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• Prof. Haynes Miller
• Dr. Nat Stapleton
• Saul Glasman

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• Mathematics

As Taught In

Learning resource types, project laboratory in mathematics.

Next: Revision and Feedback »

In this section, Prof. Haynes Miller and Susan Ruff describe the criteria for good mathematical writing and the components of the writing workshop .

A central goal of the course is to teach students how to write effective, journal-style mathematics papers. Papers are a key way in which mathematicians share research findings and learn about others’ work. For each research project, each student group writes and revises a paper in the style of a professional mathematics journal paper. These research projects are perfect for helping students to learn to write as mathematicians because the students write about the new mathematics that they discover. They own it, they are committed to it, and they put a lot of effort into writing well.

Criteria for Good Writing

In the course, we help students learn to write papers that communicate clearly, follow the conventions of mathematics papers, and are mathematically engaging.

Communicating clearly is challenging for students because doing so requires writing precisely and correctly as well as anticipating readers’ needs. Although students have read textbooks and watched lectures that are worded precisely, they are often unaware of the care with which each word or piece of notation was chosen. So when students must choose the words and notation themselves, the task can be surprisingly challenging. Writing precisely is even more challenging when students write about insights they’re still developing. Even students who do a good job of writing precisely may have a different difficulty: providing sufficient groundwork for readers. When students are deeply focused on the details of their research, it can be hard for them to imagine what the reading experience may be like for someone new to that research. We can help students to communicate clearly by pointing out places within the draft at which readers may be confused by imprecise wording or by missing context.

For most students, the conventions of mathematics papers are unfamiliar because they have not read—much less written—mathematics journal papers before. The students’ first drafts often build upon their knowledge of more familiar genres: humanities papers and mathematics textbooks and lecture notes. So the text is often more verbose or explanatory than a typical paper in a mathematics journal. To help students learn the conventions of journal papers, including appropriate concision, we provide samples and individualized feedback.

Finally, a common student preconception is that mathematical writing is dry and formal, so we encourage students to write in a way that is mathematically engaging. In Spring 2013, for example, one student had to be persuaded that he did not have to use the passive voice. In reality, effective mathematics writing should be efficient and correct, but it should also provide motivation, communicate intuition, and stimulate interest.

To summarize, instruction and feedback in the course address many different aspects of successful writing:

• Precision and correctness: e.g., mathematical terminology and notation should be used correctly.
• Audience awareness: e.g., ideas should be introduced with appropriate preparation and motivation.
• Genre conventions: e.g., in most mathematics papers, the paper’s conclusion is stated in the introduction rather than in a final section titled “Conclusion.”
• Style: e.g., writing should stimulate interest.
• Other aspects of effective writing, as needed.

To help students learn to write effective mathematics papers, we provide various resources, a writing workshop, and individualized feedback on drafts.

Writing Resources

Various resources are provided to help students learn effective mathematical writing.

The following prize-winning journal article was annotated to point out various conventions and strategies of mathematical writing. (Courtesy of Mathematical Association of America. Courtesy of a Creative Commons BY-NC-SA license.)

An Annotated Journal Article (PDF)

This document introduces the structure of a paper and provides a miscellany of common mistakes to avoid.

Notes on Writing Mathematics (PDF)

LaTeX Resources

The following PDF, TeX, and Beamer samples guide students to present their work using LaTeX, a high-quality typesetting system designed for the production of technical and scientific documentation. The content in the PDF and TeX documents highlights the structure of a generic student paper.

Sample PDF Document created by pdfLaTeX (PDF)

Sample TeX Document (TEX)

Beamer template (TEX)

The following resources are provided to help students learn and use LaTeX.

LaTeX-Project. “ Obtaining LaTeX .” August 28, 2009.

Downes, Michael. “Short Math Guide for LaTeX.” (PDF) American Mathematical Society . Version 1.09. March 22, 2002.

Oetiker, Tobias, Hubert Partl, et al. “The Not So Short Introduction to LaTeX 2ε.” (PDF) Version 5.01. April 06, 2011.

Reckdahl, Keith. “Using Imported Graphics in LaTeX and pdfLaTeX.” (PDF) Version 3.0.1. January 12, 2006.

Writing Workshop

Each semester there is a writing workshop, led by the lead instructor, which features examples to stimulate discussion about how to write well. In Spring 2013, Haynes ran this workshop during the third class session and used the following slide deck, which was developed by Prof. Paul Seidel and modified with the help of Prof. Tom Mrowka and Prof. Richard Stanley.

The 18.821 Project Report (PDF)

This workshop was held before students had begun to think about the writing component of the course, and it seemed as if the students had to be reminded of the lessons of the workshop when they actually wrote their papers. In future semesters, we plan to offer the writing workshop closer to the time that students are drafting their first paper. We may also focus the examples used in the workshop on the few most important points rather than a broad coverage.

• Download video

This video features the writing workshop from Spring 2013 and includes instruction from Haynes as well as excerpts of the class discussion.

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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.

• Resource collection:  Skills every early career academic needs
• Top tips to improve the teaching of mathematics in universities
• One write way to student success in mathematics

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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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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Home — Essay Samples — Science — Mathematics in Everyday Life — Mathematics In Everyday Life: Most Vital Discipline

Mathematics in Everyday Life: Most Vital Discipline

• Categories: Mathematics in Everyday Life

About this sample

Words: 795 |

Published: Mar 14, 2019

Words: 795 | Pages: 2 | 4 min read

Works Cited

• Benacerraf, P. (1991). Mathematics as an object of knowledge. In P. Benacerraf & H. Putnam (Eds.), Philosophy of mathematics: Selected readings (pp. 1-13). Cambridge University Press.
• EdReady. (n.d.). Home. Retrieved from https://www.edready.org/
• Puttaswamy, T. K. (2012). Engineering mathematics. Dorling Kindersley (India) Pvt. Ltd.
• Steen, L. A. (Ed.). (2001). Mathematics today: Twelve informal essays. Springer Science & Business Media.
• Suter, B. W. (2012). Mathematics education: A critical introduction. Bloomsbury Academic.
• Tucker, A. W. (2006). Applied combinatorics. John Wiley & Sons.
• Vakil, R. (2017). A mathematical mosaic: Patterns & problem solving. Princeton University Press.
• Wolfram MathWorld. (n.d.). MathWorld--The web's most extensive mathematics resource. Retrieved from http://mathworld.wolfram.com/
• Wu, H. H. (2011). The mis-education of mathematics teachers. Educational Studies in Mathematics, 77(1), 1-20.
• Ziegler, G. M., & Aigner, M. (2012). Proofs from THE BOOK. Springer Science & Business Media.

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• 20 March 2024
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Mathematician who tamed randomness wins Abel Prize

• Davide Castelvecchi

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Michel Talagrand studies stochastic processes, mathematical models of phenomena that are governed by randomness. Credit: Peter Bagde/Typos1/Abel Prize 2024

A mathematician who developed formulas to make random processes more predictable and helped to solve an iconic model of complex phenomena has won the 2024 Abel Prize, one of the field’s most coveted awards. Michel Talagrand received the prize for his “contributions to probability theory and functional analysis, with outstanding applications in mathematical physics and statistics”, the Norwegian Academy of Science and Letters in Oslo announced on 20 March.

Assaf Naor, a mathematician at Princeton University in New Jersey, says it is difficult to overestimate the impact of Talagrand’s work. “There are papers posted maybe on a daily basis where the punchline is ‘now we use Talagrand’s inequalities’,” he says.

Talagrand’s reaction on hearing the news was incredulity. “There was a total blank in my mind for at least four seconds,” he says. “If I had been told an alien ship had landed in front of the White House, I would not have been more surprised.”

The Abel Prize was modelled after the Nobel Prizes — which do not include mathematics — and was first awarded in 2003. The recipient wins a sum of 7.5 million Norwegian kroner (US$700,000).

‘Like a piece of art’

Talagrand specializes in the theory of probability and stochastic processes, which are mathematical models of phenomena governed by randomness. A typical example is a river’s water level, which is highly variable and is affected by many independent factors, including rain, wind and temperature, Talagrand says. His proudest achievement was his inequalities 1 , a set of formulas that poses limits to the swings in stochastic processes. His formulas express how the contributions of many factors often cancel each other out — making the overall result less variable, not more.

“It’s like a piece of art,” says Abel-committee chair Helge Holden, a mathematician at the Norwegian University of Science and Technology in Trondheim. “The magic here is to find a good estimate, not just a rough estimate.”

Abel Prize: pioneer of ‘smooth’ physics wins top maths award

Thanks to Talagrand’s techniques, “many things that seem complicated and random turn out to be not so random”, says Naor. His estimates are extremely powerful, for example for studying problems such as optimizing the route of a delivery truck. Finding a perfect solution would require an exorbitant amount of computation, so computer scientists can instead calculate the lengths of a limited number of random candidate routes and then take the average — and Talagrand’s inequalities ensure that the result is close to optimal.

Talagrand also completed the solution to a problem posed by theoretical physicist Giorgio Parisi — work that ultimately helped Parisi to earn a Nobel Prize in Physics in 2021. In 1979, Parisi, now at the University of Rome, proposed a complete solution for the structure of a spin glass — an abstracted model of a material in which the magnetization of each atom tends to flip up or down depending on those of its neighbours.

Parisi’s arguments were rooted in his powerful intuition in physics, and followed steps that “mathematicians would consider as sorcery”, Talagrand says, such as taking n copies of a system — with n being a negative number. Many researchers doubted that Parisi’s proof could be made mathematically rigorous. But in the early 2000s, the problem was completely solved in two separate works, one by Talagrand 2 and an earlier one by Francesco Guerra 3 , a mathematical physicist who is also at the University of Rome.

Finding motivation

Talagrand’s journey to becoming a top researcher was unconventional. Born in Béziers, France, in 1952, he lost vision in his right eye at age five because of a genetic predisposition to detachment of the retina. Although while growing up in Lyon he was a voracious reader of popular science magazines, he struggled at school, particularly with the complex rules of French spelling. “I never really made peace with orthography,” he told an interviewer in 2019 .

His turning point came at age 15, when he received emergency treatment for another retinal detachment, this time in his left eye. He had to miss almost an entire year of school. The terrifying experience of nearly losing his sight — and his father’s efforts to keep his mind busy while his eyes were bandaged — gave Talagrand a renewed focus. He became a highly motivated student after his recovery, and began to excel in national maths competitions.

Just 5 women have won a top maths prize in the past 90 years

Still, Talagrand did not follow the typical path of gifted French students, which includes two years of preparatory school followed by a national admission competition for highly selective grandes écoles such as the École Normale Supérieure in Paris. Instead, he studied at the University of Lyon, France, and then went on to work as a full-time researcher at the national research agency CNRS, first in Lyon and later in Paris, where he spent more than a decade in an entry-level job. Apart from a brief stint in Canada, followed by a trip to the United States where he met his wife, he worked at the CNRS until his retirement.

Talagrand loves to challenge other mathematicians to solve problems that he has come up with — offering cash to those who do — and he keeps a list of those problems on his website. Some have been solved, leading to publications in major maths journals . The prizes come with some conditions: “I will award the prizes below as long as I am not too senile to understand the proofs I receive. If I can’t understand them, I will not pay.”

Nature 627 , 714-715 (2024)

doi: https://doi.org/10.1038/d41586-024-00839-6

Updates & Corrections

Correction 21 March 2024 : An earlier version of this article stated that Giorgio Parisi won the Nobel Prize in Physics in 2001. He in fact won in 2021.

Talagrand, M. Publ. Math. IHES 81 , 73–205, (1995).

Article   Google Scholar  

Talagrand, M. Ann. Math. 163 , 221–263 (2006).

Guerra, F. Commun. Math. Phys. 233 , 1–12 (2003).

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Extended Essay: Group 5: Mathematics

• General Timeline
• Group 1: English Language and Literature
• Group 2: Language Acquisition
• Group 3: Individuals and Societies
• Group 4: Sciences
• Group 5: Mathematics
• Group 6: The Arts
• Interdisciplinary essays
• Brainstorming
• Pre-Writing
• Research Techniques
• The Research Question
• Paraphrasing, Summarising and Quotations
• Writing an EE Introduction
• Writing the main body of your EE
• Writing your EE Conclusion
• Six sub-categories for WSEE
• IB Interdisciplinary EE Assessment Guide
• Sources: Finding, Organising and Evaluating Them
• Conducting Interviews and Surveys
• Citing and Referencing
• Check-in Sessions
• First Formal Reflection
• Second Formal Reflection
• Final Reflection (Viva Voce)
• Researcher's Reflection Space (RRS) Examples
• Information for Supervisors
• How is the EE Graded?
• EE Online Resources
• Stavanger Public Library
• Exemplar Essays
• Extended Essay Presentations
• ISS High School Academic Honesty Policy

Mathematics

An extended essay (EE) in mathematics is intended for students who are writing on any topic that has a mathematical focus and it need not be confined to the theory of mathematics itself.

Essays in this group are divided into six categories:

• the applicability of mathematics to solve both real and abstract problems
• the beauty of mathematics—eg geometry or fractal theory
• the elegance of mathematics in the proving of theorems—eg number theory
• the history of mathematics: the origin and subsequent development of a branch of mathematics over a period of time, measured in tens, hundreds or thousands of years
• the effect of technology on mathematics:
• in forging links between different branches of mathematics,
• or in bringing about a new branch of mathematics, or causing a particular branch to flourish.

These are just some of the many different ways that mathematics can be enjoyable or useful, or, as in many cases, both.

For an Introduction in a Mathematics EE look HERE . 

Choice of topic

The EE may be written on any topic that has a mathematical focus and it need not be confined to the theory of mathematics itself.

Students may choose mathematical topics from fields such as engineering, the sciences or the social sciences, as well as from mathematics itself.

Statistical analyses of experimental results taken from other subject areas are also acceptable, provided that they focus on the modeling process and discuss the limitations of the results; such essays should not include extensive non-mathematical detail.

A topic selected from the history of mathematics may also be appropriate, provided that a clear line of mathematical development is demonstrated. Concentration on the lives of, or personal rivalries between, mathematicians would be irrelevant and would not score highly on the assessment criteria.

It should be noted that the assessment criteria give credit for the nature of the investigation and for the extent that reasoned arguments are applied to an appropriate research question.

Students should avoid choosing a topic that gives rise to a trivial research question or one that is not sufficiently focused to allow appropriate treatment within the requirements of the EE.

Students will normally be expected either to extend their knowledge beyond that encountered in the Diploma Programme mathematics course they are studying or to apply techniques used in their mathematics course to modeling in an appropriately chosen topic.

However, it is very important to remember that it is an essay that is being written, not a research paper for a journal of advanced mathematics, and no result, however impressive, should be quoted without evidence of the student’s real understanding of it.

Example and Treatment of Topic

Examples of topics

These examples are just for guidance. Students must ensure their choice of topic is focused (left-hand column) rather than broad (right-hand column

Treatment of the topic

Whatever the title of the EE, students must apply good mathematical practice that is relevant to the

chosen topic, including:

• data analysed using appropriate techniques

• arguments correctly reasoned

• situations modeled using correct methodology

• problems clearly stated and techniques at the correct level of sophistication applied to their solution.

Research methods

Students must be advised that mathematical research is a long-term and open-ended exploration of a set of related mathematical problems that are based on personal observations. 

The answers to these problems connect to and build upon each other over time.

Students’ research should be guided by analysis of primary and secondary sources.

A primary source for research in mathematics involves:

• data-gathering

• visualization

• abstraction

• conjecturing

• proof.

A secondary source of research refers to a comprehensive review of scholarly work, including books, journal articles or essays in an edited collection.

A literature review for mathematics might not be as extensive as in other subjects, but students are expected to demonstrate their knowledge and understanding of the mathematics they are using in the context of the broader discipline, for example how the mathematics they are using has been applied before, or in a different area to the one they are investigating.

Writing the essay

Throughout the EE students should communicate mathematically:

• describing their way of thinking

• writing definitions and conjectures

• using symbols, theorems, graphs and diagrams

• justifying their conclusions.

There must be sufficient explanation and commentary throughout the essay to ensure that the reader does not lose sight of its purpose in a mass of mathematical symbols, formulae and analysis.

The unique disciplines of mathematics must be respected throughout. Relevant graphs and diagrams are often important and should be incorporated in the body of the essay, not relegated to an appendix.

However, lengthy printouts, tables of results and computer programs should not be allowed to interrupt the development of the essay, and should appear separately as footnotes or in an appendix. Proofs of key results may be included, but proofs of standard results should be either omitted or, if they illustrate an important point, included in an appendix.

Examples of topics, research questions and suggested approaches

Once students have identified their topic and written their research question, they can decide how to

research their answer. They may find it helpful to write a statement outlining their broad approach. These

examples are for guidance only.

An important note on “double-dipping”

Students must ensure that their EE does not duplicate other work they are submitting for the Diploma Programme. For example, students are not permitted to repeat any of the mathematics in their IA in their EE, or vice versa.

The mathematics EE and internal assessment

An EE in mathematics is not an extension of the internal assessment (IA) task. Students must ensure that they understand the differences between the two.

• The EE is a more substantial piece of work that requires formal research
• The IA is an exploration of an idea in mathematics.

It is not appropriate for a student to choose the same topic for an EE as the IA. There would be too much danger of duplication and it must therefore be discouraged.

• << Previous: Group 4: Sciences
• Next: Group 6: The Arts >>
• Last Updated: Mar 8, 2024 1:59 PM
• URL: https://isstavanger.libguides.com/c.php?g=695888

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. 

You might also be interested in our ordinal number explainer.

“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

Martin is an avid writer specializing in editing and proofreading. He also enjoys literary analysis and writing about food and travel.

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The Best Writing on Mathematics 12

Mircea pitici,  series editor.

This annual anthology brings together the year’s finest mathematics writing from around the world. Featuring promising new voices alongside some of the foremost names in the field, The Best Writing on Mathematics makes mathematical writing available to a wide audience.

The year’s finest mathematical writing from around the world

The year's finest mathematical writing from around the world

The year's finest mathematics writing from around the world

The year's finest writing on mathematics from around the world

The year's finest writing on mathematics from around the world, with a foreword by Nobel Prize – winning physicist Roger Penrose

The year’s most memorable writing on mathematics

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Mathematics: Discovered or Created? Essay (Critical Writing)

Mathematics is a branch of science that has had far-reaching impacts on many spheres of life. Through mathematics, man has made remarkable advances in technology and other fields of life. Mathematics also provides us with a logical order for describing the various prototypes and structures that comprise nature. Mathematics is also responsible for some of the greatest breakthroughs that have been made by humanity so far.

For instance, mathematics has played a hand in humanity’s foray into the cosmos and it has been responsible for the modern internet advancements. Albert Einstein once asked, “How can it be that mathematics, being after all a product of human thought which is independent of experience, is so admirably appropriate to the objects of reality?” (Ernest 9). This question is part of a big debate on whether math is a product of human creation or human discovery. Consequently, if math is part of human discovery what are some of the laws and notions that are subject to this discovery? This paper explores the issues surrounding the debate on whether math is a product of human creation or human discovery.

First, it is important to note that math acts like the outline to our universe. Many mathematicians agree that the universe is governed by a singular order that is defined using mathematical principles. Consequently, even if the universe ceased to exist, all mathematical principles would still be true. Therefore, like other aspects of human nature, mathematics is part of human discovery. Furthermore, there are several mathematical principles that are yet to be discovered. When these principles are discovered, they “will then assist us in building models that will give us predictive power and understanding of the physical phenomena we seek to control” (Ernest 10). Therefore, math is a natural concept that is to be discovered and used by humanity. This argument is common among lovers of mathematics.

Another viable explanation of the existence of mathematics is that it is merely part of the human creation. The argument about math being part of the intricate web of nature could be easily refuted by the view that human beings invented mathematics as a tool that could aid in the description of the physical world. Therefore, mathematics is only popular among human beings because it suits their needs when they are exploring the world.

It is also true that some mathematical concepts have been changed and altered for them to be palatable to human beings. Furthermore, if the universe ceased to exist, there would be no need for mathematics and it would not exist. Mathematics has been made possible by geography, astronomy, and physics among other areas of universal studies. Mathematics exists solely to satisfy the needs of studying and understanding the universe but it is not part of these studies. Therefore, mathematics is not something that is discovered but it is a human creation.

These two arguments form the basis of our understanding of the institution of mathematics. However, in my understanding, mathematics is a human creation. The argument for mathematics being part of human discovery is far-fetched and fanatical. For instance, mathematics only describes certain variables of the physical universe. There are several other factors of the universe that cannot be defined or explained by mathematical concepts. Therefore, the argument about mathematics being part of human discovery can be nullified by the idea that there are discoveries that are outside of the mathematical realm. In my view, when discoveries about the physical world are made, man proceeds to create mathematical concepts that can help him analyze and explain these new discoveries.

Works Cited

Ernest, Paul. “Is mathematics discovered or invented.” Philosophy of Mathematics Education Journal 12.1 (2009): 9-13. Print.

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• Chicago (N-B)

IvyPanda. (2023, November 1). Mathematics: Discovered or Created? https://ivypanda.com/essays/mathematics-discovered-or-created/

"Mathematics: Discovered or Created?" IvyPanda , 1 Nov. 2023, ivypanda.com/essays/mathematics-discovered-or-created/.

IvyPanda . (2023) 'Mathematics: Discovered or Created'. 1 November.

IvyPanda . 2023. "Mathematics: Discovered or Created?" November 1, 2023. https://ivypanda.com/essays/mathematics-discovered-or-created/.

1. IvyPanda . "Mathematics: Discovered or Created?" November 1, 2023. https://ivypanda.com/essays/mathematics-discovered-or-created/.

Bibliography

IvyPanda . "Mathematics: Discovered or Created?" November 1, 2023. https://ivypanda.com/essays/mathematics-discovered-or-created/.

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What is a Video Essay? The Art of the Video Analysis Essay

I n the era of the internet and Youtube, the video essay has become an increasingly popular means of expressing ideas and concepts. However, there is a bit of an enigma behind the construction of the video essay largely due to the vagueness of the term.

What defines a video analysis essay? What is a video essay supposed to be about? In this article, we’ll take a look at the foundation of these videos and the various ways writers and editors use them creatively. Let’s dive in.

Watch: Our Best Film Video Essays of the Year

Subscribe for more filmmaking videos like this.

What is a video essay?

First, let’s define video essay.

There is narrative film, documentary film, short films, and then there is the video essay. What is its role within the realm of visual media? Let’s begin with the video essay definition. 

VIDEO ESSAY DEFINITION

A video essay is a video that analyzes a specific topic, theme, person or thesis. Because video essays are a rather new form, they can be difficult to define, but recognizable nonetheless. To put it simply, they are essays in video form that aim to persuade, educate, or critique. 

These essays have become increasingly popular within the era of Youtube and with many creatives writing video essays on topics such as politics, music, film, and pop culture. 

What is a video essay used for?

• To persuade an audience of a thesis
• To educate on a specific subject
• To analyze and/or critique 

What is a video essay based on?

Establish a thesis.

Video analysis essays lack distinguished boundaries since there are countless topics a video essayist can tackle. Most essays, however, begin with a thesis. 

How Christopher Nolan Elevates the Movie Montage  •  Video Analysis Essays

Good essays often have a point to make. This point, or thesis, should be at the heart of every video analysis essay and is what binds the video together. 

Related Posts

• Stanley Kubrick Directing Style Explained →
• A Filmmaker’s Guide to Nolan’s Directing Style →
• How to Write a Voice Over Montage in a Script →

interviews in video essay

Utilize interviews.

A key determinant for the structure of an essay is the source of the ideas. A common source for this are interviews from experts in the field. These interviews can be cut and rearranged to support a thesis. 

Roger Deakins on "Learning to Light"  •  Video Analysis Essays

Utilizing first hand interviews is a great way to utilize ethos into the rhetoric of a video. However, it can be limiting since you are given a limited amount to work with. Voice over scripts, however, can give you the room to say anything. 

How to create the best video essays on Youtube

Write voice over scripts.

Voice over (VO) scripts allow video essayists to write out exactly what they want to say. This is one of the most common ways to structure a video analysis essay since it gives more freedom to the writer. It is also a great technique to use when taking on large topics.

In this video, it would have been difficult to explain every type of camera lens by cutting sound bites from interviews of filmmakers. A voice over script, on the other hand, allowed us to communicate information directly when and where we wanted to.

Ultimate Guide to Camera Lenses  •  Video essay examples

Some of the most famous video essayists like Every Frame a Painting and Nerdwriter1 utilize voice over to capitalize on their strength in writing video analysis essays. However, if you’re more of an editor than a writer, the next type of essay will be more up your alley. 

Video analysis essay without a script

Edit a supercut.

Rather than leaning on interview sound bites or voice over, the supercut video depends more on editing. You might be thinking “What is a video essay without writing?” The beauty of the video essay is that the writing can be done throughout the editing. Supercuts create arguments or themes visually through specific sequences. 

Another one of the great video essay channels, Screen Junkies, put together a supercut of the last decade in cinema. The video could be called a portrait of the last decade in cinema.

2010 - 2019: A Decade In Film  •  Best videos on Youtube

This video is rather general as it visually establishes the theme of art during a general time period. Other essays can be much more specific. 

Critical essays

Video essays are a uniquely effective means of creating an argument. This is especially true in critical essays. This type of video critiques the facets of a specific topic. 

In this video, by one of the best video essay channels, Every Frame a Painting, the topic of the film score is analyzed and critiqued — specifically temp film score.

Every Frame a Painting Marvel Symphonic Universe  •  Essay examples

Of course, not all essays critique the work of artists. Persuasion of an opinion is only one way to use the video form. Another popular use is to educate. 

• The Different Types of Camera Lenses →
• Write and Create Professionally Formatted Screenplays →
• How to Create Unforgettable Film Moments with Music →

Video analysis essay

Visual analysis.

One of the biggest advantages that video analysis essays have over traditional, written essays is the use of visuals. The use of visuals has allowed video essayists to display the subject or work that they are analyzing. It has also allowed them to be more specific with what they are analyzing. Writing video essays entails structuring both words and visuals. 

Take this video on There Will Be Blood for example. In a traditional, written essay, the writer would have had to first explain what occurs in the film then make their analysis and repeat.

This can be extremely inefficient and redundant. By analyzing the scene through a video, the points and lessons are much more clear and efficient. 

There Will Be Blood  •   Subscribe on YouTube

Through these video analysis essays, the scene of a film becomes support for a claim rather than the topic of the essay. 

Dissect an artist

Essays that focus on analysis do not always focus on a work of art. Oftentimes, they focus on the artist themself. In this type of essay, a thesis is typically made about an artist’s style or approach. The work of that artist is then used to support this thesis.

Nerdwriter1, one of the best video essays on Youtube, creates this type to analyze filmmakers, actors, photographers or in this case, iconic painters. 

Caravaggio: Master Of Light  •  Best video essays on YouTube

In the world of film, the artist video analysis essay tends to cover auteur filmmakers. Auteur filmmakers tend to have distinct styles and repetitive techniques that many filmmakers learn from and use in their own work. 

Stanley Kubrick is perhaps the most notable example. In this video, we analyze Kubrick’s best films and the techniques he uses that make so many of us drawn to his films. 

Why We're Obsessed with Stanley Kubrick Movies  •  Video essay examples

Critical essays and analytical essays choose to focus on a piece of work or an artist. Essays that aim to educate, however, draw on various sources to teach technique and the purpose behind those techniques. 

What is a video essay written about?

Historical analysis.

Another popular type of essay is historical analysis. Video analysis essays are a great medium to analyze the history of a specific topic. They are an opportunity for essayists to share their research as well as their opinion on history. 

Our video on aspect ratio , for example, analyzes how aspect ratios began in cinema and how they continue to evolve. We also make and support the claim that the 2:1 aspect ratio is becoming increasingly popular among filmmakers. 

Why More Directors are Switching to 18:9  •  Video analysis essay

Analyzing the work of great artists inherently yields a lesson to be learned. Some essays teach more directly.

• Types of Camera Movements in Film Explained →
• What is Aspect Ratio? A Formula for Framing Success →
• Visualize your scenes with intuitive online shotlist software →

Writing video essays about technique

Teach technique.

Educational essays designed to teach are typically more direct. They tend to be more valuable for those looking to create art rather than solely analyze it.

In this video, we explain every type of camera movement and the storytelling value of each. Educational essays must be based on research, evidence, and facts rather than opinion.

Ultimate Guide to Camera Movement  •  Best video essays on YouTube

As you can see, there are many reasons why the video essay has become an increasingly popular means of communicating information. Its ability to use both sound and picture makes it efficient and effective. It also draws on the language of filmmaking to express ideas through editing. But it also gives writers the creative freedom they love. 

Writing video essays is a new art form that many channels have set high standards for. What is a video essay supposed to be about? That’s up to you. 

Organize Post Production Workflow

The quality of an essay largely depends on the quality of the edit. If editing is not your strong suit, check out our next article. We dive into tips and techniques that will help you organize your Post-Production workflow to edit like a pro. 

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IB Maths EE examples

Filter exemplars, to what extent prime counting function and the riemann zeta function are similar, and what is the importance of their similarities, how are elliptic curves used in cryptography to make information secure in today’s world, want to get full marks for your ee allow us to review it for you 🎯, how does elliptic curve cryptography ensure secure communication of information on the internet, to what extent is the naive bayes classifier effective in classifying iris plants data set, to what extent is the insight into the concepts of consonance and dissonance in music theory provided by the mathematical descriptions of the string motions within stringed instruments described by the fourier series, fast track your coursework with mark schemes moderated by ib examiners. upgrade now 🚀, how can laplace transformation be used to solve differential equations in undamped vibration and kirchhoff's laws of current and voltage, to what length does the lotka-volterra model help us understand the predator-prey relation in an ecosystem, how does the implementation of pell's equation in rsa cryptography affect its efficiency, and what is the security of the prime fake modulus variant against fermat's factorization and wiener's attack, dans quelle mesure, l’utilisation de pi (π) est-il devenu un facteur important dans la vie quotidienne et l’évolution du monde, how can matrix analysis of game theory be used to guide foreign policy in the ongoing us-iran nuclear tensions, how does the idea of transpositions from group theory apply itself to the solution of the futurama problem, how can the surface area of a violin's top plate be calculated, what is the height and number of towers in a suspension bridge between tuas and jurong island such that it will bear the heaviest possible load and have the lowest cost, how trigonomotry applied in astronomy, how do laplace transformations and complex exponential substitution enable the solution of a first order differential equation to obtain the sinusoidal current in a basic rl circuit, the analysis of approaches and extension of a combinatorial geometry problem, to what extent, statistically, are the causal effects of parenting programs on rural chinese toddlers’ cognition different between genders, to what extent is the mathematical proof of ‘ac ohm’s law’ applicable to ac circuits, to what extent do trigonometry, elliptical geometry and calculus aid forensic analysts in blood spatter analysis and the estimation of the time of death of a corpse, how does the fourier series is used as a musical signal for chord structure, what is modular arithmetic, and how can it be applied to solve problems in the field of number theory, to what extent do the motion of strings within stringed instruments described by fourier series give insight into consonance and dissonance in music theory, how can we use fourier series to analyse and produce an electrocardiogram signal, (35/36) hyperbolic flyby trajectories in orbital mechanicss, analyzing the distribution of cards in the "egg game”, to what extent the areas of mathematics such as differ- ential geometry and calculus of variations can be used to generalize the brachis- tochrone problem at planes to curved surfaces embedded in three dimensions, generating arbitrary uniform probability distributions, what are some ways the riemann zeta function is connected to the prime numbers, that helps us investigate and better understand them, probability factors that influence the game of roulette, we will investigate whether the supply and demand affect the performance of a stock in the us equity market, to what extent does the distance between the path that goes through the gold nucleus and one of the asymptotes of the α particle’s hyperbolic trajectory affect the trajectory of the α particle in rutherford's gold foil experiment, what is the most optimal point on football field to score a goal, how does abstract mathematics apply to physical phenomena in the process of the development of schrodinger’s equations, the rsa algorithm and its vulnerabilities, how can mathematics be used to work out the optimal distance from the try line to position the ball for a conversion kick in rugby union.

ESSAY SAUCE

FOR STUDENTS : ALL THE INGREDIENTS OF A GOOD ESSAY

• Mathematics essays

Our free mathematics essay examples include popular topics such as algorithms, applied mathematics, calculus, knot theory, linear algebra, and more.

Euler’s identity

Euler’s identity is an equality found in mathematics that has been compared to a Shakespearean sonnet and described as “the most beautiful equation.” It is a special case of a foundational equation in complex arithmetic called Euler’s Formula, which the late great physicist Richard Feynman called in his lectures “our jewel” and “the most remarkable formula in … Read more

The Banach-Tarski paradox

Mathematics is seen by many as a mysterious and often unsettling subject. Answers often hide behind layers and layers of complicated equations, formulas and ciphers, the application of advanced concepts to real life is limited and I often find myself more confused after class than when I first entered. However, the real beauty of Mathematics … Read more

Pascal’s triangle, binomial theorem

What is Pascal’s Triangle? Pascal’s Triangle was named after Blaise Pascal. Pascal’s triangle starts with the number 1 and goes down the scale. When you start with one, add more numbers in a triangular shape, like a pyramid of some sort. All the numbers on the surrounding right and left sides of the triangle are … Read more

My journey of teaching and learning mathematics since embarking on a PGCE Mathematics course

Before I came to study a Post Graduate Certificate (PGCE) Mathematics course at University College London Institute of Education (UCL IOE), I had been working as an Academic Tutor at a behavioural centre, linked to a mainstream secondary school for the past 7 months. Students placed here had either learning difficulties or behaviour issues experienced … Read more

Aircraft – mathematics

Math SL Internal Assessment Lift and Drag Introduction When you look at aircrafts, they look like they shouldn’t be able to leave the ground because of how big they are. I always watched aircrafts, take off and land, over and over. According to Newton’s Third Law, every action has an equal and opposite reaction, lift … Read more

The World of Mathematics

Mathematics is often considered a useless discipline because people think they do not use advanced math in their life. It is a misunderstanding. Not using advanced math does not mean it is not vital. If you trade stocks, you will read many stock analysis reports. These reports use mathematical knowledge. Many students in the United … Read more

The history of algebra

We all use algebra. Even if it’s for the simple stuff, we use some form of algebra in our everyday lives. While reading chapters 1-10, I came across the word algebra and became quite curious about the subject for I have never really understood nor cared for it honestly, I just figured it’s the usual … Read more

Mathematics introduction

Mathematics belongs to the science discourse community. The word science means knowledge and comes from the Latin “Scientia”. In university, science is made up of a lot of discourse communities, such as Mathematics, Physics, and Chemistry. By searching the definition of science in Webster’s New Collegiate Dictionary, science is “knowledge covering general truths of the … Read more

Niels Henrik Abel

For over two centuries, mathematicians had trouble in finding a solution to the quintic equation, that is until Niels Henrik Abel formulated a theory. Abel was a Norwegian mathematician born on August 5, 1802, and his talent and potential in the field of mathematics was already present at a young age, leading him to become … Read more

The narrative of zero

Numbers surround us. They stamp our days, light our evenings, foresee our climate, and keep us on course. They drive business and support human progress. The beginning of the numerals makes disarray between the historical backdrop of mathematics and the historical backdrop of our modern numerals. The narrative of zero alludes to something can be … Read more

Emmy Noether

She was more than a mathematician to the people she met and to the people she inspired. She even has managed to inspire people long after she has passed. Emmy Noether was born on March 23, 1882 in Bavaria Germany. Growing up she wanted to go to college but back then women weren’t allowed to … Read more

Bitopological Approximation Space with Application to Data Reduction in Multivalued Information Systems

Abstract: In this work we generalize Pawlak approximation space to bitopological approximation space. One binary relation can define two subbases of two topological spaces. Membership, equillity and inclusion relations using rough approximations are defined and studied in bitopological aapproximation space. Some new measures that measure the accuracy and the quality of approximations are defined and … Read more

Statistics overview

Statistics is a form of mathematical analysis that uses quantified models, representations and synopses for a given set of experimental data or real life studies. Statistical analysis involves the process of gathering and evaluating data and then summarizing the data into a mathematical form. Statistics is a term used to summarize a process that a … Read more

Numerical Weather Prediction

You turn on the television, and often the first channel that pops up is the weather. It’s going 24/7 with predictions that go from weekly all the way down to hourly, with conditions that go from humidity to temperature. But what goes on behind the scenes is heavily entrenched in mathematics– meteorology’s backbone is a … Read more

The Mathematics of Our Universe

Abstract In this report, we start by defining key aspects of classical Lagrangian mechanics including the principle of least action and how one can use this to derive the Euler-Lagrange equations. Momentum and Conservation laws shall also be introduced, deriving relations between position, momenta and the Lagrangian of a given system. Following this, we develop … Read more

Ideas for your next mathematics essay

Stuck for a title for your next essay? Here are some ideas to inspire you:

• The Mathematics of Music: Exploring the Relationship between Mathematics and Music – This essay would examine the connections between music and mathematics, including the use of mathematical concepts in musical composition and the study of the mathematics of sound.
• The Golden Ratio: A Mathematical and Aesthetic Marvel – This essay would discuss the concept of the golden ratio and its applications in art, architecture, and design. It would explore the beauty and symmetry of this mathematical principle.
• Mathematics in Sports: Analyzing the Numbers Behind Athletic Performance – This essay would explore the use of mathematics in sports, including the use of statistics and analytics to analyze athletic performance and predict outcomes.
• Chaos Theory: The Science of Nonlinear Systems – This essay would discuss the concept of chaos theory and its applications in various fields, such as meteorology, physics, and economics. It would explore the idea that small changes in initial conditions can have a significant impact on the final outcome of a system.
• The Mathematics of Cryptography: Securing Information in the Digital Age – This essay would examine the use of mathematics in cryptography, including the principles of encryption and decryption, and how these concepts are applied to secure information in the digital age.
• Fractals: The Beauty of Infinite Complexity – This essay would explore the concept of fractals and their applications in art, nature, and science. It would discuss the beauty and complexity of these repeating patterns found in nature and how they are used in various fields of study.
• Mathematical Models in Biology: Understanding the Complexities of Life – This essay would discuss the use of mathematical models in biology, including the modeling of population growth, the spread of disease, and the behavior of organisms. It would explore how these models help scientists understand the complex systems that make up living organisms.
• The Mathematics of Finance: Analyzing Investments and Markets – This essay would examine the use of mathematics in finance, including the principles of financial analysis, investments, and risk management. It would explore how mathematics is used to understand and predict market trends.
• Geometry in Art: The Intersection of Math and Creativity – This essay would discuss the use of geometry in art, including the use of shapes, patterns, and symmetry. It would explore how artists use mathematical concepts to create beautiful and compelling works of art.
• The History of Mathematics: From Ancient Times to Modern-Day Advances – This essay would trace the history of mathematics, from its origins in ancient civilizations to modern-day advancements in the field. It would explore the contributions of key mathematicians throughout history and the evolution of mathematical concepts and principles over time.

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