examples of essay questions in mathematics

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
• Six sub-categories for WSEE
• IB Interdisciplinary EE Assessment Guide
• 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
• 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.

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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. 

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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How to Choose an EE Topic (Mathematics)

The Extended Essay is undoubtedly one of the most feared components of the IB program. A 4,000 word research paper can, in fact, seem daunting to those who have only written 500-1000 word essays. Therefore, students should choose a topic that they can not only find sources for, but are also passionate about it.

Mathematics Extended Essays are rare — of the 87,519 Extended Essays submitted in the 2020 May Examination Session only 2,454 were done over Mathematics (2.8%) ( IB Statistical Bulletin 2020 ). Despite the rarity, I chose to write a Mathematics EE because maths is something that fascinates me. To many students, Mathematics EEs sound scary and barely consider writing one. There were many people that told me I was insane and that it was impossible. In the end, I put in the work to make it happen. 

I chose to write my paper on Game Theory and my research question was: “To what extent does Game Theory play a role in Modern Warfare?” 

I found this topic not unlike the way students writing History EEs find their own specific topics. Just as history has countless events in which one can write about, Mathematics is similar with its various branches. I chose a branch that interested me (Game Theory) and used it to solve a real-world problem (Modern Warfare). My economics teacher actually suggested this idea.  They said that, while Game Theory is primarily used in economics, it has numerous applications to maths when discussed alongside warfare. This qualified my essay as a Category 1 Mathematics Extended Essay, which is a paper that discusses “the applicability of mathematics to solve both real and abstract problems” (p. 96, IB Extended Essay Guide ). 

Writing the essay is where, I admit, it got challenging. During the process I had no peers to help me as only a few others had chosen a Mathematics EE, but none of their topics related to mine. Fortunately, my mentor was extremely helpful and I was able to find several books at my local university that were very useful.

Mathematics Extended Essays are bizarre in many ways as things such as word count, varied sentence structure, and high vocabulary do not matter. However, it should be noted that effective communication is key even if that’s done through mathematical expressions. Despite these challenges, I strongly believe that Mathematics EEs are doable, and more people would do them if there was not such a negative stigma about them. I encourage all future IB sessions to consider doing one as the feeling when you have finished is unlike any other. The pride and satisfaction I felt knowing that I took the path less travelled and still found success is something that I hope all future IB students will experience.

You may also like…

• Our Extended Essay series
• Tiffany’s tips for Mathematics HL

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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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Sat / act prep online guides and tips, the complete ib extended essay guide: examples, topics, and ideas.

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

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IB Math Extended Essay Topics: 20+ Ideas for Inspiration

by  Antony W

September 3, 2022

Do you feel stuck on searching for and choosing the best IB Math Extended Essay topics? Or maybe you already have a topic for consideration but it isn’t viable enough to fit the scope of the assignment?

You’ve come to the right place.

In this guide, we’ll give you 15+ IB Math ideas that you can use as inspiration to come up with your own topic or modify and investigate further in your extended essay.

What’s the Purpose of IB Math Extended Essay?

An extended essay in mathematics gives you the chance to demonstrate an understanding of any part of the subject.

You can give an expression on the beauty of mathematics in geometry or fractal theory, the elegance of mathematics in the proving of theorems, and the origin and subsequent development of a branch of mathematics over a period.

The extended essay also allows you to demonstrate the link between the different branches of mathematics and the powerful structures that enable many different problems to be solved by a single theory and the way in which mathematics is applied to real-world situations.

Your essay requires a well-defined and focused research question. An abstract is no longer necessary in an extended essay , but you’re welcome to include it if you believe it will summarizes your strategy to solving the research question and your findings

Math Extended Essay Writing Assistance

While Math opens up an opportunity to explore complex issues beyond the IB Diploma course , the subject can be extremely challenging for some IB students.

If you’re one of the students who chose Math for the Extended Essay project but you find the subject challenging, you can get help online from experts in the subject.

Help for Assessment offers the most  comprehensive Extended Essay help   in Mathematics, even on a topic that you would consider too complex to handle. With our help, you’ll find complex concepts easy to understand, not to mention you’ll get your Math assignment completed on time.

We understand that Math tasks can be costly and involving. However, we’ve made our writing service as affordable as possible, so you can get professional writing help.

We can write you first draft before the first reflection session with your supervisor and equally help you fine-tune the last draft for the final submission.

IB Math Extended Essay Topics

The following are examples of IB Math Extended Essay topics that you might find worth investigating further: 

• What is the return percentage of a certain three-reel slot machine?
• What are the alternatives to Euclidean geometry and what are their practical applications?
• Comparison of population growth models for Country X for the past n years, with projections for the future.
• The exploration of geometric series in musical instruments, such as the fret position on a guitar
• How many convex polygons can you construct from seven tangram pieces?
• An examination of the alteration of a message's truthful substance during transmission between persons
• Is there a connection between the golden ratio and human’s perception on natural beauty, with a focus on the human face and form?
• Is there a relationship between SAT scores and school test results/GPA?
• Leibniz and Newton independently developed calculus at around the same time. Compare their techniques and analyze which notation is currently more prevalent.
• What is the Binomial Theorem, and how has it contributed to human history?
• Complex number problem-solving techniques: What types of real-world issues do complex numbers assist solve?
• Applying Newton's Forward Difference Formula to predict the number of triangles created by subdividing the sides of an equilateral triangle n times.
• RSA Public Key Cryptography's use of modular arithmetic and huge prime integers to achieve anonymity
• Investigating the link between Pascal's Triangle and the Fibonacci sequence
• How can mathematical modeling that employs differential equations determine population growth patterns for a predator and its prey?
• How can the population of cells be determined throughout time? Which mathematical model approximates an actual experiment more precisely?
• A study of Riemann Sums (conventional integration to get areas) and Numerical Integration
• Vedic Mathematics: an investigation of its effectiveness and exploration of its applications
• How are Laplace transforms utilized in the solution of second-order differential equations?
• A statistical examination of the impact of background music on pupils' short-term memory ability
• Analytical and geometric formulations of parabolic and cubic Bezier curves as used in computer graphics software
• A quantitative analysis of the efficacy of two herbs for treating impetigo skin condition
• A study of the nature of beats and the relative consonance of pure-tone dyads
• The link between logical-mathematical intelligence and academic achievement at the undergraduate level
• A study of the link between a bond's coupon rate, yield to maturity, and its clean price
• Using the addition of sine curves to analyze the harmony of Chinese and Western musical scales
• The correlation between students' attitudes toward mathematics and their mathematical performance
• How near is the approximation of the Taylor Series to the original function
• What criteria determine whether the movement of employees on a building site achieves "equilibrium"?
• The efficacy of an English Tuition Program in enhancing the English skills of participants
• A statistical examination of the causes of fatal traffic accidents throughout the holiday season
• Does studying a third language have any influence on the short-term memory retention of lower secondary students?

Keep in mind that this list is not exhaustive by any means. So if none of these topic ideas appeals to you, doing additional research can make a difference.

Related Reading

• The Complete Guide for IB Math Extended Essay
• Get a List of Psychology Extended Essay Topics Here
• Learn More About Physics Extended Essay Assignment

Some Tips to Help You Choose a Relevant Math EE Topic

You can write an extended essay in math on any subject with a mathematical focus. Because IB doesn’t limit the assignment to mathematical theories, you may select mathematical themes from engineering, sciences, and the social sciences.

Statistical analyses of experimental results from other disciplines are also appropriate, as long as they focus on the modeling method and address the limits of the results.

A topic chosen from the history of mathematics may also be acceptable, provided you bring out a clear progression of mathematical growth.

Focusing on the lives of mathematicians or their personal rivalry would be irrelevant and would not score highly on the grading criteria.

Notably, the evaluation criteria provide points for the nature of the inquiry and the extent to which reasoned arguments are suitable for a research issue.

You need to avoid selecting a topic that generates a trivial research question or is insufficiently concentrated to permit suitable presentation in an essay of the right length.

Typically, you will have to challenge yourself to either extend their knowledge beyond the Diploma Program course or apply techniques learned in their mathematics course to the modeling of an adequately chosen topic.

Final Thoughts

One of the most important thing to keep in mind once you find a suitable Math EE topic is that you will be working on an essay, not a research article for a journal of advanced mathematics.

Also, no finding, no matter how remarkable, should appear in your work without proof of your actual understanding of it. 

About the author 

Antony W is a professional writer and coach at Help for Assessment. He spends countless hours every day researching and writing great content filled with expert advice on how to write engaging essays, research papers, and assignments.

SAT Essay Questions

We have a collection of the new SAT Essay Questions from March 2005 till the most recent test released by College Board.

October 2007

If you took the October 2007 SAT Reasoning Test, you would have been given one of the essay prompts below:

Think carefully about the issue presented in the following excerpt and the assignment below.

A person does not simply "receive" his or her identity. Identity is much more than the name or features one is born with. True identity is something people must create for themselves by making choices that are significant and that require a courageous commitment in the face of challenges. Identity means having ideas and values that one lives by.

Adapted from Thomas Merton, Contemplation in a World of Action

Assignment: Is identity something people are born with or given, or is it something people create for themselves? Plan and write an essay in which you develop your point of view on this issue. Support your position with reasoning and examples taken from your reading, studies, experience, or observations.

We value uniqueness and originality, but it seems that everywhere we turn, we are surrounded by ideas and things that are copies or even copies of copies. Writers, artists, and musicians seek new ideas for paintings, books, songs, and movies, but many sadly realize, "It's been done." The same is true for scientists, scholars, and businesspeople. Everyone wants to create something new, but at best we can hope only to repeat or imitate what has already been done.

Assignment: Can people ever be truly original? Plan and write an essay in which you develop your point of view on this issue. Support your position with reasoning and examples taken from your reading, studies, experience, or observations.

All people who have achieved greatness in something knew what they excelled at. These people identified the skills that made them special—good judgment, or courage, or a special artistic or literary talent—and focused on developing these skills. Yet most people achieve superiority in nothing because they fail to identify and develop their greatest attribute.

Adapted from Baltasar Gracián y Morales, The Art of Worldly Wisdom

Adapted from Stephen J. Carter, Integrity

Assignment: Do people achieve greatness only by finding out what they are especially good at and developing that attribute above all else? Plan and write an essay in which you develop your point of view on this issue. Support your position with reasoning and examples taken from your reading, studies, experience, or observations.

Having many admirers is one way to become a celebrity, but it is not the way to become a hero. Heroes are self-made. Yet in our daily lives we see no difference between "celebrities" and "heroes." For this reason, we deprive ourselves of real role models. We should admire heroes—people who are famous because they are great—but not celebrities—people who simply seem great because they are famous.

Adapted from Daniel Boorstin, The Image: A Guide to Pseudo-Events in America

Assignment: Should we admire heroes but not celebrities? Plan and write an essay in which you develop your point of view on this issue. Support your position with reasoning and examples taken from your reading, studies, experience, or observations.

More SAT essay prompts at SAT preparation.

We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.

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12 Strong Topic Ideas For A Math Extended Essay

Writing a math extended essay can be quite a challenge unless you are using an IB extended essay writing service . You have many factors to consider such as following the right format, choosing the best approach for your study, and defending your thesis (if required). So choosing an engaging topic that pertains to today’s issues is a crucial first step when you are in the planning stages.

Obviously, mathematics are your primary interest or else you wouldn’t have this assignment, to begin with due to not being enrolled in a course that goes above and beyond Algebra 102 or Geometry 104. (Even if you’re forced to endure a statistics course, you would have some interest in mathematical data or at least possess an awareness of working with numbers in your chosen field.) So one bit of advice on selecting a topic for your extended essay topics is to combine your intrigue with math with a problem, scenario or specific career domain (e.g.: medical, technology, sociology, business, etc.) that will not only hold your attention but also relate to current trends or events.

So here some suggestions for fascinating math essay topics to get you started:

In the area of education, some possible themes are:

• Possible correlation between district-level standardized test scores or GPA’s and performance on the SAT
• Prevalence of stress and coping skills of secondary university-bound students (Think ratios and statistics)
• Effectiveness of literacy programs (school or community-wide) towards improving reading skills (You can probably narrow down to an age range or grade level(s))

For the medical field, the possibilities are endless. Consider these three suggestions:

• Possible direct correlation between usage of “antibacterial” products, like hand sanitizer for instance and the rise of the “Super Bug.”
• The odds of another pandemic, similar to the 1918 worldwide influenza outbreak, occurring
• The impact of advertising on childhood obesity (Again, think ratios, statistics, and probability)

In the realm of computer technology, you can look into any one of these subjects:

• Best formula and combinations for SEO
• The use of prime numbers and modular arithmetic to maintain privacy with RSA Public Key Cryptography
• Correlation between the use of electronic pay services (Skrill for example) and users’ professions.

Of course, there are a variety of areas to explore within the content of math itself and its applications. Some possibilities include the following:

• Study of alternatives to Euclidean geometry and their applications
• Close study of Sophie Germain’s Theorem
• Real life dilemmas that can be solved with strategies of complex number problem-solving

As you can see, there are many different subjects to explore when writing about mathematical concepts and how they relate to the real world. You can dive more into the content area of science and hypothesize the route(s) of a comet that could impact the earth. Concerning sociological and psychological studies, you can look into various statistical investigations of human behavior. Another rather amusing numerical investigation could involve a study of probability in gambling venues or about other types of gaming, like Fantasy Football. (Be careful with your finances, though.)

However, some tips to remember as you examine these topics is to choose the “sub-area” that interests you the most (unless it’s all about the math), as you will devote a lot of time to this project; make sure you have a clear and measurable hypothesis; and clarify any questions on format with your instructor. With these recommendations and a lot of calculating, you will compose the perfect paper.

Helpful Sources

Writing Tips

• Essay intro on math algorithms
• Paper about the chemistry of water

IB Maths EE examples

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260 Interesting Math Topics for Essays & Research Papers

Mathematics is the science of numbers and shapes. Writing about it can give you a fresh perspective and help to clarify difficult concepts. You can even use mathematical writing as a tool in problem-solving.

Our specialists will write a custom essay specially for you!

In this article, you will find plenty of interesting math topics. Besides, you will learn about branches of mathematics that you can choose from. And if the thought of letters and numbers makes your head swim, try our custom writing service . Our professionals will craft a paper for you in no time!

And now, let’s proceed to math essay topics and tips.

🔝 Top 10 Interesting Math Topics

✅ branches of mathematics, ✨ fun math topics.

• 🏫 Math Topics for High School
• 🎓 College Math Topics
• 🤔 Advanced Math
• 📚 Math Research
• ✏️ Math Education
• 💵 Business Math

🔍 References

• Number theory in everyday life.
• Logicist definitions of mathematics.
• Multivariable vs. vector calculus.
• 4 conditions of functional analysis.
• Random variable in probability theory.
• How is math used in cryptography?
• The purpose of homological algebra.
• Concave vs. convex in geometry.
• The philosophical problem of foundations.
• Is numerical analysis useful for machine learning?

What exactly is mathematics ? First and foremost, it is very old. Ancient Greeks and Persians were already utilizing mathematical tools. Nowadays, we consider it an interdisciplinary language.

Biologists, linguists, and sociologists alike use math in their work. And not only that, we all deal with it in our daily lives. For instance, it manifests in the measurement of time. We often need it to calculate how much our groceries cost and how much paint we need to buy to cover a wall.

Simply put, mathematics is a universal instrument for problem-solving. We can divide pure math into three branches: geometry, arithmetic, and algebra. Let’s take a closer look:

Just in 1 hour! We will write you a plagiarism-free paper in hardly more than 1 hour

• Geometry By studying geometry, we try to comprehend our physical surroundings. Geometric shapes can be simple, like a triangle. Or, they can form complicated figures, like a rhombicosidodecahedron.
• Arithmetic Arithmetic deals with numbers and simple operations: subtraction, addition, division, and multiplication.
• Algebra Algebra is used when the exact numbers are unclear. Instead, they are replaced with letters. Businesses often need algebra to predict their sales.

It’s true that most high school students don’t like math. However, that doesn’t mean it can’t be a fun and compelling subject. In the following section, you will find plenty of enthralling mathematical topics for your paper.

If you’re struggling to start working on your essay, we have some fun and cool math topics to offer. They will definitely engage you and make the writing process enjoyable. Besides, fun math topics can show everyone that even math can be entertaining or even a bit silly.

• The link between mathematics and art – analyzing the Golden Ratio in Renaissance-era paintings.
• An evaluation of Georg Cantor’s set theory.
• The best approaches to learning math facts and developing number sense.
• Different approaches to probability as explored through analyzing card tricks.
• Chess and checkers – the use of mathematics in recreational activities.
• The five types of math used in computer science .
• Real-life applications of the Pythagorean Theorem .
• A study of the different theories of mathematical logic .
• The use of game theory in social science.
• Mathematical definitions of infinity and how to measure it.
• What is the logic behind unsolvable math problems?
• An explanation of mean, mode, and median using classroom math grades.
• The properties and geometry of a Möbius strip.
• Using truth tables to present the logical validity of a propositional expression.
• The relationship between Pascal’s Triangle and The Binomial Theorem.
• The use of different number types: the history.
• The application of differential geometry in modern architecture.
• A mathematical approach to the solution of a Rubik’s Cube.
• Comparison of predictive and prescriptive statistical analyses.
• Explaining the iterations of the Koch snowflake.
• The importance of limits in calculus.
• Hexagons as the most balanced shape in the universe.
• The emergence of patterns in chaos theory.
• What were Euclid’s contributions to the field of mathematics?
• The difference between universal algebra and abstract algebra.

🏫 Math Essay Topics for High School

When writing a math paper, you want to demonstrate that you understand a concept. It can be helpful if you need to prepare for an exam. Choose a topic from this section and decide what you want to discuss.

• Explain what we need Pythagoras’ theorem for. 
• What is a hyperbola? 
• Describe the difference between algebra and arithmetic. 
• When is it unnecessary to use a calculator ? 
• Find a connection between math and the arts. 
• How do you solve a linear equation? 
• Discuss how to determine the probability of rolling two dice. 
• Is there a link between philosophy and math? 
• What types of math do you use in your everyday life? 
• What is the numerical data? 
• Explain how to use the binomial theorem. 
• What is the distributive property of multiplication? 
• Discuss the major concepts in ancient Egyptian mathematics . 
• Why do so many students dislike math? 
• Should math be required in school? 
• How do you do an equivalent transformation? 
• Why do we need imaginary numbers? 
• How can you calculate the slope of a curve? 
• What is the difference between sine, cosine, and tangent? 
• How do you define the cross product of two vectors? 
• What do we use differential equations for? 
• Investigate how to calculate the mean value. 
• Define linear growth. 
• Give examples of different number types. 
• How can you solve a matrix? 

🎓 College Math Topics for a Paper

Sometimes you need more than just formulas to explain a complex idea. That’s why knowing how to express yourself is crucial. It is especially true for college-level mathematics. Consider the following ideas for your next research project:

• What do we need n-dimensional spaces for?
• Explain how card counting works.
• Discuss the difference between a discrete and a continuous probability distribution .
• How does encryption work?
• Describe extremal problems in discrete geometry.
• What can make a math problem unsolvable?
• Examine the topology of a Möbius strip.

• What is K-theory?  
• Discuss the core problems of computational geometry. 
• Explain the use of set theory . 
• What do we need Boolean functions for? 
• Describe the main topological concepts in modern mathematics. 
• Investigate the properties of a rotation matrix. 
• Analyze the practical applications of game theory.  
• How can you solve a Rubik’s cube mathematically? 
• Explain the math behind the Koch snowflake. 
• Describe the paradox of Gabriel’s Horn. 
• How do fractals form? 
• Find a way to solve Sudoku using math. 
• Why is the Riemann hypothesis still unsolved? 
• Discuss the Millennium Prize Problems. 
• How can you divide complex numbers? 
• Analyze the degrees in polynomial functions. 
• What are the most important concepts in number theory? 
• Compare the different types of statistical methods . 

🤔 Advanced Topics in Math to Write a Paper on

Once you have passed the trials of basic math, you can move on to the advanced section. This area includes topology, combinatorics, logic, and computational mathematics. Check out the list below for enticing topics to write about:

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• What is an abelian group?
• Explain the orbit-stabilizer theorem.
• Discuss what makes the Burnside problem influential.
• What fundamental properties do holomorphic functions have?
• How does Cauchy’s integral theorem lead to Cauchy’s integral formula?
• How do the two Picard theorems relate to each other?
• When is a trigonometric series called a Fourier series?
• Give an example of an algorithm used for machine learning .
• Compare the different types of knapsack problems.
• What is the minimum overlap problem?
• Describe the Bernoulli scheme.
• Give a formal definition of the Chinese restaurant process.
• Discuss the logistic map in relation to chaos .
• What do we need the Feigenbaum constants for?
• Define a difference equation.
• Explain the uses of the Fibonacci sequence.
• What is an oblivious transfer?
• Compare the Riemann and the Ruelle zeta functions.
• How can you use elementary embeddings in model theory?
• Analyze the problem with the wholeness axiom and Kunen’s inconsistency theorem.
• How is Lie algebra used in physics ?
• Define various cases of algebraic cycles.
• Why do we need étale cohomology groups to calculate algebraic curves?
• What does non-Euclidean geometry consist of?
• How can two lines be ultraparallel?

📚 Math Research Topics for a Paper

Choosing the right topic is crucial for a successful research paper in math. It should be hard enough to be compelling, but not exceeding your level of competence. If possible, stick to your area of knowledge. This way your task will become more manageable. Here are some ideas:

• Write about the history of calculus.
• Why are unsolved math problems significant?
• Find reasons for the gender gap in math students.
• What are the toughest mathematical questions asked today?
• Examine the notion of operator spaces.
• How can we design a train schedule for a whole country?
• What makes a number big?

• How can infinities have various sizes?
• What is the best mathematical strategy to win a game of Go?
• Analyze natural occurrences of random walks in biology.
• Explain what kind of mathematics was used in ancient Persia.
• Discuss how the Iwasawa theory relates to modular forms.
• What role do prime numbers play in encryption ?
• How did the study of mathematics evolve?
• Investigate the different Tower of Hanoi solutions.
• Research Napier’s bones. How can you use them?
• What is the best mathematical way to find someone who is lost in a maze?
• Examine the Traveling Salesman Problem. Can you find a new strategy?
• Describe how barcodes function.
• Study some real-life examples of chaos theory. How do you define them mathematically?
• Compare the impact of various ground-breaking mathematical equations .
• Research the Seven Bridges of Königsberg. Relate the problem to the city of your choice.
• Discuss Fisher’s fundamental theorem of natural selection.
• How does quantum computing work?
• Pick an unsolved math problem and say what makes it so difficult.

✏️ Math Education Research Topics

For many teachers, the hardest part is to keep the students interested. When it comes to math, it can be especially challenging. It’s crucial to make complicated concepts easy to understand. That’s why we need research on math education.

• Compare traditional methods of teaching math with unconventional ones.
• How can you improve mathematical education in the U.S.?
• Describe ways of encouraging girls to pursue careers in STEM fields.
• Should computer programming be taught in high school?
• Define the goals of mathematics education .
• Research how to make math more accessible to students with learning disabilities .
• At what age should children begin to practice simple equations?
• Investigate the effectiveness of gamification in algebra classes.
• What do students gain from taking part in mathematics competitions?
• What are the benefits of moving away from standardized testing ?
• Describe the causes of “ math anxiety .” How can you overcome it?
• Explain the social and political relevance of mathematics education.
• Define the most significant issues in public school math teaching.
• What is the best way to get children interested in geometry?
• How can students hone their mathematical thinking outside the classroom?
• Discuss the benefits of using technology in math class.
• In what way does culture influence your mathematical education?
• Explore the history of teaching algebra .
• Compare math education in various countries.

• How does dyscalculia affect a student’s daily life?
• Into which school subjects can math be integrated?
• Has a mathematics degree increased in value over the last few years?
• What are the disadvantages of the Common Core Standards ?
• What are the advantages of following an integrated curriculum in math?
• Discuss the benefits of Mathcamp.

🧮 Algebra Topics for a Paper

The elegance of algebra stems from its simplicity. It gives us the ability to express complex problems in short equations. The world was changed forever when Einstein wrote down the simple formula E=mc². Now, if your algebra seminar requires you to write a paper, look no further! Here are some brilliant prompts:

• Give an example of an induction proof.
• What are F-algebras used for?
• What are number problems?
• Show the importance of abstract algebraic thinking .
• Investigate the peculiarities of Fermat’s last theorem.
• What are the essentials of Boolean algebra?
• Explore the relationship between algebra and geometry.
• Compare the differences between commutative and noncommutative algebra.
• Why is Brun’s constant relevant?
• How do you factor quadratics?
• Explain Descartes’ Rule of Signs.
• What is the quadratic formula?
• Compare the four types of sequences and define them.
• Explain how partial fractions work.
• What are logarithms used for?
• Describe the Gaussian elimination.
• What does Cramer’s rule state?
• Explore the difference between eigenvectors and eigenvalues.
• Analyze the Gram-Schmidt process in two dimensions.
• Explain what is meant by “range” and “domain” in algebra.
• What can you do with determinants?
• Learn about the origin of the distance formula.
• Find the best way to solve math word problems.
• Compare the relationships between different systems of equations.
• Explore how the Rubik’s cube relates to group theory .

📏 Geometry Topics for a Research Paper

Shapes and space are the two staples of geometry. Since its appearance in ancient times, it has evolved into a major field of study. Geometry’s most recent addition, topology, explores what happens to an object if you stretch, shrink, and fold it. Things can get pretty crazy from here! The following list contains 25 interesting geometry topics:

• What are the Archimedean solids? 
• Find real-life uses for a rhombicosidodecahedron. 
• What is studied in projective geometry? 
• Compare the most common types of transformations. 
• Explain how acute square triangulation works. 
• Discuss the Borromean ring configuration. 
• Investigate the solutions to Buffon’s needle problem. 
• What is unique about right triangles? 

• Describe the notion of Dirac manifolds.
• Compare the various relationships between lines.
• What is the Klein bottle?
• How does geometry translate into other disciplines, such as chemistry and physics?
• Explore Riemannian manifolds in Euclidean space.
• How can you prove the angle bisector theorem?
• Do a research on M.C. Escher’s use of geometry.
• Find applications for the golden ratio .
• Describe the importance of circles.
• Investigate what the ancient Greeks knew about geometry.
• What does congruency mean?
• Study the uses of Euler’s formula.
• How do CT scans relate to geometry?
• Why do we need n-dimensional vectors?
• How can you solve Heesch’s problem?
• What are hypercubes?
• Analyze the use of geometry in Picasso’s paintings.

➗ Calculus Topics to Write a Paper on

You can describe calculus as a more complicated algebra. It’s a study of change over time that provides useful insights into everyday problems. Applied calculus is required in a variety of fields such as sociology, engineering, or business. Consult this list of compelling topics on a calculus paper:

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• What are the differences between trigonometry, algebra, and calculus?
• Explain the concept of limits.
• Describe the standard formulas needed for derivatives.
• How can you find critical points in a graph?
• Evaluate the application of L’Hôpital’s rule.
• How do you define the area between curves?
• What is the foundation of calculus?

• How does multivariate calculus work?
• Discuss the use of Stokes’ theorem.
• What does Leibniz’s integral rule state?
• What is the Itô stochastic integral?
• Explore the influence of nonstandard analysis on probability theory.
• Research the origins of calculus.
• Who was Maria Gaetana Agnesi?
• Define a continuous function.
• What is the fundamental theorem of calculus?
• How do you calculate the Taylor series of a function?
• Discuss the ways to resolve Runge’s phenomenon.
• Explain the extreme value theorem.
• What do we need predicate calculus for?
• What are linear approximations?
• When does an integral become improper?
• Describe the Ratio and Root Tests.
• How does the method of rings work?
• Where do we apply calculus in real-life situations?

💵 Business Math Topics to Write About

You don’t have to own a company to appreciate business math. Its topics range from credits and loans to insurance, taxes, and investment. Even if you’re not a mathematician, you can use it to handle your finances. Sounds interesting? Then have a look at the following list:

• What are the essential skills needed for business math?
• How do you calculate interest rates?
• Compare business and consumer math.
• What is a discount factor?
• How do you know that an investment is reasonable?
• When does it make sense to pay a loan with another loan?
• Find useful financing techniques that everyone can use.
• How does critical path analysis work?
• Explain how loans work.
• Which areas of work utilize operations research?
• How do businesses use statistics?
• What is the economic lot scheduling problem?
• Compare the uses of different chart types.
• What causes a stock market crash?
• How can you calculate the net present value?
• Explore the history of revenue management .
• When do you use multi-period models?
• Explain the consequences of depreciation.
• Are annuities a good investment?
• Would the U.S. financially benefit from discontinuing the penny?
• What caused the United States housing crash in 2008?
• How do you calculate sales tax?
• Describe the notions of markups and markdowns.
• Investigate the math behind debt amortization.
• What is the difference between a loan and a mortgage?

With all these ideas, you are perfectly equipped for your next math paper. Good luck!

• What Is Calculus?: Southern State Community College
• What Is Mathematics?: Tennessee Tech University
• What Is Geometry?: University of Waterloo
• What Is Algebra?: BBC
• Ten Simple Rules for Mathematical Writing: Ohio State University
• Practical Algebra Lessons: Purplemath
• Topics in Geometry: Massachusetts Institute of Technology
• The Geometry Junkyard: All Topics: Donald Bren School of Information and Computer Sciences
• Calculus I: Lamar University
• Business Math for Financial Management: The Balance Small Business
• What Is Mathematics: Life Science
• What Is Mathematics Education?: University of California, Berkeley
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Mathematics Extended Essay Topics for IB

Table of contents

• Writing Metier

Ever felt the exhilaration that comes with cracking a complex math problem? That’s the sheer beauty of mathematics – it’s a world where numbers dance, patterns emerge, and solutions await the keen observer. Felt that? Hah?

Now, imagine channeling that same enthusiasm and zest into your Math Extended essay. It might sound like a challenge, but isn’t that what we thrive on? With the right Math EE topic, you can showcase your mathematical prowess and leave an indelible mark on your IB evaluators following the general criteria. 

To help you with that, I’ve curated a list of Math extended essay ideas that span the spectrum from the accessible to the intricate. 

So, let’s begin.

IB Math extended essay ideas

These aren’t just topics; they’re gateways to exploration, understanding, and innovation. 

Ready to get started?

Easy-to-approach topics

For those looking for a gentler introduction to the Math Extended essay, below is a list of 10 engaging and manageable IB Math EE topic ideas, each with a research question and a brief description on how to approach it:

Patterns in Pascal’s Triangle

Research Question: 

How do patterns emerge in Pascal’s Triangle?

Description: 

Begin with the construction of Pascal’s Triangle, then delve into the exploration of its patterns, such as triangular numbers and the Fibonacci sequence.

Mathematics of Voting Systems

How do different voting systems weigh individual votes mathematically?

Introduce various voting systems, then analyze the mathematical principles behind each, discussing fairness and potential biases.

Geometry in Art

Research Question:  

How is geometry used to create visual appeal in art?

Explore various art pieces, highlighting the geometric principles employed, and discuss their impact on aesthetics.

The Math Behind Baking

How do ratios in baking recipes affect the final product?

Investigate the importance of maintaining specific ratios in baking recipes and experiment with variations to observe changes in outcomes.

Probability in Card Games

How does understanding probability enhance success in card games like Poker?

Delve into the rules of Poker and then analyze various hands and scenarios using probability principles.

Symmetry in Nature

How is symmetry exhibited in natural formations?

Explore the concept of symmetry mathematically and then identify and analyze its presence in various natural formations like leaves, flowers, and animals.

Mathematics of Music

How do mathematical patterns influence musical scales and rhythms?

Investigate the structure of musical scales, rhythms, and time signatures, highlighting the underlying mathematical patterns.

Simple Interest vs. Compound Interest

How do simple and compound interest methods impact savings over time?

Define both interest methods and then use mathematical modeling to compare their effects on savings over various periods.

The Golden Ratio in Architecture

How is the Golden Ratio applied in iconic architectural designs?

Introduce the concept of the Golden Ratio and then analyze its application in various famous architectural structures.

Mathematics of Juggling

How do mathematical patterns and sequences dictate juggling techniques?

Explore basic juggling techniques and patterns, analyzing the mathematical sequences that jugglers use to maintain rhythm and control.

Each of these topic ideas and RQs is approachable yet offers ample scope for exploration and analysis within the realm of mathematics.

Intermediate topics

For those seeking a bit more challenge without diving into the deep end, the topics below offer a balanced blend of complexity and accessibility.

Here’s a list of 10 average-difficulty IB Math Extended essay topics, each with a research question and a brief description of how to approach it:

Game Theory in Economics

How does game theory provide insights into competitive market behaviors?

Introduce game theory principles and use business world case studies to show strategic decision-making influenced by game theory.

Fractals and Nature

How do fractal patterns manifest in natural phenomena?

Description:  

Delve into the mathematical concept of fractals and explore their appearance in various natural settings, such as coastlines, mountains, and plants.

Mathematics of Population Growth Models

How do mathematical models accurately predict population growth in urban areas?

Introduce population growth models and use real urban area data to validate these models, discussing influencing factors.

Cryptography and Internet Security

How do modern cryptographic techniques ensure data security on the internet?

Explore the evolution of cryptography, focusing on modern techniques, and discuss their role in ensuring data security in online transactions.

Mathematical Modeling of Epidemics

How can mathematical models predict the spread of infectious diseases?

Introduce basic epidemiological models and analyze their effectiveness in predicting disease spread using real-world data.

Topology and Coffee Cups

How does topology explain the mathematical similarity between a coffee cup and a donut?

Dive into the basics of topology and use it to explain the often-cited comparison between coffee cups and donuts, emphasizing the concept of homeomorphism.

Chaos Theory and Weather Forecasting

How does chaos theory impact the accuracy of long-term weather forecasts?

Introduce chaos theory, then delve into its application in meteorology, discussing the challenges and limitations in predicting weather.

Mathematics Behind Neural Networks

How do mathematical algorithms drive the functioning of neural networks in artificial intelligence?

Explore the structure of neural networks and delve into the mathematical algorithms that enable their learning and functioning.

Optimization Problems in Logistics

How can mathematical optimization improve efficiency in supply chain logistics?

Investigate real-world logistics challenges and demonstrate how mathematical optimization techniques can offer solutions.

Number Theory in Modern Cryptography

How does advanced number theory underpin modern cryptographic techniques?

Delve into number theory concepts and their application in modern cryptographic methods, emphasizing their role in ensuring data security.

These topics and research questions offer a balanced blend of complexity and accessibility, making them suitable for students seeking a moderate challenge in their Math Extended essay.

Advanced topics (with potential for higher rewards)

For the brave hearts ready to dive deep, these topics are challenging but can yield impressive results when tackled effectively.

The list of 10 challenging IB Math Extended essay ideas, each with a research question and a brief description:

Navier–Stokes Existence and Smoothness

What are the mathematical implications of the unsolved Navier–Stokes existence and smoothness problem in fluid dynamics?

Delve deep into the Navier–Stokes equations, exploring their significance in fluid dynamics and the challenges surrounding their unsolved problems.

Riemann Hypothesis and Prime Numbers

How does the Riemann Hypothesis relate to the distribution of prime numbers?

Investigate the Riemann Hypothesis, its historical context, and its profound implications for the distribution of prime numbers.

Quantum Cryptography and Key Distribution

How does quantum cryptography enhance security in key distribution?

Explore the principles of quantum mechanics applied to cryptography, focusing on the advantages and challenges of quantum key distribution.

Elliptic Curves and Cryptography

How do elliptic curves underpin modern cryptographic techniques?

Dive into the mathematics of elliptic curves and their pivotal role in modern cryptographic algorithms.

Four Color Theorem and Graph Theory

How does the Four Color Theorem demonstrate the complexities of graph coloring?

Investigate the history and proof of the Four Color Theorem, discussing its implications and challenges in graph theory.

Complex Analysis in Quantum Mechanics

How does complex analysis influence the mathematical foundations of quantum mechanics?

Delve into the principles of complex analysis and explore their applications and significance in quantum mechanics.

Twin Prime Conjecture

What are the implications and challenges of the Twin Prime Conjecture in number theory?

Investigate the Twin Prime Conjecture, its history, and its significance in the realm of number theory.

Knot Theory and DNA Replication

How does knot theory provide insights into the process of DNA replication?

Explore the mathematical intricacies of knot theory and its applications in understanding the complexities of DNA replication.

Ergodic Theory and Thermodynamics

How does ergodic theory connect with the principles of statistical thermodynamics?

Dive deep into ergodic theory, exploring its foundational concepts and its connections to statistical thermodynamics.

Langlands Program and Number Theory

What is the Langlands Program, and how does it seek to unify different areas of mathematics?

Investigate the Langlands Program, its objectives, and its profound implications in unifying disparate areas of mathematics, particularly number theory.

These topics are undoubtedly challenging but can yield impressive results when tackled effectively. They offer a deep dive into complex mathematical concepts and theories, making them ideal for students aiming for the highest grades in their Math Extended essay.

Get extended essay help

Before continuing to the next block, I suggest our Math EE writing or editing services . Our company has been working with numerous IB students and helped them write custom IB extended essays.

Join a team of happy IB students who have followed the IB extended essay rubric and criteria and gained better results with Writing Metier and our Math assignments help !

Overused Math EE topics (proceed with caution)

While these topics are popular, they’ve been explored extensively. If you choose one, ensure you bring a fresh perspective:

• The Fibonacci Sequence in Nature.
• Pi and its Mysteries.
• The Monty Hall Problem.
• The Birthday Paradox.
• Exploring Pascal’s Triangle.
• The Mathematics of the Pyramids.
• The Tower of Hanoi Problem.
• Benford’s Law.
• The Four Color Theorem.
• The Mathematics of the Rubik’s Cube.

Keep in mind that selecting such a topic will require hard work to find a new custom angle of research and sometimes might not lead to higher grades .

In Conclusion

Alright, IB champs, that wraps up our curated selection of Math EE topics, each with its unique flavor and challenge. The topic is just the starting point. The real magic happens when you infuse it with your insights, analysis, and unique perspective. 

Mathematics isn’t just about numbers; it’s about stories and trips within the confines of equations and graphs. As you gear up to tackle your Extended essay, keep that passion alive, keep questioning, and most importantly, enjoy the process. 

Don’t forget to reserve extra space because it may take time to write an extended essay . And if you’re ever in doubt, remember that Writing Metier is here to guide you through every step of the process.

Free topic suggestions

Vasy kafidoff.

Vasyl Kafidoff is a co-founder and CEO at WritingMetier. He is interested in education and how modern technology makes it more accessible. He wants to bring awareness about new learning possibilities as an educational specialist. When Vasy is not working, he’s found behind a drum kit.

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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.

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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

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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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181 Mathematics Research Topics From PhD Experts

If you are reading this blog post, it means you are looking for some exceptional math research topics. You want them to be original, unique even. If you manage to find topics like this, you can be sure your professor will give you a top grade (if you write a decent paper, that is). The good news is that you have arrived at just the right place – at the right time. We have just finished updating our list of topics, so you will find plenty of original ideas right on this page. All our topics are 100 percent free to use as you see fit. You can reword them and you don’t need to give us any credit.

And remember: if you need assistance from a professional, don’t hesitate to reach out to us. We are not just the best place for math research topics for high school students; we are also the number one choice for students looking for top-notch research paper writing services.

Our Newest Research Topics in Math

We know you probably want the best and most recent research topics in math. You want your paper to stand out from all the rest. After all, this is the best way to get some bonus points from your professor. On top of this, finding some great topics for your next paper makes it easier for you to write the essay. As long as you know at least something about the topic, you’ll find that writing a great paper or buy phd thesis isn’t as difficult as you previously thought.

So, without further ado, here are the 181 brand new topics for your next math research paper:

Cool Math Topics to Research

Are you looking for some cool math topics to research? We have a list of original topics for your right here. Pick the one you like and start writing now:

• Roll two dice and calculate a probability
• Discuss ancient Greek mathematics
• Is math really important in school?
• Discuss the binomial theorem
• The math behind encryption
• Game theory and its real-life applications
• Analyze the Bernoulli scheme
• What are holomorphic functions and how do they work?
• Describe big numbers
• Solving the Tower of Hanoi problem

Undergraduate Math Research Topics

If you are an undergraduate looking for some research topics for your next math paper, you will surely appreciate our list of interesting undergraduate math research topics:

• Methods to count discrete objects
• The origins of Greek symbols in mathematics
• Methods to solve simultaneous equations
• Real-world applications of the theorem of Pythagoras
• Discuss the limits of diffusion
• Use math to analyze the abortion data in the UK over the last 100 years
• Discuss the Knot theory
• Analyze predictive models (take meteorology as an example)
• In-depth analysis of the Monte Carlo methods for inverse problems
• Squares vs. rectangles (compare and contrast)

Number Theory Topics to Research

Interested in writing about number theory? It is not an easy subject to discuss, we know. However, we are sure you will appreciate these number theory topics:

• Discuss the greatest common divisor
• Explain the extended Euclidean algorithm
• What are RSA numbers?
• Discuss Bézout’s lemma
• In-depth analysis of the square-free polynomial
• Discuss the Stern-Brocot tree
• Analyze Fermat’s little theorem
• What is a discrete logarithm?
• Gauss’s lemma in number theory
• Analyze the Pentagonal number theorem

Math Research Topics for High School

High school students shouldn’t be too worried about their math papers because we have some unique, and quite interesting, math research topics for high school right here:

• Discuss Brun’s constant
• An in-depth look at the Brahmagupta–Fibonacci identity
• What is derivative algebra?
• Describe the Symmetric Boolean function
• Discuss orders of approximation in limits
• Solving Regiomontanus’ angle maximization problem
• What is a Quadratic integral?
• Define and describe complementary angles
• Analyze the incircle and excircles of a triangle
• Analyze the Bolyai–Gerwien theorem in geometry
• Math in our everyday life

Complex Math Topics

If you want to give some complex math topics a try, we have the best examples below. Remember, these topics should only be attempted by students who are proficient in mathematics:

• Mathematics and its appliance in Artificial Intelligence
• Try to solve an unsolved problem in math
• Discuss Kolmogorov’s zero-one law
• What is a discrete random variable?
• Analyze the Hewitt–Savage zero-one law
• What is a transferable belief model?
• Discuss 3 major mathematical theorems
• Describe and analyze the Dempster-Shafer theory
• An in-depth analysis of a continuous stochastic process
• Identify and analyze Gauss-Markov processes

Easy Math Research Paper Topics

Perhaps you don’t want to spend too much time working on your next research paper. Who can blame you? Check out these easy math research paper topics:

• Define the hyperbola
• Do we need to use a calculator during math class?
• The binomial theorem and its real-world applications
• What is a parabola in geometry?
• How do you calculate the slope of a curve?
• Define the Jacobian matrix
• Solving matrix problems effectively
• Why do we need differential equations?
• Should math be mandatory in all schools?
• What is a Hessian matrix?

Logic Topics to Research

We have some interesting logical topics for research papers. These are perfect for students interested in writing about math logic. Pick one right now:

• Discuss the reductio ad absurdum approach
• Discuss Boolean algebra
• What is consistency proof?
• Analyze Trakhtenbrot’s theorem (the finite model theory)
• Discuss the Gödel completeness theorem
• An in-depth analysis of Morley’s categoricity theorem
• How does the Back-and-forth method work?
• Discuss the Ehrenfeucht–Fraïssé game technique
• Discuss Aleph numbers (Aleph-null and Aleph-one)
• Solving the Suslin problem

Algebra Topics for a Research Paper

Would you like to write about an algebra topic? No problem, our seasoned writers have compiled a list of the best algebra topics for a research paper:

• Discuss the differential equation
• Analyze the Jacobson density theorem
• The 4 properties of a binary operation in algebra
• Analyze the unary operator in depth
• Analyze the Abel–Ruffini theorem
• Epimorphisms vs. monomorphisms: compare and contrast
• Discuss the Morita duality in algebraic structures
• Idempotent vs. nilpotent in Ring theory
• Discuss the Artin-Wedderburn theorem
• What is a commutative ring in algebra?
• Analyze and describe the Noetherian ring

Math Education Research Topics

There is nothing wrong with writing about math education, especially if your professor did not give you writing prompts. Here are some very nice math education research topics:

• What are the goals a mathematics professor should have?
• What is math anxiety in the classroom?
• Teaching math in UK schools: the difficulties
• Computer programming or math in high school?
• Is math education in Europe at a high enough level?
• Common Core Standards and their effects on math education
• Culture and math education in Africa
• What is dyscalculia and how does it manifest itself?
• When was algebra first thought in schools?
• Math education in the United States versus the United Kingdom

Computability Theory Topics to Research

Writing about computability theory can be a very interesting adventure. Give it a try! Here are some of our most interesting computability theory topics to research:

• What is a multiplication table?
• Analyze the Scholz conjecture
• Explain exponentiating by squaring
• Analyze the Myhill-Nerode theorem
• What is a tree automaton?
• Compare and contrast the Pushdown automaton and the Büchi automaton
• Discuss the Markov algorithm
• What is a Turing machine?
• Analyze the post correspondence problem
• Discuss the linear speedup theorem
• Discuss the Boolean satisfiability problem

Interesting Math Research Topics

We know you want topics that are interesting and relatively easy to write about. This is why we have a separate list of our most interesting math research topics:

• What is two-element Boolean algebra?
• The life of Gauss
• The life of Isaac Newton
• What is an orthodiagonal quadrilateral?
• Tessellation in Euclidean plane geometry
• Describe a hyperboloid in 3D geometry
• What is a sphericon?
• Discuss the peculiarities of Borel’s paradox
• Analyze the De Finetti theorem in statistics
• What are Martingales?
• The basics of stochastic calculus

Applied Math Research Topics

Interested in writing about applied mathematics? Our team managed to create a list of awesome applied math research topics from scratch for you:

• Discuss Newton’s laws of motion
• Analyze the perpendicular axes rule
• How is a Galilean transformation done?
• The conservation of energy and its applications
• Discuss Liouville’s theorem in Hamiltonian mechanics
• Analyze the quantum field theory
• Discuss the main components of the Lorentz symmetry
• An in-depth look at the uncertainty principle

Geometry Topics for a Research Paper

Geometry can be a very captivating subject, especially when you know plenty about it. Check out our list of geometry topics for a research paper and pick the best one today:

• Most useful trigonometry functions in math
• The life of Archimedes and his achievements
• Trigonometry in computer graphics
• Using Vincenty’s formulae in geodesy
• Define and describe the Heronian tetrahedron
• The math behind the parabolic microphone
• Discuss the Japanese theorem for concyclic polygons
• Analyze Euler’s theorem in geometry

Math Research Topics for Middle School

Yes, even middle school children can write about mathematics. We have some original math research topics for middle school right here:

• Finding critical points in a graph
• The basics of calculus
• What makes a graph ultrahomogeneous?
• How do you calculate the area of different shapes?
• What contributions did Euclid have to the field of mathematics?
• What is Diophantine geometry?
• What makes a graph regular?
• Analyze a full binary tree

Math Research Topics for College Students

As you’ve probably already figured out, college students should pick topics that are a bit more complex. We have some of the best math research topics for college students right here:

• What are extremal problems and how do you solve them?
• Discuss an unsolvable math problem
• How can supercomputers solve complex mathematical problems?
• An in-depth analysis of fractals
• Discuss the Boruvka’s algorithm (related to the minimum spanning tree)
• Discuss the Lorentz–FitzGerald contraction hypothesis in relativity
• An in-depth look at Einstein’s field equation
• The math behind computer vision and object recognition

Calculus Topics for a Research Paper

Let’s face it: calculus is not a very difficult field. So, why don’t you pick one of our excellent calculus topics for a research paper and start writing your essay right away:

• When do we need to apply the L’Hôpital rule?
• Discuss the Leibniz integral rule
• Calculus in ancient Egypt
• Discuss and analyze linear approximations
• The applications of calculus in real life
• The many uses of Stokes’ theorem
• Discuss the Borel regular measure
• An in-depth analysis of Lebesgue’s monotone convergence theorem

Simple Math Research Paper Topics for High School

This is the place where you can find some pretty simple topics if you are a high school student. Check out our simple math research paper topics for high school:

• The life and work of the famous Pierre de Fermat
• What are limits and why are they useful in calculus?
• Explain the concept of congruency
• The life and work of the famous Jakob Bernoulli
• Analyze the rhombicosidodecahedron and its applications
• Calculus and the Egyptian pyramids
• The life and work of the famous Jean d’Alembert
• Discuss the hyperplane arrangement in combinatorial computational geometry
• The smallest enclosing sphere method in combinatorics

Business Math Topics

If you want to surprise your professor, why don’t you write about business math? We have some exceptional topics that nobody has thought about right here:

• Is paying a loan with another loan a good approach?
• Discuss the major causes of a stock market crash
• Best debt amortization methods in the US
• How do bank loans work in the UK?
• Calculating interest rates the easy way
• Discuss the pros and cons of annuities
• Basic business math skills everyone should possess
• Business math in United States schools
• Analyze the discount factor

Probability and Statistics Topics for Research

Probability and statistics are not easy fields. However, you can impress your professor with one of our unique probability and statistics topics for research:

• What is the autoregressive conditional duration?
• Applying the ANOVA method to ranks
• Discuss the practical applications of the Bates distribution
• Explain the principle of maximum entropy
• Discuss Skorokhod’s representation theorem in random variables
• What is the Factorial moment in the Theory of Probability?
• Compare and contrast Cochran’s C test and his Q test
• Analyze the De Moivre-Laplace theorem
• What is a negative probability?

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