251+ Math Research Topics [2024 Updated]

Math research topics

Mathematics, often dubbed as the language of the universe, holds immense significance in shaping our understanding of the world around us. It’s not just about crunching numbers or solving equations; it’s about unraveling mysteries, making predictions, and creating innovative solutions to complex problems. In this blog, we embark on a journey into the realm of math research topics, exploring various branches of mathematics and their real-world applications.

How Do You Write A Math Research Topic?

Writing a math research topic involves several steps to ensure clarity, relevance, and feasibility. Here’s a guide to help you craft a compelling math research topic:

  • Identify Your Interests: Start by exploring areas of mathematics that interest you. Whether it’s pure mathematics, applied mathematics, or interdisciplinary topics, choose a field that aligns with your passion and expertise.
  • Narrow Down Your Focus: Mathematics is a broad field, so it’s essential to narrow down your focus to a specific area or problem. Consider the scope of your research and choose a topic that is manageable within your resources and time frame.
  • Review Existing Literature: Conduct a thorough literature review to understand the current state of research in your chosen area. Identify gaps, controversies, or unanswered questions that could form the basis of your research topic.
  • Formulate a Research Question: Based on your exploration and literature review, formulate a clear and concise research question. Your research question should be specific, measurable, achievable, relevant, and time-bound (SMART).
  • Consider Feasibility: Assess the feasibility of your research topic in terms of available resources, data availability, and research methodologies. Ensure that your topic is realistic and achievable within the constraints of your project.
  • Consult with Experts: Seek feedback from mentors, advisors, or experts in the field to validate your research topic and refine your ideas. Their insights can help you identify potential challenges and opportunities for improvement.
  • Refine and Iterate: Refine your research topic based on feedback and further reflection. Iterate on your ideas to ensure clarity, coherence, and relevance to the broader context of mathematics research.
  • Craft a Title: Once you have finalized your research topic, craft a compelling title that succinctly summarizes the essence of your research. Your title should be descriptive, engaging, and reflective of the key themes of your study.
  • Write a Research Proposal: Develop a comprehensive research proposal outlining the background, objectives, methodology, and expected outcomes of your research. Your research proposal should provide a clear roadmap for your study and justify the significance of your research topic.

By following these steps, you can effectively write a math research topic that is well-defined, relevant, and poised to make a meaningful contribution to the field of mathematics.

251+ Math Research Topics: Beginners To Advanced

  • Prime Number Distribution in Arithmetic Progressions
  • Diophantine Equations and their Solutions
  • Applications of Modular Arithmetic in Cryptography
  • The Riemann Hypothesis and its Implications
  • Graph Theory: Exploring Connectivity and Coloring Problems
  • Knot Theory: Unraveling the Mathematics of Knots and Links
  • Fractal Geometry: Understanding Self-Similarity and Dimensionality
  • Differential Equations: Modeling Physical Phenomena and Dynamical Systems
  • Chaos Theory: Investigating Deterministic Chaos and Strange Attractors
  • Combinatorial Optimization: Algorithms for Solving Optimization Problems
  • Computational Complexity: Analyzing the Complexity of Algorithms
  • Game Theory: Mathematical Models of Strategic Interactions
  • Number Theory: Exploring Properties of Integers and Primes
  • Algebraic Topology: Studying Topological Invariants and Homotopy Theory
  • Analytic Number Theory: Investigating Properties of Prime Numbers
  • Algebraic Geometry: Geometry Arising from Algebraic Equations
  • Galois Theory: Understanding Field Extensions and Solvability of Equations
  • Representation Theory: Studying Symmetry in Linear Spaces
  • Harmonic Analysis: Analyzing Functions on Groups and Manifolds
  • Mathematical Logic: Foundations of Mathematics and Formal Systems
  • Set Theory: Exploring Infinite Sets and Cardinal Numbers
  • Real Analysis: Rigorous Study of Real Numbers and Functions
  • Complex Analysis: Analytic Functions and Complex Integration
  • Measure Theory: Foundations of Lebesgue Integration and Probability
  • Topological Groups: Investigating Topological Structures on Groups
  • Lie Groups and Lie Algebras: Geometry of Continuous Symmetry
  • Differential Geometry: Curvature and Topology of Smooth Manifolds
  • Algebraic Combinatorics: Enumerative and Algebraic Aspects of Combinatorics
  • Ramsey Theory: Investigating Structure in Large Discrete Structures
  • Analytic Geometry: Studying Geometry Using Analytic Methods
  • Hyperbolic Geometry: Non-Euclidean Geometry of Curved Spaces
  • Nonlinear Dynamics: Chaos, Bifurcations, and Strange Attractors
  • Homological Algebra: Studying Homology and Cohomology of Algebraic Structures
  • Topological Vector Spaces: Vector Spaces with Topological Structure
  • Representation Theory of Finite Groups: Decomposition of Group Representations
  • Category Theory: Abstract Structures and Universal Properties
  • Operator Theory: Spectral Theory and Functional Analysis of Operators
  • Algebraic Number Theory: Study of Algebraic Structures in Number Fields
  • Cryptanalysis: Breaking Cryptographic Systems Using Mathematical Methods
  • Discrete Mathematics: Combinatorics, Graph Theory, and Number Theory
  • Mathematical Biology: Modeling Biological Systems Using Mathematical Tools
  • Population Dynamics: Mathematical Models of Population Growth and Interaction
  • Epidemiology: Mathematical Modeling of Disease Spread and Control
  • Mathematical Ecology: Dynamics of Ecological Systems and Food Webs
  • Evolutionary Game Theory: Evolutionary Dynamics and Strategic Behavior
  • Mathematical Neuroscience: Modeling Brain Dynamics and Neural Networks
  • Mathematical Physics: Mathematical Models in Physical Sciences
  • Quantum Mechanics: Foundations and Applications of Quantum Theory
  • Statistical Mechanics: Statistical Methods in Physics and Thermodynamics
  • Fluid Dynamics: Modeling Flow of Fluids Using Partial Differential Equations
  • Mathematical Finance: Stochastic Models in Finance and Risk Management
  • Option Pricing Models: Black-Scholes Model and Beyond
  • Portfolio Optimization: Maximizing Returns and Minimizing Risk
  • Stochastic Calculus: Calculus of Stochastic Processes and Itô Calculus
  • Financial Time Series Analysis: Modeling and Forecasting Financial Data
  • Operations Research: Optimization of Decision-Making Processes
  • Linear Programming: Optimization Problems with Linear Constraints
  • Integer Programming: Optimization Problems with Integer Solutions
  • Network Flow Optimization: Modeling and Solving Flow Network Problems
  • Combinatorial Game Theory: Analysis of Games with Perfect Information
  • Algorithmic Game Theory: Computational Aspects of Game-Theoretic Problems
  • Fair Division: Methods for Fairly Allocating Resources Among Parties
  • Auction Theory: Modeling Auction Mechanisms and Bidding Strategies
  • Voting Theory: Mathematical Models of Voting Systems and Social Choice
  • Social Network Analysis: Mathematical Analysis of Social Networks
  • Algorithm Analysis: Complexity Analysis of Algorithms and Data Structures
  • Machine Learning: Statistical Learning Algorithms and Data Mining
  • Deep Learning: Neural Network Models with Multiple Layers
  • Reinforcement Learning: Learning by Interaction and Feedback
  • Natural Language Processing: Statistical and Computational Analysis of Language
  • Computer Vision: Mathematical Models for Image Analysis and Recognition
  • Computational Geometry: Algorithms for Geometric Problems
  • Symbolic Computation: Manipulation of Mathematical Expressions
  • Numerical Analysis: Algorithms for Solving Numerical Problems
  • Finite Element Method: Numerical Solution of Partial Differential Equations
  • Monte Carlo Methods: Statistical Simulation Techniques
  • High-Performance Computing: Parallel and Distributed Computing Techniques
  • Quantum Computing: Quantum Algorithms and Quantum Information Theory
  • Quantum Information Theory: Study of Quantum Communication and Computation
  • Quantum Error Correction: Methods for Protecting Quantum Information from Errors
  • Topological Quantum Computing: Using Topological Properties for Quantum Computation
  • Quantum Algorithms: Efficient Algorithms for Quantum Computers
  • Quantum Cryptography: Secure Communication Using Quantum Key Distribution
  • Topological Data Analysis: Analyzing Shape and Structure of Data Sets
  • Persistent Homology: Topological Invariants for Data Analysis
  • Mapper Algorithm: Method for Visualization and Analysis of High-Dimensional Data
  • Algebraic Statistics: Statistical Methods Based on Algebraic Geometry
  • Tropical Geometry: Geometric Methods for Studying Polynomial Equations
  • Model Theory: Study of Mathematical Structures and Their Interpretations
  • Descriptive Set Theory: Study of Borel and Analytic Sets
  • Ergodic Theory: Study of Measure-Preserving Transformations
  • Combinatorial Number Theory: Intersection of Combinatorics and Number Theory
  • Additive Combinatorics: Study of Additive Properties of Sets
  • Arithmetic Geometry: Interplay Between Number Theory and Algebraic Geometry
  • Proof Theory: Study of Formal Proofs and Logical Inference
  • Reverse Mathematics: Study of Logical Strength of Mathematical Theorems
  • Nonstandard Analysis: Alternative Approach to Analysis Using Infinitesimals
  • Computable Analysis: Study of Computable Functions and Real Numbers
  • Graph Theory: Study of Graphs and Networks
  • Random Graphs: Probabilistic Models of Graphs and Connectivity
  • Spectral Graph Theory: Analysis of Graphs Using Eigenvalues and Eigenvectors
  • Algebraic Graph Theory: Study of Algebraic Structures in Graphs
  • Metric Geometry: Study of Geometric Structures Using Metrics
  • Geometric Measure Theory: Study of Measures on Geometric Spaces
  • Discrete Differential Geometry: Study of Differential Geometry on Discrete Spaces
  • Algebraic Coding Theory: Study of Error-Correcting Codes
  • Information Theory: Study of Information and Communication
  • Coding Theory: Study of Error-Correcting Codes
  • Cryptography: Study of Secure Communication and Encryption
  • Finite Fields: Study of Fields with Finite Number of Elements
  • Elliptic Curves: Study of Curves Defined by Cubic Equations
  • Hyperelliptic Curves: Study of Curves Defined by Higher-Degree Equations
  • Modular Forms: Analytic Functions with Certain Transformation Properties
  • L-functions: Analytic Functions Associated with Number Theory
  • Zeta Functions: Analytic Functions with Special Properties
  • Analytic Number Theory: Study of Number Theoretic Functions Using Analysis
  • Dirichlet Series: Analytic Functions Represented by Infinite Series
  • Euler Products: Product Representations of Analytic Functions
  • Arithmetic Dynamics: Study of Iterative Processes on Algebraic Structures
  • Dynamics of Rational Maps: Study of Dynamical Systems Defined by Rational Functions
  • Julia Sets: Fractal Sets Associated with Dynamical Systems
  • Mandelbrot Set: Fractal Set Associated with Iterations of Complex Quadratic Polynomials
  • Arithmetic Geometry: Study of Algebraic Geometry Over Number Fields
  • Diophantine Geometry: Study of Solutions of Diophantine Equations Using Geometry
  • Arithmetic of Elliptic Curves: Study of Elliptic Curves Over Number Fields
  • Rational Points on Curves: Study of Rational Solutions of Algebraic Equations
  • Galois Representations: Study of Representations of Galois Groups
  • Automorphic Forms: Analytic Functions with Certain Transformation Properties
  • L-functions: Analytic Functions Associated with Automorphic Forms
  • Selberg Trace Formula: Tool for Studying Spectral Theory and Automorphic Forms
  • Langlands Program: Program to Unify Number Theory and Representation Theory
  • Hodge Theory: Study of Harmonic Forms on Complex Manifolds
  • Riemann Surfaces: One-dimensional Complex Manifolds
  • Shimura Varieties: Algebraic Varieties Associated with Automorphic Forms
  • Modular Curves: Algebraic Curves Associated with Modular Forms
  • Hyperbolic Manifolds: Manifolds with Constant Negative Curvature
  • Teichmüller Theory: Study of Moduli Spaces of Riemann Surfaces
  • Mirror Symmetry: Duality Between Calabi-Yau Manifolds
  • Kähler Geometry: Study of Hermitian Manifolds with Special Symmetries
  • Algebraic Groups: Linear Algebraic Groups and Their Representations
  • Lie Algebras: Study of Algebraic Structures Arising from Lie Groups
  • Representation Theory of Lie Algebras: Study of Representations of Lie Algebras
  • Quantum Groups: Deformation of Lie Groups and Lie Algebras
  • Algebraic Topology: Study of Topological Spaces Using Algebraic Methods
  • Homotopy Theory: Study of Continuous Deformations of Spaces
  • Homology Theory: Study of Algebraic Invariants of Topological Spaces
  • Cohomology Theory: Study of Dual Concepts to Homology Theory
  • Singular Homology: Homology Theory Defined Using Simplicial Complexes
  • Sheaf Theory: Study of Sheaves and Their Cohomology
  • Differential Forms: Study of Multilinear Differential Forms
  • De Rham Cohomology: Cohomology Theory Defined Using Differential Forms
  • Morse Theory: Study of Critical Points of Smooth Functions
  • Symplectic Geometry: Study of Symplectic Manifolds and Their Geometry
  • Floer Homology: Study of Symplectic Manifolds Using Pseudoholomorphic Curves
  • Gromov-Witten Invariants: Invariants of Symplectic Manifolds Associated with Pseudoholomorphic Curves
  • Mirror Symmetry: Duality Between Symplectic and Complex Geometry
  • Calabi-Yau Manifolds: Ricci-Flat Complex Manifolds
  • Moduli Spaces: Spaces Parameterizing Geometric Objects
  • Donaldson-Thomas Invariants: Invariants Counting Sheaves on Calabi-Yau Manifolds
  • Algebraic K-Theory: Study of Algebraic Invariants of Rings and Modules
  • Homological Algebra: Study of Homology and Cohomology of Algebraic Structures
  • Derived Categories: Categories Arising from Homological Algebra
  • Stable Homotopy Theory: Homotopy Theory with Stable Homotopy Groups
  • Model Categories: Categories with Certain Homotopical Properties
  • Higher Category Theory: Study of Higher Categories and Homotopy Theory
  • Higher Topos Theory: Study of Higher Categorical Structures
  • Higher Algebra: Study of Higher Categorical Structures in Algebra
  • Higher Algebraic Geometry: Study of Higher Categorical Structures in Algebraic Geometry
  • Higher Representation Theory: Study of Higher Categorical Structures in Representation Theory
  • Higher Category Theory: Study of Higher Categorical Structures
  • Homotopical Algebra: Study of Algebraic Structures in Homotopy Theory
  • Homotopical Groups: Study of Groups with Homotopical Structure
  • Homotopical Categories: Study of Categories with Homotopical Structure
  • Homotopy Groups: Algebraic Invariants of Topological Spaces
  • Homotopy Type Theory: Study of Foundations of Mathematics Using Homotopy Theory

In conclusion, the world of mathematics is vast and multifaceted, offering endless opportunities for exploration and discovery. Whether delving into the abstract realms of pure mathematics or applying mathematical principles to solve real-world problems, mathematicians play a vital role in advancing human knowledge and shaping the future of our world.

By embracing diverse math research topics and interdisciplinary collaborations, we can unlock new possibilities and harness the power of mathematics to address the challenges of today and tomorrow. So, let’s embark on this journey together as we unravel the mysteries of numbers and explore the boundless horizons of mathematical inquiry.

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260 Interesting Math Topics for Essays & Research Papers

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

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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.

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:

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  • 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.

Three main types of geometry.

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

🤔 Advanced Topics in Math to Write a Paper on

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

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

📚 Math Research Topics for a Paper

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

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

Mathematical writing should be well-structured, precise, and easy readable

  • 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.

E. T. Bell quote.

  • 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? 

The role of study of non-Euclidean geometry

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

➗ Calculus Topics to Write a Paper on

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

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

Calculus was developed by Isaac Newton and Gottfried Leibnitz.

  • 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
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  • 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
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220 Cause and Effect Essay Topics: Fun & Interesting

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A narrative essay tells a story about a series of events. At the core of this kind of essay can be a personal experience or a fictional plot. Any story can be a basis for a narrative essay! Narratives can look similar to descriptions. Still, they are different. A descriptive...

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Similar to the instructions in a recipe book, process essays convey information in a step-by-step format. In this type of paper, you follow a structured chronological process. You can also call it a how-to essay. A closely related type is a process analysis essay. Here you have to carefully consider...

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In a classification essay, you divide the subject into categories. To create these categories, you single out certain attributes of things. You can classify them according to their characteristics, themes, or traits. Sounds complicated? Be sure that any high school or college student can manage this type of essay!

200 Excellent Evaluation Essay Topics

Throughout your high school years, you are likely to write many evaluative papers. In an evaluation essay you aim is to justify your point of view through evidence.

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181 Mathematics Research Topics From PhD Experts

math research topics

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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Home > College of Natural Sciences > Mathematics > Mathematics Theses, Projects, and Dissertations

Mathematics Theses, Projects, and Dissertations

Theses/projects/dissertations from 2024 2024.

On Cheeger Constants of Knots , Robert Lattimer

Information Based Approach for Detecting Change Points in Inverse Gaussian Model with Applications , Alexis Anne Wallace

Theses/Projects/Dissertations from 2023 2023


An Exposition of the Curvature of Warped Product Manifolds , Angelina Bisson

Jackknife Empirical Likelihood Tests for Equality of Generalized Lorenz Curves , Anton Butenko


Statistical Analysis of Health Habits for Incoming College Students , Wendy Isamara Lizarraga Noriega

Reverse Mathematics of Ramsey's Theorem , Nikolay Maslov

Distance Correlation Based Feature Selection in Random Forest , Jose Munoz-Lopez

Constructing Hyperbolic Polygons in the Poincaré Disk , Akram Zakaria Samweil


Theses/Projects/Dissertations from 2022 2022


The Examination of the Arithmetic Surface (3, 5) Over Q , Rachel J. Arguelles

Error Terms for the Trapezoid, Midpoint, and Simpson's Rules , Jessica E. Coen

de Rham Cohomology, Homotopy Invariance and the Mayer-Vietoris Sequence , Stacey Elizabeth Cox

Symmetric Generation , Ana Gonzalez


Simple Groups and Related Topics , Simrandeep Kaur

Homomorphic Images and Related Topics , Alejandro Martinez



Verifying Sudoku Puzzles , Chelsea Schweer


Theses/Projects/Dissertations from 2021 2021

Non-Abelian Finite Simple Groups as Homomorphic Images , Sandra Bahena

Matroids Determinable by Two Partial Representations , Aurora Calderon Dojaquez


Symmetric Presentation of Finite Groups, and Related Topics , Marina Michelle Duchesne


A Study in Applications of Continued Fractions , Karen Lynn Parrish

Partial Representations for Ternary Matroids , Ebony Perez

Theses/Projects/Dissertations from 2020 2020

Sum of Cubes of the First n Integers , Obiamaka L. Agu

Permutation and Monomial Progenitors , Crystal Diaz

Tile Based Self-Assembly of the Rook's Graph , Ernesto Gonzalez

Research In Short Term Actuarial Modeling , Elijah Howells

Hyperbolic Triangle Groups , Sergey Katykhin

Exploring Matroid Minors , Jonathan Lara Tejeda


Modeling the Spread of Measles , Alexandria Le Beau

Symmetric Presentations and Related Topics , Mayra McGrath

Minimal Surfaces and The Weierstrass-Enneper Representation , Evan Snyder


Excluded minors for nearly-paving matroids , Vanessa Natalie Vega

Theses/Projects/Dissertations from 2019 2019

Fuchsian Groups , Bob Anaya

Tribonacci Convolution Triangle , Rosa Davila


Analogues Between Leibniz's Harmonic Triangle and Pascal's Arithmetic Triangle , Lacey Taylor James

Geodesics on Generalized Plane Wave Manifolds , Moises Pena

Algebraic Methods for Proving Geometric Theorems , Lynn Redman

Pascal's Triangle, Pascal's Pyramid, and the Trinomial Triangle , Antonio Saucedo Jr.



Theses/Projects/Dissertations from 2018 2018


Monomial Progenitors and Related Topics , Madai Obaid Alnominy

Progenitors Involving Simple Groups , Nicholas R. Andujo

Simple Groups, Progenitors, and Related Topics , Angelica Baccari

Exploring Flag Matroids and Duality , Zachary Garcia

Images of Permutation and Monomial Progenitors , Shirley Marina Juan


Progenitors, Symmetric Presentations, and Related Topics , Joana Viridiana Luna

Symmetric Presentations, Representations, and Related Topics , Adam Manriquez

Toroidal Embeddings and Desingularization , LEON NGUYEN


Tutte-Equivalent Matroids , Maria Margarita Rocha

Symmetric Presentations and Double Coset Enumeration , Charles Seager


Theses/Projects/Dissertations from 2017 2017

Investigation of Finite Groups Through Progenitors , Charles Baccari


Making Models with Bayes , Pilar Olid

An Introduction to Lie Algebra , Amanda Renee Talley



Theses/Projects/Dissertations from 2016 2016

Upset Paths and 2-Majority Tournaments , Rana Ali Alshaikh

Regular Round Matroids , Svetlana Borissova



Solving Absolute Value Equations and Inequalities on a Number Line , Melinda A. Curtis



LIFE EXPECTANCY , Ali R. Hassanzadah


A Dual Fano, and Dual Non-Fano Matroidal Network , Stephen Lee Johnson

Mathematical Reasoning and the Inductive Process: An Examination of The Law of Quadratic Reciprocity , Nitish Mittal

The Kauffman Bracket and Genus of Alternating Links , Bryan M. Nguyen

Probabilistic Methods In Information Theory , Erik W. Pachas


Indicators of Future Mathematics Proficiency: Literature Review & Synthesis , Claudia Preciado

Ádám's Conjecture and Arc Reversal Problems , Claudio D. Salas


The Evolution of Cryptology , Gwendolyn Rae Souza

Theses/Projects/Dissertations from 2015 2015


Homomorphic Images And Related Topics , Kevin J. Baccari

Geometric Constructions from an Algebraic Perspective , Betzabe Bojorquez

Discovering and Applying Geometric Transformations: Transformations to Show Congruence and Similarity , Tamara V. Bonn

Symmetric Presentations and Generation , Dustin J. Grindstaff



Simple Groups and Related Topics , Manal Abdulkarim Marouf Ms.

Elliptic Curves , Trinity Mecklenburg

A Fundamental Unit of O_K , Susana L. Munoz


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mini research topics in mathematics

Department members engage in cutting-edge research on a wide variety of topics in mathematics and its applications. Topics continually evolve to reflect emerging interests and developments, but can roughly grouped into the following areas.

Algebra, Combinatorics, and Geometry

Algebra, combinatorics, and geometry are areas of very active research at the University of Pittsburgh.

Analysis and Partial Differential Equations

The research of the analysis group covers functional analysis, harmonic analysis, several complex variables, partial differential equations, and analysis on metric and Carnot-Caratheodory spaces.

Applied Analysis

The department is a leader in the analysis of systems of nonlinear differential equations and dynamical systems  that arise in modeling a variety of physical phenomena. They include problems in biology, chemistry, phase transitions, fluid flow, flame propagation, diffusion processes, and pattern formation in nonlinear stochastic partial differential equations.

Mathematical Biology

The biological world stands as the next great frontier for mathematical modeling and analysis. This group studies complex systems and dynamics arising in various biological phenomena.

Mathematical Finance

A rapidly growing area of mathematical finance is Quantitative Behavioral Finance. The high-tech boom and bust of the late 1990s followed by the housing and financial upheavals of 2008 have made a convincing case for the necessity of adopting broader assumptions in finance.

Numerical Analysis and Scientific Computing

The diversity of this group is reflected in its research interests: numerical analysis of partial differential equations , adaptive methods for scientific computing, computational methods of fluid dynamics and turbulence, numerical solution of nonlinear problems arising from porous media flow and transport, optimal control, and simulation of stochastic reaction diffusion systems.

Topology and Differential Geometry

Research in analytic topology continues in the broad area of generalized metric spaces. This group studies relativity theory and differential geometry, with emphasis on twistor methods, as well as geometric and topological aspects of quantum field theory, string theory, and M-theory.

mini research topics in mathematics

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Math 380: Research Methods in Mathematics


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Pure mathematics articles from across Nature Portfolio

Pure mathematics uses mathematics to explore abstract ideas, mathematics that does not necessarily describe a real physical system. This can include developing the fundamental tools used by mathematicians, such as algebra and calculus, describing multi-dimensional space, or better understanding the philosophical meaning of mathematics and numbers themselves.

Latest Research and Reviews

mini research topics in mathematics

Max-mixed EWMA control chart for joint monitoring of mean and variance: an application to yogurt packing process

  • Seher Malik
  • Muhammad Hanif
  • Jumanah Ahmed Darwish

mini research topics in mathematics

Computation and convergence of fixed-point with an RLC-electric circuit model in an extended b-suprametric space

  • Sumati Kumari Panda
  • Vijayakumar Velusamy
  • Shafiullah Niazai

mini research topics in mathematics

Spectral shifted Chebyshev collocation technique with residual power series algorithm for time fractional problems

  • Saad. Z. Rida
  • Anas. A. M. Arafa
  • Marwa. M. M. Mostafa

mini research topics in mathematics

A novel group decision making method based on CoCoSo and interval-valued Q-rung orthopair fuzzy sets

mini research topics in mathematics

Entropy for q-rung linear diophantine fuzzy hypersoft set with its application in MADM

  • Mohd Asif Shah

mini research topics in mathematics

A stochastic model of preventive maintenance strategies for wind turbine gearboxes considering the incomplete maintenance

  • Hongsheng Su


News and Comment

mini research topics in mathematics

The real value of numbers

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166 Extraordinary Math Research Topics For Your Papers

math research topics

Math research topics cover various genres from which students can choose. Many people think that a research project on a math topic is dull. However, mathematics can be a wonderful and vivid field. Since it’s a universal language, mathematics can describe anything and everything, from galaxies that orbit each other to music. However, the broad nature of this study field also makes selecting a research paper difficult. That’s because learners want to pick interesting topics that will impress educators to award them top scores. This article lists the best math research paper topics. It’s useful because it inspires students to select or customize topics for their academic essays without much struggle.

What Are The Different Types Of Math?

As hinted, math covers several genres. Here are the primary types of mathematics:

Geometry: It’s a math branch that deals with the shapes, size, and relative position of figures. Many people consider geometry a practical math branch because it examines figures, shapes, sizes, and features of various entities, including parts like solids, lines, surfaces, lines, and angles. Algebra: It assists in solving equations and manipulating symbols. This branch helps students represent unknown quantities with alphabets and use them alongside numbers. Calculus: This area is vital in determining rates of change, such as velocity and acceleration. Arithmetic: Arithmetic is the most common and oldest math branch, encompassing basis number operations. These operations include subtraction, addition, divisions, and multiplications, and some schools shorten it as BODMAS. Statistics and Probability: They help analyze numerical data to make predictions. Probability is about chances, while statistics entails handling different data using various techniques. Trigonometry: It assists in calculating angles and distances between points. It mainly deals with triangles’ relationships, sides, and curves.

Now that you understand the types of mathematics, it’s easier to select a suitable research topic. The following are some of the best topic ideas in math. 

 Undergraduate Math Research Topics

Maybe you’re pursuing your undergraduate studies. However, you have challenges comprehending math topics, yet the professor expects you to write a superior paper. In that case, here’s a list of engaging research topics in math to consider for your essays.

  • An in-depth comprehension of the meaning of discrete random variables in math and their identification
  • Math evolution- Comprehending the Gauss-Markov
  • Primary math theorems- Investigating how they work
  • Continuous stochastic process- Exploring its role in the math process
  • Analyzing the Dempster-Shafer theory
  • The application of the transferable belief model
  • Exploring the use of math in artificial intelligence
  • The application of mathematics in daily life
  • Algebra and its history
  • Math and culture- What’s the relationship?
  • How drawing and painting could help with mathematics
  • Ways to boost math interest among learners
  • The social and political significance of learning mathematics
  • Circles and their relevance in mathematics
  • Challenges to math learning in public schools
  • Prove the use of F-Algebras
  • Understanding the meaning of abstract algebra
  • Discuss geometry and algebra
  • How acute square triangulation works
  • Discuss the essence of right triangles
  • Why non-Euclidean geometry should be compulsory for math students
  • Investigating number problems
  • Discuss the meaning of Dirac manifolds
  • How geometry influences chemistry and physics
  • Riemannian manifolds’ application in the Euclidean space

These are exciting math topics for undergraduate students. Nevertheless, prepare adequate time and resources to investigate any of these titles to draft a winning essay. You might have to provide theoretical and practical assessments when writing your essay.

Math Research Topics for High School Learners

Maybe your high school teacher asked you to write a research paper. Choosing a familiar topic is an excellent way to get a high grade. Here are some of the best math research paper topics for high school.

  • How to draw a chart representing the financial analysis of a prominent company over the last five years
  • How to solve a matrix- The vital principles and formulas to embrace
  • Exploring various techniques for solving finance and mathematical gaps
  • Discount factor- Why it’s crucial for learners and ways to achieve it
  • Calculating the interest rate and its essence in the banking industry
  • Why imaginary numbers are important
  • Investigating the application of math in the workplace
  • Explain why learners hate mathematics teachers
  • What makes math a complex subject?
  • Is making math compulsory in high school a good thing?
  • How to solve a dice question from a probability perspective
  • Understanding the Binomial theorem and its essence
  • Investigating Egyptian mathematics
  • Hyperbola- Understanding it and its use in math
  • When should students use calculators in class?
  • How to solve linear equations
  • Is the Pythagoras theorem important in math?
  • The interdependence between math and art
  • Philosophy’s role in math
  • Numerical data overview

High school learners can pick any of these titles and develop them into an essay. Nevertheless, they should prepare to spend some time investigating their topics to write pieces that will impress their educators. Titles that address math history and its influence on education can also suit high school students. However, learners should select titles that fulfil the academic requirements set by the educators.

Applied Math Research Topics

As a branch, applied math deals with mathematical methods and their real-life applications. These methods are manifest in engineering, finance, medicine, biology, physics, and others. Here are some of the exciting topics in this field.

  • Dimensions for examining fingerprints
  • Computer tomography and its significance
  • Step-stress modelling- What is its importance?
  • Explain the essence of data mining- How does it benefit the banking sector?
  • A detailed examination of nonlinear models
  • How genes discovery helps determine unhealthy and healthy patients
  • Algorithms and their role in probabilistic modelling
  • Mathematicians and their importance in robots’ development
  • Mathematicians’ role in crime prevention and data analysis
  • The essence of Law of Motion by Isaac in real life
  • The importance of math in energy conservation
  • Math and its role in quantum theory
  • Analyzing the Lorentz symmetry features
  • Evaluating the processing of the statistical signal in detail
  • Explain the achievement of Galilean Transformation

These are exciting ideas to explore when writing a research paper in applied math. Nevertheless, take your time to carefully and extensively research your preferred title to write a high-quality essay. Students should also note that some topics in this category require specialized knowledge to write superior papers.

It’s a challenge to write a paper for a high grade. Sometimes every student need a professional help with college paper writing. Therefore, don’t be afraid to hire a writer to complete your assignment. Just write a message “Please, write custom research paper for me” and get time to relax. Contact us today and get a 100% original paper. 

Interesting Math Research Topics

Maybe you’re among the learners that prefer working with exciting ideas. In that case, this category has topics that will interest you.

  • The uses of numerical analysis in machine learning
  • Foundations and philosophical problems
  • Convex versus Concave in geometry
  • Homological algebra- What is its purpose?
  • Is math useful in cryptography
  • Probability theory and random variable
  • Functional analysis- What are its four conditions?
  • Vector calculus versus multivariable
  • Mathematics and logicist definitions
  • Ways to apply the number theory in daily life
  • Studying complex math equations
  • How to calculate mode, median, and mean
  • Understanding the meaning of the Scholz conjecture
  • The definition of the past correspondence problem
  • Computational maths- What are its classes?
  • Multiplication table and its importance
  • What the Boolean satisfiability problem means for a learner
  • Understanding the linear speedup theory in mathematics
  • The Turing machine description
  • Understanding the Markov algorithm
  • Investigating the similarities and differences between Buchi automation and Pushdown automation
  • What is the meaning of Tree automation?
  • Describing the enclosing sphere method and its use in combinations
  • Egyptian pyramids and calculus
  • Analyzing De Finetti theorem in statistics and probability
  • Examining the congruence meaning in math
  • Application and purpose of calculus in the banking industry
  • Jean d’Alembert’s most famous works
  • Boolean algebra- What are its essential elements
  • Isaac Newton- His contribution, life, and time in math
  • Understanding the meaning of Sphericon
  • What is the purpose of Martingales?
  • Gauss times, energy, and contributions to math
  • Jakob Bernoulli- Exploring his famous works
  • A brief history of math

Some learners think writing a math essay is complex and tedious. However, you can find a topic you will enjoy working with throughout the project. These are exciting ideas to explore in research papers. However, prepare to spend sufficient time investigating your chosen title to write a winning paper, although these are generally relaxing titles for math papers and essays.

Math Research Topics for Middle School

Some middle school students worry about the math topics for their research. However, they can choose unique titles that will impress their teachers. Here are some of these ideas.

  • The impacts of standard exam curriculum on math education
  • Why is learning math so tricky?
  • What is the meaning of the commutative ring in algebra?
  • The Artin-Wedderburn theorem and its meaning
  • How monopolists and epimorphisms differ
  • Understanding the Jacobson density theorem
  • How linear approximations work
  • Root and ratio test definition
  • Statistics role in business
  • Economic lot scheduling- What does it mean?
  • Causes of the stock market crash
  • How many traders contribute to the New York Stock Exchange
  • The history of revenue management
  • Financial signs of an excellent investment
  • Depreciation and its odds
  • How a poor currency can benefit a country
  • How math helps with debt amortization
  • Ways to calculate a person’s net worth
  • Distinctions in algebra, trigonometry, and calculus
  • Discussing the beginning of calculus
  • The essence of stochastic in math
  • The meaning of limits in math
  • Ways to identify a critical point in a graph
  • Nonstandard analysis- What does it mean in the probability theory?
  • Continuous function description and meaning
  • Calculus- What are its primary principles?
  • Pythagoras theorem- What are its central tenets?
  • Calculus applications in finance
  • Theorem value in math
  • The application of linear approximations

This list has some of the best titles for middle school learners. But they also require some research to write superior essays. However, finding information on such topics is relatively easy, making them suitable for middle school students.

Math Research Topics for College Students

Maybe you’re pursuing college studies and need a title for a math research paper. In that case, here are exciting titles to consider for your essay.

  • What is the purpose of n-dimensional spaces?
  • Card counting- How does it work?
  • How continuous probability and discrete distribution differ
  • Understanding encryption- How Does it work?
  • Extremal problems- Investigating them in discrete geometry
  • The Mobius strip- Examining the topology
  • Why can a math problem be unsolvable?
  • Comparing different statistical methods
  • Explain the vital number theory concepts
  • Analyzing the polynomial functions’ degrees
  • Ways to divide complex numbers
  • Describe the prize problems with the millennium
  • The reasons for the unsolved Riemann hypothesis
  • Methods of solving Sudoku with math
  • Explain the fractals formation
  • Describe the evolution of math
  • Explore different types of Tower of Hanoi solutions
  • Discuss the uses of Napier’s bones
  • With examples, explain the chaos theory
  • Why are mathematical equations important all the time?
  • Fisher’s fundamental theorem and natural selection- Why are they important?

College professors expect students to draft papers with relevant and valuable information. These are relevant titles for college students. However, they require extensive research to write winning papers.

Cool Math Topics to Research

Maybe you don’t need a complex topic for your research paper. In that case, consider any of these ideas for your essay. If you have a problem writing even with these topics and you’re thinking: “solve my math for me,” you can always reach out to our service.

  • How contemporary architectural designs use geometry
  • What makes some math equations complex?
  • Ways to solve the Rubik’s cube
  • Discuss the meaning of prescriptive statistical and predictive analysis
  • Understanding the purpose of the chaos theory
  • What limits calculus?- Provide relevant examples
  • A comparison of universal and abstract algebra- How do they differ?
  • The relationship between probability and card tricks
  • Pascal’s Triangle- What does it mean?
  • Mobius strip- What are its features in geometry?
  • Multiple probability ideas- A brief overview
  • Discuss the meaning of the Golden Ration in Renaissance period paintings
  • How checkers and chess matter in understanding mathematics
  • Ways to measure infinity
  • Evaluating the Georg Contor theory
  • Are hexagons the most balanced shapes in the world?
  • The Koch snowflake- Explain the iterations
  • The history of various number types and their use
  • Game theory use in social science
  • Five math types with significant benefits in computer science

These are some of the most excellent math education research topics. However, they also require extensive research to write high-quality papers.

Enlist the Best College Research Paper Writing Service

Perhaps, you have a topic for your paper but not the time to write a winning piece. Maybe you’re not confident in your research, analytical, and writing skills. Thus, you’re unsure that you can write an essay that will compel your educator to award you the highest grade in your class. Well, you’re not the only one. Many students seek cheap research papers due to varied reasons. Whether it’s limited time and resources or a lack of the necessary skills and experience in academic paper writing, our crew can help you. We offer affordable college paper writing services and help in various math branches. Our experts can assist you if you need help with math research topics for high school students, college, or undergraduates. We are a professional team with a reputation for providing the best-rated academic writing assistance. Whether in university, college, or high school, our crew will offer the service you need to excel academically. Contact us now for cheap and reliable help with your academic essays.

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100+ Amazing Algebra Topics for Research Papers

Algebra Topics

Many students seek algebra topics when writing research papers in this mathematical field. Algebra is the study field that entails studying mathematical symbols and rules for their manipulation. Algebra is the unifying thread for most mathematics, including solving elementary equations to learning abstractions like rings, groups, and fields.

In most cases, people use algebra when unsure about the exact numbers. Therefore, they replace those numbers with letters. In business, algebra helps with sales prediction. While many students dislike mathematics, avoiding algebra research paper topics is almost impossible at an advanced study level.

Therefore, this article lists topics to consider when writing a research paper in this academic field. It’s helpful because many learners struggle to find suitable topics when writing research papers in this field.

How to Write Theses on Advanced Algebra Topics

A thesis on an algebra topic is an individual project that the learner writes after investigating and studying a specific idea. Here’s a step-by-step guide for writing a thesis on an algebra topic.

Pick a topic: Start by selecting a title for your algebra thesis. Your topic should relate to your research interests and your supervisor’s guidelines. Investigate your topic: Once you’ve chosen a topic, research it extensively to know the relevant theories, formulas, and texts. Your thesis should be an extension of a particular topic’s analysis and a report on your research. Write the thesis: Once you’ve explored the topic extensively, start writing your paper. Your dissertation should have an abstract, an introduction, the body, and a conclusion.

The abstract should summarise your thesis’ aims, scope, and conclusions. The introduction should introduce the topic, size, and significance while providing relevant literature and outlining the logical structure. The body should have several chapters with details and proofs of numerical implementations, while the conclusion should restate your main arguments and tell readers the effects. Also, it should suggest future work.

College Algebra Topics

You may need topics to consider if you’re in college and want to write an algebra research paper. Here’s a list of titles worth considering for your essay.

  • Exploring the relationship between Rubik’s cube and the group theory
  • Comparing the relationship between various equation systems
  • Finding the most appropriate way to solve mathematical word problems
  • Investigating the distance formula and its origin
  • Exploring the things you can achieve with determinants
  • Explaining what “domain” and “range” mean in algebra
  • A two-dimension analysis of the Gram-Schmidt process
  • Exploring the differences between eigenvalues and eigenvectors
  • What the Cramer’s rule states, and why does it matter
  • Describing the Gaussian elimination
  • Provide an induction-proof example
  • Describe the uses of F-algebras
  • Understanding the number problems in algebra
  • What’s the essence of abstract algebra?
  • Investigating Fermat’s last theorem peculiarities
  • Exploring the algebra essentials
  • Investigating the relationship between geometry and algebra

These are exciting topics in college algebra. However, writing a winning paper about any of them requires careful research and analysis. Therefore, prepare to spend sufficient time working on any of these titles.

Cool Topics in Algebra

Perhaps, you want to write about an excellent topic in this mathematical field. If so, consider the following ideas for your algebra paper.

  • Discussing a differential equation with illustrations
  • Describing and analysing the Noetherian ring
  • Explain the commutative ring from an algebra viewpoint
  • Describe the Artin-Weddderburn theorem
  • Studying the Jacobson density theorem
  • Describe the four properties of any binary operation from an algebra viewpoint
  • A detailed analysis of the unary operator
  • Analysing the Abel-Ruffini theorem
  • Monomorphisms versus Epimorphisms: Contrast and comparison
  • Discus Morita duality with algebraic structures in mind
  • Nilpotent versus Idempotent in Ring theory

Pick any idea from this list and develop it into a research topic. Your educator will love your paper and award you a good grade if you research it and write an informative essay.

Linear Algebra Topics

Linear algebra covers vector spaces and the linear mapping between them. Linear equation systems have unknowns, and mathematicians use vectors and matrices to represent them. Here are exciting topics in linear algebra to consider for your research paper.

  • Decomposition of singular value
  • Investigating linear independence and dependence
  • Exploring projections in linear algebra
  • What are linear transformations in linear algebra?
  • Describe positive definite matrices
  • What are orthogonal matrices?
  • Describe Euclidean vector spaces with examples
  • Explain how you can solve equation systems with matrices
  • Determinants versus matrix inverses
  • Describe mathematical operations using matrices
  • Functional analysis of linear algebra
  • Exploring linear algebra and its fundamentals

These are some of the exciting project topics in linear algebra. Nevertheless, prepare sufficient resources and time to investigate any of these titles to write a winning paper.

Pre Algebra Topics

Are you interested in a pre-algebra research topic? If so, this category has some of the most exciting ideas to explore.

  • Investigating the importance of pre-algebra
  • The best way to start pre-algebra for a beginner
  • Pre-algebra and algebra- Which is the hardest and why?
  • Core lessons in pre-algebra
  • What follows pre-algebra?
  • The first things to learn in pre-algebra
  • Investigating the standard form in pre-algebra
  • Provide pre-algebra examples using the basic rules to evaluate expressions
  • Differentiate pre-algebra and algebra
  • Describe five pre-algebra formulas

Consider exploring any of these ideas if you’re interested in pre-algebra. Nevertheless, choose a title you’re comfortable with to develop a winning paper.

Intermediate Algebra Topics for Research

Perhaps, you’re interested in intermediate algebra. If so, consider any of these ideas for your research paper.

  • Reviewing absolute value and real numbers
  • Investigating real numbers’ operations
  • Exploring the cube and square roots of real numbers
  • Analysing algebraic formulas and expressions
  • What are the rules of scientific notation and exponents?
  • How to solve a linear inequality with a single variable
  • Exploring relations, functions, and graphics from an algebraic viewpoint
  • Investigating linear systems with two variables and solutions
  • How to solve a linear system with two variables
  • Exploring linear systems applications with two variables
  • How to solve a linear system with three variables
  • Gaussian elimination and matrices
  • How to simplify a radical expression
  • How to add and subtract a radical expression
  • How to multiply and divide a radical expression
  • How to extract a square root and complete the square
  • Investigating quadratic functions and graphs
  • How to solve a polynomial and rational inequality
  • How to solve logarithmic and exponential equations
  • Exploring arithmetic series and sequences

These are exciting topics in intermediate algebra to consider for research papers. Nevertheless, learners should prepare to solve equations in their work.

Algebra Topics High School Students Can Explore

Are you in high school and want to explore algebra? If yes, consider these topics for your research, they could be a great coursework help to you.

  • Crucial principles and formulas to embrace when solving a matrix
  • Ways to create charts on a firm’s financial analysis for the past five years
  • How to find solutions to finance and mathematical gaps
  • Ways to solve linear equations
  • What is a linear equation- Provide examples
  • Describe the substitution and elimination methods for solving equations
  • How to solve logarithmic equations
  • What are partial fractions?
  • Describe linear inequalities with examples
  • How to solve a quadratic equation by factoring
  • How to solve a quadratic equation by formula
  • How to solve a quadratic equation with a square completion method
  • How to frame a worksheet for a quadratic equation
  • Explain the relationship between roots and coefficients
  • Describe rational expressions and ways to simplify them
  • Describe a cubic equation roots
  • What is the greatest common factor- Provide examples
  • What is the least common multiple- Provide examples
  • Describe the remainder theorem with examples

Explore any of these titles for your high school paper. However, pick a title you’re comfortable working with from the beginning to the end to make your work easier.

Advanced Topics in Algebra and Geometry

Maybe you want to explore something more advanced in your paper. In that case, the following list has advanced topics in geometry and algebra worth considering.

  • Arithmetical structures and their algorithmic aspects
  • Fractional thermoentropy spaces in topological quantum fields
  • Fractional thermoentripy spaces in large-scale systems
  • Eigenpoints configurations
  • Investigating the higher dimension aperiodic domino problem
  • Exploring math anxiety, executive functions, and math performance
  • Coherent quantiles and lifting elements
  • Absolute values extension on two subfields
  • Reviewing the laws of form and Majorana fermions
  • Studying the specialisation and rational maps degree
  • Investigating mathematical-pedagogical knowledge of prospective teachers in ECD programs
  • The adeles I model theory
  • Exploring logarithmic vector fields, arrangements, and divisors’ freeness
  • How to reconstruct curves from Hodge classes
  • Investigating Eigen points configuration

These are advanced topics in algebra and geometry worth investigating. However, please prepare to explore your topic extensively to write a strong essay.

Abstract Algebra Topics

Most people study abstract algebra in college. If you’re interested in research in this area, consider these topics for your project.

  • Describe abstract algebra applications
  • Why is abstract algebra essential?
  • Describe ring theory and its application
  • What is group theory, and why does it matter?
  • Describe the critical conceptual algebra levels
  • Describe the fundamental theorem of the finite Abelian groups
  • Describe Sylow’s theorems
  • What is Polya counting?
  • Describe the RSA algorithm
  • What are the homomorphisms and ideals of Rings?
  • Describe integral domains and factorisation
  • Describe Boolean algebra and its importance
  • State and explain Cauchy’s Theorem- Why is it important?

This algebra topics list is not exhaustive. You can find more ideas worth exploring in your project. Nevertheless, pick an idea you will work with comfortably to deliver a winning paper.

Get Professional Math Homework Help!

Perhaps, you don’t have the time to find accurate algebra homework solutions. Maybe you need math thesis help from an expert. If so, you’ve no reason to search further. Our thesis writing services in USA can help you write a winning assignment. We offer custom help with math assignments at cheap prices.

If you want to get a quality algebra dissertation without sweating, place an order with us. We’re an online team providing homework help to students across educational levels. We guarantee you a top-notch service once you approach us, saying, “Please do my math assignment.” We’re fast and can beat even a tight deadline without compromising quality. And whether you’re in high school, university, or college, we will write a paper that will compel your teacher to award you the best grade in your class. Contact us now!

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research mini overview

RESEARCH MINIS – AN OVERVIEW ( get this info as a single-page PDF )

A research mini is a side-by-side comparison of two different pedagogical approaches for the same content topic.

For example, look at the two different approaches to the topic of Area Representations of Fractions at

The goal is not to show that one approach is better than the other. Often, students benefit from seeing a topic through various approaches and perspectives.

The goal is to showcase a new approach that you have designed that you feel is worth sharing, and to compare it to an approach that educators have likely seen before.

The audience for a research mini are educators. They are busy people who are looking for cool ideas to try out in their classrooms.

Here are some suggestions for designing these side-by-side comparisons:

  • Show them as classroom dialogues, with speech bubbles.
  • Use stick figures to represent generic students / teachers.
  • Give educators enough information to be able to try each approach in their classroom.
  • Be as succinct as possible.

You will find more examples of research minis at

Geometry learning with dynamic software in pre-service mathematics teacher education: A systematic review

  • Published: 13 May 2024

Cite this article

mini research topics in mathematics

  • Juan Luis Prieto-González   ORCID: 1 &
  • Rafael Enrique Gutiérrez-Araujo   ORCID: 2  

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Providing an overview of the accumulated scientific knowledge regarding the learning of geometry with dynamic software by pre-service mathematics teachers is currently a pertinent issue in Mathematics Education. The interest in this topic within the field is reflected in the significance attributed to the role of the teacher as a pivotal actor in their students learning. Considering this, we present a systematic review that seeks to understand how the learning of school geometry content with dynamic software has been promoted and studied during pre-service mathematics teacher education. To do so, we have reviewed a group of journal articles, published between 2017 and 2023, following the principles of PRISMA declaration. The results reveal how researchers understand such learning, the pre-service teachers, the teacher educator, the tasks that promote it, and the production and analysis of data. Given these findings, we identify gaps in the research on this topic, among which stand out the view of pre-service teachers as autonomous subjects, the instrumentalist conception of dynamic software, and methodological approaches to data analysis that do not fully consider the role of the body in the act of knowing. These gaps reveal that the promotion of and study of learning of school geometry content with dynamic software have been explored little from sociocultural perspectives. Because of this, we believe it necessary to develop studies regarding learning from theoretical and methodological perspectives that demonstrate pathways for future explorations on the addressed topic and thus allow for the reduction of these gaps.

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Abrantes, P. (1999). Investigações em geometria na sala de aula. In E. Veloso, H. Fonseca, J. Ponte, & P. Abrantes (Eds.), Ensino da Geometria no virar do milénio (pp. 51–62). Departamento de Educação da Faculdade de Ciências da Universidade de Lisboa.

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Bairral, M. A., & Silvano, T. S. (2023). Licenciandos em matemática interagindo no VMTcG em uma tarefa sobre translação. Educação Matemática Pesquisa, 25 (1), 305–335.

Bartolini, M. G., & Mariotti, M. A. (2008). Semiotic mediation in the mathematics classroom. Artifacts and signs after a Vygotskian perspective. In L. English (Ed.), Handbook of International Research in Mathematics Education (pp. 746–805). Routledge.

Bautista, A., & Roth, W.-M. (2012). Conceptualizing sound as a form of incarnate mathematical consciousness. Educational Studies in Mathematics, 79 (1), 1–19.

Bretscher, N. (2017). Beyond a positive stance: Integrating technology is demanding on teachers’ mathematical knowledge for teaching. In T. Dooley, & G. Gueudet (Eds.), Proceedings of the 10th Congress of the European Society for Research in Mathematics Education (pp. 2358–2365). ERME.

Bretscher, N. (2023). Conceptualising TPACK within mathematics education: Teachers’ strategies for capitalising on transitions within and beyond dynamic geometry software. Digital Experiences in Mathematics Education, 9 , 232–254.

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Prieto-González, J.L., Gutiérrez-Araujo, R.E. Geometry learning with dynamic software in pre-service mathematics teacher education: A systematic review. Educ Inf Technol (2024).

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Highlight links, change contrast, increase text size, increase letter spacing, readability bar, dyslexia friendly font, increase cursor size, the cmp team shares research at the 2024 create for stem mini-conference.

  • May 8, 2024

The CMP Team presented at the 10th Annual CREATE for STEM Mini-Conference at The STEM Teaching and Learning Center on May 6, 2024.

It was a great day to showcase our CMP4 and NSF projects. Learning and connecting with other Spartans and hearing an inspirational talk by Shirley Malcom were just a few of the highlights from the day.

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Connected mathematics4 : a contextualized, problem-based middle grades mathematics curriculum for students and teachers  .

Authors : Elizabeth Phillips, Glenda Lappan, James Fey, Susan Friel, Yvonne Slanger-Grant, & Alden J. Edson   CMP Staff : Elizabeth Phillips, Alden J. Edson, Taren Going, Elizabeth Lozen, Sunyoung Park, & Chris Waston   CMP Graduate Assistants : Ashley Fabry, Ahmad Wachidul Kohar, Sasha Rudow, & Samantha Wald  

For over thirty years the team at Michigan State University has been designing, field-testing, and evaluating four revisions of the Connected Mathematics Project’s curriculum, Connected Mathematics . CMP4 is a contextualized, problem-based mathematics curriculum. Important mathematical ideas are identified and embedded in a sequence of contextual problems. This poster reports on the design features, development, field testing, professional learning, and feedback from over 500 teachers and their students.  

CMP4 A Contextualized, Problem-Based Math Curriculum

Enhancing the Teacher-Curriculum Relationship in Problem-Based Mathematics Classrooms by Connecting Teacher and Student Digital Collaborative Environments   

  PIs : Elizabeth Phillips, Alden J. Edson, Kristen Bieda, Chad Dorsey, Nathan Kimball   Research Team : Ashley Fabry, Taren Going, Ahmad Wachidul Kohar, Sunyoung Park, Sasha Rudow, and Samantha Wald  

The project is extending a digital collaborative platform for networks of teachers to create, use, and share resources for planning, teaching, and reflecting. The resources online include problem-based curriculum, classroom artifacts from students, and resources created by teachers. This poster reports on our research efforts to examine the extent to which teachers and students use the digital collaborative platform as a resource during the whole-class summary discussions.  

Enhancing the Teacher-Curriculum Relationship

Using Problem-Based Learning Analytics to Investigate Individual and Collaborative Mathematics Learning in a Digital Environment Over Time   

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The project aims to understand how engagement in learning proportional reasoning is enhanced by a digital collaborative platform with an embedded problem-based curriculum and a digital mathematics notebook. This poster reports on our research efforts to use artificial intelligence/machine learning techniques to provide teachers with (1) real-time information on evidence of students’ mathematical thinking, (2) interactive features for using evidence of students’ thinking during whole-group summary discussions, and (3) artificial intelligence suggestions of student thinking.  

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I just read the ANN newsletter and it's full of real gems. There are examples of using visual representations for assorted challenging concepts so that students can build understanding and think mathematically :)     I just signed up for the SABES sessions (yay!  I don't have to be in Massachusetts to go!).   

I dropped in at an online conference from the folks at Just Equations, about rectifying inequities in math education.  I was wondering if anybody 'round here had been there.  I went with cautious skepticism and was inspired by the opening speaker who encouraged us to not just think of the "low hanging fruit."   Alas, both of the sessions about adults and math were definitely all about "low hanging fruit" -- improving success at elite schools (Cal Tech, Johns Hopkins and another), and improving things for students transferring to four-year programs.   Since some of the folks speaking and sponsoring have preached loudly about remedial math in postsecondary being a "quagmire," I was intrigued that they simply didn't address students needing math foundations at all (except when talking about K-12 and how that was the result of inequities).     I've sent an email but haven't gotten a response.  

That said,  I wonder if the big push to eliminate remedial math in postsecondary could mean more folks going to different "adult ed" programs and how that's going to play out. Career specific courses for certificates?  

I also went to a face-to-face gathering of tutoring center people and it was wonderful to be with folks I didn't have to explain adult learners to ;)   They are also facing big challenges w/ the students whose needs are not met by "just put 'em in college level with co-requisite" options. THe best session was the "accessibility" session where we talked about some of the exact topics in the ANN newsletter -- using visuals to build understanding, and the idea that many students need slower, not faster.        Our semester's winding down and I'll be taking some days off but summer is also when I can do more exploring and creating and sharing online, so I'm looking forward to it! 

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This article is part of the research topic.

Spotlight on Nanotechnology: the African Continent

Nanoscience Teaching and Research program in South Africa Provisionally Accepted

  • 1 University of the Western Cape, South Africa
  • 2 Université de Lorraine, France

The final, formatted version of the article will be published soon.

Since 2012, the National Nanoscience Teaching and Training Platform (NNPTTP), funded by the South African Department of Science and Innovation (DSI), has been responsible for overseeing Africa's first-ever master's in nanoscience program. For over a decade, the NNPTTP has seen the cooperation of four partner universities across South Africa, namely the University of Johannesburg (UJ), University of the Free State (UFS), University of the Western Cape (UWC), and Nelson Mandela University (NMU), culminating in over 250 graduates trained in either nanophysics, nanochemistry, or nanobiology. Originally established to train professionals for a nanotechnologybased industry, both in South Africa and internationally, the program and platform has evolved into a testament to scientific collaboration. This paper discusses the program's framework, successes and challenges, related research, and future plans.

Keywords: nanoscience, Nanotechnology, nanophysics, Nanochemistry, nanobiology, Entrepreneurship

Received: 15 Mar 2024; Accepted: 15 May 2024.

Copyright: © 2024 Lindsay and Nel. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY) . The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

* Correspondence: Mx. Robert Lindsay, University of the Western Cape, Bellville, South Africa

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    Department members engage in cutting-edge research on a wide variety of topics in mathematics and its applications. Topics continually evolve to reflect emerging interests and developments, but can roughly grouped into the following areas. Algebra, Combinatorics, and Geometry Algebra, combinatorics, and geometry are areas of very active research at the University of Pittsburgh.

  7. Math 380: Research Methods in Mathematics

    Metadata. Math 380: Research Methods was developed for Fall semester of 2015 by Dr. Dandrielle Lewis, Dr. Carolyn Otto, and three undergraduate mentors. The main premise of this course is to instruct future mathematicians on the art and procedures of mathematics research. This course prepares students for student/faculty research collaboration ...

  8. Future themes of mathematics education research: an international

    Before the pandemic (2019), we asked: On what themes should research in mathematics education focus in the coming decade? The 229 responses from 44 countries led to eight themes plus considerations about mathematics education research itself. The themes can be summarized as teaching approaches, goals, relations to practices outside mathematics education, teacher professional development ...

  9. Pure mathematics

    Pure mathematics uses mathematics to explore abstract ideas, mathematics that does not necessarily describe a real physical system. This can include developing the fundamental tools used by ...

  10. Frontiers in Applied Mathematics and Statistics

    Computational Methods for Spatial Biomedical Data Analysis. Qiwei Li. Himel Mallick, PhD, FASA. Xiaowei Zhan. Guanyu Hu. 730 views. Explores how the application of mathematics and statistics can drive scientific developments across data science, engineering, finance, physics, biology, ecology, business, medicine, and beyond.

  11. 166 Math Research Topics for Academic Papers and Essays

    Here are some of the best math research paper topics for high school. How to draw a chart representing the financial analysis of a prominent company over the last five years. How to solve a matrix- The vital principles and formulas to embrace. Exploring various techniques for solving finance and mathematical gaps.

  12. Research

    In applied mathematics, we look for important connections with other disciplines that may inspire interesting and useful mathematics, and where innovative mathematical reasoning may lead to new insights and applications. Combinatorics. Computational Biology. Physical Applied Mathematics. Computational Science & Numerical Analysis.

  13. Math/Stats Thesis and Colloquium Topics

    An outstanding student who writes a mini-thesis, or pursues actuarial honors and writes a paper, might also be considered. In all cases, the award of honors and highest honors is the decision of the Department. ... One of my research topics is variable selection for high-dimensional data. ... Any interesting topic in mathematics. Leo Goldmakher.

  14. 1164588 PDFs

    Mathematics, Pure and Applied Math | Explore the latest full-text research PDFs, articles, conference papers, preprints and more on MATHEMATICS. Find methods information, sources, references or ...

  15. Trends in mathematics education and insights from a meta ...

    Review studies are vital for advancing knowledge in many scientific fields, including mathematics education, amid burgeoning publications. Based on an extensive consideration of existing review typologies, we conducted a meta-review and bibliometric analysis to provide a comprehensive overview of and deeper insights into review studies within mathematics education. After searching Web of ...

  16. 100-Plus Exciting Algebra Topics for Research Papers

    College Algebra Topics. You may need topics to consider if you're in college and want to write an algebra research paper. Here's a list of titles worth considering for your essay. Exploring the relationship between Rubik's cube and the group theory. Comparing the relationship between various equation systems.


    Learning Task 2Conduct a mini-research on students' performance in their third-quarter summative test in Mathematics. Apply the knowledge and skills you have...


    The high school dropout. rate in 2006 was 6.3% while the chronic truancy rate was at 7.4%. The financial earnings of the teachers and administrators at this district average at. $62, 452 per year. The teachers in this district have been working for an average for 12.5. years.

  19. A Mini Research For Math Grade 10

    A Mini Research for Math Grade 10(1) - Free download as Word Doc (.doc / .docx), PDF File (.pdf), Text File (.txt) or read online for free. Research

  20. A Mini Statistical Research On The Performance of Grade10 ...

    This document summarizes a mini-statistical research on the performance of grade 10 students in mathematics for the third quarter. It analyzes students' grades and survey responses. The research found that 88% of students scored below 92.25% with an average grade of 85.73%. Most students reported difficulties understanding mathematical processes. Nearly half found the topic of conditional ...

  21. research mini overview

    A research mini is a side-by-side comparison of two different pedagogical approaches for the same content topic. ... hosted by the Centre for Mathematics Education at the Fields Institute for Research in Mathematical Sciences. The views expressed on this website belong to the authors and do not necessarily reflect the opinions of the Ministry ...

  22. Geometry learning with dynamic software in pre-service mathematics

    2.3 Stage 3: Critical review of articles. This stage took place in three phases. First, we defined categories and descriptors for the review of the articles, which we organized in two classes derived from our research question: promotion and study of the learning of school geometry content with dynamic software. The categories of each class account for different aspects of the promotion and ...

  23. Applied Mathematics Research

    Applied Mathematics Research. In applied mathematics, we look for important connections with other disciplines that may inspire interesting and useful mathematics, and where innovative mathematical reasoning may lead to new insights and applications. ... Department of Mathematics Headquarters Office Simons Building (Building 2), Room 106 77 ...

  24. A mini research Presented to Malinta National High school

    Christian A Hesse. The purpose of this book is to acquaint the reader with the increasing number of applications of statistics in engineering and the social sciences. It can be used as a textbook for a first course in statistical methods in Universities and Polytechnics. The book can also be used by decision makers and researchers to either ...

  25. MATHEMATICS Quarter 4

    MATHEMATICS Quarter 4 - Module 5 Statistical Mini-Research. Last updated on May 29, 2021 Grade 10. Math 10 4th Quarter. Related. MATHEMATICS Quarter 4 - Module 4 Solving Problems Involving Measures of Position; MATHEMATICS Quarter 4 - Module 1 Illustrating The Measures of Position for Ungrouped Data;

  26. The CMP Team Shares Research at the 2024 CREATE for STEM Mini-Conference

    CMP Staff, Graduate Students, and Undergraduate Students presented at the 10th Annual CREATE for STEM Mini-Conference at The STEM Teaching and Learning Center on May 6, 2024. It was a great day to showcase our CMP4 and NSF projects. Learning and connecting with other Spartans and hearing an inspirational talk by Shirley Malcom were just a few of the highlights from the day.

  27. Parental early math support: The role of parental knowledge about early

    We hypothesized that parents' knowledge about the development of two critical early math topics would help explain some of this variability in their early math support. U.S. parents of 3- and 4-year-olds ( N = 196 mothers and 148 fathers, 94% identified as the child's primary caregiver and 77% as White; 79% had at least a bachelor's degree ...

  28. Electronics

    With the rapid development of artificial intelligence in recent years, intelligent evaluation of college students' growth by means of the monitoring data from training processes is becoming a promising technique in the field intelligent education. Current studies, however, tend to utilize course grades, which are objective, to predict students' grade-point averages (GPAs), but usually ...

  29. Sharing Math Ideas

    Sharing Math Ideas. Submitted by Susan Jones on Thu, 05/09/2024 - 15:19. I just read the ANN newsletter and it's full of real gems. There are examples of using visual representations for assorted challenging concepts so that students can build understanding and think mathematically :) I just signed up for the SABES sessions (yay!

  30. Nanoscience Teaching and Research program in South Africa

    Since 2012, the National Nanoscience Teaching and Training Platform (NNPTTP), funded by the South African Department of Science and Innovation (DSI), has been responsible for overseeing Africa's first-ever master's in nanoscience program. For over a decade, the NNPTTP has seen the cooperation of four partner universities across South Africa, namely the University of Johannesburg (UJ ...