Do you have to submit a math research paper? Are you looking for the best math research topics? Well, in this blog post, we have shared a list of 150+ interesting math research topics to consider for assignments and academic projects. If you are a student who is pursuing a degree in mathematics, then you can very well use the topic ideas suggested here. Also, you can check this blog post and get to know the important steps for writing a brilliant math research paper.
What is Mathematics?
Mathematics is a broad academic discipline that focuses on numbers, structures, spaces, and shapes. This subject contains many analysis and calculation methods. Especially in the real world, math is considered an effective problem-solving tool. By using math, you can find solutions for both simple and complex problems.
Basically, mathematics is an integrated language that is widely used in several fields such as engineering, physics, medicine, finance, computer, business, and biology. Apart from the complex scientific fields, even math plays a vital role in the basic cost and time calculation in our everyday life.
Different Branches of Mathematics
Listed below are some popular branches of mathematics.
Arithmetic: It is a basic branch of math that focuses on numbers and their associated operations such as addition, subtraction, multiplication, and division.
Algebra: When the numbers are unknown, algebra steps in. Generally, along with numbers, algebra uses the letters such as A, B, X, and Y to represent unknown quantities. Mainly, businesses depend on algebra concepts to predict their sales.
Geometry: It is a popular branch of mathematics that deals with shapes, sizes, and figures. The concept commonly revolves around lines, points, solids, angles, and surfaces.
Apart from all these common branches, mathematics also includes more advanced types such as calculus, trigonometry, statistics, topology, probability, etc.
How to Write a Math Research Paper?
In general, a math research paper is an academic paper that is prepared to explain a mathematical concept with proper results. For writing a math research paper, first, you must have a good research topic from any branch of mathematics. As math is a vast discipline, you can easily search and find plenty of research topics from it. But when you have many topics, then it will be more tedious to identify one perfect topic out of them all.
Right now, are you searching for a perfect math research topic? Well, then this is what you should do during the topic selection process to spot the right topic.
Topic Selection
Whenever you are asked to come up with a research paper topic on your own, initially, restrict yourself to the research area that you have strong knowledge of and are passionate about. Next, in that research area, explore and identify one great topic that has a broad scope to evaluate and express your ideas.
Remember, the topic you select should be comfortable for you to perform research and write about. Never pick a topic with less or no research scope. The topic should support the research method of your choice. Most importantly, give preference to the topic that has wide research information, references, and evidence. Also, before finalizing the topic, check whether your topic satisfies your instructor’s guidelines.
Research Paper Writing
After you have found a good math research topic, you can proceed to write the research paper. The research paper you write should follow a proper format and structure. So, in the math research paper, make sure to include the following essential sections.
- Introduction
- Body
- Implications
Introduction
In the introduction section, you should first give brief background information about your topic to familiarize your readers. Here, mainly you should explain the primary concepts along with the history of its terms. Also, you should state the basic research problem and discuss the symbols and principles that you are going to use in the essay.
Body
The body of your research paper should elaborate on all your findings. Particularly, in the body paragraphs, you should talk about the formulas, theories, and mathematical analysis methods you have used to find solutions for the research problem.
Implications
The implication is the last or closing part of your research paper. Here, you should share your research insights with the readers. Also, you should include a brief summary of all the important points that you have discussed in the entire essay.
List of the Best Math Research Topics
Are you struggling to come up with a good math research paper topic for your assignment? No worries! Here we have shared a list of top-rated math research topic ideas on various branches of mathematics.
Explore them all and find a topic that suits you perfectly.
Simple and Easy Math Topics
- Explain the working of Partial fractions.
- Discuss the application of Mathematics in daily life.
- What is the basis of Cramer’s rule?
- How to solve Heesch’s problem?
- Explain the history of calculus.
- What is Euler’s formula?
- Explain the working of Logarithms.
- What are the different types of sequences?
- Explain the different types of Transformations.
- Define Brun’s constant.
- What are the methods of factoring quadratics?
- Examine Archimedean solids.
- Explain Gaussian elimination.
- Write about encryption and prime numbers.
- How does Hypercube work?
- Analyze Pygaoethores Theorem
- Describe the logicist definitions of mathematics
- Describe the purpose of homological algebra
- Compare and contrast Concave and Convex in geometry
- The study and contributions of Blaise Pascal to Probability
- Explain the Fibonacci series briefly
- How the Ancient Greek architecture influenced by mathematics?
- Discuss the ancient Egyptian mathematical applications and accomplishments
- Discuss the easiest ways to memorize algebraic expressions
- Algebra is an exposition on the invariants of matrices – Explain
Basic Math Topics for Middle School Students
- Define the Artin-Wedderburn theorem.
- How to calculate net worth?
- How to identify critical points in graphs?
- What is the role of statistics in business?
- Describe the principles of the Pythagoras theorem.
- What are the applications of finance in math?
- What do limits in math mean?
- Explain the ratio and root test.
- Define Jacobson’s density theorem.
- What are the principles of calculus?
Interesting Math Topics for High School Students
- What are the different number types? Explain with examples.
- Explain the need for imaginary numbers.
- How to calculate the interest rate?
- How to solve a matrix?
- How to prepare a chart of a company’s financial analysis?
- When to use a calculator in class?
- Explain the importance of the Binomial theorem.
- Write about Egyptian mathematics.
- Describe the applications of math in the workplace.
- How to solve linear equations?
- Describe the usage of hyperbola in math.
- Why do so many students hate math?
- What is the difference between algebra and arithmetic?
- How to calculate the mean value?
- What is the numerical data?
Math Research Paper Topics for Undergraduate Students
- Explain the different theories of mathematical logic.
- Discuss the origins of Greek symbols in mathematics.
- Explain the significance of circles.
- Analyze predictive models.
- Explain the emergence of patterns in chaos theory.
- Define abstract algebra.
- What is a continuous stochastic process?
- Write about the history of algebra.
- Analyze Monte Carlo methods for inverse problems.
- What are the goals of standardized testing?
- Define the Pentagonal number theorem.
- Discuss the Lorentz–FitzGerald contraction hypothesis in relativity.
- How to solve simultaneous equations.
- How do supercomputers solve complex mathematical problems?
- What is a parabola in geometry?
Math Research Topics for College Students
- Explain the Fibonacci sequence.
- What are the core problems of computational geometry?
- Discuss the practical applications of game theory.
- What is the Traveling Salesman Problem?
- Describe the Influence of math in biology.
- Analyze the meaning of fractals.
- Discuss the origin and evolution of mathematics.
- What is quantum computing?
- Explain Einstein’s field equation theory.
- What is the influence of math on chemistry?
- How to solve a Rubik’s cube mathematically?
- How to do complex numbers division?
- Explain the use of Boolean functions.
- Analyze the degrees in polynomial functions.
- How to solve Sudoku using mathematics?
- Explain the use of set theory.
- Explain the math behind the Koch snowflake.
- Explore the varieties of the Tower of Hanoi solutions.
- What is the difference between a discrete and a continuous probability distribution?
- How does encryption work?
Applied Math Research Topics
- What is the role of algorithms in probabilistic modeling?
- Explain the significance of step-stress modeling.
- Describe Newton’s laws of motion.
- What dimensions are used to examine fingerprints?
- Analyze statistical signal processing.
- How to do Galilean transformation?
- What is the role of mathematicians in crime data analysis and prevention?
- Explain the uncertainty principle.
- Discuss Liouville’s theorem in Hamiltonian mechanics.
- Analyze the perpendicular axes rule.
Business Math Research Topics
- What is the difference between a loan and a mortgage?
- How to calculate sales tax?
- Explore the math behind debt amortization.
- How do businesses use statistics?
- What is the economic lot scheduling problem?
- Explain how loans work.
- Discuss the significance of business math in real life.
- Define discount factor.
- What are the major causes of a stock market crash?
- Compare the uses of different types of charts.
- Describe the notions of markups and markdowns.
- How does critical path analysis work?
- What are the pros and cons of annuities?
- When to use multi-period models?
- Compare business and consumer math.
Advanced Math Research Paper Topics
- What is an oblivious transfer?
- Compare the Riemann and the Ruelle zeta functions.
- What are the different types of knapsack problems?
- Define an abelian group.
- What are the algorithms used for machine learning?
- Define various cases of algebraic cycles.
- When a trigonometric series is called a Fourier series?
- What is the minimum overlap problem?
- What are the basic properties of holomorphic functions?
- Describe the Bernoulli scheme.
Complex Math Research Topics
- Write about Napier’s bones.
- What makes a number big?
- Examine the notion of operator spaces.
- How do barcodes function?
- Define Fisher’s fundamental theorem of natural selection.
- What are the peculiarities of Borel’s paradox?
- How to design a train schedule for a whole country?
- Describe a hyperboloid in 3D geometry.
- What is an orthodiagonal quadrilateral?
- Explain how the Iwasawa theory relates to modular forms.
Math Research Ideas on Probability and Statistics
- Roll two dice and calculate a probability.
- Write about the Factorial moment in the Theory of Probability.
- Explain the principle of maximum entropy.
- Compare and contrast Cochran’s C test and his Q test.
- Discuss Skorokhod’s representation theorem in random variables
- How to apply the ANOVA method to rank.
- Analyze the De Moivre-Laplace theorem.
- What is the autoregressive conditional duration?
- Explain a negative probability.
- Discuss the practical applications of the Bates distribution.
Algebra Research Topics
- Explain Descartes’ Rule of Signs.
- How to factor quadratics?
- What is the use of F-algebras?
- Discuss the differential equation.
- What is the difference between eigenvectors and eigenvalues?
- What are the properties of a binary operation in algebra?
- What is a commutative ring in algebra?
- Discuss the origin of the distance formula.
- Explain the quadratic formula.
- Analyze the unary operator.
- Define range and domain in algebra.
- Describe the Noetherian ring.
- Discuss the Morita duality in algebraic structures.
- Define the Abel–Ruffini theorem.
- What is the use of determinants?
Math Research Paper Topics on Geometry
- Research the real-life uses of a rhombicosidodecahedron.
- Find out the solutions to Buffon’s needle problem.
- What is unique about right triangles?
- What is the Klein bottle?
- What are the Archimedean solids?
- What does congruency mean?
- Discuss the role of trigonometry in computer graphics.
- What is the need for n-dimensional vectors?
- Explain the Japanese theorem for concyclic polygons.
- Prove the angle bisector theorem.
- Identify the applications for the golden ratio.
- Explain the Heronian tetrahedron.
- Describe the notion of Dirac manifolds.
- What is the use of geometry in Picasso’s paintings?
- How do CT scans relate to geometry?
Calculus Research Topics
- How to calculate the Taylor series of a function?
- What is the role of calculus in real life?
- Discuss the Leibniz integral rule
- Discuss and analyze linear approximations.
- What is the use of predicate calculus?
- What is the foundation of calculus?
- How to calculate the area between curves?
- Describe the standard formulas needed for derivatives.
- Explain the working of multivariate calculus.
- Define the fundamental theorem of calculus.
Outstanding Math Research Topics
- What is a sphericon?
- What is the role of Mathematics in Artificial Intelligence?
- Define De Finetti’s theorem in probability and statistics.
- How to calculate the slope of a curve?
- Discuss the Stern-Brocot tree.
- Explain Pascal’s Triangle.
- Analyze the Georg Cantor set theory.
- How to measure infinity?
- Explain the Scholz conjecture.
- How is geometry used in contemporary architectural designs?
- How to solve the Suslin problem?
- What is a tree automaton?
- Explain the working of the Back-and-forth method.
- What is a Turing machine?
- Discuss the linear speedup theorem.
- Discuss the benefits of using truth tables to present the logical validity of a propositional expression
- Critical analysis of the major concepts in ancient Egyptian mathematics
- Discuss the similarities and differences between a continuous and a discrete probability distribution
- Analysis of the problem with the wholeness axiom and Kunen’s inconsistency theorem
- Develop a study focusing on the Seven Bridges of Königsberg and relate the problem to the city or state of your choice
Latest Math Research Topics
- What does point zero reflect on a graph where the vertical and horizontal lines meet?
- How to recognize adjacent angles easily without any trouble?
- Compare the differential vs. analytic geometry by citing relevant examples.
- Explain how to use a graphics system for solving various types of equations.
- How to divide the feasible and non-feasible regions in linear programming?
- What are confidence intervals and how it helps in statistical math?
- How to differentiate the effect of a magnetic field on a given point of the circle by using appropriate differential formula?
- What are the different types of identities that are used in trigonometric functions?
- Why polynomials are difficult to solve as compared to monomials? Give examples.
- Explain radical expressions and their significance with examples.
Final Words
We hope you have identified an ideal topic from the list of math research topics and ideas recommended above. If you haven’t found a unique research topic or need assistance to complete your math research paper, then contact us.
