

Eddie Glaude Jr. is a professor of African American studies at Princeton University and author of the 2020 book "Begin Again: James Baldwin's America and Its Urgent Lessons for Our Own."

Eddie Glaude Jr.:

I think, if you read Baldwin closely, there is this underlying idea that we have yet to discover who we are, right, because the ghosts of the past in so many ways, not only blind us, but they have us by the throat.

James Arthur Baldwin was born in Harlem in 1924 and raised there by his mother and stepfather, a Baptist preacher. The oldest of nine children, he excelled in school and served as a junior minister.

A man on the margins, Black and queer, he spent years of his life abroad, much of it in France, beginning at age 24. He wrote novels, including "Go Tell It on the Mountain," an autobiographical book about growing up in Harlem, and "Giovanni's Room" about a tormented love affair between two men living in Paris, and powerful essays exploring race and American identity, including "Notes of a Native Son" and "The Fire Next Time."

He's one of the greatest essayists we have ever produced, the world has ever produced I think, and his subject is us. But his vantage point, it's not that of a victim. His vantage point is from those who've had to bear the burden of America's refusal to look itself squarely in the face.

He was also a playwright and poet, an activist who marched and spoke out for civil rights, including on television, here on "The Dick Cavett Show" in 1969.

James Baldwin:

And the word Negro in this country really is designed, finally, to disguise the fact that one is talking about another man, a man like you, who wants what you want.

And insofar as the American public wants to think there has been progress, they overlook one very simple thing. I don't want to be given anything by you. I just want you to leave me alone, so I can do it myself.

Baldwin died in 1987, but he's remained a powerful cultural presence, one that's only grown in the past decade.

There are days — this is one of them — when you wonder what your role is in this country and what your future is in it.

In the 2016 documentary "I Am Not Your Negro," director Raoul Peck drew from Baldwin's own words. As he told me then:

Raoul Peck, Director:

He was already a classic, and he wrote those things 40, 50 years ago. And watching the film, you think that he would have — he wrote that in the morning, the morning before watching the film, because those words are so accurate, they are so prescient and so impactful, that you can't do it better.

In 2018, Baldwin's 1974 novel "If Beale Street Could Talk" was adapted by Oscar-winning director Barry Jenkins.

Barry Jenkins, Director:

Whether I had won eight Oscars or no Oscars, it's James damn Baldwin, you know? It's James Baldwin. That's pressure enough, in and of itself, because I wanted to honor his legacy in the way that I thought it should be honored.

And now a celebration of the centennial of his birth, including an exhibition at the National Portrait Gallery called This Morning, This Evening, So Soon: James Baldwin and the Voices of Queer Resistance, which takes its name from a short story he published in 1960, another at the Schomburg Center for Research in Black Culture titled Jimmy: Gods Black Revolutionary Mouth, presenting Baldwin's archive of personal papers.

There's a new album by singer-songwriter and bassist Meshell Ndegeocello called No More Water: The Gospel of James Baldwin, and reissues of seminal works with new introductions and artwork.

Cree Myles, Host, "The Baldwin 100": What is the best lesson you have learned being in the spiritual community that you are in with James Baldwin?

Along with a podcast, "The Baldwin 100," in which host Cree Myles talks with contemporary writers and thinkers.

What is his relevance today, especially when you think about younger people, younger readers, younger citizens?

Cree Myles:

Despite the time that has passed, his amount of truth is still relatively radical. When I think about his novels and "Giovanni's Room," and we're thinking about the ways that he grappled with, like, sexuality, those are things were still coming to terms with.

Acclaimed Irish novelist Colm Toibin contributed the new book "On James Baldwin."

Colm Toibin, Author, "On James Baldwin": I'm interested in him as, I suppose, someone who really found ways of dealing with individuality versus community, with being an artist in a difficult time.

But more than anything, more than anything, he wrote well.

Toibin saw connections to his own upbringing and told us how Baldwin has influenced him as writer and man.

Colm Toibin:

It's a question of engaging with this great intelligence and with the sensuous intelligence, with someone sort of thinking brilliantly and glittering sort of way.

But it is also, of course, developing strategies, which he did in relation to his family, in relation to Harlem, in relation to Black America, in relation to exile, in relation to attempting to being an artist in a time of flux, and also in a way of being a gay artist, a homosexual artist coming out of a world which is very conservative and very religious, and attempting also to build strategies around that that give you energy, rather than ones that take you down.

One deeply resonant thread through all the commemorations, Baldwin's focus on the fragility of democracy itself.

Baldwin's exposing the lie that is the source of the suffering, that defines this fragile project, it seems to me. He's committed to democracy. He's committed to America. After all, we are deeply American. But, by virtue of that commitment, he has to relentlessly critique it.

It comes as a great shock to discover the country, which is your birthplace and to which you owe your life and your identity, has not, in its whole system of reality, evolved any place for you.

A commitment, as Glaude puts it, to the complex experiment called America.

For the "PBS News Hour," I'm Jeffrey Brown.

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In his more than 30-year career with the News Hour, Brown has served as co-anchor, studio moderator, and field reporter on a wide range of national and international issues, with work taking him around the country and to many parts of the globe. As arts correspondent he has profiled many of the world's leading writers, musicians, actors and other artists. Among his signature works at the News Hour: a multi-year series, “Culture at Risk,” about threatened cultural heritage in the United States and abroad; the creation of the NewsHour’s online “Art Beat”; and hosting the monthly book club, “Now Read This,” a collaboration with The New York Times.

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