how do you start 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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Math Essay Ideas for Students: Exploring Mathematical Concepts

Are you a student who's been tasked with writing a math essay? Don't fret! While math may seem like an abstract and daunting subject, it's actually full of fascinating concepts waiting to be explored. In this article, we'll delve into some exciting math essay ideas that will not only pique your interest but also impress your teachers. So grab your pens and calculators, and let's dive into the world of mathematics!

• The Beauty of Fibonacci Sequence

Have you ever wondered why sunflowers, pinecones, and even galaxies exhibit a mesmerizing spiral pattern? It's all thanks to the Fibonacci sequence! Explore the origin, properties, and real-world applications of this remarkable mathematical sequence. Discuss how it manifests in nature, art, and even financial markets. Unveil the hidden beauty behind these numbers and show how they shape the world around us.

• The Mathematics of Music

Did you know that music and mathematics go hand in hand? Dive into the relationship between these two seemingly unrelated fields and develop your writing skills . Explore the connection between harmonics, frequencies, and mathematical ratios. Analyze how musical scales are constructed and why certain combinations of notes create pleasant melodies while others may sound dissonant. Explore the fascinating world where numbers and melodies intertwine.

• The Geometry of Architecture

Architects have been using mathematical principles for centuries to create awe-inspiring structures. Explore the geometric concepts that underpin iconic architectural designs. From the symmetry of the Parthenon to the intricate tessellations in Islamic art, mathematics plays a crucial role in creating visually stunning buildings. Discuss the mathematical principles architects employ and how they enhance the functionality and aesthetics of their designs.

• Fractals: Nature's Infinite Complexity

Step into the mesmerizing world of fractals, where infinite complexity arises from simple patterns. Did you know that the famous Mandelbrot set , a classic example of a fractal, has been studied extensively and generated using computers? In fact, it is estimated that the Mandelbrot set requires billions of calculations to generate just a single image! This showcases the computational power and mathematical precision involved in exploring the beauty of fractal geometry.

Explore the beauty and intricacy of fractal geometry, from the famous Mandelbrot set to the Sierpinski triangle. Discuss the self-similarity and infinite iteration that define fractals and how they can be found in natural phenomena such as coastlines, clouds, and even in the structure of our lungs. Examine how fractal mathematics is applied in computer graphics, art, and the study of chaotic systems. Let the captivating world of fractals unfold before your eyes.

• The Game Theory Revolution

Game theory isn't just about playing games; it's a powerful tool used in various fields, from economics to biology. Dive into the world of strategic decision-making and explore how game theory helps us understand human behavior and predict outcomes. Discuss in your essay classic games like The Prisoner's Dilemma and examine how mathematical models can shed light on complex social interactions. Explore the cutting-edge applications of game theory in diverse fields, such as cybersecurity and evolutionary biology. If you still have difficulties choosing an idea for a math essay, find a reliable expert online. Ask them to write me an essay or provide any other academic assistance with your math assignments.

• Chaos Theory and the Butterfly Effect

While writing an essay, explore the fascinating world of chaos theory and how small changes can lead to big consequences. Discuss the famous Butterfly Effect and how it exemplifies the sensitive dependence on initial conditions. Delve into the mathematical principles behind chaotic systems and their applications in weather forecasting, population dynamics, and cryptography. Unravel the hidden order within apparent randomness and showcase the far-reaching implications of chaos theory.

• The Mathematics Behind Cryptography

In an increasingly digital world, cryptography plays a vital role in ensuring secure communication and data protection. Did you know that the global cybersecurity market is projected to reach a staggering $248.26 billion by 2023? This statistic emphasizes the growing importance of cryptography in safeguarding sensitive information.

Explore the mathematical foundations of cryptography and how it allows for the creation of unbreakable codes and encryption algorithms. Discuss the concepts of prime numbers, modular arithmetic, and public-key cryptography. Delve into the fascinating history of cryptography, from ancient times to modern-day encryption methods. In your essay, highlight the importance of mathematics in safeguarding sensitive information and the ongoing challenges faced by cryptographers.

Writing a math essay doesn't have to be a daunting task. By choosing a captivating topic and exploring the various mathematical concepts, you can turn your essay into a fascinating journey of discovery. Whether you're uncovering the beauty of the Fibonacci sequence, exploring the mathematical underpinnings of music, or delving into the game theory revolution, there's a world of possibilities waiting to be explored. So embrace the power of mathematics and let your creativity shine through your words!

Remember, these are just a few math essay ideas to get you started. Feel free to explore other mathematical concepts that ignite your curiosity. The world of mathematics is vast, and each concept has its own unique story to tell. So go ahead, unleash your inner mathematician, and embark on an exciting journey through the captivating realm of mathematical ideas!

Tobi Columb, a math expert, is a dedicated educator and explorer. He is deeply fascinated by the infinite possibilities of mathematics. Tobi's mission is to equip his students with the tools needed to excel in the realm of numbers. He also advocates for the benefits of a gluten-free lifestyle for students and people of all ages. Join Tobi on his transformative journey of mathematical mastery and holistic well-being.

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Introduction to writing in mathematics

Writing in mathematics is an essential skill that serves to communicate abstract concepts, proofs, and problem-solving methodologies effectively. Unlike writing in literature, mathematical writing demands precision, clarity, and logical coherence to convey mathematical ideas accurately. This distinct approach to writing underscores the importance of articulating mathematical reasoning and procedures concisely, ensuring that mathematical arguments are both comprehensible and rigorous

Writing an essay in a math class? Not sure where to begin? Here is a helpful resource for engaging in mathematical writing: A Guide to Writing Mathematics (UC Davis).

A General Outline for a Mathematical Essay

• Background Information: Provide context around the problem. Careful not to assume that the reader has full knowledge on the topic. Avoid words such as “ obvious ” since this assumes the knowledge of your reader. You may include relevant details that will help the reader understand the problem you are presenting. In addition, this section is where specific vocabulary or notation/ symbols are defined. Establishing the definitions, it is safe to use throughout the body of the paper.  
• Thesis Statement: Restate the goal of the problem in one sentence. This serves as a quick reminder to the reader what you will be attempting to answer. 
• Supporting Paragraphs: A good approach to this section would be to break down the problem into various subproblems. The more details that you provide, the more clarity the reader has into your perspective. You should be as elaborate as possible! 
• Summarize/Review key points: In this section you want to cycle back to the original objective of the problem, that is return to the thesis statement. Provide a small synopsis of your perspective of the problem, and provide emphasis of the conclusion. Make sure that your reader understands how you arrived at your final solution. 
• Concluding thoughts : You may want to conclude with other ideas that you considered while thinking about the problem. Alternatively, you may leave your reader with questions that you have after the analysis of the problem. This is a good place to provide your experiences of reasoning throughout the problem.

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How to Write a Math Essay

Adam jefferys.

Before taking a college-level math class, many students have never needed to write a mathematics essay. However, professional mathematicians, along with others working with higher-level math, must be able to communicate their ideas in ways that are comprehensible to others. Being able to write well about math is as important to mathematicians as being able to solve problems.

Explore this article

• Choosing a Topic
• Structuring Your Essay
• Writing Formulas
• Punctuation and Grammar

1 Choosing a Topic

The topic of your mathematics essay should be something that involves doing actual math -- not a history of Euclidean geometry or a biographical essay on Pierre de Fermat. In some cases, your instructor might provide you with a list of topics or problems. Otherwise, ask yourself what topics discussed in class have particularly interested you. Consider topics or ideas brought up in discussion that the instructor did not have time to explain in detail, or ways of applying ideas from class to new problems.

2 Structuring Your Essay

A well-structured mathematical essay will both show the connections between your work and the wider world of mathematics, and will carefully lead your reader through the logical structure of your work. A standard organizational form consists of four sections: background, introduction, body and implications. The background section gives the reader the history of the problem or ideas you're working with. The introduction introduces the reader to your work specifically and introduces any special definitions or symbols needed for your work. The body section contains most of your work, leading the reader through the specific problem or idea you're considering. The implications section gives your reader an idea of the consequences of your work, and what future work remains to be done.

3 Writing Formulas

Some instructors might allow students to write complex mathematical formulations by hand, though of course the main text of the paper should be typed. Formulas written by hand should be legible. To type formulas in Microsoft Word 2010, on the Insert tab, in the Symbols group, click the “Equation” arrow, then click “Insert New Equation.” If you're going to be writing many mathematics essays or other writing involving complex formulas, it might be worthwhile to learn a mathematical typesetting language such as TeX or LaTeX.

4 Punctuation and Grammar

Follow the rules of punctuation and grammar throughout your mathematics essay. Formulas are generally indented and given a separate line, but otherwise should be treated as elements of the composition, following the same rules of grammar that apply to words. Treat an equation, inequality or other “complete” mathematical statement as a sentence, followed by a period. Equations that do not constitute complete mathematical statements, such as “5x + 1,” should be treated as nouns.

• 1 Oregon State University: How to Write a Math Essay
• 2 UC Davis Computer Science: A Guide to Writing Mathematics
• 3 Massachusetts Institute of Technology: Writing a Research Paper in Mathematics
• 4 Microsoft Office: Write, Insert or Change an Equation

About the Author

Based in Chicago, Adam Jefferys has been writing since 2007. He teaches college writing and literature, and has tutored students in ESL. He holds a Masters of Fine Arts in creative writing, and is currently completing a PhD in English Studies.

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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 2 months ago (category: Blog )

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GED Mathematical Reasoning Prep 2020-2021 The Most Comprehensive Review and Ultimate Guide to the GED Math Test

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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 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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Essays About Math: Top 10 Examples and Writing Prompts 

Love it or hate it, an understanding of math is said to be crucial to success. So, if you are writing essays about math , read our top essay examples .  

Mathematics is the study of numbers, shapes, and space using reason and usually a special system of symbols and rules for organizing them . It can be used for a variety of purposes, from calculating a business’s profit to estimating the mass of a black hole. However, it can be considered “controversial” to an extent.

Most students adore math or regard it as their least favorite. No other core subject has the same infamy as math for generating passionate reactions both for and against it. It has applications in every field, whether basic operations or complex calculus problems. Knowing the basics of math is necessary to do any work properly. 

If you are writing essays about Math , we have compiled some essay examples for you to get started. 

1. Mathematics: Problem Solving and Ideal Math Classroom by Darlene Gregory 

2. math essay by prasanna, 3. short essay on the importance of mathematics by jay prakash.

• 4.  Math Anxiety by Elias Wong

5. Why Math Isn’t as Useless as We Think by Murtaza Ali

1. mathematics – do you love or hate it, 2. why do many people despise math, 3. how does math prepare you for the future, 4. is mathematics an essential skill, 5. mathematics in the modern world.

“The trait of the teacher that is being strict is we know that will really help the students to change. But it will give a stress and pressure to students and that is one of the causes why students begin to dislike math. As a student I want a teacher that is not so much strict and giving considerations to his students. A teacher that is not giving loads of things to do and must know how to understand the reasons of his students.”

Gregory discusses the reasons for most students’ hatred of math and how teachers handle the subject in class. She says that math teachers do not explain the topics well, give too much work, and demand nothing less than perfection. To her, the ideal math class would involve teachers being more considerate and giving less work. 

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“ Math is complicated to learn, and one needs to focus and concentrate more. Math is logical sometimes, and the logic needs to be derived out. Maths make our life easier and more straightforward. Math is considered to be challenging because it consists of many formulas that have to be learned, and many symbols and each symbol generally has its significance.”

In her essay , Prasanna gives readers a basic idea of what math is and its importance. She additionally lists down some of the many uses of mathematics in different career paths, namely managing finances, cooking, home modeling and construction, and traveling. Math may seem “useless” and “annoying” to many, but the essay gives readers a clear message: we need math to succeed. 

“In this modern age of Science and Technology, emphasis is given on Science such as Physics, Chemistry, Biology, Medicine and Engineering. Mathematics , which is a Science by any criterion, also is an efficient and necessary tool being employed by all these Sciences. As a matter of fact, all these Sciences progress only with the aid of Mathematics . So it is aptly remarked, ‘ Mathematics is a Science of all Sciences and art of all arts.’”

As its title suggests, Prakash’s essay briefly explains why math is vital to human nature. As the world continues to advance and modernize, society emphasizes sciences such as medicine, chemistry, and physics. All sciences employ math; it cannot be studied without math. It also helps us better our reasoning skills and maximizes the human mind. It is not only necessary but beneficial to our everyday lives. 

4.   Math Anxiety by Elias Wong

“ Math anxiety affects different not only students but also people in different ways. It’s important to be familiar with the thoughts you have about yourself and the situation when you encounter math. If you are aware of unrealistic or irrational thoughts you can work to replace those thoughts with more positive and realistic ones.”

Wong writes about the phenomenon known as “math anxiety.” This term is used to describe many people’s hatred or fear of math- they feel that they are incapable of doing it. This anxiety is caused mainly by students’ negative experiences in math class, which makes them believe they cannot do well. Wong explains that some people have brains geared towards math and others do not, but this should not stop people from trying to overcome their math anxiety. Through review and practice of basic mathematical skills , students can overcome them and even excel at math. 

“We see that math is not an obscure subject reserved for some pretentious intellectual nobility. Though we may not be aware of it, mathematics is embedded into many different aspects of our lives and our world — and by understanding it deeply, we may just gain a greater understanding of ourselves.”

Similar to some of the previous essays, Ali’s essay explains the importance of math. Interestingly, he tells a story of the life of a person name Kyle. He goes through the typical stages of life and enjoys typical human hobbies, including Rubik’s cube solving. Throughout this “Kyle’s” entire life, he performed the role of a mathematician in various ways. Ali explains that math is much more prevalent in our lives than we think, and by understanding it, we can better understand ourselves. 

Writing Prompts on Essays about Math

Math is a controversial subject that many people either passionately adore or despise. In this essay , reflect on your feelings towards math, and state your position on the topic. Then, give insights and reasons as to why you feel this way. Perhaps this subject comes easily to you, or perhaps it’s a subject that you find pretty challenging. For an insightful and compelling essay , you can include personal anecdotes to relate to your argument. 

It is well-known that many people despise math. In this essay , discuss why so many people do not enjoy maths and struggle with this subject in school. For a compelling essay , gather interview data and statistics to support your arguments. You could include different sections correlating to why people do not enjoy this subject .

In this essay , begin by reading articles and essays about the importance of studying math. Then, write about the different ways that having proficient math skills can help you later in life. Next, use real-life examples of where maths is necessary, such as banking, shopping, planning holidays, and more! For an engaging essay , use some anecdotes from your experiences of using math in your daily life.

Many people have said that math is essential for the future and that you shouldn’t take a math class for granted. However, many also say that only a basic understanding of math is essential; the rest depends on one’s career. Is it essential to learn calculus and trigonometry? Choose your position and back up your claim with evidence. 

Prasanna’s essay lists down just a few applications math has in our daily lives. For this essay , you can choose any activity, whether running, painting, or playing video games, and explain how math is used there. Then, write about mathematical concepts related to your chosen activity and explain how they are used. Finally, be sure to link it back to the importance of math, as this is essentially the topic around which your essay is based. 

If you are interested in learning more, check out our essay writing tips !

For help with your essays, check out our round-up of the best essay checkers

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How to Start a College Essay to Hook Your Reader

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What is the purpose of the college essay introduction, tips for getting started on your essay, 6 effective techniques for starting your college essay.

• Cliche College Essay Introduction to Avoid

Where to Get Your Essay Edited for Free

Have you sat down to write your essay and just hit a wall of writer’s block? Do you have too many ideas running around your head, or maybe no ideas at all?

Starting a college essay is potentially the hardest part of the application process. Once you start, it’s easy to keep writing, but that initial hurdle is just so difficult to overcome. We’ve put together a list of tips to help you jump that wall and make your essay the best it can be.

The introduction to a college essay should immediately hook the reader. You want to give admissions officers a reason to stay interested in your story and encourage them to continue reading your essay with an open mind. Remember that admissions officers are only able to spend a couple minutes per essay, so if you bore them or turn them off from the start, they may clock out for the rest of the essay.

As a whole, the college essay should aim to portray a part of your personality that hasn’t been covered by your GPA, extracurriculars, and test scores. This makes the introduction a crucial part of the essay. Think of it as the first glimpse, an intriguing lead on, into the read rest of your essay which also showcases your voice and personality. 

Brainstorm Topics

Take the time to sit down and brainstorm some good topic ideas for your essay. You want your topic to be meaningful to you, while also displaying a part of you that isn’t apparent in other aspects of your application. The essay is an opportunity to show admissions officers the “real you.” If you have a topic in mind, do not feel pressured to start with the introduction. Sometimes the best essay openings are developed last, once you fully grasp the flow of your story.

Do a Freewrite

Give yourself permission to write without judgment for an allotted period of time. For each topic you generated in your brainstorm session, do a free-write session. Set a time for one minute and write down whatever comes to mind for that specific topic. This will help get the juices flowing and push you over that initial bit of writer’s block that’s so common when it comes time to write a college essay. Repeat this exercise if you’re feeling stuck at any point during the essay writing process. Freewriting is a great way to warm up your creative writing brain whilst seeing which topics are flowing more naturally onto the page.

Create an Outline

Once you’ve chosen your topic, write an outline for your whole essay. It’s easier to organize all your thoughts, write the body, and then go back to write the introduction. That way, you already know the direction you want your essay to go because you’ve actually written it out, and you can ensure that your introduction leads directly into the rest of the essay. Admissions officers are looking for the quality of your writing alongside the content of your essay. To be prepared for college-level writing, students should understand how to logically structure an essay. By creating an outline, you are setting yourself up to be judged favorably on the quality of your writing skills.

1. The Scriptwriter

“No! Make it stop! Get me out!” My 5-year-old self waved my arms frantically in front of my face in the darkened movie theater.

Starting your essay with dialogue instantly transports the reader into the story, while also introducing your personal voice. In the rest of the essay, the author proposes a class that introduces people to insects as a type of food. Typically, one would begin directly with the course proposal. However, the author’s inclusion of this flashback weaves in a personal narrative, further displaying her true self.

Read the full essay.

2. The Shocker

A chaotic sense of sickness and filth unfolds in an overcrowded border station in McAllen, Texas. Through soundproof windows, migrants motion that they have not showered in weeks, and children wear clothes caked in mucus and tears. The humanitarian crisis at the southern border exists not only in photographs published by mainstream media, but miles from my home in South Texas.

This essay opener is also a good example of “The Vivid Imaginer.” In this case, the detailed imagery only serves to heighten the shock factor. While people may be aware of the “humanitarian crisis at the southern border,” reading about it in such stark terms is bound to capture the reader’s attention. Through this hook, the reader learns a bit about the author’s home life; an aspect of the student that may not be detailed elsewhere in their application. The rest of the essay goes on to talk about the author’s passion for aiding refugees, and this initial paragraph immediately establishes the author’s personal connection to the refugee crisis.

3. The Vivid Imaginer

The air is crisp and cool, nipping at my ears as I walk under a curtain of darkness that drapes over the sky, starless. It is a Friday night in downtown Corpus Christi, a rare moment of peace in my home city filled with the laughter of strangers and colorful lights of street vendors. But I cannot focus. 

Starting off with a bit of well-written imagery transports the reader to wherever you want to take them. By putting them in this context with you, you allow the reader to closely understand your thoughts and emotions in this situation. Additionally, this method showcases the author’s individual way of looking at the world, a personal touch that is the baseline of all college essays.

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4. The Instant Plunger

The flickering LED lights began to form into a face of a man when I focused my eyes. The man spoke of a ruthless serial killer of the decade who had been arrested in 2004, and my parents shivered at his reaccounting of the case. I curiously tuned in, wondering who he was to speak of such crimes with concrete composure and knowledge. Later, he introduced himself as a profiler named Pyo Chang Won, and I watched the rest of the program by myself without realizing that my parents had left the couch.

Plunging readers into the middle of a story (also known as in medias res ) is an effective hook because it captures attention by placing the reader directly into the action. The descriptive imagery in the first sentence also helps to immerse the reader, creating a satisfying hook while also showing (instead of telling) how the author became interested in criminology. With this technique, it is important to “zoom out,” so to speak, in such a way that the essay remains personal to you.

5. The Philosopher 

Saved in the Notes app on my phone are three questions: What can I know? What must I do? What may I hope for? First asked by Immanuel Kant, these questions guide my pursuit of knowledge and organization of critical thought, both skills that are necessary to move our country and society forward in the right direction.

Posing philosophical questions helps present you as someone with deep ideas while also guiding the focus of your essay. In a way, it presents the reader with a roadmap; they know that these questions provide the theme for the rest of the essay. The more controversial the questions, the more gripping a hook you can create. 

Providing an answer to these questions is not necessarily as important as making sure that the discussions they provoke really showcase you and your own values and beliefs.

6. The Storyteller

One Christmas morning, when I was nine, I opened a snap circuit set from my grandmother. Although I had always loved math and science, I didn’t realize my passion for engineering until I spent the rest of winter break creating different circuits to power various lights, alarms, and sensors. Even after I outgrew the toy, I kept the set in my bedroom at home and knew I wanted to study engineering.

Beginning with an anecdote is a strong way to establish a meaningful connection with the content itself. It also shows that the topic you write about has been a part of your life for a significant amount of time, and something that college admissions officers look for in activities is follow-through; they want to make sure that you are truly interested in something. A personal story such as the one above shows off just that.

Cliche College Essay Introductions to Avoid

Ambiguous introduction.

It’s best to avoid introductory sentences that don’t seem to really say anything at all, such as “Science plays a large role in today’s society,” or “X has existed since the beginning of time.” Statements like these, in addition to being extremely common, don’t demonstrate anything about you, the author. Without a personal connection to you right away, it’s easy for the admissions officer to write off the essay before getting past the first sentence.

Quoting Someone Famous

While having a quotation by a famous author, celebrity, or someone else you admire may seem like a good way to allow the reader to get to know you, these kinds of introductions are actually incredibly overused. You also risk making your essay all about the quotation and the famous person who said it; admissions officers want to get to know you, your beliefs, and your values, not someone who isn’t applying to their school. There are some cases where you may actually be asked to write about a quotation, and that’s fine, but you should avoid starting your essay with someone else’s words outside of this case. It is fine, however, to start with dialogue to plunge your readers into a specific moment.

Talking About Writing an Essay

This method is also very commonplace and is thus best avoided. It’s better to show, not tell, and all this method allows you to do is tell the reader how you were feeling at the time of writing the essay. If you do feel compelled to go this way, make sure to include vivid imagery and focus on grounding the essay in the five senses, which can help elevate your introduction and separate it from the many other meta essays.

Childhood Memories

Phrases like “Ever since I was young…” or “I’ve always wanted…” also lend more to telling rather than showing. If you want to talk about your childhood or past feelings in your essay, try using one of the techniques listed earlier (such as the Instant Plunger or the Vivid Imaginer) to elevate your writing.

CollegeVine has a peer essay review page where peers can tell you if your introduction was enough to hook them. Getting feedback from someone who hasn’t read your essay before, and thus doesn’t have any context which may bias them to be more forgiving to your introduction, is helpful because it mimics the same environment in which an admissions officer will be reading your essay. 

Writing a college essay is hard, but with these tips hopefully starting it will be a little easier!

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International Baccalaureate (IB)

IB students around the globe fear writing the Extended Essay, but it doesn't have to be a source of stress! In this article, I'll get you excited about writing your Extended Essay and provide you with the resources you need to get an A on it.

If you're reading this article, I'm going to assume you're an IB student getting ready to write your Extended Essay. If you're looking at this as a potential future IB student, I recommend reading our introductory IB articles first, including our guide to what the IB program is and our full coverage of the IB curriculum .

IB Extended Essay: Why Should You Trust My Advice?

I myself am a recipient of an IB Diploma, and I happened to receive an A on my IB Extended Essay. Don't believe me? The proof is in the IBO pudding:

If you're confused by what this report means, EE is short for Extended Essay , and English A1 is the subject that my Extended Essay topic coordinated with. In layman's terms, my IB Diploma was graded in May 2010, I wrote my Extended Essay in the English A1 category, and I received an A grade on it.

What Is the Extended Essay in the IB Diploma Programme?

The IB Extended Essay, or EE , is a mini-thesis you write under the supervision of an IB advisor (an IB teacher at your school), which counts toward your IB Diploma (learn more about the major IB Diploma requirements in our guide) . I will explain exactly how the EE affects your Diploma later in this article.

For the Extended Essay, you will choose a research question as a topic, conduct the research independently, then write an essay on your findings . The essay itself is a long one—although there's a cap of 4,000 words, most successful essays get very close to this limit.

Keep in mind that the IB requires this essay to be a "formal piece of academic writing," meaning you'll have to do outside research and cite additional sources.

The IB Extended Essay must include the following:

• A title page
• Contents page
• Introduction
• Body of the essay
• References and bibliography

Additionally, your research topic must fall into one of the six approved DP categories , or IB subject groups, which are as follows:

• Group 1: Studies in Language and Literature
• Group 2: Language Acquisition
• Group 3: Individuals and Societies
• Group 4: Sciences
• Group 5: Mathematics
• Group 6: The Arts

Once you figure out your category and have identified a potential research topic, it's time to pick your advisor, who is normally an IB teacher at your school (though you can also find one online ). This person will help direct your research, and they'll conduct the reflection sessions you'll have to do as part of your Extended Essay.

As of 2018, the IB requires a "reflection process" as part of your EE supervision process. To fulfill this requirement, you have to meet at least three times with your supervisor in what the IB calls "reflection sessions." These meetings are not only mandatory but are also part of the formal assessment of the EE and your research methods.

According to the IB, the purpose of these meetings is to "provide an opportunity for students to reflect on their engagement with the research process." Basically, these meetings give your supervisor the opportunity to offer feedback, push you to think differently, and encourage you to evaluate your research process.

The final reflection session is called the viva voce, and it's a short 10- to 15-minute interview between you and your advisor. This happens at the very end of the EE process, and it's designed to help your advisor write their report, which factors into your EE grade.

Here are the topics covered in your viva voce :

• A check on plagiarism and malpractice
• Your reflection on your project's successes and difficulties
• Your reflection on what you've learned during the EE process

Your completed Extended Essay, along with your supervisor's report, will then be sent to the IB to be graded. We'll cover the assessment criteria in just a moment.

We'll help you learn how to have those "lightbulb" moments...even on test day!  

What Should You Write About in Your IB Extended Essay?

You can technically write about anything, so long as it falls within one of the approved categories listed above.

It's best to choose a topic that matches one of the IB courses , (such as Theatre, Film, Spanish, French, Math, Biology, etc.), which shouldn't be difficult because there are so many class subjects.

Here is a range of sample topics with the attached extended essay:

• Biology: The Effect of Age and Gender on the Photoreceptor Cells in the Human Retina
• Chemistry: How Does Reflux Time Affect the Yield and Purity of Ethyl Aminobenzoate (Benzocaine), and How Effective is Recrystallisation as a Purification Technique for This Compound?
• English: An Exploration of Jane Austen's Use of the Outdoors in Emma
• Geography: The Effect of Location on the Educational Attainment of Indigenous Secondary Students in Queensland, Australia
• Math: Alhazen's Billiard Problem
• Visual Arts: Can Luc Tuymans Be Classified as a Political Painter?

You can see from how varied the topics are that you have a lot of freedom when it comes to picking a topic . So how do you pick when the options are limitless?

How to Write a Stellar IB Extended Essay: 6 Essential Tips

Below are six key tips to keep in mind as you work on your Extended Essay for the IB DP. Follow these and you're sure to get an A!

#1: Write About Something You Enjoy

You can't expect to write a compelling essay if you're not a fan of the topic on which you're writing. For example, I just love British theatre and ended up writing my Extended Essay on a revolution in post-WWII British theatre. (Yes, I'm definitely a #TheatreNerd.)

I really encourage anyone who pursues an IB Diploma to take the Extended Essay seriously. I was fortunate enough to receive a full-tuition merit scholarship to USC's School of Dramatic Arts program. In my interview for the scholarship, I spoke passionately about my Extended Essay; thus, I genuinely think my Extended Essay helped me get my scholarship.

But how do you find a topic you're passionate about? Start by thinking about which classes you enjoy the most and why . Do you like math classes because you like to solve problems? Or do you enjoy English because you like to analyze literary texts?

Keep in mind that there's no right or wrong answer when it comes to choosing your Extended Essay topic. You're not more likely to get high marks because you're writing about science, just like you're not doomed to failure because you've chosen to tackle the social sciences. The quality of what you produce—not the field you choose to research within—will determine your grade.

Once you've figured out your category, you should brainstorm more specific topics by putting pen to paper . What was your favorite chapter you learned in that class? Was it astrophysics or mechanics? What did you like about that specific chapter? Is there something you want to learn more about? I recommend spending a few hours on this type of brainstorming.

One last note: if you're truly stumped on what to research, pick a topic that will help you in your future major or career . That way you can use your Extended Essay as a talking point in your college essays (and it will prepare you for your studies to come too!).

#2: Select a Topic That Is Neither Too Broad nor Too Narrow

There's a fine line between broad and narrow. You need to write about something specific, but not so specific that you can't write 4,000 words on it.

You can't write about WWII because that would be a book's worth of material. You also don't want to write about what type of soup prisoners of war received behind enemy lines, because you probably won’t be able to come up with 4,000 words of material about it. However, you could possibly write about how the conditions in German POW camps—and the rations provided—were directly affected by the Nazis' successes and failures on the front, including the use of captured factories and prison labor in Eastern Europe to increase production. WWII military history might be a little overdone, but you get my point.

If you're really stuck trying to pinpoint a not-too-broad-or-too-narrow topic, I suggest trying to brainstorm a topic that uses a comparison. Once you begin looking through the list of sample essays below, you'll notice that many use comparisons to formulate their main arguments.

I also used a comparison in my EE, contrasting Harold Pinter's Party Time with John Osborne's Look Back in Anger in order to show a transition in British theatre. Topics with comparisons of two to three plays, books, and so on tend to be the sweet spot. You can analyze each item and then compare them with one another after doing some in-depth analysis of each individually. The ways these items compare and contrast will end up forming the thesis of your essay!

When choosing a comparative topic, the key is that the comparison should be significant. I compared two plays to illustrate the transition in British theatre, but you could compare the ways different regional dialects affect people's job prospects or how different temperatures may or may not affect the mating patterns of lightning bugs. The point here is that comparisons not only help you limit your topic, but they also help you build your argument.

Comparisons are not the only way to get a grade-A EE, though. If after brainstorming, you pick a non-comparison-based topic and are still unsure whether your topic is too broad or narrow, spend about 30 minutes doing some basic research and see how much material is out there.

If there are more than 1,000 books, articles, or documentaries out there on that exact topic, it may be too broad. But if there are only two books that have any connection to your topic, it may be too narrow. If you're still unsure, ask your advisor—it's what they're there for! Speaking of advisors...

Don't get stuck with a narrow topic!

#3: Choose an Advisor Who Is Familiar With Your Topic

If you're not certain of who you would like to be your advisor, create a list of your top three choices. Next, write down the pros and cons of each possibility (I know this sounds tedious, but it really helps!).

For example, Mr. Green is my favorite teacher and we get along really well, but he teaches English. For my EE, I want to conduct an experiment that compares the efficiency of American electric cars with foreign electric cars.

I had Ms. White a year ago. She teaches physics and enjoyed having me in her class. Unlike Mr. Green, Ms. White could help me design my experiment.

Based on my topic and what I need from my advisor, Ms. White would be a better fit for me than would Mr. Green (even though I like him a lot).

The moral of my story is this: do not just ask your favorite teacher to be your advisor . They might be a hindrance to you if they teach another subject. For example, I would not recommend asking your biology teacher to guide you in writing an English literature-based EE.

There can, of course, be exceptions to this rule. If you have a teacher who's passionate and knowledgeable about your topic (as my English teacher was about my theatre topic), you could ask that instructor. Consider all your options before you do this. There was no theatre teacher at my high school, so I couldn't find a theatre-specific advisor, but I chose the next best thing.

Before you approach a teacher to serve as your advisor, check with your high school to see what requirements they have for this process. Some IB high schools require your IB Extended Essay advisor to sign an Agreement Form , for instance.

Make sure that you ask your IB coordinator whether there is any required paperwork to fill out. If your school needs a specific form signed, bring it with you when you ask your teacher to be your EE advisor.

#4: Pick an Advisor Who Will Push You to Be Your Best

Some teachers might just take on students because they have to and aren't very passionate about reading drafts, only giving you minimal feedback. Choose a teacher who will take the time to read several drafts of your essay and give you extensive notes. I would not have gotten my A without being pushed to make my Extended Essay draft better.

Ask a teacher that you have experience with through class or an extracurricular activity. Do not ask a teacher that you have absolutely no connection to. If a teacher already knows you, that means they already know your strengths and weaknesses, so they know what to look for, where you need to improve, and how to encourage your best work.

Also, don't forget that your supervisor's assessment is part of your overall EE score . If you're meeting with someone who pushes you to do better—and you actually take their advice—they'll have more impressive things to say about you than a supervisor who doesn't know you well and isn't heavily involved in your research process.

Be aware that the IB only allows advisors to make suggestions and give constructive criticism. Your teacher cannot actually help you write your EE. The IB recommends that the supervisor spends approximately two to three hours in total with the candidate discussing the EE.

#5: Make Sure Your Essay Has a Clear Structure and Flow

The IB likes structure. Your EE needs a clear introduction (which should be one to two double-spaced pages), research question/focus (i.e., what you're investigating), a body, and a conclusion (about one double-spaced page). An essay with unclear organization will be graded poorly.

The body of your EE should make up the bulk of the essay. It should be about eight to 18 pages long (again, depending on your topic). Your body can be split into multiple parts. For example, if you were doing a comparison, you might have one third of your body as Novel A Analysis, another third as Novel B Analysis, and the final third as your comparison of Novels A and B.

If you're conducting an experiment or analyzing data, such as in this EE , your EE body should have a clear structure that aligns with the scientific method ; you should state the research question, discuss your method, present the data, analyze the data, explain any uncertainties, and draw a conclusion and/or evaluate the success of the experiment.

#6: Start Writing Sooner Rather Than Later!

You will not be able to crank out a 4,000-word essay in just a week and get an A on it. You'll be reading many, many articles (and, depending on your topic, possibly books and plays as well!). As such, it's imperative that you start your research as soon as possible.

Each school has a slightly different deadline for the Extended Essay. Some schools want them as soon as November of your senior year; others will take them as late as February. Your school will tell you what your deadline is. If they haven't mentioned it by February of your junior year, ask your IB coordinator about it.

Some high schools will provide you with a timeline of when you need to come up with a topic, when you need to meet with your advisor, and when certain drafts are due. Not all schools do this. Ask your IB coordinator if you are unsure whether you are on a specific timeline.

Below is my recommended EE timeline. While it's earlier than most schools, it'll save you a ton of heartache (trust me, I remember how hard this process was!):

• January/February of Junior Year: Come up with your final research topic (or at least your top three options).
• February of Junior Year: Approach a teacher about being your EE advisor. If they decline, keep asking others until you find one. See my notes above on how to pick an EE advisor.
• April/May of Junior Year: Submit an outline of your EE and a bibliography of potential research sources (I recommend at least seven to 10) to your EE advisor. Meet with your EE advisor to discuss your outline.
• Summer Between Junior and Senior Year: Complete your first full draft over the summer between your junior and senior year. I know, I know—no one wants to work during the summer, but trust me—this will save you so much stress come fall when you are busy with college applications and other internal assessments for your IB classes. You will want to have this first full draft done because you will want to complete a couple of draft cycles as you likely won't be able to get everything you want to say into 4,000 articulate words on the first attempt. Try to get this first draft into the best possible shape so you don't have to work on too many revisions during the school year on top of your homework, college applications, and extracurriculars.
• August/September of Senior Year: Turn in your first draft of your EE to your advisor and receive feedback. Work on incorporating their feedback into your essay. If they have a lot of suggestions for improvement, ask if they will read one more draft before the final draft.
• September/October of Senior Year: Submit the second draft of your EE to your advisor (if necessary) and look at their feedback. Work on creating the best possible final draft.
• November-February of Senior Year: Schedule your viva voce. Submit two copies of your final draft to your school to be sent off to the IB. You likely will not get your grade until after you graduate.

Remember that in the middle of these milestones, you'll need to schedule two other reflection sessions with your advisor . (Your teachers will actually take notes on these sessions on a form like this one , which then gets submitted to the IB.)

I recommend doing them when you get feedback on your drafts, but these meetings will ultimately be up to your supervisor. Just don't forget to do them!

The early bird DOES get the worm!

How Is the IB Extended Essay Graded?

Extended Essays are graded by examiners appointed by the IB on a scale of 0 to 34 . You'll be graded on five criteria, each with its own set of points. You can learn more about how EE scoring works by reading the IB guide to extended essays .

• Criterion A: Focus and Method (6 points maximum)
• Criterion B: Knowledge and Understanding (6 points maximum)
• Criterion C: Critical Thinking (12 points maximum)
• Criterion D: Presentation (4 points maximum)
• Criterion E: Engagement (6 points maximum)

How well you do on each of these criteria will determine the final letter grade you get for your EE. You must earn at least a D to be eligible to receive your IB Diploma.

Although each criterion has a point value, the IB explicitly states that graders are not converting point totals into grades; instead, they're using qualitative grade descriptors to determine the final grade of your Extended Essay . Grade descriptors are on pages 102-103 of this document .

Here's a rough estimate of how these different point values translate to letter grades based on previous scoring methods for the EE. This is just an estimate —you should read and understand the grade descriptors so you know exactly what the scorers are looking for.

Here is the breakdown of EE scores (from the May 2021 bulletin):

How Does the Extended Essay Grade Affect Your IB Diploma?

The Extended Essay grade is combined with your TOK (Theory of Knowledge) grade to determine how many points you get toward your IB Diploma.

To learn about Theory of Knowledge or how many points you need to receive an IB Diploma, read our complete guide to the IB program and our guide to the IB Diploma requirements .

This diagram shows how the two scores are combined to determine how many points you receive for your IB diploma (3 being the most, 0 being the least). In order to get your IB Diploma, you have to earn 24 points across both categories (the TOK and EE). The highest score anyone can earn is 45 points.

Let's say you get an A on your EE and a B on TOK. You will get 3 points toward your Diploma. As of 2014, a student who scores an E on either the extended essay or TOK essay will not be eligible to receive an IB Diploma .

Prior to the class of 2010, a Diploma candidate could receive a failing grade in either the Extended Essay or Theory of Knowledge and still be awarded a Diploma, but this is no longer true.

Figuring out how you're assessed can be a little tricky. Luckily, the IB breaks everything down here in this document . (The assessment information begins on page 219.)

40+ Sample Extended Essays for the IB Diploma Programme

In case you want a little more guidance on how to get an A on your EE, here are over 40 excellent (grade A) sample extended essays for your reading pleasure. Essays are grouped by IB subject.

• Business Management 1
• Chemistry 1
• Chemistry 2
• Chemistry 3
• Chemistry 4
• Chemistry 5
• Chemistry 6
• Chemistry 7
• Computer Science 1
• Economics 1
• Design Technology 1
• Design Technology 2
• Environmental Systems and Societies 1
• Geography 1
• Geography 2
• Geography 3
• Geography 4
• Geography 5
• Geography 6
• Literature and Performance 1
• Mathematics 1
• Mathematics 2
• Mathematics 3
• Mathematics 4
• Mathematics 5
• Philosophy 1
• Philosophy 2
• Philosophy 3
• Philosophy 4
• Philosophy 5
• Psychology 1
• Psychology 2
• Psychology 3
• Psychology 4
• Psychology 5
• Social and Cultural Anthropology 1
• Social and Cultural Anthropology 2
• Social and Cultural Anthropology 3
• Sports, Exercise and Health Science 1
• Sports, Exercise and Health Science 2
• Visual Arts 1
• Visual Arts 2
• Visual Arts 3
• Visual Arts 4
• Visual Arts 5
• World Religion 1
• World Religion 2
• World Religion 3

What's Next?

Trying to figure out what extracurriculars you should do? Learn more about participating in the Science Olympiad , starting a club , doing volunteer work , and joining Student Government .

Studying for the SAT? Check out our expert study guide to the SAT . Taking the SAT in a month or so? Learn how to cram effectively for this important test .

Not sure where you want to go to college? Read our guide to finding your target school . Also, determine your target SAT score or target ACT score .

As an SAT/ACT tutor, Dora has guided many students to test prep success. She loves watching students succeed and is committed to helping you get there. Dora received a full-tuition merit based scholarship to University of Southern California. She graduated magna cum laude and scored in the 99th percentile on the ACT. She is also passionate about acting, writing, and photography.

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What is an essay in mathematics?

Hi everyone, hopefully it is okay to ask this question here. I have an assignment to write “an essay about some topic in mathematics I find interesting”. I have already chosen the topic (hamming codes), but I am having trouble with what I should actually write. What does an essay in mathematics normally cover?

I’m thinking the reader should be assumed to be unfamiliar with the topic so a part of the essay should probably go to introducing the theory with some short examples, but what should be the “goal” of the essay?

I’m sorry for the vague questions, but the teacher has not given more exact instructions. I’m thankful for any help/advice I can get. :)

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Math Essay | Essay on Math for Students and Children in English

February 13, 2024 by Prasanna

Math Essay: Mathematics is generally defined as the science that deals with numbers. It involves operations among numbers, and it also helps you to calculate the product price, how many discounted prizes here, and If you good in maths so you can calculate very fast. Mathematicians and scientists rely on mathematics principles in their real-life to experiments with new things every day. Many students say that ” I hate mathematics ” and maths is a useless subject, but it is wrong because without mathematics your life is tough to survive. Math has its applications in every field.

You can also find more  Essay Writing  articles on events, persons, sports, technology and many more.

Long and Short Essays on Math for Students and Kids in English

We are presenting students with essay samples on an extended essay of 500 words and a short of 150 words on the topic of math for reference.

Long Essay on Math 500 Words in English

Long Essay on Math is usually given to classes 7, 8, 9, and 10.

Mathematics is one of the common subjects that we study since our childhood. It is generally used in our daily life. Every person needs to learn some basics of it. Even counting money also includes math. Every work is linked with math in some way or the other. A person who does math is called a Mathematician.

Mathematics can be divided into two parts. The first is Pure mathematics, and the second is Applied mathematics. In Pure mathematics, we need to study the basic concept and structures of mathematics. But, on the other side, Applied mathematics involves the application of mathematics to solve problems that arise in various areas,(e.g.), science, engineering, and so on.

One couldn’t imagine the world without math. Math makes our life systematic, and every invention involves math. No matter what action a person is doing, he should know some basic maths. Every profession involves maths. Our present-day world runs on computers, and even computer runs with the help of maths. Every development that happens requires math.

Mathematics has a wide range of applications in our daily life. Maths generally deals with numbers. There are various topics in math, such as trigonometry; integration; differentiation, etc. All the subjects such as physics; chemistry; economy; commerce involve maths in some way or the other. Math is also used to find the relation between two numbers, and math is considered to be one of the most challenging subjects to learn. Math includes various numbers, and many symbols are used to show the relation between two different numbers.

Math is complicated to learn, and one needs to focus and concentrate more. Math is logical sometimes, and the logic needs to be derived out. Maths make our life easier and more straightforward. Math is considered to be challenging because it consists of many formulas that have to be learned, and many symbols and each symbol generally has its significance.

Some of the advantages of Math in our daily life

• Managing Money: Counting money and calculating simple interest, compound interest includes the usage of mathematics. Profit and loss are also computed using maths. Anything related to maths contains maths.
• Cooking: Maths is even used in cooking as estimating the number of ingredients that have to be used is calculated in numbers. Proportions also include maths.
• Home modelling: Calculating the area is essential in the construction of the home or home modelling. The size is also measured using maths. Even heights are also measured using maths.
• Travelling: Distance between two places and time taken to travel also includes maths. The amount of time taken revolves around maths. Almost every work is related to maths in some way or another. Maths contains some conditions that need to be followed, and maths has several formulas that have to be learned to become a mathematician.

Short Essay on Math 150 Words in English

Short Essay on Math is usually given to classes 1, 2, 3, 4, 5, and 6.

Maths is generally defined as the science of numbers and the operations performed among them. It deals with both alphabets along with numbers and involves addition, subtraction, multiplication, division, comparison, etc. It is used in every field. Maths consists of finding a relation between numbers, calculating the distance between two places, counting money, calculating profit and loss.

It is of two types pure and applied. Pure math deals with the basic structure and concept of maths, whereas applied mathematics deals with how maths is used it involves the application of maths in our daily life. All the subjects include maths, and hence maths is considered to be one of the primary and joint issues which need to be learned by everyone. One couldn’t imagine their life using maths. It has made our experience easy and straightforward. It has prevented chaos in our daily life. Hence learning maths is mandatory for everyone.

10 Lines on Math in English

• Father of Mathematics was Archimedes.
• Hypatia is the first woman know to know to have taught mathematics.
• From 0-1000 ,letter “A” only appears first in 1,000 ( “one thousand “).
• Zero (0) is the only number that can not be represented by Roman numerals.
• The Sign plus (+) and Minus(-) were discovered in 1489 A.D.
• Do you know that a Baseball field is of the perfect shape of a Rhombus.
• Jiffy is considered to be a unit of time for 1/100th of a second.
• 14th March International Day of Mathematics.
• Most mathematics symbols weren’t invented until the 16th century.
• The symbols for the division is called an Obelus.

FAQ’s on Math Essay

Question 1. What is Mathematics in simple words?

Answer: Mathematics is the study of shapes, patterns, numbers, and more. It involves a comparison between two numbers and calculating the distance between two places.

Question 2. Do we need mathematics every day?

Answer: Yes, we need mathematics every day, from buying a product to sell anything you want. Maths is present in our daily life, and no matter what work we do, maths is involved, and the application of maths is current in our everyday life.

Question 3. Who was the No.1 Mathematicians in the world?

Answer: Isaac Newton, who was a profound mathematician, is considered to be one of the best mathematicians in the world.

Question 4. What are the applications of maths?

Answer: Maths have various applications in our daily life. Maths is present everywhere from counting money to the calculating distance between two places. We could find math applications around.

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How to Structure an Essay

Essay writing is a fundamental skill, a basic task, that is expected of those who choose to pursue their undergraduate and master’s degrees. It constitutes a key requirement for students to complete a given course credit. However, many students and early career researchers find themselves struggling with the challenge of organizing their thoughts into a coherent, engaging structure. This article is especially for those who see essay writing as a daunting task and face problems in presenting their work in an impactful way.  

Table of Contents

• Writing an essay: basic elements and some key principles  
• Essay structure template 
• Chronological structure 
• Problem-methods-solutions structure 
• Compare and contrast structures 
• Frequently asked questions on essay structure 

Read on as we delve into the basic elements of essay writing, outline key principles for organizing information, and cover some foundational features of writing essays.  

Writing an essay: basic elements and some key principles

Essays are written in a flowing and continuous pattern but with a structure of its own. An introduction, body and conclusion are integral to it. The key is to balance the amount and kind of information to be presented in each part. Various disciplines may have their own conventions or guidelines on the information to be provided in the introduction.  

A clear articulation of the context and background of the study is important, as is the definition of key terms and an outline of specific models or theories used. Readers also need to know the significance of the study and its implications for further research. Most importantly, the thesis or the main proposition should be clearly presented.  

The body of the essay is therefore organized into paragraphs that hold the main ideas and arguments and is presented and analyzed in a logical manner. Ideally, each paragraph of the body focuses on one main point or a distinct topic and must be supported by evidence and analysis. The concluding paragraph should bring back to the reader the key arguments, its significance and food for thought. It is best not to re-state all the points of the essay or introduce a new concept here. 

In other words, certain general guidelines help structure the information in the essay. The information must flow logically with the context or the background information presented in the introductory part of the essay. The arguments are built organically where each paragraph in the body of the essay deals with a different point, yet closely linked to the para preceding and following it. Importantly, when writing essays, early career researchers must be careful in ensuring that each piece of information relates to the main thesis and is a building block to the arguments. 

Essay structure template

• Introduction 
• Provide the context and share significance of the study 
• Clearly articulate the thesis statement 
• Body  
• Paragraph 1 consisting of the first main point, followed by supporting evidence and an analysis of the findings. Transitional words and phrases can be used to move to the next main point. 
• There can be as many paragraphs with the above-mentioned elements as there are points and arguments to support your thesis. 
• Conclusion  
• Bring in key ideas and discuss their significance and relevance 
• Call for action 
• References 

Essay structures

The structure of an essay can be determined by the kind of essay that is required.  

Chronological structure

Also known as the cause-and-effect approach, this is a straightforward way to structure an essay. In such essays, events are discussed sequentially, as they occurred from the earliest to the latest. A chronological structure is useful for discussing a series of events or processes such as historical analyses or narratives of events. The introduction should have the topic sentence. The body of the essay should follow a chorological progression with each para discussing a major aspect of that event with supporting evidence. It ends with a summarizing of the results of the events.  

Problem-methods-solutions structure

Where the essay focuses on a specific problem, the problem-methods-solutions structure can be used to organize the essay. This structure is ideal for essays that address complex issues. It starts with presenting the problem, the context, and thesis statement as introduction to the essay. The major part of the discussion which forms the body of the essay focuses on stating the problem and its significance, the author’s approach or methods adopted to address the problem along with its relevance, and accordingly proposing solution(s) to the identified problem. The concluding part offers a recap of the research problem, methods, and proposed solutions, emphasizing their significance and potential impact. 

Compare and contrast structures

This structure of essay writing is ideally used when two or more key subjects require a comparison of ideas, theories, or phenomena. The three crucial elements, introduction, body, and conclusion, remain the same. The introduction presents the context and the thesis statement. The body of the essay seeks to focus on and highlight differences between the subjects, supported by evidence and analysis. The conclusion is used to summarize the key points of comparison and contrast, offering insights into the significance of the analysis.  

Depending on how the subjects will be discussed, the body of the essay can be organized according to the block method or the alternating method. In the block method, one para discusses one subject and the next para the other subject. In the alternative method, both subjects are discussed in one para based on a particular topic or issue followed by the next para on another issue and so on.  

Frequently asked questions on essay structure

An essay structure serves as a framework for presenting ideas coherently and logically. It comprises three crucial elements: an introduction that communicates the context, topic, and thesis statement; the body focusing on the main points and arguments supported with appropriate evidence followed by its analysis; and a conclusion that ties together the main points and its importance .  

An essay structure well-defined essay structure enhances clarity, coherence, and readability, and is crucial for organizing ideas and arguments to effectively communicate key aspects of a chosen topic. It allows readers to better understand arguments presented and demonstrates the author’s ability to organize and present information systematically. 

Yes, while expert recommend following an essay structure, early career researchers may choose how best to adapt standard essay structures to communicate and share their research in an impactful and engaging way. However, do keep in mind that deviating too far from established structures can hinder comprehension and weaken the overall effectiveness of the essay,  By understanding the basic elements of essay writing and employing appropriate structures such as chronological, problem-methods-solutions, or compare and contrast, researchers can effectively organize their ideas and communicate their findings with clarity and precision. 

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