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 ideas for your next math essay. 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!

✅  Branches of Mathematics

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.

Albert Einstein quote.

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.

🏫  Mathematics 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.

  1. Explain what we need Pythagoras’ theorem for.
  2. What is a hyperbola?
  3. Describe the difference between algebra and arithmetic.
  4. When is it unnecessary to use a calculator?
  5. Find a connection between math and the arts.
  6. How do you solve a linear equation?
  7. Discuss how to determine the probability of rolling two dice.
  8. Is there a link between philosophy and math?
  9. What types of math do you use in your everyday life?
  10. What is the numerical data?
  11. Explain how to use the binomial theorem.
  12. What is the distributive property of multiplication?
  13. Discuss the major concepts in ancient Egyptian mathematics.
  14. Why do so many students dislike math?
  15. Should math be required in school?
  16. How do you do an equivalent transformation?
  17. Why do we need imaginary numbers?
  18. How can you calculate the slope of a curve?
  19. What is the difference between sine, cosine, and tangent?
  20. How do you define the cross product of two vectors?
  21. What do we use differential equations for?
  22. Investigate how to calculate the mean value.
  23. Define linear growth.
  24. Give examples of different number types.
  25. 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:

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

Three main types of geometry.

  1. What is K-theory?
  2. Discuss the core problems of computational geometry.
  3. Explain the use of set theory.
  4. What do we need Boolean functions for?
  5. Describe the main topological concepts in modern mathematics.
  6. Investigate the properties of a rotation matrix.
  7. Analyze the practical applications of game theory.
  8. How can you solve a Rubik’s cube mathematically?
  9. Explain the math behind the Koch snowflake.
  10. Describe the paradox of Gabriel’s Horn.
  11. How do fractals form?
  12. Find a way to solve Sudoku using math.
  13. Why is the Riemann hypothesis still unsolved?
  14. Discuss the Millennium Prize Problems.
  15. How can you divide complex numbers?
  16. Analyze the degrees in polynomial functions.
  17. What are the most important concepts in number theory?
  18. 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:

  1. What is an abelian group?
  2. Explain the orbit-stabilizer theorem.
  3. Discuss what makes the Burnside problem influential.
  4. What fundamental properties do holomorphic functions have?
  5. How does Cauchy’s integral theorem lead to Cauchy’s integral formula?
  6. How do the two Picard theorems relate to each other?
  7. When is a trigonometric series called a Fourier series?
  8. Give an example of an algorithm used for machine learning.
  9. Compare the different types of knapsack problems.
  10. What is the minimum overlap problem?
  11. Describe the Bernoulli scheme.
  12. Give a formal definition of the Chinese restaurant process.
  13. Discuss the logistic map in relation to chaos.
  14. What do we need the Feigenbaum constants for?
  15. Define a difference equation.
  16. Explain the uses of the Fibonacci sequence.
  17. What is an oblivious transfer?
  18. Compare the Riemann and the Ruelle zeta functions.
  19. How can you use elementary embeddings in model theory?
  20. Analyze the problem with the wholeness axiom and Kunen’s inconsistency theorem.
  21. How is Lie algebra used in physics?
  22. Define various cases of algebraic cycles.
  23. Why do we need étale cohomology groups to calculate algebraic curves?
  24. What does non-Euclidean geometry consist of?
  25. 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:

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

Mathematical writing should be.

  1. How can infinities have various sizes?
  2. What is the best mathematical strategy to win a game of Go?
  3. Analyze natural occurrences of random walks in biology.
  4. Explain what kind of mathematics was used in ancient Persia.
  5. Discuss how the Iwasawa theory relates to modular forms.
  6. What role do prime numbers play in encryption?
  7. How did the study of mathematics evolve?
  8. Investigate the different Tower of Hanoi solutions.
  9. Research Napier’s bones. How can you use them?
  10. What is the best mathematical way to find someone who is lost in a maze?
  11. Examine the Traveling Salesman Problem. Can you find a new strategy?
  12. Describe how barcodes function.
  13. Study some real-life examples of chaos theory. How do you define them mathematically?
  14. Compare the impact of various ground-breaking mathematical equations.
  15. Research the Seven Bridges of Königsberg. Relate the problem to the city of your choice.
  16. Discuss Fisher’s fundamental theorem of natural selection.
  17. How does quantum computing work?
  18. 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.

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

E. T. Bell quote.

  1. How does dyscalculia affect a student’s daily life?
  2. Into which school subjects can math be integrated?
  3. Has a mathematics degree increased in value over the last few years?
  4. What are the disadvantages of the Common Core Standards?
  5. What are the advantages of following an integrated curriculum in math?
  6. 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:

  1. Give an example of an induction proof.
  2. What are F-algebras used for?
  3. What are number problems?
  4. Show the importance of abstract algebra.
  5. Investigate the peculiarities of Fermat’s last theorem.
  6. What are the essentials of algebra?
  7. Explore the relationship between algebra and geometry.
  8. Compare the differences between commutative and noncommutative algebra.
  9. Why is Brun’s constant relevant?
  10. How do you factor quadratics?
  11. Explain Descartes’ Rule of Signs.
  12. What is the quadratic formula?
  13. Compare the four types of sequences and define them.
  14. Explain how partial fractions work.
  15. What are logarithms used for?
  16. Describe the Gaussian elimination.
  17. What does Cramer’s rule state?
  18. Explore the difference between eigenvectors and eigenvalues.
  19. Analyze the Gram-Schmidt process in two dimensions.
  20. Explain what is meant by “range” and “domain” in algebra.
  21. What can you do with determinants?
  22. Learn about the origin of the distance formula.
  23. Find the best way to solve math word problems.
  24. Compare the relationships between different systems of equations.
  25. 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:

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

The study of non-Euclidean geometry.

  1. Describe the notion of Dirac manifolds.
  2. Compare the various relationships between lines.
  3. What is the Klein bottle?
  4. How does geometry translate into other disciplines, such as chemistry and physics?
  5. Explore Riemannian manifolds in Euclidean space.
  6. How can you prove the angle bisector theorem?
  7. Do a research on M.C. Escher’s use of geometry.
  8. Find applications for the golden ratio.
  9. Describe the importance of circles.
  10. Investigate what the ancient Greeks knew about geometry.
  11. What does congruency mean?
  12. Study the uses of Euler’s formula.
  13. How do CT scans relate to geometry?
  14. Why do we need n-dimensional vectors?
  15. How can you solve Heesch’s problem?
  16. What are hypercubes?
  17. 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:

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

Calculus was developed by Isaac Newton and Gottfried Leibnitz.

  1. How does multivariate calculus work?
  2. Discuss the use of Stokes’ theorem.
  3. What does Leibniz’s integral rule state?
  4. What is the Itô stochastic integral?
  5. Explore the influence of nonstandard analysis on probability theory.
  6. Research the origins of calculus.
  7. Who was Maria Gaetana Agnesi?
  8. Define a continuous function.
  9. What is the fundamental theorem of calculus?
  10. How do you calculate the Taylor series of a function?
  11. Discuss the ways to resolve Runge’s phenomenon.
  12. Explain the extreme value theorem.
  13. What do we need predicate calculus for?
  14. What are linear approximations?
  15. When does an integral become improper?
  16. Describe the Ratio and Root Tests.
  17. How does the method of rings work?
  18. 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:

  1. What are the essential skills needed for business math?
  2. How do you calculate interest rates?
  3. Compare business and consumer math.
  4. What is a discount factor?
  5. How do you know that an investment is reasonable?
  6. When does it make sense to pay a loan with another loan?
  7. Find useful financing techniques that everyone can use.
  8. How does critical path analysis work?
  9. Explain how loans work.
  10. Which areas of work utilize operations research?
  11. How do businesses use statistics?
  12. What is the economic lot scheduling problem?
  13. Compare the uses of different chart types.
  14. What causes a stock market crash?
  15. How can you calculate the net present value?
  16. Explore the history of revenue management.
  17. When do you use multi-period models?
  18. Explain the consequences of depreciation.
  19. Are annuities a good investment?
  20. Would the U.S. financially benefit from discontinuing the penny?
  21. What caused the United States housing crash in 2008?
  22. How do you calculate sales tax?
  23. Describe the notions of markups and markdowns.
  24. Investigate the math behind debt amortization.
  25. 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!

🔍  References