math related essay

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.

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:

• 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:

• 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:

• 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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What I Like About Math: 5 Best Essay Examples

Mathematics is often seen as a challenging subject, yet it has a captivating side that many come to appreciate. From the elegance of equations to the joy of problem-solving, math holds a special place for those who engage with its beauty. In this article, we’ll explore what makes math fascinating through five essay examples that you can use as inspiration for your own writing.

• Why People Love Math

The Beauty of Patterns and Structures

At its core, math is about recognizing patterns and understanding structures. Whether it’s the symmetry of a snowflake or the geometric precision of a crystal, math unlocks the secrets of nature’s designs. Take the Fibonacci sequence, for instance, with its presence in flowers, shells, and galaxies. Recognizing these patterns can evoke a sense of wonder and connection to the universe's grand design.

Problem-Solving Thrills

For many, the thrill of solving a challenging problem is unparalleled. The satisfaction of deciphering a complex equation or proving a theorem provides a rush that’s akin to completing a tough puzzle. It's this challenge that keeps the mind engaged and continually growing.

Practical Applications

Math isn’t just abstract; it’s incredibly practical. From calculating tips at a restaurant to engineering marvels like bridges and skyscrapers, math’s applications are vast and varied. Its utility in everyday life makes it an indispensable skill.

• What is a Good Math Essay?

A good math essay isn’t just about numbers and equations; it’s a narrative that conveys your passion for the subject. Here are some key elements to consider:

Engaging Introduction

Start with a hook that grabs the reader’s attention. You might open with a compelling quote, an interesting fact, or a personal anecdote that highlights your connection to math.

Clear Thesis Statement

Your thesis should succinctly state what you love about math and lay the groundwork for your arguments. This central idea will guide the rest of your essay.

Personal Insights

Share your personal experiences and insights that demonstrate your appreciation for math. Whether it’s a memorable moment in a math class or a particular concept that excites you, personal stories make your essay more relatable.

Logical Structure

Organize your essay logically. Use clear headings and subheadings to guide the reader through your thoughts. Each paragraph should flow naturally into the next.

Strong Conclusion

Summarize your key points and restate your thesis in a way that reinforces the message of your essay. Leave the reader with something to ponder.

• Essay Example 1: The Joy of Discovery

Introduction

Mathematics has always been a subject of discovery for me. From the moment I first solved a simple addition problem to understanding complex calculus equations, each step has been a journey filled with excitement and joy. This essay explores the reasons why I find math so intriguing.

Personal Engagement

Growing up, puzzles and brain teasers were my favorite pastime. Math felt like an extension of these activities, offering endless problems to solve and mysteries to uncover. Whether it was through games or formal education, math kept my curiosity alive.

The Challenge

The challenges posed by mathematical problems are exhilarating. Every equation is a puzzle waiting to be solved, and every theorem is a mystery waiting to be proved. The struggle and eventual triumph provide a unique sense of accomplishment.

Practical Benefits

Understanding math has practical benefits. It sharpens analytical thinking and enhances problem-solving skills, which are essential in everyday life. From calculating expenses to making informed decisions, math plays a vital role.

In conclusion, math is much more than numbers and formulas. It’s a world of discovery, challenge, and practicality. My love for math continues to grow as I delve deeper into its complexities and applications.

• Essay Example 2: Math and Its Artistic Beauty

Art and math may seem like polar opposites, but they share a profound connection. This essay explores the artistic beauty of mathematics and how it has influenced my perspective on both disciplines.

Patterns in Nature

Mathematics is the language of nature’s patterns. From the spirals of galaxies to the symmetry of leaves, math explains the aesthetic structures we observe. This connection between math and nature’s beauty has always fascinated me.

Geometric Art

Geometric art is an excellent example of the confluence between math and creativity. Artists like M.C. Escher have used mathematical principles to create visually stunning works that challenge perceptions and captivate minds.

Symmetry and Proportion

Symmetry and proportion are core principles in both math and art. The Golden Ratio, for instance, is a mathematical concept that has been used in art and architecture for centuries, creating balance and harmony in design.

Math’s artistic beauty lies in its ability to explain and create patterns and structures. This intersection of disciplines has deepened my appreciation for both art and math, revealing the elegance that lies in their union.

• Essay Example 3: The Universality of Math

Mathematics is a universal language that transcends cultural and linguistic barriers. This essay examines how math connects people across the globe and why this universality makes it so appealing to me.

A Common Language

No matter where you go, mathematical principles remain the same. This consistency allows people from different backgrounds to communicate and collaborate effortlessly. Math bridges gaps that words cannot.

Historical Connections

Throughout history, civilizations have contributed to the development of math. From ancient Egypt to modern-day scientists, the collective effort to understand math has connected humanity through time and space.

Modern Technology

Today's technology relies heavily on math. Computers, smartphones, and the internet—all functions on mathematical principles. This universality brings us closer, creating a technologically connected world.

Math's universality is a testament to its power to unite. Its principles are consistent across cultures, making it a shared language that connects us all. This global reach is one of the many reasons I love math.

• Essay Example 4: The Logical Nature of Math

The logical structure of mathematics is both fascinating and reassuring. This essay delves into the logical aspects of math and why they resonate with me so deeply.

Clear and Definitive

Math offers clear and definitive answers. Unlike subjective disciplines, where interpretations vary, math provides certainty. This clarity is comforting and appealing.

Logical Progression

Mathematical concepts build logically, each one laying the foundation for the next. This structured progression makes learning math a coherent and systematic process, enhancing comprehension and enjoyment.

Critical Thinking

Math sharpens critical thinking. It trains the mind to analyze, reason, and solve problems systematically. These skills are invaluable and extend beyond math into everyday decision-making.

The logical nature of math is one of its most compelling aspects. Its clarity, structured progression, and emphasis on critical thinking make it a rewarding subject to study and appreciate.

Essay Example 5: Math's Role in Innovation

Math is a driving force behind innovation and technological advancement. This essay explores the crucial role math plays in fostering innovation and why this aspect makes it so appealing.

Technological Advancements

From the development of algorithms to artificial intelligence, math is at the heart of technological progress. Its principles are applied to solve complex problems and create groundbreaking solutions.

Engineering Marvels

Engineering, which relies heavily on math, has brought about incredible advancements. Bridges, skyscrapers, and space exploration all owe their existence to mathematical calculations and theories.

Future Prospects

The future of innovation continues to depend on math. Emerging fields like quantum computing and nanotechnology are grounded in mathematical theories. Being part of this exciting progression is both motivating and fascinating.

Math’s role in innovation is undeniable. Its principles drive technological progress and pave the way for future advancements. This critical role is a significant reason for my ongoing interest and enthusiasm for math.

• Wrap-up: The Multifaceted Appeal of Math

Math's appeal is multifaceted, drawing people for various reasons—its beauty, challenge, practicality, universality, logical structure, and role in innovation, to name a few. Whether you see patterns in nature or enjoy solving complex puzzles, math offers something for everyone. Through these essay examples, it's clear that math is not just a subject but a passion that many holds dear. Its influence spans from everyday applications to groundbreaking innovations, making it a truly fascinating and invaluable field of study.

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We’ll explore a personal essay, how you can write one, and what admissions officers seek when they read your personal statement. We’ll also look at the current Common App essay prompts so you can prepare to write a stellar essay ahead of time. We’ll also cover some examples of what your personal statement might look like. Are you ready? Let’s start with the most critical question: what is a personal statement?

• Essay Example 5: Math's Role in Innovation

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

writing good math essay

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

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

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

Why Write About Mathematics

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

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

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

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

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

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

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

 25 Interesting Math Topics to Write On

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

How to Write a Good Math Essay

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

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

1. Understanding the Essay Prompt

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

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

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

2. Research and Gather Information

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

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

3. Structuring Your Math Essay

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

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

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

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

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

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

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

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

4. Proofreading and Editing

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

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

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

5. Presentation and Formatting

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

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

6. Mathematical Notation and Symbols

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

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

7. Seek Clarification

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

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

8. Practice and Feedback

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

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

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

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

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How to Write a Math Extended Essay? A Comprehensive Guide

Ah, the Math extended essay! It’s an excellent opportunity for students in the IB program to showcase their knack for numbers. From my experience, crafting an impactful essay requires mathematical talent and a solid understanding of what makes a paper genuinely resonate.

Throughout this article, you’ll find gems on selecting Math extended essay topics , how to structure your essay, and even some common pitfalls to avoid. So, let’s jump right in, shall we?

What is a Math Extended Essay?

You may be pondering, “What is a Math extended essay?” According to the IB criteria, this piece is a 4,000-word research document that prompts students to research a mathematical topic of interest thoroughly. It’s not just an ordinary research paper; think of it as your gateway to mastering a subject you’re genuinely passionate about. Trust me, from my experience, it’s a pivotal component of your academic growth.

Let’s clarify further. Math extended essay isn’t just a routine school assignment you might complete on a typical day. Instead, it’s a comprehensive exploration of a distinct topic within Mathematics. But remember, it’s not all about numbers or equations. It’s about showcasing your ability to reason, analyze, and communicate your findings in writing.

Here are all the critical elements of a top-notch Math extended essay :

• Clear Thesis . A strong paper begins with a defined proposition or statement set for investigation.
• Thorough Research . Look into reputable sources, journals, and academic papers. Absorb as much relevant information as possible.
• Logical Flow . Your essay should transition smoothly from one topic to the next, ensuring readers can follow your train of thought easily.
• In-depth Analysis . Beyond stating facts, analyze them critically and draw your conclusions.
• Personal Touch . Reflect on your genuine interest and connection with the topic.
• Effective Expression . Aim for clarity in your writing, ensuring readers can quickly grasp your points.
• Ethical Standards . Properly cite all your sources and avoid any form of plagiarism.
• Reflection . Share insights on your learning process, the challenges faced, and the strategies you employed to address them.

So, you might wonder, “Why take on such a demanding task?” Here’s the thing: based on what I’ve learned and observed, the Math extended essay plays a significant role in the IB program. It’s essential for obtaining your IB diploma and can significantly enhance your college application. More importantly, it’s an opportunity to challenge yourself academically, fostering intellectual growth.

Committing to this task and seeing it through will be a significant academic accomplishment. Best of luck!

Getting Started with Your Math Extended Essay

The inception of any great essay starts with topic selection and understanding the guidelines, naturally.

Topic Selection

Choosing the right topic is the first milestone. Think about the Mathematical areas that captivate your interest. Whether it’s the logic of algebra, the complexity of calculus, or any other field, there’s a vast Mathematical universe to explore. While broad subjects might seem tempting, concentrating on specific IB Math extended essay topics is often more effective. Your issue should be clear-cut and straightforward and uphold strong academic integrity in line with IB standards.

Understanding Guidelines

After settling on a topic, it’s essential to acquaint yourself with the IB’s precise expectations . From my experience, grasping these guidelines is foundational to the essay’s success:

• The IB has detailed guidelines regarding the structure and layout of extended essays. Ensure you’re well-versed in font choice, spacing, and the like.
• While the IB often leans towards MLA or APA citation styles, be sure to check the style preferred by your institution. Accurate citations aren’t just about avoiding plagiarism; they lend authenticity to your work.
• IB evaluates your extended essay based on distinct criteria, such as clarity, depth of knowledge, presentation, and personal connection to the topic. Familiarizing yourself with these parameters can guide your research and writing trajectory.
• The extended essay process in the IB program includes consultations with a designated supervisor. These sessions are golden opportunities to glean insights and refine your approach.

In essence, the proper groundwork ensures a smoother path ahead. With a compelling topic and a robust grasp of the IB guidelines, you’re primed to craft a stellar Math extended essay. Embrace the process and aim for excellence!

Math Extended Essay: Research and Planning

Research is the backbone of your essay! Adequate preparation is necessary for a subject as complex and layered as Math.

Behind every successful essay is a bedrock of meticulous research and detailed planning. Given the intricate nature of Mathematics, gathering your tools and strategies is paramount before plunging into the writing phase. First, seek out robust platforms that offer a plethora of verified information :

• Online Databases . Websites like JSTOR , Google Scholar , and MathSciNet host a rich collection of articles, papers, and journals dedicated to Mathematics.
• Academic Journals . Publications such as the “American Journal of Mathematics” or the “European Journal of Mathematics” provide peer-reviewed papers on many topics.
• University Libraries . Many universities offer access to their digital libraries, which can be goldmines for in-depth research.
• Professors and Mentors . Never underestimate the power of a conversation. Sometimes, discussing your topic with experts can lead to new insights and perspectives.

Remember, the depth and breadth of your research directly influence the strength of your arguments. Always verify the authenticity of your sources; a well-researched essay stands tall among its peers.

Timeline for Writing Math Extended Essay

Managing time is a lifesaver in the whirlwind of IB coursework, deadlines, and extracurriculars. Crafting a detailed timeline ensures you stay on track and prevents last-minute scrambles.

• Exploration . Dedicate the initial phase to exploring potential topics, understanding guidelines, and preliminary reading.
• Intensive Research . This phase involves deep diving into your chosen topic, gathering data, and organizing your findings.
• Drafting . Begin with an initial draft. Lay down your arguments, flesh out your thoughts, and structure your content.
• Review and Refinement . Revisit your draft, make necessary revisions, and incorporate feedback from peers or mentors.
• Finalization . Proofread, ensure adherence to guidelines, and prepare for submission.

Breaking down your process into manageable chunks alleviates stress and enhances the quality of your work.

Need help with your IB extended essay?

From research and analysis to structuring and editing, our skilled mentors will be by your side, helping you craft an exceptional extended essay that not only meets the wordcount and stringent IB criteria but also reflects your passion for selected IB group .

To wrap it up, remember that while the task might seem daunting, meticulous research and detailed planning are your allies. Harness them wisely; your Math extended essay will meet and exceed expectations. Happy researching!

Structuring Your Math Extended Essay

Organization is key, folks! How you structure your essay could make or break your grade.

Introduction

Your introduction should present the issue you’re investigating, why it matters, and how you plan to tackle it. This part is the roadmap of your essay; it sets the tone for the reader.

In this section, present your research, arguments, and findings. Dabble in some theory, show your equations or models, and remember to analyze their relevance. As you go, remember to build a logical flow. Use transition words to guide your reader through your discussion.

It is where you tie all your findings together. A well-crafted conclusion leaves a lasting impression, briefly highlighting your significant discoveries and their implications.

Math Extended Essay: Common Mistakes to Avoid

When creating an essay of the caliber expected for the IB program, the devil is often in the details. Many students have sailed through the bulk of their paper writing only to stumble near the finish line due to seemingly minor oversights. Awareness of these pitfalls is essential, especially in an undertaking as significant as the Math extended essay.

A common trap that students often fall into is vagueness. One might use ambiguous phrases or general statements to sound sophisticated or cover a wide range of ideas. Instead of making broad claims, focus on your main idea and flesh it out with detail and precision. 

Another critical area that cannot be overemphasized is plagiarism. While it’s tempting to borrow a perfectly phrased sentence or a well-structured argument, doing so without proper attribution is academically dishonest and can jeopardize your entire essay. When in doubt, always give credit where credit is due.

Another often overlooked aspect is the flow and structure of the essay. Transitioning smoothly from one point to the next, ensuring that each segment of your paper leads seamlessly into the next, can make a difference in your work’s overall quality and readability.

Review and Revision in Math Extended Essay

One of the most powerful tools in this phase is peer review. While you’ve been deeply engrossed in your essay and every argument, equation, and citation, there’s immense value in having another set of eyes scan your work. It doesn’t necessarily mean someone who’s an expert in your topic but can provide a fresh perspective. They can identify areas that might be unclear to a new reader.

Following peer review, there’s the intricate task of editing and proofreading. While these terms are often used interchangeably, they serve distinct purposes. Editing is all about refining the content. Proofreading, on the other hand, is about the nitty-gritty. It ensures that your grammar is spot-on and that there are no misplaced punctuations.

In all of this, reflection is a vital element often overlooked. Taking a step back, setting your essay aside for a day or two, and returning to it with renewed vigor is immensely beneficial. With a fresh mindset, you might find new angles to consider or realize there are redundant points that can be removed.

To Sum It Up

Writing a Math extended essay can be challenging but also incredibly rewarding. So, according to general IB criteria and years of personal experience, the time and effort you invest in this project will be well worth it. Good luck, young scholars!

Luke MacQuoid

Luke MacQuoid has extensive experience teaching English as a foreign language in Japan, having worked with students of all ages for over 12 years. Currently, he is teaching at the tertiary level. Luke holds a BA from the University of Sussex and an MA in TESOL from Lancaster University, both located in England. As well to his work as an IB Examiner and Master Tutor, Luke also enjoys sharing his experiences and insights with others through writing articles for various websites, including extendedessaywriters.com blog

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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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Getting cheap online help with research papers has never been easier. College students should just get in touch with us and tell us what they need. We will assign them our most affordable and experienced math writer in minutes, even during the night. We are the best-rated online writing company on the Internet because we always deliver high-quality academic content at the most competitive prices. Give us a try today!

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Math Essay Examples and Topics

Mathematics: discovered or created, the importance of geometry in our daily life.

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Debate on Mathematics: An Art or a Science

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History of Algebra Brief Overview

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Spatial Modeling: Types, Pros and Cons

Parabolas and their application in the real life, statistics: chi-square test and regression analysis.

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Statistics Abuse: How, Why, and When

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Measurements’ Standarts

The life and works of archimedes.

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Mathematical Analysis of the Pyramid of the Louvre

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Pythagorean Theorem: History, Formula, and Proof

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Mathematics: The Language of Nature

Correlation.

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Order of Operations: Connecting to Real Life

Leonardo pisano fibonacci’s life and contributions, the value of mathematics in antonsen’s ted talk, arthur cayley: life, career, and achievements, oblique triangles in everyday life, the use of polynomials in the real world, linear equations comprehensive study, sofia kovalevskaya’s contributions to math, math functions in economics.

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Construction of Regular Polygons: Octagon

Quantitative approach to research, fibonacci sequence and related mathematical concepts.

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Mathematics – Concept of Multiplication

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Mathematical and Statistical Investigation

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Algebra in the Real World and Everyday Life

Pythagoras theories.

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Exponential and Logarithmic Functions

Problem solving process in mathematics, the formal mathematical language and its importance, the use of mathematics in advertisements, optimizing the cross-section of a gutter, bouncing ball as an example of a conic section, fourier transform: the behavior of the image in the frequency domain.

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Reflection on Statistics Learning Goals

Fundamental theorem of calculus in modern world, importance of math during trip from us to japan, implicit differentiation in the business sector, practical usages of scientific notation, data results of statistics, quantitative data analysis, the discipline of criminal justice: the use of mathematics, mathematical explorations: quantitative reasoning, compound interest as mathematical fact.

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Number Theory and Major Contributors to the Field

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Applications of Algebraic Functions in an Environmental Agency

Historical data analysis: various variables trends.

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Qualitative Research Method Analysis

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History of Pythagoras Theorem

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Sir Isaac Newton Mathematical Theory

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History of Calculus: Brief Review One of the Branches of Mathematics

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Math Essay Writing Guide

It is often met that students feel wondered when they are asked to write essays in math classes. Actually, the tasks of math essay writing want to make students demonstrate their knowledge and understanding of mathematical concepts and ideas.

This kind of essay is what students of both college and high school students can be asked to create. Yes, this type of writing is quite special, and having its own tricks and demands. Still, guides for writing a math essay is mostly the same as for those of other subjects.

If you think you do not have enough time or skill to complete a math essay on your own, remember about the possibility to ask for essay help online .

Set Up Your Topic

Just like any other essay, math writing is to be started from choosing a topic. Here are several possible ways to go. First one wants you to choose any mathematical concept that seems to be interesting for you, like one of those you discussed with a teacher and classmates and want to investigate it a bit deeper. Another way is, you can choose any math problem you have solved in the past.

For this type of writing, you show up a problem, and then show your way towards solving it and getting the right answer. Whatever the type of essay is, you need to provide a brainstorm and find the topic worrying your mind the most, as to write about something you need to research it seriously. For instance think about any particular concept or equation of mathematics you would like to spend a bit more time to investigate, and then note your thoughts on a paper.

Consider the Audience

Thinking about the audience that is going to read your essay is a must for any essay, same thing goes for math paper writing. Mathematician P. R. Halmos offers the way to think about the particular person while writing an essay, in the text of his article “How to Write Mathematics”.

Halmos says it is good to think about someone who has math ways that “can stand mending”. To say in other words, when writing an essay, do not try jumping above your head and write the text for the audience that has the same skill in math as you do. Yes, you write a math essay in order to present the idea or to explain a problem solution. But still, you want to prove your method to be the best one. Try convincing the reader in that, and the essay is guaranteed to be interesting.

Concept Essay in Math

In case of math, concept essays look similar to those for other classes. In fact, you need to write a regular expository essay to complete your task. To do that, you research a certain math concept, analyze it, then form and develop your upcoming theoretical ideas basing on the experience and knowledge you could get when providing the investigation, and then claim it as a usual thesis statement.

Start writing your essay with the intro, importing the topic through it. include your claim about the theory there. The, you need to develop your claim in the further text, and to present reliable evidences you found during the research to prove your viewpoint. Write a conclusion, tie up any loose ends and readdress your theoretical info according to the way how it was provided before.

Math Equation Essay

To complete an equation essay successfully, you should show up the problem and solution at once, in the essay intro. Then, explain the problem significance and factors that made you choose your certain way towards the solution. Both significance and rationale are the same with a thesis statement, they serve as the base ground for your argumentation here.

Compose a paragraph that clearly shows the reader how to solve the problem according to your vision, make a “how-to” user guide for the chosen problem. If the problem is complex, set up a helpful graph that could demonstrate your equation result. Explain what can be seen on that graph. Same thing: define variables carefully and precisely with sentences like “Let’s think n is any real number.” Show up your problem solving methodical, guide the reader through the used formulas and explain why you used exactly those ones.

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How mathematical practices can improve your writing

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

Caroline Yoon

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

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

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

Three mathematical practices that can improve your writing

Mathematical modelling.

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

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

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

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

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

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Problem-solving

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

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

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

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

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

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

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

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

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

Practical tips for productive writing beliefs and behaviours

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

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

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

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How to Apply a Mathematical Approach to Essay Writing

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

Beneficial Impact on Your Writing

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

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

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

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

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

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

Where It Will Come in Very Handy

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

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

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

Math Techniques to Apply in Writing Papers

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

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

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

A Few More Things to Consider

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

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

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

Final Thoughts

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

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

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Essay on Importance of Mathematics in our Daily Life in 100, 200, and 350 words.

• Updated on  
• Dec 22, 2023

Mathematics is one of the core aspects of education. Without mathematics, several subjects would cease to exist. It’s applied in the science fields of physics, chemistry, and even biology as well. In commerce accountancy, business statistics and analytics all revolve around mathematics. But what we fail to see is that not only in the field of education but our lives also revolve around it. There is a major role that mathematics plays in our lives. Regardless of where we are, or what we are doing, mathematics is forever persistent. Let’s see how maths is there in our lives via our blog essay on importance of mathematics in our daily life. 

Table of Contents

• 1 Essay on Importance of Mathematics in our Daily life in 100 words 
• 2 Essay on Importance of Mathematics in our Daily life in 200 words
• 3 Essay on Importance of Mathematics in our Daily Life in 350 words

Essay on Importance of Mathematics in our Daily life in 100 words 

Mathematics is a powerful aspect even in our day-to-day life. If you are a cook, the measurements of spices have mathematics in them. If you are a doctor, the composition of medicines that make you provide prescription is made by mathematics. Even if you are going out for just some groceries, the scale that is used for weighing them has maths, and the quantity like ‘dozen apples’ has maths in it. No matter the task, one way or another it revolves around mathematics. Everywhere we go, whatever we do, has maths in it. We just don’t realize that. Maybe from now on, we will, as mathematics is an important aspect of our daily life.

Also Read:- Importance of Internet

Essay on Importance of Mathematics in our Daily life in 200 words

Mathematics, as a subject, is one of the most important subjects in our lives. Irrespective of the field, mathematics is essential in it. Be it physics, chemistry, accounts, etc. mathematics is there. The use of mathematics proceeds in our daily life to a major extent. It will be correct to say that it has become a vital part of us. Imagining our lives without it would be like a boat without a sail. It will be a shock to know that we constantly use mathematics even without realising the same. 

From making instalments to dialling basic phone numbers it all revolves around mathematics. 

Let’s take an example from our daily life. In the scenario of going out shopping, we take an estimate of hours. Even while buying just simple groceries, we take into account the weight of vegetables for scaling, weighing them on the scale and then counting the cash to give to the cashier. We don’t even realise it and we are already counting numbers and doing calculations. 

Without mathematics and numbers, none of this would be possible.

Hence we can say that mathematics helps us make better choices, more calculated ones throughout our day and hence make our lives simpler. 

Also Read:-   My Aim in Life

Also Read: How to Prepare for UPSC in 6 Months?

Essay on Importance of Mathematics in our Daily Life in 350 words

Mathematics is what we call a backbone, a backbone of science. Without it, human life would be extremely difficult to imagine. We cannot live even a single day without making use of mathematics in our daily lives. Without mathematics, human progress would come to a halt. 

Maths helps us with our finances. It helps us calculate our daily, monthly as well as yearly expenses. It teaches us how to divide and prioritise our expenses. Its knowledge is essential for investing money too. We can only invest money in property, bank schemes, the stock market, mutual funds, etc. only when we calculate the figures. Let’s take an example from the basic routine of a day. Let’s assume we have to make tea for ourselves. Without mathematics, we wouldn’t be able to calculate how many teaspoons of sugar we need, how many cups of milk and water we have to put in, etc. and if these mentioned calculations aren’t made, how would one be able to prepare tea? 

In such a way, mathematics is used to decide the portions of food, ingredients, etc. Mathematics teaches us logical reasoning and helps us develop problem-solving skills. It also improves our analytical thinking and reasoning ability. To stay in shape, mathematics helps by calculating the number of calories and keeping the account of the same. It helps us in deciding the portion of our meals. It will be impossible to think of sports without mathematics. For instance, in cricket, run economy, run rate, strike rate, overs bowled, overs left, number of wickets, bowling average, etc. are calculated. It also helps in predicting the result of the match. When we are on the road and driving, mathetics help us keep account of our speeds, the distance we have travelled, the amount of fuel left, when should we refuel our vehicles, etc. 

We can go on and on about how mathematics is involved in our daily lives. In conclusion, we can say that the universe revolves around mathematics. It encompasses everything and without it, we cannot imagine our lives. 

Also Read:- Essay on Pollution

Ans: Mathematics is a powerful aspect even in our day-to-day life. If you are a cook, the measurements of spices have mathematics in them. If you are a doctor, the composition of medicines that make you provide prescription is made by mathematics. Even if you are going out for just some groceries, the scale that is used for weighing them has maths, and the quantity like ‘dozen apples’ has maths in it. No matter the task, one way or another it revolves around mathematics. Everywhere we go, whatever we do, has maths in it. We just don’t realize that. Maybe from now on, we will, as mathematics is an important aspect of our daily life.

Ans: Mathematics, as a subject, is one of the most important subjects in our lives. Irrespective of the field, mathematics is essential in it. Be it physics, chemistry, accounts, etc. mathematics is there. The use of mathematics proceeds in our daily life to a major extent. It will be correct to say that it has become a vital part of us. Imagining our lives without it would be like a boat without a sail. It will be a shock to know that we constantly use mathematics even without realising the same.  From making instalments to dialling basic phone numbers it all revolves around mathematics. Let’s take an example from our daily life. In the scenario of going out shopping, we take an estimate of hours. Even while buying just simple groceries, we take into account the weight of vegetables for scaling, weighing them on the scale and then counting the cash to give to the cashier. We don’t even realise it and we are already counting numbers and doing calculations. Without mathematics and numbers, none of this would be possible. Hence we can say that mathematics helps us make better choices, more calculated ones throughout our day and hence make our lives simpler.  

Ans: Archimedes is considered the father of mathematics.

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The Best Writing on Mathematics 12

Mircea pitici,  series editor.

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

The year’s finest mathematical writing from around the world

The year's finest mathematical writing from around the world

The year's finest mathematics writing from around the world

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

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

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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.

Home — Essay Samples — Science — Mathematics in Everyday Life — Importance of Math

Importance of Math

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Published: Jun 13, 2024

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Mathematics in education, mathematics in professional fields, mathematics in everyday life, mathematics and critical thinking.

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• Instructions Followed To The Letter
• Deadlines Met At Every Stage
• Unique And Plagiarism Free

Browse Course Material

Course info, instructors.

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

Departments

• Mathematics

As Taught In

Learning resource types, project laboratory in mathematics.

Next: Revision and Feedback »

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

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

Criteria for Good Writing

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

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

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

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

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

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

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

Writing Resources

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

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

An Annotated Journal Article (PDF)

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

Notes on Writing Mathematics (PDF)

LaTeX Resources

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

Sample PDF Document created by pdfLaTeX (PDF)

Sample TeX Document (TEX)

Beamer template (TEX)

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

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

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

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

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

Writing Workshop

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

The 18.821 Project Report (PDF)

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

• Download video

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

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

February 13, 2024 by Prasanna

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

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

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

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

Long Essay on Math 500 Words in English

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

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

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

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

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

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

Some of the advantages of Math in our daily life

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

Short Essay on Math 150 Words in English

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

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

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

10 Lines on Math in English

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

FAQ’s on Math Essay

Question 1. What is Mathematics in simple words?

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

Question 2. Do we need mathematics every day?

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

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

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

Question 4. What are the applications of maths?

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

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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
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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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What Students Are Saying About the Value of Math

We asked teenagers: Do you see the point in learning math? The answer from many was “yes.”

By The Learning Network

“Mathematics, I now see, is important because it expands the world,” Alec Wilkinson writes in a recent guest essay . “It is a point of entry into larger concerns. It teaches reverence. It insists one be receptive to wonder. It requires that a person pay close attention.”

In our writing prompt “ Do You See the Point in Learning Math? ” we wanted to know if students agreed. Basic arithmetic, sure, but is there value in learning higher-level math, such as algebra, geometry and calculus? Do we appreciate math enough?

The answer from many students — those who love and those who “detest” the subject alike — was yes. Of course math helps us balance checkbooks and work up budgets, they said, but it also helps us learn how to follow a formula, appreciate music, draw, shoot three-pointers and even skateboard. It gives us different perspectives, helps us organize our chaotic thoughts, makes us more creative, and shows us how to think rationally.

Not all were convinced that young people should have to take higher-level math classes all through high school, but, as one student said, “I can see myself understanding even more how important it is and appreciating it more as I get older.”

Thank you to all the teenagers who joined the conversation on our writing prompts this week, including students from Bentonville West High School in Centerton, Ark, ; Harvard-Westlake School in Los Angeles ; and North High School in North St. Paul, Minn.

Please note: Student comments have been lightly edited for length, but otherwise appear as they were originally submitted.

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Popular Math Terms and Definitions

A to Z Mathematics Glossary

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Understanding math terms is important because mathematics is often referred to as the language of science and the universe, and it's not just about numbers. It encapsulates a vast array of concepts, principles, and terminology—from the foundational basics of counting to the complexities of calculus and beyond.

In this A to Z glossary, you'll find fundamental math concepts ranging from absolute value to zero slope. There's also a bit of history, with terms named after famous mathematicians.

A to Z Glossary of Math Terms

Abacus : An early counting tool used for basic arithmetic.

Absolute Value : Always a positive number, absolute value refers to the distance of a number from 0.

Acute Angle : An angle whose measure is between zero degrees and 90 degrees, or with less than 90-degree radians.

Addend : A number involved in an addition problem; numbers being added are called addends.

Algebra : The branch of mathematics that substitutes letters for numbers to solve for unknown values.

Algorithm : A procedure or set of steps used to solve a mathematical computation.

Angle : Two rays sharing the same endpoint (called the angle vertex).

Angle Bisector : The line dividing an angle into two equal angles.

Area : The two-dimensional space taken up by an object or shape, given in square units.

Array : A set of numbers or objects that follow a specific pattern.

Attribute : A characteristic or feature of an object—such as size, shape, color, etc.—that allows it to be grouped.

Average : The average is the same as the mean. Add up a series of numbers and divide the sum by the total number of values to find the average.

Base : The bottom of a shape or three-dimensional object, what an object rests on.

Base 10 : Number system that assigns place value to numbers.

Bar Graph : A graph that represents data visually using bars of different heights or lengths.

BEDMAS or PEMDAS Definition : An acronym used to help people remember the correct order of operations for solving algebraic equations. BEDMAS stands for "Brackets, Exponents, Division, Multiplication, Addition, and Subtraction" and PEMDAS stands for "Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction".

Bell Curve : The bell shape created when a line is plotted using data points for an item that meets the criteria of normal distribution. The center of a bell curve contains the highest value points.

Binomial : A polynomial equation with two terms usually joined by a plus or minus sign.

Box and Whisker Plot/Chart : A graphical representation of data that shows differences in distributions and plots data set ranges.

Calculus : The branch of mathematics involving derivatives and integrals, Calculus is the study of motion in which changing values are studied.

Capacity : The volume of substance that a container will hold.

Centimeter : A metric unit of measurement for length, abbreviated as cm. 2.5 cm is approximately equal to an inch.

Circumference : The complete distance around a circle or a square.

Chord : A segment joining two points on a circle.

Coefficient : A letter or number representing a numerical quantity attached to a term (usually at the beginning). For example, x is the coefficient in the expression x (a + b) and 3 is the coefficient in the term 3 y.

Common Factors : A factor shared by two or more numbers, common factors are numbers that divide exactly into two different numbers.

Complementary Angles: Two angles that together equal 90 degrees.

Composite Number : A positive integer with at least one factor aside from its own. Composite numbers cannot be prime because they can be divided exactly.

Cone : A three-dimensional shape with only one vertex and a circular base.

Conic Section : The section formed by the intersection of a plane and cone.

Constant : A value that does not change.

Coordinate : The ordered pair that gives a precise location or position on a coordinate plane.

Congruent : Objects and figures that have the same size and shape. Congruent shapes can be turned into one another with a flip, rotation, or turn.

Cosine : In a right triangle, cosine is a ratio that represents the length of a side adjacent to an acute angle to the length of the hypotenuse.

Cylinder : A three-dimensional shape featuring two circle bases connected by a curved tube.

Decagon : A polygon or shape with ten angles and ten straight lines.

Decimal : A real number on the base ten standard numbering system.

Denominator : The bottom number of a fraction. The denominator is the total number of equal parts into which the numerator is being divided.

Degree : The unit of an angle's measure represented with the symbol °.

Diagonal : A line segment that connects two vertices in a polygon.

Diameter : A line that passes through the center of a circle and divides it in half.

Difference : The difference is the answer to a subtraction problem, in which one number is taken away from another.

Digit : Digits are the numerals 0-9 found in all numbers. 176 is a 3-digit number featuring the digits 1, 7, and 6.

Dividend : A number divided into equal parts (inside the bracket in long division).

Divisor : A number that divides another number into equal parts (outside of the bracket in long division).

Edge : A line is where two faces meet in a three-dimensional structure.

Ellipse : An ellipse looks like a slightly flattened circle and is also known as a plane curve. Planetary orbits take the form of ellipses.

End Point : The "point" at which a line or curve ends.

Equilateral : A term used to describe a shape whose sides are all of equal length.

Equation : A statement that shows the equality of two expressions by joining them with an equals sign.

Even Number : A number that can be divided or is divisible by 2.

Event : This term often refers to an outcome of probability; it may answer questions about the probability of one scenario happening over another.

Evaluate : This word means "to calculate the numerical value".

Exponent : The number that denotes repeated multiplication of a term, shown as a superscript above that term. The exponent of 3 4 is 4.

Expressions : Symbols that represent numbers or operations between numbers.

Face : The flat surfaces on a three-dimensional object.

Factor : A number that divides into another number exactly. The factors of 10 are 1, 2, 5, and 10 (1 x 10, 2 x 5, 5 x 2, 10 x 1).

Factoring : The process of breaking numbers down into all of their factors.

Factorial Notation : Often used in combinatorics, factorial notations require that you multiply a number by every number smaller than it. The symbol used in factorial notation is ! When you see x !, the factorial of x is needed.

Factor Tree : A graphical representation showing the factors of a specific number.

Fibonacci Sequence : Named after Italian number theorist Leonardo Pisano Fibonacci, it's a sequence beginning with a 0 and 1 whereby each number is the sum of the two numbers preceding it. For example, "0, 1, 1, 2, 3, 5, 8, 13, 21, 34..." is a Fibonacci sequence.

Figure : Two-dimensional shapes.

Finite : Not infinite; has an end.

Flip : A reflection or mirror image of a two-dimensional shape.

Formula : A rule that numerically describes the relationship between two or more variables.

Fraction : A quantity that is not whole that contains a numerator and denominator. The fraction representing half of 1 is written as 1/2.

Frequency : The number of times an event can happen in a given period of time; often used in probability calculations.

Furlong : A unit of measurement representing the side length of one square acre. One furlong is approximately 1/8 of a mile, 201.17 meters, or 220 yards.

Geometry : The study of lines, angles, shapes, and their properties. Geometry studies physical shapes and object dimensions.

Graphing Calculator : A calculator with an advanced screen capable of showing and drawing graphs and other functions.

Graph Theory : A branch of mathematics focused on the properties of graphs.

Greatest Common Factor : The largest number common to each set of factors that divides both numbers exactly. The greatest common factor of 10 and 20 is 10.

Hexagon : A six-sided and six-angled polygon.

Histogram : A graph that uses bars that equal ranges of values.

Hyperbola : A type of conic section or symmetrical open curve. The hyperbola is the set of all points in a plane, the difference of whose distance from two fixed points in the plane is a positive constant.

Hypotenuse : The longest side of a right-angled triangle, always opposite to the right angle itself.

Identity : An equation that is true for variables of any value.

Improper Fraction : A fraction whose numerator is equal to or greater than the denominator, such as 6/4.

Inequality : A mathematical equation expressing inequality and containing a greater than (>), less than (<), or not equal to (≠) symbol.

Integers : All whole numbers, positive or negative, including zero.

Irrational : A number that cannot be represented as a decimal or fraction. A number like pi is irrational because it contains an infinite number of digits that keep repeating. Many square roots are also irrational numbers.

Isosceles : A polygon with two sides of equal length.

Kilometer : A unit of measure equal to 1000 meters.

Knot : A closed three-dimensional circle that is embedded and cannot be untangled.

Like Terms : Terms with the same variable and same exponents/powers.

Like Fractions : Fractions with the same denominator.

Line : A straight infinite path joining an infinite number of points in both directions.

Line Segment : A straight path that has two endpoints, a beginning, and an end.

Linear Equation : An equation that contains two variables and can be plotted on a graph as a straight line.

Line of Symmetry : A line that divides a figure into two equal shapes.

Logic : Sound reasoning and the formal laws of reasoning.

Logarithm : The power to which a base must be raised to produce a given number. If nx = a , the logarithm of a , with n as the base, is x . Logarithm is the opposite of exponentiation.

Mean : The mean is the same as the average. Add up a series of numbers and divide the sum by the total number of values to find the mean.

Median : The median is the middle value in a series of numbers ordered from least to greatest. When the total number of values in a list is odd, the median is the middle entry. When the total number of values in a list is even, the median is equal to the sum of the two middle numbers divided by two.

Midpoint : A point that is exactly halfway between two locations.

Mixed Numbers : Mixed numbers refer to whole numbers combined with fractions or decimals. Example 3 1 / 2 or 3.5.

Mode : The mode in a list of numbers are the values that occur most frequently.

Modular Arithmetic : A system of arithmetic for integers where numbers "wrap around" upon reaching a certain value of the modulus.

Monomial : An algebraic expression made up of one term.

Multiple : The multiple of a number is the product of that number and any other whole number. 2, 4, 6, and 8 are multiples of 2.

Multiplication : Multiplication is the repeated addition of the same number denoted with the symbol x. 4 x 3 is equal to 3 + 3 + 3 + 3.

Multiplicand : A quantity multiplied by another. A product is obtained by multiplying two or more multiplicands.

Natural Numbers : Regular counting numbers.

Negative Number : A number less than zero denoted with the symbol -. Negative 3 = -3.

Net : A two-dimensional shape that can be turned into a two-dimensional object by gluing/taping and folding.

Nth Root : The n th root of a number is how many times a number needs to be multiplied by itself to achieve the value specified. Example: the 4th root of 3 is 81 because 3 x 3 x 3 x 3 = 81.

Norm : The mean or average; an established pattern or form.

Normal Distribution : Also known as Gaussian distribution, normal distribution refers to a probability distribution that is reflected across the mean or center of a bell curve.

Numerator : The top number in a fraction. The numerator is divided into equal parts by the denominator.

Number Line : A line whose points correspond to numbers.

Numeral : A written symbol denoting a number value.

Obtuse Angle : An angle measuring between 90° and 180°.

Obtuse Triangle : A triangle with at least one obtuse angle.

Octagon : A polygon with eight sides.

Odds : The ratio or likelihood of a probability event happening. The odds of flipping a coin and having it land on heads are one in two.

Odd Number : A whole number that is not divisible by 2.

Operation : Refers to addition, subtraction, multiplication, or division.

Ordinal : Ordinal numbers give relative positions in a set: first, second, third, etc.

Order of Operations : A set of rules used to solve mathematical problems in the correct order. This is often remembered with acronyms BEDMAS and PEMDAS.

Outcome : Used in probability to refer to the result of an event.

Parallelogram : A quadrilateral with two sets of opposite sides that are parallel.

Parabola : An open curve whose points are equidistant from a fixed point called the focus and a fixed straight line called the directrix.

Pentagon : A five-sided polygon. Regular pentagons have five equal sides and five equal angles.

Percent : A ratio or fraction with the denominator 100.

Perimeter : The total distance around the outside of a polygon. This distance is obtained by adding together the units of measure from each side.

Perpendicular : Two lines or line segments intersecting to form a right angle.

Pi : Pi is used to represent the ratio of the circumference of a circle to its diameter, denoted with the Greek symbol π.

Plane : When a set of points join together to form a flat surface that extends in all directions, this is called a plane.

Polynomial : The sum of two or more monomials.

Polygon : Line segments joined together to form a closed figure. Rectangles, squares, and pentagons are just a few examples of polygons.

Prime Numbers : Prime numbers are integers greater than one that are only divisible by themselves and 1.

Probability : The likelihood of an event happening.

Product : The sum obtained through the multiplication of two or more numbers.

Proper Fraction : A fraction whose denominator is greater than its numerator.

Protractor : A semi-circle device used for measuring angles. The edge of a protractor is subdivided into degrees.

Quadrant : One quarter ( qua) of the plane on the Cartesian coordinate system. The plane is divided into 4 sections, each called a quadrant.

Quadratic Equation : An equation that can be written with one side equal to 0. Quadratic equations ask you to find the quadratic polynomial that is equal to zero.

Quadrilateral : A four-sided polygon.

Quadruple : To multiply or to be multiplied by 4.

Qualitative : Properties that must be described using qualities rather than numbers.

Quartic : A polynomial having a degree of 4.

Quintic : A polynomial having a degree of 5.

Quotient : The solution to a division problem.

Radius : A distance found by measuring a line segment extending from the center of a circle to any point on the circle; the line extending from the center of a sphere to any point on the outside edge of the sphere.

Ratio : The relationship between two quantities. Ratios can be expressed in words, fractions, decimals, or percentages. Example: the ratio given when a team wins 4 out of 6 games is 4/6, 4:6, four out of six, or ~67%.

Ray : A straight line with only one endpoint that extends infinitely.

Range : The difference between the maximum and minimum in a set of data.

Rectangle : A parallelogram with four right angles.

Repeating Decimal : A decimal with endlessly repeating digits. Example: 88 divided by 33 equals 2.6666666666666... ("2.6 repeating").

Reflection : The mirror image of a shape or object, obtained from flipping the shape on an axis.

Remainder : The number left over when a quantity cannot be divided evenly. A remainder can be expressed as an integer, fraction, or decimal.

Right Angle : An angle equal to 90 degrees.

Right Triangle : A triangle with one right angle.

Rhombus : A parallelogram with four sides of equal length and no right angles.

Scalene Triangle : A triangle with three unequal sides.

Sector : The area between an arc and two radii of a circle, sometimes referred to as a wedge.

Slope : Slope shows the steepness or incline of a line and is determined by comparing the positions of two points on the line (usually on a graph).

Square Root : A number squared is multiplied by itself; the square root of a number is whatever integer gives the original number when multiplied by itself. For instance, 12 x 12 or 12 squared is 144, so the square root of 144 is 12.

Stem and Leaf : A graphic organizer used to organize and compare data. Similar to a histogram, stem and leaf graphs organize intervals or groups of data.

Subtraction : The operation of finding the difference between two numbers or quantities by "taking away" one from the other.

Supplementary Angles : Two angles are supplementary if their sum is equal to 180°.

Symmetry : Two halves that match perfectly and are identical across an axis.

Tangent : A straight line touching a curve from only one point.

Term : Piece of an algebraic equation; a number in a sequence or series; a product of real numbers and/or variables.

Tessellation : Congruent plane figures/shapes that cover a plane completely without overlapping.

Translation : A translation, also called a slide, is a geometrical movement in which a figure or shape is moved from each of its points the same distance and in the same direction.

Transversal : A line that crosses/intersects two or more lines.

Trapezoid : A quadrilateral with exactly two parallel sides.

Tree Diagram : Used in probability to show all possible outcomes or combinations of an event.

Triangle : A three-sided polygon.

Trinomial : A polynomial with three terms.

Unit : A standard quantity used in measurement. Inches and centimeters are units of length, pounds, and kilograms are units of weight, and square meters and acres are units of area.

Uniform : Term meaning "all the same". It can be used to describe size, texture, color, design, and more.

Variable : A letter used to represent a numerical value in equations and expressions. Example: in the expression 3 x + y , both y and x are the variables.

Venn Diagram : A Venn diagram is usually shown as two overlapping circles and is used to compare two sets. The overlapping section contains information that is true of both sides or sets and the non-overlapping portions each represent a set and contain information that is only true of their set.

Volume : A unit of measure describing how much space a substance occupies or the capacity of a container, provided in cubic units.

Vertex : The point of intersection between two or more rays, often called a corner. A vertex is where two-dimensional sides or three-dimensional edges meet.

Weight : The measure of how heavy something is.

Whole Number : A whole number is a positive integer.

X-Axis : The horizontal axis in a coordinate plane.

X-Intercept : The value of x where a line or curve intersects the x-axis.

X : The Roman numeral for 10.

x : A symbol used to represent an unknown quantity in an equation or expression.

Y-Axis : The vertical axis in a coordinate plane.

Y-Intercept : The value of y where a line or curve intersects the y-axis.

Yard : A unit of measure that is equal to approximately 91.5 centimeters or 3 feet.

Zero Slope: The slope of a horizontal line. Its slope is zero because a horizontal line has no incline.

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‘Groups’ Underpin Modern Math. Here’s How They Work.

September 6, 2024

Adam Nickel for  Quanta Magazine

Introduction

Mathematics started with numbers — clear, concrete, intuitive. Over the last two centuries, however, it has become a far more abstract enterprise. One of the first major steps down this road was taken in the late 18th and early 19th centuries. It involved a field called group theory, and it changed math — theoretical and applied — as we know it.

Groups generalize essential properties of the whole numbers. They have transformed geometry, algebra and analysis, the mathematical study of smoothly changing functions. They’re used to encrypt messages and study the shapes of viruses . Physicists rely on them to unify the fundamental forces of nature: At high energies, group theory can be used to show that electromagnetism and the forces that hold atomic nuclei together and cause radioactivity are all manifestations of a single underlying force.

The term “group” in a mathematical context was coined in 1830 by Évariste Galois, a French prodigy, just 18 years old at the time. (Two years later, he would be killed in a duel, having already changed the course of mathematical history.) But he didn’t discover groups single-handed. “It’s not like a bunch of mathematicians got together one day and said, ‘Let’s create an abstract structure just for a laugh,’” said Sarah Hart, a group theorist at Gresham College in London. “It emerged gradually, over maybe 50 years in the 19th century, that these were the right rules to require. They give you the most flexibility and generality, while still allowing you to prove things.”

Évariste Galois helped lay the foundations for group theory as a teenager.

Public domain

A group is a set, or collection of objects, together with an operation that takes in two objects and outputs a third. Arguably the simplest example is the integers and the operation of addition. Groups must satisfy four rules.

• The first is called closure: Add any two integers and you’ll get another integer.
• The second rule is called associativity: If you add three numbers together, the result doesn’t depend on how you group them. You can add 3 and 4 to get 7, then add 5 to get 12. Or you can add 3 to the sum of 4 and 5. Either way, you’ll still get the same answer: 12 = (3 + 4) + 5 = 3 + (4 + 5).
• The third rule is that the group must contain an element that leaves other group elements unchanged, called an identity element. The number zero is the identity for addition, since adding zero to a number keeps that number the same.
• Finally, each group element must have an inverse — add an element and its inverse, and you’ll get the identity. In the integers, the inverse of a number is its negative. For example, 3 + (−3) = 0.

To understand the significance of these four properties, it helps to consider a noteworthy omission. When adding two numbers together, you can change the order without affecting the outcome: 3 + 5 is the same as 5 + 3. This property is called commutativity. But there’s no requirement that groups be commutative. By making this property optional, mathematicians have been able to explore a rich variety of structures.

For an example of a noncommutative group, consider an equilateral triangle with labeled corners. If you rotate the triangle a third of the way around or flip it along its vertical axis, the only thing that will change about the image is the locations of the labels. There are six of these transformations that leave the shape otherwise unchanged, called symmetries of the triangle. They form a group called D 6 . (More generally, D 2 n is a group formed by the symmetries of a regular shape with n sides, so D 8 is the group of symmetries of a square.)

5W Infographics/Mark Belan for Quanta Magazine

To “add” two symmetries, just do one after another. You will quickly find that D 6 is not commutative: Flipping then rotating leaves the labels in different places than they will be if you rotate then flip.

D 6 is one of only two possible groups with six elements. For the other example of a six-element group, take the numbers {0, 1, 2, 3, 4, 5} as the set. For the operation, add two numbers in the usual way and then divide by 6, ignoring the quotient but retaining the remainder. So 3 and 5 deliver 2, since 8 leaves a remainder of 2 when divided by 6. This is called addition modulo 6, and the group is called Z 6 . In general, Z n is a group with n elements obtained from the numbers {0, 1, 2, 3, …,  n − 1} together with addition modulo n . Unlike D 6 , Z 6 is commutative, because 3 + 5 = 5 + 3, and so forth.

Z 6 and D 6 have different structures. Not only is one commutative and the other not, but you can generate any element of Z 6 using just one of its elements, the number 1: Start with 1, then keep adding 1. In D 6 , no element has this property. Figuring out the possible structures of groups has been one of the central projects of algebra over the last century.

To do this, mathematicians try to identify smaller groups contained within a group, called subgroups. These must retain the operation used for the full group. For example, the even integers form a subgroup within the integers. An even integer plus an even integer always results in another even integer. On the other hand, the odd numbers are not a subgroup, since if you add two odd numbers, you’ll get an even number. The identity element always forms a subgroup by itself, called the trivial subgroup.

Figuring out what subgroups a group contains is one way to understand its structure. For example, the subgroups of Z 6 are {0}, {0, 2, 4} and {0, 3} — the trivial subgroup, the multiples of 2, and the multiples of 3. In the group D 6 , rotations form a subgroup, but reflections don’t. That’s because two reflections performed in sequence produce a rotation, not a reflection, just as adding two odd numbers results in an even one.

Certain types of subgroups called “normal” subgroups are especially helpful to mathematicians. In a commutative group, all subgroups are normal, but this isn’t always true more generally. These subgroups retain some of the most useful properties of commutativity, without forcing the entire group to be commutative. If a list of normal subgroups can be identified, groups can be broken up into components much the way integers can be broken up into products of primes. Groups that have no normal subgroups are called simple groups and cannot be broken down any further, just as prime numbers can’t be factored. The group Z n is simple only when n is prime — the multiples of 2 and 3, for instance, form normal subgroups in Z 6 .

However, simple groups are not always so simple. “It’s the biggest misnomer in mathematics,” Hart said. In 1892, the mathematician Otto Hölder proposed that researchers assemble a complete list of all possible finite simple groups. (Infinite groups such as the integers form their own field of study.)

It turns out that almost all finite simple groups either look like Z n (for prime values of n ) or fall into one of two other families. And there are 26 exceptions, called sporadic groups. Pinning them down, and showing that there are no other possibilities, took over a century.

The largest sporadic group, aptly called the monster group, was discovered in 1973. It has more than 8 × 10 54 elements and represents geometric rotations in a space with nearly 200,000 dimensions. “It’s just crazy that this thing could be found by humans,” Hart said.

By the 1980s, the bulk of the work Hölder had called for appeared to have been completed, but it was tough to show that there were no more sporadic groups lingering out there. The classification was further delayed when, in 1989, the community found gaps in one 800-page proof from the early 1980s. A new proof was finally published in 2004, finishing off the classification.

Many structures in modern math — rings, fields and vector spaces, for example — are created when more structure is added to groups. In rings, you can multiply as well as add and subtract; in fields, you can also divide. But underneath all of these more intricate structures is that same original group idea, with its four axioms. “The richness that’s possible within this structure, with these four rules, is mind-blowing,” Hart said.

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Also in Mathematics

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Mathematicians Prove Hawking Wrong About the Most Extreme Black Holes

The Geometric Tool That Solved Einstein’s Relativity Problem

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• Copy URL https://www.pbs.org/newshour/nation/regulators-turn-to-math-to-determine-when-ai-is-powerful-enough-to-be-dangerous

Regulators turn to math to determine when AI is powerful enough to be dangerous

How do you know if an artificial intelligence system is so powerful that it poses a security danger and shouldn’t be unleashed without careful oversight?

For regulators trying to put guardrails on AI, it’s mostly about the arithmetic. Specifically, an AI model trained on 10 to the 26th floating-point operations per second must now be reported to the U.S. government and could soon trigger even stricter requirements in California.

Say what? Well, if you’re counting the zeroes, that’s 100,000,000,000,000,000,000,000,000, or 100 septillion, calculations each second, using a measure known as flops.

What it signals to some lawmakers and AI safety advocates is a level of computing power that might enable rapidly advancing AI technology to create or proliferate weapons of mass destruction, or conduct catastrophic cyberattacks.

Those who’ve crafted such regulations acknowledge they are an imperfect starting point to distinguish today’s highest-performing generative AI systems — largely made by California-based companies like Anthropic, Google, Meta Platforms and ChatGPT-maker OpenAI — from the next generation that could be even more powerful.

WATCH:  As artificial intelligence rapidly advances, experts debate level of threat to humanity

Critics have pounced on the thresholds as arbitrary — an attempt by governments to regulate math.

“Ten to the 26th flops,” said venture capitalist Ben Horowitz on a podcast this summer. “Well, what if that’s the size of the model you need to, like, cure cancer?”

An executive order signed by President Joe Biden last year relies on that threshold. So does California’s newly passed AI safety legislation — which Gov. Gavin Newsom has until Sept. 30 to sign into law or veto. California adds a second metric to the equation: regulated AI models must also cost at least $100 million to build.

Following Biden’s footsteps, the European Union’s sweeping AI Act also measures floating-point operations per second, or flops, but sets the bar 10 times lower at 10 to the 25th power. That covers some AI systems already in operation. China’s government has also looked at measuring computing power to determine which AI systems need safeguards.

No publicly available models meet the higher California threshold, though it’s likely that some companies have already started to build them. If so, they’re supposed to be sharing certain details and safety precautions with the U.S. government. Biden employed a Korean War-era law to compel tech companies to alert the U.S. Commerce Department if they’re building such AI models.

AI researchers are still debating how best to evaluate the capabilities of the latest generative AI technology and how it compares to human intelligence. There are tests that judge AI on solving puzzles, logical reasoning or how swiftly and accurately it predicts what text will answer a person’s chatbot query. Those measurements help assess an AI tool’s usefulness for a given task, but there’s no easy way of knowing which one is so widely capable that it poses a danger to humanity.

“This computation, this flop number, by general consensus is sort of the best thing we have along those lines,” said physicist Anthony Aguirre, executive director of the Future of Life Institute, which has advocated for the passage of California’s Senate Bill 1047 and other AI safety rules around the world.

Floating point arithmetic might sound fancy “but it’s really just numbers that are being added or multiplied together,” making it one of the simplest ways to assess an AI model’s capability and risk, Aguirre said.

“Most of what these things are doing is just multiplying big tables of numbers together,” he said. “You can just think of typing in a couple of numbers into your calculator and adding or multiplying them. And that’s what it’s doing — ten trillion times or a hundred trillion times.”

For some tech leaders, however, it’s too simple and hard-coded a metric. There’s “no clear scientific support” for using such metrics as a proxy for risk, argued computer scientist Sara Hooker, who leads AI company Cohere’s nonprofit research division, in a July paper.

“Compute thresholds as currently implemented are shortsighted and likely to fail to mitigate risk,” she wrote.

Venture capitalist Horowitz and his business partner Marc Andreessen, founders of the influential Silicon Valley investment firm Andreessen Horowitz, have attacked the Biden administration as well as California lawmakers for AI regulations they argue could snuff out an emerging AI startup industry.

For Horowitz, putting limits on “how much math you’re allowed to do” reflects a mistaken belief there will only be a handful of big companies making the most capable models and you can put “flaming hoops in front of them and they’ll jump through them and it’s fine.”

In response to the criticism, the sponsor of California’s legislation sent a letter to Andreessen Horowitz this summer defending the bill, including its regulatory thresholds.

Regulating at over 10 to the 26th flops is “a clear way to exclude from safety testing requirements many models that we know, based on current evidence, lack the ability to cause critical harm,” wrote state Sen. Scott Wiener of San Francisco. Existing publicly released models “have been tested for highly hazardous capabilities and would not be covered by the bill,” Wiener said.

Both Wiener and the Biden executive order treat the metric as a temporary one that could be adjusted later.

Yacine Jernite, who leads policy research at the AI company Hugging Face, said the flops metric emerged in “good faith” ahead of last year’s Biden order but is already starting to grow obsolete. AI developers are doing more with smaller models requiring less computing power, while the potential harms of more widely used AI products won’t trigger California’s proposed scrutiny.

“Some models are going to have a drastically larger impact on society, and those should be held to a higher standard, whereas some others are more exploratory and it might not make sense to have the same kind of process to certify them,” Jernite said.

Aguirre said it makes sense for regulators to be nimble, but he characterizes some opposition to the flops threshold as an attempt to avoid any regulation of AI systems as they grow more capable.

“This is all happening very fast,” Aguirre said. “I think there’s a legitimate criticism that these thresholds are not capturing exactly what we want them to capture. But I think it’s a poor argument to go from that to, ‘Well, we just shouldn’t do anything and just cross our fingers and hope for the best.'”

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Grants to 16 Michigan Districts and ISDs Will Add Up to Better Math Teaching, Learning

September 03, 2024

LANSING – Children across Michigan will benefit from grants to improve mathematics teaching and learning.

The Michigan Department of Education (MDE) is announcing that it has awarded nearly $25 million in grants to 16 local education agencies.

Funding is from Section 388.1623h of the Fiscal Year 2024 State School Aid Act, approved by the state legislature and signed into law by Gov. Gretchen Whitmer, and was awarded through a competitive process to improve mathematics teaching and learning.

“It’s exciting to see the enormous interest of local and intermediate school districts in these math grants,” said State Superintendent Dr. Michael F. Rice. “These grants will help improve mathematics teaching and learning throughout the state.”

Among the grant awardees is Wayne Regional Educational Service Agency (RESA), which is receiving more than $1.8 million that it will use to ensure educators and students have access to high-quality, highly aligned, and culturally relevant math instructional materials through a guided six-step adoption process. By the end of a pilot phase, participating districts will have tested and proven resources that are not only effective but also resonate with the diverse needs of their students to fully implement in the 2025-26 school year.

"In order for our students to thrive, they must see themselves in culturally relevant and rich instruction, and we must support our educators as they implement research-based and evolving curriculum," said Dr. Daveda Colbert, Wayne RESA superintendent.” We are grateful for this critical funding that will undoubtedly strengthen our math instruction and our students' learning by enriching the way we involve teachers in adopting teaching tools and materials to best serve our students in a constantly evolving landscape."

Applicants could apply in the following categories designated in state statute:

• Continued system development, capacity building, and networking spaces for early math specialists in districts and intermediate school districts.
• Incentives and supports for grades K-5 schools in purchasing and implementing high-quality mathematics instructional materials programs to engage students in equitable, high-quality mathematics learning experiences using a guided adoption process through intermediate districts.
• Supports for expanding math recovery specialists statewide through intermediate school districts.
• Supports for secondary schools in offering supplemental just-in-time, personalized support programs that are designed to keep students on track in their math classes and for graduation.

All the funded agencies are listed below and organized by the category for which they are funded.

• Systems development:
• Gogebic-Ontonagon Intermediate School District, $10.4 million.
• Ypsilanti Community Schools, $809,800.
• High-quality mathematics instructional materials:
• Pickford Public Schools, $66,151.
• Pontiac School District, 181,346.
• Walkerville Public Schools, $77,110.
• West Branch-Rose City Area Schools, $142,000.
• Gratiot-Isabella Regional Education Service District, $963,327.
• Wayne RESA, $1,847,740.
• Math recovery:
• Kalamazoo Regional Educational Service Agency, $3,556,834.
• Muskegon Area Intermediate School District, $334,600.
• Just-in-time supports:
• Dearborn Public Schools, $3,717,878.
• Fennville Public Schools, $81,457.
• Lincoln Consolidated Schools, $482,500.
• Northview Public Schools, $206,501.
• Genesee Intermediate School District, $108,993.
• Washtenaw Intermediate School District, $2,019,400.

Eligible applicants – intermediate school districts, traditional school districts, and public charter schools – submitted over 100 applications through the competitive process.

The grants to Gogebic-Ontonagon Intermediate School District and Kalamazoo Regional Educational Service Agency support teachers across the state.

“On behalf of our children and ISDs, in collaboration with the Michigan Association of Intermediate School Administrators, we are excited to support K-5 educators and leaders throughout Michigan in implementing research-supported mathematics practices,” said Mr. Alan Tulppo, superintendent of the Gogebic-Ontonagon Intermediate School District.

Five grants support teachers and students within their county – Genesee Intermediate School District, Gratiot-Isabella Regional Education Service District, Muskegon Area Intermediate School District, Washtenaw Intermediate School District, and Wayne Regional Educational Service Agency. The rest of the funding supports individual district efforts to improve mathematics teaching and learning.

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