math research problems

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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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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“Teachers should teach math in a way that encourages students to engage in sense-making and not merely to memorize or internalize exactly what the teacher says or does,” says Jon R. Star.

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One way is the wrong way to do math. Here’s the right way.

Harvard Staff Writer

Research by Ed School psychologist reinforces case for stressing multiple problem-solving paths over memorization

There’s never just one way to solve a math problem, says Jon R. Star , a psychologist and professor of education at the Harvard Graduate School of Education. With researchers from Vanderbilt University, Star found that teaching students multiple ways to solve math problems instead of using a single method improves teaching and learning. In an interview with the Gazette, Star, a former math teacher, outlined the research and explained how anyone, with the right instruction, can develop a knack for numbers.

Jon R. Star

GAZETTE: What is the most common misconception about math learning?

STAR: That you’re either a math person or you’re not a math person — that some people are just born with math smarts, and they can do math, and other people are just not, and there’s not much you can do about it.

GAZETTE: What does science say about the process of learning math?

STAR: One thing we know from psychology about the learning process is that the act of reaching into your brain, grabbing some knowledge, pulling it out, chewing on it, talking about it, and putting it back helps you learn. Psychologists call this elaborative encoding. The more times you can do that process — putting knowledge in, getting it out, elaborating on it, putting it back in — the more you will have learned, remembered, and understood the material. We’re trying to get math teachers to help students engage in that process of elaborative encoding.

GAZETTE: How did you learn math yourself?

STAR: Learning math should involve some sense-making. It’s necessary that we listen to what our teacher tells us about the math and try to make sense of it in our minds. Math learning is not about pouring the words directly from the teacher’s mouth into the students’ ears and brains. That’s not the way it works. I think that’s how I learned math. But that’s not how I hope students learn math and that’s not how I hope teachers think about the teaching of math. Teachers should teach math in a way that encourages students to engage in sense-making and not merely to memorize or internalize exactly what the teacher says or does.

GAZETTE: Tell us about the teaching method described in the research.

STAR: One of the strategies that some teachers may use when teaching math is to show students how to solve problems and expect that the student is going to end up using the same method that the teacher showed. But there are many ways to solve math problems; there’s never just one way.

The strategy we developed asks that teachers compare two ways for solving a problem, side by side, and that they follow an instructional routine to lead a discussion to help students understand the difference between the two methods. That discussion is really the heart of this routine because it is fundamentally about sharing reasoning: Teachers ask students to explain why a strategy works, and students must dig into their heads and try to say what they understand. And listening to other people’s reasoning reinforces the process of learning.

GAZETTE: Why is this strategy an improvement over just learning a single method?

STAR: We think that learning multiple strategies for solving problems deepens students’ understanding of the content. There is a direct benefit to learning through comparing multiple methods, but there are also other types of benefits to students’ motivation. In this process, students come to see math a little differently — not just as a set of problems, each of which has exactly one way to solve it that you must memorize, but rather, as a terrain where there are always decisions to be made and multiple strategies that one might need to justify or debate. Because that is what math is.

For teachers, this can also be empowering because they are interested in increasing their students’ understanding, and we’ve given them a set of tools that can help them do that and potentially make the class more interesting as well. It’s important to note, too, that this approach is not something that we invented. In this case, what we’re asking teachers to do is something that they do a little bit of already. Every high school math teacher, for certain topics, is teaching students multiple strategies. It’s built into the curriculum. All that we’re saying is, first, you should do it more because it’s a good thing, and second, when you do it, this is a certain way that we found to be especially effective, both in terms of the visual materials and the pedagogy. It’s not a big stretch for most teachers. Conversations around ways to teach math for the past 30 or 40 years, and perhaps longer, have been emphasizing the use of multiple strategies.

GAZETTE: What are the potential challenges for math teachers to put this in practice?

STAR: If we want teachers to introduce students to multiple ways to solve problems, we must recognize that that is a lot of information for students and teachers. There is a concern that there could be information overload, and that’s very legitimate. Also, a well-intentioned teacher might take our strategy too far. A teacher might say something like, “Well, if comparing two strategies is good, then why don’t I compare three or four or five?” Not that that’s impossible to do well. But the visual materials you would have to design to help students manage that information overload are quite challenging. We don’t recommend that.

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Categories within Mathematics

math.AG - Algebraic Geometry ( new , recent , current month ) Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
math.AT - Algebraic Topology ( new , recent , current month ) Homotopy theory, homological algebra, algebraic treatments of manifolds
math.AP - Analysis of PDEs ( new , recent , current month ) Existence and uniqueness, boundary conditions, linear and non-linear operators, stability, soliton theory, integrable PDE's, conservation laws, qualitative dynamics
math.CT - Category Theory ( new , recent , current month ) Enriched categories, topoi, abelian categories, monoidal categories, homological algebra
math.CA - Classical Analysis and ODEs ( new , recent , current month ) Special functions, orthogonal polynomials, harmonic analysis, ODE's, differential relations, calculus of variations, approximations, expansions, asymptotics
math.CO - Combinatorics ( new , recent , current month ) Discrete mathematics, graph theory, enumeration, combinatorial optimization, Ramsey theory, combinatorial game theory
math.AC - Commutative Algebra ( new , recent , current month ) Commutative rings, modules, ideals, homological algebra, computational aspects, invariant theory, connections to algebraic geometry and combinatorics
math.CV - Complex Variables ( new , recent , current month ) Holomorphic functions, automorphic group actions and forms, pseudoconvexity, complex geometry, analytic spaces, analytic sheaves
math.DG - Differential Geometry ( new , recent , current month ) Complex, contact, Riemannian, pseudo-Riemannian and Finsler geometry, relativity, gauge theory, global analysis
math.DS - Dynamical Systems ( new , recent , current month ) Dynamics of differential equations and flows, mechanics, classical few-body problems, iterations, complex dynamics, delayed differential equations
math.FA - Functional Analysis ( new , recent , current month ) Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory
math.GM - General Mathematics ( new , recent , current month ) Mathematical material of general interest, topics not covered elsewhere
math.GN - General Topology ( new , recent , current month ) Continuum theory, point-set topology, spaces with algebraic structure, foundations, dimension theory, local and global properties
math.GT - Geometric Topology ( new , recent , current month ) Manifolds, orbifolds, polyhedra, cell complexes, foliations, geometric structures
math.GR - Group Theory ( new , recent , current month ) Finite groups, topological groups, representation theory, cohomology, classification and structure
math.HO - History and Overview ( new , recent , current month ) Biographies, philosophy of mathematics, mathematics education, recreational mathematics, communication of mathematics, ethics in mathematics
math.IT - Information Theory ( new , recent , current month ) math.IT is an alias for cs.IT. Covers theoretical and experimental aspects of information theory and coding.
math.KT - K-Theory and Homology ( new , recent , current month ) Algebraic and topological K-theory, relations with topology, commutative algebra, and operator algebras
math.LO - Logic ( new , recent , current month ) Logic, set theory, point-set topology, formal mathematics
math.MP - Mathematical Physics ( new , recent , current month ) math.MP is an alias for math-ph. Articles in this category focus on areas of research that illustrate the application of mathematics to problems in physics, develop mathematical methods for such applications, or provide mathematically rigorous formulations of existing physical theories. Submissions to math-ph should be of interest to both physically oriented mathematicians and mathematically oriented physicists; submissions which are primarily of interest to theoretical physicists or to mathematicians should probably be directed to the respective physics/math categories
math.MG - Metric Geometry ( new , recent , current month ) Euclidean, hyperbolic, discrete, convex, coarse geometry, comparisons in Riemannian geometry, symmetric spaces
math.NT - Number Theory ( new , recent , current month ) Prime numbers, diophantine equations, analytic number theory, algebraic number theory, arithmetic geometry, Galois theory
math.NA - Numerical Analysis ( new , recent , current month ) Numerical algorithms for problems in analysis and algebra, scientific computation
math.OA - Operator Algebras ( new , recent , current month ) Algebras of operators on Hilbert space, C^*-algebras, von Neumann algebras, non-commutative geometry
math.OC - Optimization and Control ( new , recent , current month ) Operations research, linear programming, control theory, systems theory, optimal control, game theory
math.PR - Probability ( new , recent , current month ) Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
math.QA - Quantum Algebra ( new , recent , current month ) Quantum groups, skein theories, operadic and diagrammatic algebra, quantum field theory
math.RT - Representation Theory ( new , recent , current month ) Linear representations of algebras and groups, Lie theory, associative algebras, multilinear algebra
math.RA - Rings and Algebras ( new , recent , current month ) Non-commutative rings and algebras, non-associative algebras, universal algebra and lattice theory, linear algebra, semigroups
math.SP - Spectral Theory ( new , recent , current month ) Schrodinger operators, operators on manifolds, general differential operators, numerical studies, integral operators, discrete models, resonances, non-self-adjoint operators, random operators/matrices
math.ST - Statistics Theory ( new , recent , current month ) Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
math.SG - Symplectic Geometry ( new , recent , current month ) Hamiltonian systems, symplectic flows, classical integrable systems

Mathematics at MIT is administratively divided into two categories: Pure Mathematics and Applied Mathematics. They comprise the following research areas:

Pure Mathematics

Algebra & Algebraic Geometry
Algebraic Topology
Analysis & PDEs
Mathematical Logic & Foundations
Number Theory
Probability & Statistics
Representation Theory

Applied Mathematics

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
Theoretical Computer Science
Mathematics of Data

AIM Problem Lists

Noncommutative surfaces and Artin’s conjecture
Global rigidity of actions by higher-rank groups

Algebraic geometry

Components of Hilbert schemes
Deformation theory and the Brauer group
Test ideals and multiplier ideals
Singular learning theory
Cohomological methods in abelian varieties
Brauer groups and obstruction problems
The minimal model program in characteristic p
Algebraic vision
Equivariant derived algebraic geometry
Positivity of cycles
Rational subvarieties in positive characteristic
Stability and moduli spaces
Foundations of tropical schemes
Singular geometry and Higgs bundles in string theory
Categorified Hecke algebras, link homology, and Hilbert schemes
Rationality problems in algebraic geometry
Double ramification cycles and integrable systems
K-stability and related topics
Mapping theory in metric spaces
Stability and hyperbolicity
Cauchy-Riemann equations in several variables
Painleve equations and their applications
Fisher-Hartwig asymptotics and Szego expansions
Mathematical questions in wave turbulence theory
Crouzeix’s conjecture
Sparse domination of singular integral operators
Analysis and geometry on pseudohermitian manifolds
Steklov eigenproblems
Nonlocal differential equations in collective behavior
Problems on holomorphic function spaces and complex dynamics
Shape optimization with surface interactions
Minimal energy problems with Riesz potentials
Noncommutative inequalities
Criticality and stochasticity in quasilinear fluid systems
Analysis on the hypercube with applications to quantum computing
Effective methods in measure and dimension
Modeling the eye as a window on the body

Combinatorics

Rational Catalan combinatorics
Geometry of large networks
Hypergraph Turán problem
Graph Ramsey Theory
Hereditary discrepancy and factorization norms
Polyhedral geometry and partition theory
Zero forcing and its applications
Connecting communities via the block model
Additive combinatorics and its applications
Ehrhart polynomials: inequalities and extremal constructions

Cryptography

Quantum algorithms for analysis of public-key crypto

Functional analysis

Set theory and C* algebras
Invariants in convex geometry and Banach space theory
Symmetry and convexity in geometric inequalities

Geometric group theory

JSJ Decompositions
$L^2$ invariants for finitely generated groups
Amenability of discrete groups
Boundaries of groups
Classification of group von Neumann algebras
Random walks beyond hyperbolic groups
Geometric flows and Riemannian geometry
Spectral data for Higgs bundles
Soft packings, nested clusters, and condensed matter
Arborealization of singularities of Lagrangian skeleta
Non-Hermitian quantum mechanics and symplectic geometry
Fourier analytic methods in convex geometry
Manifolds with non-negative sectional curvature
Nonlinear PDEs in real and complex geometry
Discrete geometry and automorphic forms
Equilibrium states for dynamical systems arising from geometry
Rigidity and flexibility of microstructures
Partial differential equations and conformal geometry
Descriptive graph theory

Number theory

The Tate Conjecture
Automorphic forms on covering groups
Gromov-Witten invariants and number theory
The Galois theory of orbits in arithmetic dynamics
Moments of zeta and correlations of divisor sums
Arithmetic golden gates
Nonstandard methods in combinatorial number theory
Constructing cryptographic multilinear maps
Sarnak’s conjecture
Definability and decidability problems in number theory
Geometric realizations of Jacquet-Langlands correspondences
Arithmetic reflection groups and crystallographic packings

Probability

Kardar-Parisi-Zhang equation and universality class
Vector equilibrium problems and random matrix models
Markov chain mixing times
First passage percolation
Entropy power inequalities
Phase transitions in randomized computational problems
Stein’s method and applications in high-dimensional statistics
Boltzmann Machines
Zeros of random polynomials
Self-interacting processes, supersymmetry, and Bayesian statistics
Deep learning and partial differential equations

Representation theory

Sheaves and modular representations of reductive groups
Representation stability

Several complex variables

Complexity of CR Mappings
Surfaces of infinite type
Trisections and low-dimensional topology
Engel structures
Symplectic four-manifolds through branched coverings
Smooth concordance classes of topologically slice knots
Configuration spaces of graphs
Stability in mirror symmetry
Equivariant techniques in stable homotopy theory
Floer theory of symmetric products and Hilbert schemes
Try out this list!
Integrable systems in Gromov-Witten and symplectic field theory
Systems approaches to drug discovery and development in oncology
Classifying fusion categories
Postcritically finite maps in complex and arithmetic dynamics
The Maslov index
High and Low forcing
Moduli spaces for algebraic dynamical systems
Computational mathematics in computer assisted proofs
Higher categories and topological order
Invariant descriptive computability theory

Research Areas

Analysis and PDE are a major strength of Stanford’s Department of Mathematics, with strong connections to geometry and applied mathematics (since PDE describe fundamental aspects...

Applied mathematics at the Stanford Department of Mathematics focuses, very broadly, on the areas of scientific computing, stochastic modeling, and applied analysis. Some of the more specific...

Combinatorics concerns the study of discrete objects. It has applications to diverse areas of mathematics and science, and has played a particularly important role in...

Currently research in financial mathematics at Stanford is in two broad areas. One is on mathematical problems arising from the analysis of financial data; it involves...

Modern geometry takes many different guises, ranging from geometric topology and algebraic geometry and symplectic geometry to geometric analysis (which has a significant overlap with...

Contemporary number theory is developing rapidly through its interactions with many other areas of mathematics. Insights from ergodic theory have led to dramatic progress in...

The probability group at Stanford is engaged in numerous research activities, including problems from statistical mechanics, analysis of Markov chains, mathematical finance, problems at the...

Representation theory is fundamental in the study of objects with symmetry. It arises in contexts as diverse as card shuffling and quantum mechanics. An early...

Symplectic topology is at the crossroads of several mathematical disciplines such as low-dimensional topology, algebraic geometry, representation theory, Hamiltonian dynamics, integrable systems, mirror symmetry, and string theory. It...

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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.

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.

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Applied mathematics articles from across Nature Portfolio

Applied mathematics is the application of mathematical techniques to describe real-world systems and solve technologically relevant problems. This can include the mechanics of a moving body, the statistics governing the atoms in a gas or developing more efficient algorithms for computational analysis. These ideas are closely linked with those of theoretical physics.

Latest Research and Reviews

Entropy optimization of lid-driven micropolar hybrid nanofluid flow in a partially porous hexagonal-shaped cavity with relevance to energy efficient storage processes

Anil Ahlawat
Shilpa Chaudhary
Allam Balaram

Computational modeling reveals key factors driving treatment-free remission in chronic myeloid leukemia patients

Xiaopei Jiao

Fractional analysis of non-linear fuzzy partial differential equations by using a direct procedure

Muhammad Arshad
Shahbaz Khan

A logistic-tent chaotic mapping Levenberg Marquardt algorithm for improving positioning accuracy of grinding robot

Yonghong Deng

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

Real space iterative reconstruction for vector tomography (RESIRE-V)

Xingyuan Lu
Jianwei Miao

News and Comment

The curious case of the test set AUROC

The area under the receiver operating characteristic curve (AUROC) of the test set is used throughout machine learning (ML) for assessing a model’s performance. However, when concordance is not the only ambition, this gives only a partial insight into performance, masking distribution shifts of model outputs and model instability.

Michael Roberts
Carola-Bibiane Schönlieb

The role of computational science in digital twins

Digital twins hold immense promise in accelerating scientific discovery, but the publicity currently outweighs the evidence base of success. We summarize key research opportunities in the computational sciences to enable digital twin technologies, as identified by a recent National Academies of Sciences, Engineering, and Medicine consensus study report.

Karen Willcox
Brittany Segundo

Distilling data into code

One of the greatest limitations of deep neural networks is the difficulty of interpreting what they learn from the data. Deep distilling addresses this problem by extracting human-comprehensible and executable code from observations.

Joseph Bakarji

Why even specialists struggle with black hole proofs

Mathematical proofs of black hole physics are becoming too complex even for specialists.

Alejandro Penuela Diaz

Packing finite numbers of spheres efficiently

A paper in Nature Communications reports experiments and simulations of spherical particles that help show how finite numbers of spheres pack in practice.

Zoe Budrikis

Graph theory captures hard-core exclusion

Physical networks, composed of nodes and links that occupy a spatial volume, are hard to study with conventional techniques. A meta-graph approach that elucidates the impact of physicality on network structure has now been introduced.

Zoltán Toroczkai

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What’s the point of maths research? It’s the abstract nonsense behind tomorrow’s breakthroughs

Director of Research for Mathematics, University of Hull

Disclosure statement

Wolfram Bentz does not work for, consult, own shares in or receive funding from any company or organisation that would benefit from this article, and has disclosed no relevant affiliations beyond their academic appointment.

University of Hull provides funding as a member of The Conversation UK.

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Whenever I tell people I’m a mathematical researcher, I’m usually met with some form of bewilderment. Occasionally that’s followed by the immediate end of the conversation. If there is a follow-up question, it’s usually not about the type of research I’m doing or how it’s funded but whether there’s anything left to discover in maths at all.

True, maths rarely makes the headlines and so most people probably don’t think of it as carrying out cutting-edge research. But neither does, say, geology and people don’t assume there’s nothing left to discover in that field. The difference is that everyone is familiar with maths from their schooldays in a way that contrasts vastly from the work of actual mathematicians. In school we learn formulas that are then used to calculate answers to specific problems. The right method correctly calculated will never fail.

Maths research, on the other hand, looks at the myriad problems for which we don’t have such a method. It’s about finding the tools and systems that other subject areas find so useful in formulating their own work. And sometimes it stumbles across facts about numbers that we have no conceivable use for at the moment but that one day could become vital to the world.

Any mathematical method used at school (or work or anywhere) was figured out at some point by a mathematician. Another mathematician may have proven that it always works. And another may have worked out how to use the method in the real world. Someone else might then have shown that it’s not a very efficient way to solve larger problems and developed a different approach instead.

The method may also have relied on several properties of the underlying number system discovered over a long stretch of time. Others before them will have accomplished the important but unglamorous task of precisely defining that number system, perhaps a very long time ago .

Prime purpose

Research mathematicians essentially still discover similar types of results today. We have simply moved on to different questions that have become important, to new methods for existing questions, to different systems that draw our attention, and to more advanced questions about things that have already been researched.

Here is an example of such a recent result. It deals with the distribution of prime numbers, like 7, 11, 23, or 37, which you cannot divide by another natural number other than 1 or themselves. We’ve found prime numbers as large as 22m digits long, and researchers are still looking .

If you look at a table of numbers, the prime numbers seem to be almost randomly mixed into the non-prime ones. For a long time, we have been able to describe the typical characteristics of prime numbers. As it turns out, prime numbers slowly but steadily appear less frequently – they “thin out” – among the larger numbers. What’s more, we can quantify this process in surprisingly precise terms.

With the average primes being further and further apart as we look at ever larger numbers, a typical question for maths researchers to ask is whether this process of thinning out also carries over to the smallest gaps between primes. In other words, will all large primes come at increasing distances from each other, or will we always find primes that are close to each other?

A breakthrough result in 2014 showed that no matter how high we go among the numbers, we will always find two primes that are closer to each other than some constant number. That number was initially a whopping 70m. This might not seem very close but the fact that we could identify a finite number was an important breakthrough. Other mathematicians then set out to reduce this value, and the best I am currently aware of is a much more manageable 246 .

Real applications – eventually

You might wonder how solving such abstract problems helps anyone outside of mathematics. First, there is a trickle-down effect. A fundamental result is useful in obtaining other pure mathematical results, which in turn are used to develop applied mathematics, which are then used by non-mathematicians. Second – and more importantly – mathematical theory is often ahead of its time, and the abstract nonsense of yesterday underpins the applied mathematics of today.

For example, number theory is the area that examines, among other items, questions like our prime number example. For many years this was considered the ultimate pure mathematics topic and completely unusable for any purpose other than satisfying human curiosity. The eminent early 20th-century number theorist and pacifist, G.H Hardy, was very proud to say : “No discovery of mine has made, or is likely to make, directly or indirectly, for good or ill, the least difference to the amenity of the world.” In other words, he was glad his work could not be used for military purposes.

Nowadays, the number theory results that seemed so useless less than a century ago are at the heart of the encryption algorithms that let us securely order a product or check our bank accounts online. In a way that would have horrified Hardy, British intelligence services had actually already discovered the same method in secret ahead of their civil colleagues.

When the next technological or scientific breakthrough requires a new type of mathematical model, it is likely that the subject already has the underlying theory in hand, waiting to be adapted to a new setting.

Underlying all of this is one of the fundamental truths about mathematical research. The applications of mathematics might change with scientific progress, making some mathematical topics more useful at times than others. But because mathematical results are based on logical deductions alone, they actually never become wrong, never get obsolete, and never truly get old. They are just waiting for the right application to arrive.

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Exploring Best Math Research Topics That Push the Boundaries

Mathematics is a vast and fascinating field that encompasses a wide range of topics and research areas. Whether you are an undergraduate student, graduate student, or a professional mathematician, engaging in math research opens doors to exploration, discovery, and the advancement of knowledge. The world of math research is filled with exciting challenges, unsolved problems, and groundbreaking ideas waiting to be explored.

In this guide, we will delve into the realm of math research topics, providing you with a glimpse into the diverse areas of mathematical inquiry. From pure mathematics to applied mathematics, this guide will present a variety of research areas that span different branches and interdisciplinary intersections. Whether you are interested in algebra, analysis, geometry, number theory, statistics, or computational mathematics, there is a wealth of captivating topics to consider.

Math research topics are not only intellectually stimulating but also have significant real-world applications. Mathematical discoveries and advancements underpin various fields such as engineering, physics, computer science, finance, cryptography, and data analysis. By immersing yourself in math research, you have the opportunity to contribute to the development of these applications and make a meaningful impact on society.

Throughout this guide, we will explore different research areas, discuss their significance, and provide insights into potential research questions and directions. However, keep in mind that this is not an exhaustive list, and there are countless other exciting topics awaiting exploration.

Embarking on a math research journey requires dedication, perseverance, and a passion for discovery. As you dive into the world of math research, embrace the challenges, seek guidance from mentors and experts, and foster a curious and open mindset. Math research is a dynamic and ever-evolving field, and by engaging in it, you become part of a vibrant community of mathematicians pushing the boundaries of knowledge.

So, let us embark on this exploration of math research topics together, where new ideas, connections, and insights await. Prepare to unravel the mysteries of numbers, patterns, and structures, and embrace the thrill of contributing to the ever-expanding tapestry of mathematical understanding.

What is math research?

Table of Contents

Math research is the process of investigating new mathematical problems and developing new mathematical theories. It is a vital part of mathematics, as it helps to expand our understanding of the world and to develop new mathematical tools that can be used in other fields, such as science, engineering, and technology.

Math research is a challenging but rewarding endeavor. It requires a deep understanding of mathematics and a strong ability to think logically and creatively. Math researchers must be able to identify new problems, develop new ideas, and prove their ideas correct.

There are many different ways to get involved in math research. One way is to attend a math research conference. Another way is to join a math research group. You can also get involved in math research by working on a math research project with a mentor.

Math Research Topics

A few examples of math research topics:

Number theory

Number theory is a branch of mathematics that studies the properties of integers and other related objects. It is a vast and active field of research, with many open problems that have yet to be solved. Some of the current research topics in number theory include:

The Riemann hypothesis

This is one of the most important unsolved problems in mathematics. It states that the non-trivial zeros of the Riemann zeta function have real part 1/2.

The Birch and Swinnerton-Dyer conjecture

This conjecture relates the zeta function of an elliptic curve to the behavior of its rational points.

The Langlands program

This is a vast program in number theory that seeks to unify many different areas of the field.

The classification of finite simple groups

This is a complete classification of all finite simple groups, which are the building blocks of all other finite groups.

The study of cryptography

Number theory is used in many cryptographic algorithms, such as RSA and Diffie-Hellman.

The study of prime numbers

Prime numbers are fundamental to number theory, and there are many open problems related to them, such as the Goldbach conjecture and the twin prime conjecture.

The study of algebraic number theory

This is a branch of number theory that studies the properties of algebraic numbers, which are roots of polynomials with integer coefficients.

The study of combinatoric number theory

This is a branch of number theory that uses tools from combinatorics to study problems in number theory.

The study of computational number theory

This is a branch of number theory that uses computers to solve problems in number theory.

These are just a few of the many research topics in number theory. The field is constantly evolving, and new problems are being discovered all the time.

Topology is a branch of mathematics that studies the properties of spaces that are preserved under continuous deformations. Some of the most important research topics in topology include:

Algebraic topology

This branch of topology studies topological spaces using algebraic tools, such as homology and cohomology. Algebraic topology has been used to great effect in the study of knot theory, 3-manifolds, and other important topological spaces.

Geometric topology

This branch of topology studies topological spaces using geometric tools, such as triangulations and manifolds. Geometric topology has been used to great effect in the study of surfaces, 3-manifolds, and other important topological spaces.

Differential topology

This branch of topology studies topological spaces using differential geometry. Differential topology has been used to great effect in the study of manifolds, including the study of their smooth structures and their underlying topological structures.

Knot theory

This branch of topology studies knots, which are closed curves in 3-space. Knot theory has applications in many other areas of mathematics, including physics, chemistry, and computer science.

Low-dimensional topology

This branch of topology studies topological spaces of low dimension, such as surfaces and 3-manifolds. Low-dimensional topology has been used to great effect in the study of knot theory, 3-manifolds, and other important topological spaces.

Topological quantum field theory

This branch of mathematics studies the relationship between topology and quantum field theory. Topological quantum field theory has applications in many areas of physics, including string theory and quantum gravity.

Topological data analysis

This branch of mathematics studies the use of topological methods to analyze data. Topological data analysis has applications in many areas, including machine learning, computer vision, and bioinformatics.

These are just a few of the many research topics in topology. Topology is a vast and growing field, and there are many exciting new directions for research.

Differential geometry research topics

Differential geometry is a branch of mathematics that studies the geometry of smooth manifolds. Some of the most important research topics in differential geometry include:

Riemannian geometry

This branch of differential geometry studies Riemannian manifolds, which are smooth manifolds equipped with a Riemannian metric. Riemannian geometry has applications in many areas of mathematics, including physics, chemistry, and computer science.

Complex geometry

This branch of differential geometry studies complex manifolds, which are smooth manifolds that are holomorphically equivalent to a complex vector space. Complex geometry has applications in many areas of mathematics, including physics, chemistry, and computer science.

Geometric analysis

This branch of differential geometry studies the interplay between differential geometry and analysis. Geometric analysis has applications in many areas of mathematics, including physics, chemistry, and computer science.

Mathematical physics

This branch of mathematics uses differential geometry to study physical systems. Mathematical physics has applications in many areas of physics, including general relativity, quantum field theory, and string theory.

Computer graphics

This field of computer science uses differential geometry to create realistic images and animations. Computer graphics has applications in many areas, including video games, movies, and simulations.

Medical imaging

This field of medicine uses differential geometry to create images of the human body. Medical imaging has applications in many areas, including diagnosis, treatment, and research.

These are just a few of the many research topics in differential geometry. Differential geometry is a vast and growing field, and there are many exciting new directions for research.

Algebraic geometry research topics

Algebraic geometry is a branch of mathematics that studies geometric objects using the tools of abstract algebra. Some of the most important research topics in algebraic geometry include:

Algebraic curves

This branch of algebraic geometry studies curves, which are one-dimensional algebraic varieties. Algebraic curves have applications in many areas of mathematics, including number theory, representation theory, and mathematical physics.

Algebraic surfaces

This branch of algebraic geometry studies surfaces, which are two-dimensional algebraic varieties. Algebraic surfaces have applications in many areas of mathematics, including topology, differential geometry, and number theory.

Algebraic threefolds

This branch of algebraic geometry studies threefolds, which are three-dimensional algebraic varieties. Algebraic threefolds have applications in many areas of mathematics, including topology, differential geometry, and number theory.

Algebraic varieties

This branch of algebraic geometry studies varieties, which are arbitrary-dimensional algebraic sets. Algebraic varieties have applications in many areas of mathematics, including topology, differential geometry, and number theory.

Algebraic groups

This branch of algebraic geometry studies groups that are also algebraic varieties. Algebraic groups have applications in many areas of mathematics, including number theory, representation theory, and mathematical physics.

Moduli spaces

This branch of algebraic geometry studies moduli spaces, which are spaces that parameterize objects of a certain type. Moduli spaces have applications in many areas of mathematics, including number theory, representation theory, and mathematical physics.

Arithmetic geometry

This branch of algebraic geometry studies the intersection of algebraic geometry and number theory. Arithmetic geometry has applications in many areas of mathematics, including number theory, representation theory, and mathematical physics.

Complex algebraic geometry

This branch of algebraic geometry studies algebraic varieties over the complex numbers. Complex algebraic geometry has applications in many areas of mathematics, including topology, differential geometry, and mathematical physics.

Algebraic combinatorics

This branch of algebraic geometry studies the intersection of algebraic geometry and combinatorics. Algebraic combinatorics has applications in many areas of mathematics, including combinatorics, computer science, and mathematical physics.

These are just a few of the many research topics in algebraic geometry. Algebraic geometry is a vast and growing field, and there are many exciting new directions for research.

Mathematical physics research topics

Mathematical physics is a field of study that uses the tools of mathematics to study physical systems. Some of the most important research topics in mathematical physics include:

Quantum mechanics

This branch of physics studies the behavior of matter and energy at the atomic and subatomic level. Quantum mechanics has applications in many areas of physics, including chemistry, biology, and engineering.

This branch of physics studies the relationship between space and time. Relativity has applications in many areas of physics, including cosmology, astrophysics, and nuclear physics.

Statistical mechanics

This branch of physics studies the behavior of systems of many particles. Statistical mechanics has applications in many areas of physics, including thermodynamics, chemistry, and biology.

Chaos theory

This branch of physics studies the behavior of systems that are sensitive to initial conditions. Chaos theory has applications in many areas of physics, including meteorology, economics, and biology.

Mathematical finance

This field of mathematics uses the tools of mathematics to study financial markets. Mathematical finance has applications in many areas of finance, including investment banking, insurance, and risk management.

Computational physics

This field of mathematics uses the tools of mathematics to solve physical problems. Computational physics has applications in many areas of physics, including materials science, engineering, and medicine.

Mathematical biology

This field of mathematics uses the tools of mathematics to study biological systems. Mathematical biology has applications in many areas of biology, including genetics, ecology, and evolution.

Mathematical chemistry

This field of mathematics uses the tools of mathematics to study chemical systems. Mathematical chemistry has applications in many areas of chemistry, including materials science, biochemistry, and pharmacology.

Mathematical engineering

This field of mathematics uses the tools of mathematics to study engineering systems. Mathematical engineering has applications in many areas of engineering, including civil engineering, mechanical engineering, and electrical engineering.

These are just a few of the many research topics in mathematical physics. Mathematical physics is a vast and growing field, and there are many exciting new directions for research.

Mathematical biology research topics

Mathematical biology is a field of study that uses the tools of mathematics to study biological systems. Some of the most important research topics in mathematical biology include:

Modeling of biological systems

This branch of mathematical biology uses mathematical models to study the behavior of biological systems. Mathematical models can be used to understand the dynamics of biological systems, to predict how they will respond to changes in their environment, and to design new interventions to improve their health.

Computational biology

This field of mathematical biology uses computational methods to study biological systems. Computational methods can be used to analyze large amounts of biological data, to simulate biological systems, and to design new experiments.

Biostatistics

This field of mathematical biology uses statistical methods to study biological data. Biostatistical methods can be used to identify patterns in biological data, to test hypotheses about biological systems, and to design clinical trials.

Mathematical epidemiology

This field of mathematical biology uses mathematical models to study the spread of diseases. Mathematical models can be used to predict the course of an epidemic, to design public health interventions, and to assess the effectiveness of those interventions.

Mathematical ecology

This field of mathematical biology uses mathematical models to study the interactions between species in an ecosystem. Mathematical models can be used to predict how ecosystems will respond to changes in their environment, to design conservation strategies, and to assess the effectiveness of those strategies.

Mathematical neuroscience

This field of mathematical biology uses mathematical models to study the nervous system. Mathematical models can be used to understand how the nervous system works, to design new treatments for neurological disorders, and to assess the effectiveness of those treatments.

Mathematical genetics

This field of mathematical biology uses mathematical models to study genetics. Mathematical models can be used to understand how genes work, to design new treatments for genetic disorders, and to assess the effectiveness of those treatments.

Mathematical evolution

This field of mathematical biology uses mathematical models to study evolution. Mathematical models can be used to understand how evolution works, to design new conservation strategies, and to assess the effectiveness of those strategies.

These are just a few of the many research topics in mathematical biology. Mathematical biology is a vast and growing field, and there are many exciting new directions for research.

Mathematical finance research topics

Mathematical finance is a field of study that uses the tools of mathematics to study financial markets. Some of the most important research topics in mathematical finance include:

Asset pricing

This branch of mathematical finance studies the prices of assets, such as stocks, bonds, and options. Asset pricing models are used to price new financial products, to manage risk, and to make investment decisions.

Portfolio optimization

This branch of mathematical finance studies how to allocate money between different assets in a portfolio. Portfolio optimization models are used to maximize returns, to minimize risk, and to achieve other investment goals.

Derivative pricing

This branch of mathematical finance studies the prices of derivatives, such as options and futures. Derivatives are used to hedge risk, to speculate on future prices, and to generate income.

Risk management

This branch of mathematical finance studies how to measure and manage risk. Risk management models are used to identify and quantify risks, to develop strategies to mitigate risks, and to comply with regulations.

Market microstructure

This branch of mathematical finance studies the structure and dynamics of financial markets. Market microstructure models are used to understand how markets work, to design new trading systems, and to improve market efficiency.

Financial econometrics

This branch of mathematical finance uses statistical methods to study financial data. Financial econometrics models are used to identify patterns in financial data, to test hypotheses about financial markets, and to forecast future prices.

Computational finance

This field of mathematical finance uses computational methods to solve financial problems. Computational finance methods are used to price financial products, to manage risk, and to simulate financial markets.

Mathematical finance and machine learning

This field of mathematical finance uses machine learning methods to study financial markets and to make financial predictions. Machine learning methods are used to identify patterns in financial data, to predict future prices, and to develop new trading strategies.

These are just a few of the many research topics in mathematical finance. Mathematical finance is a vast and growing field, and there are many exciting new directions for research.

Numerical analysis research topics

Numerical analysis is a branch of mathematics that deals with the approximation of functions and solutions to differential equations using numerical methods. Some of the most important research topics in numerical analysis include:

Error analysis

This branch of numerical analysis studies the errors that are introduced when approximate solutions are used to represent exact solutions. Error analysis is used to design numerical methods that are accurate and efficient.

Stability analysis

This branch of numerical analysis studies the stability of numerical methods. Stability analysis is used to design numerical methods that are guaranteed to converge to the correct solution.

Convergence analysis

This branch of numerical analysis studies the convergence of numerical methods. Convergence analysis is used to design numerical methods that will converge to the correct solution in a finite number of steps.

Adaptive methods

This branch of numerical analysis studies adaptive methods. Adaptive methods are numerical methods that can automatically adjust their step size or mesh size to improve accuracy.

Parallel methods

This branch of numerical analysis studies parallel methods. Parallel methods are numerical methods that can be used to solve problems on multiple processors.

Heterogeneous computing

This branch of numerical analysis studies heterogeneous computing. Heterogeneous computing is the use of multiple processors with different architectures to solve problems.

Nonlinear problems

This branch of numerical analysis studies nonlinear problems. Nonlinear problems are problems that cannot be solved using linear methods.

Optimization

This branch of numerical analysis studies methods for finding the best solution to a problem. Optimization methods are used to find the best parameters for a numerical method, to find the best solution to a problem, and to find the best way to solve a problem.

Scientific computing

This branch of numerical analysis studies the use of numerical methods to solve problems in science and engineering. Scientific computing is used to solve problems in areas such as physics, chemistry, biology, and engineering.

This branch of numerical analysis studies the use of numerical methods to solve problems in physics. Computational physics is used to solve problems in areas such as fluid dynamics, solid mechanics, and quantum mechanics.

Computational chemistry

This branch of numerical analysis studies the use of numerical methods to solve problems in chemistry. Computational chemistry is used to solve problems in areas such as molecular dynamics, quantum chemistry, and materials science.

This branch of numerical analysis studies the use of numerical methods to solve problems in biology. Computational biology is used to solve problems in areas such as genetics, molecular biology, and neuroscience.

These are just a few of the many research topics in numerical analysis. Numerical analysis is a vast and growing field, and there are many exciting new directions for research.

Probability research topics

Probability is a branch of mathematics that deals with the analysis of random phenomena. Some of the most important research topics in probability include:

Foundations of probability

This branch of probability studies the axioms and foundations of probability theory. Foundations of probability is important for understanding the basic concepts of probability and for developing new probability theories.

Stochastic processes

This branch of probability studies the evolution of random phenomena over time. Stochastic processes are used to model a wide variety of phenomena, such as stock prices, traffic patterns, and disease outbreaks.

Random graphs

This branch of probability studies graphs whose vertices and edges are chosen randomly. Random graphs are used to model a wide variety of networks, such as social networks, computer networks, and biological networks.

Markov chains

This branch of probability studies stochastic processes whose future state depends only on its current state. Markov chains are used to model a wide variety of phenomena, such as queuing systems, genetics, and epidemiology.

Queueing theory

This branch of probability studies the behavior of queues. Queues are used to model a wide variety of systems, such as call centers, hospitals, and traffic systems.

Optimal stopping theory

This branch of probability studies the problem of choosing when to stop a stochastic process. Optimal stopping theory is used to make decisions in a wide variety of situations, such as gambling, investing, and medical diagnosis.

Information theory

This branch of probability studies the quantification and manipulation of information. Information theory is used in a wide variety of fields, such as communication, cryptography, and machine learning.

Computational probability

This branch of probability studies the use of computers to solve probability problems. Computational probability is used to solve a wide variety of problems, such as simulating random phenomena, computing probabilities, and designing algorithms .

Applied probability

This branch of probability studies the use of probability in other fields, such as physics, chemistry, biology, and economics. Applied probability is used to solve a wide variety of problems in these fields.

These are just a few of the many research topics in probability. Probability is a vast and growing field, and there are many exciting new directions for research.

Statistics research topics

Statistics is a field of study that deals with the collection, analysis, interpretation, presentation, and organization of data. Some of the most important research topics in statistics include:

This branch of statistics studies the analysis of large and complex datasets. Big data is used in a wide variety of fields, such as business, finance, healthcare, and government.

Machine learning

This branch of statistics studies the development of algorithms that can learn from data without being explicitly programmed. Machine learning is used in a wide variety of fields, such as natural language processing, computer vision, and fraud detection.

Data mining

This branch of statistics studies the extraction of knowledge from data. Data mining is used in a wide variety of fields, such as marketing, customer relationship management, and fraud detection.

Bayesian statistics

This branch of statistics uses Bayes’ theorem to update beliefs in the face of new evidence. Bayesian statistics is used in a wide variety of fields, such as medical diagnosis, finance, and weather forecasting.

Nonparametric statistics

This branch of statistics uses methods that do not make assumptions about the distribution of the data. Nonparametric statistics is used in a wide variety of fields, such as social science, medical research, and environmental science.

Multivariate statistics

This branch of statistics studies the analysis of data that has multiple variables. Multivariate statistics is used in a wide variety of fields, such as marketing, finance, and environmental science.

Time series analysis

This branch of statistics studies the analysis of data that changes over time. Time series analysis is used in a wide variety of fields, such as economics, finance, and meteorology.

Survival analysis

This branch of statistics studies the analysis of data that records the time until an event occurs. Survival analysis is used in a wide variety of fields, such as medical research, epidemiology, and finance.

Quality control

This branch of statistics studies the methods used to ensure that products or services meet a certain level of quality. Quality control is used in a wide variety of fields, such as manufacturing, healthcare, and government.

These are just a few of the many research topics in statistics. Statistics is a vast and growing field, and there are many exciting new directions for research.

How to find math research topics

Here are some tips on how to find math research topics:

Talk to your professors and advisors

They will be able to give you insights into current research in your area of interest and help you identify potential topics.

Read math journals and conferences

This will help you stay up-to-date on the latest research and identify areas where you could make a contribution.

Attend math conferences and workshops

This is a great way to meet other mathematicians and learn about their research.

Think about your own interests and passions

What are you curious about? What do you want to learn more about? These can be great starting points for research topics.

Don’t be afraid to ask for help. If you’re struggling to find a research topic, talk to your professors, advisors, or other mathematicians. They will be happy to help you get started.

How to get started with math research

Getting started with math research can be daunting, but it doesn’t have to be. Here are some tips to help you get started:

Find a mentor

A mentor can help you find a research topic, develop your research skills, and navigate the research process. Talk to your professors, advisors, or other mathematicians to find someone who is interested in your research interests.

Do your research

Read articles, books, and papers on your topic. Talk to experts in the field. The more you know about your topic, the better equipped you will be to conduct research.

Develop a research plan

A research plan will help you stay organized and on track. It should include your research goals, methods, and timeline.

Research can be a slow and challenging process. Don’t get discouraged if you don’t make progress immediately. Just keep working hard and you will eventually reach your goals.

Start small

Don’t try to tackle too much at once. Start with a small research project that you can complete in a reasonable amount of time.

Get feedback

Share your work with others and get their feedback. This will help you identify areas where you can improve.

Don’t be afraid to ask for help

If you’re struggling with something, don’t be afraid to ask for help from your mentor, advisor, or other mathematicians.

Research can be a rewarding experience. By following these tips, you can increase your chances of success.

In conclusion, exploring math research topics provides an opportunity to delve into the fascinating world of mathematics and contribute to its advancement.

The wide range of potential research areas ensures that there is something for everyone, whether you are interested in pure mathematics, applied mathematics, or interdisciplinary studies. By engaging in math research, you can deepen your understanding of mathematical principles, develop problem-solving skills, and contribute to the collective knowledge of the field.

Remember to choose a research topic that aligns with your interests and goals, and seek guidance from mentors and experts in the field to maximize your research potential. Embrace the challenge, curiosity, and creativity that math research offers, and embark on a journey that can lead to exciting discoveries and breakthroughs in the realm of mathematics.

Frequently Asked Question

How do i choose a math research topic.

When choosing a math research topic, consider your interests, background knowledge, and future goals. Explore various branches of mathematics and identify areas that intrigue you. Additionally, consult with professors, mentors, and professionals in the field for guidance and suggestions.

Can I pursue research in math as an undergraduate student?

Yes, many universities and research institutions offer opportunities for undergraduate students to engage in math research. Reach out to your professors or department advisors to inquire about available research programs or projects suitable for undergraduates.

What are some emerging areas in math research?

Math research is a constantly evolving field. Some emerging areas include computational mathematics, data science, cryptography, mathematical biology, quantum computing, and mathematical physics. Staying updated with current research trends and attending conferences or seminars can help you identify new and exciting research avenues.

How can I conduct math research effectively?

Effective math research involves a systematic approach. Start by thoroughly understanding the existing literature on your chosen topic. Develop clear research questions and hypotheses, and apply appropriate mathematical techniques and methodologies.

Can math research have real-world applications?

Absolutely! Math research has numerous real-world applications in fields such as engineering, finance, computer science, cryptography, data analysis, and physics. Mathematical models and algorithms play a crucial role in solving complex problems and optimizing various processes in diverse industries.

What resources can I use for math research?

Utilize academic journals, online databases, research papers, books, and mathematical software to access relevant information and tools. Libraries, online platforms, and research institutions also provide access to valuable resources and databases specific to mathematical research.

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202 Math Research Topics: List To Vary Your Ideas

$202 Math Research Topics$

Mathematics is an exceptional field of study dealing primarily with numbers. It also deals with structures, formulas, shapes, spaces, and quantities of where they are contained.

Maths encompasses different types of computations that are applied in the real world.

Math requires a lot of analysis. This is why there are different types of maths. They all encompass different subjects and deal with different things. What are the types of maths?

Arithmetic This is perhaps the commonest type or branch of maths. It is one of the oldest and it encompasses basic numbers operations. These are addition, subtraction, multiplication, and divisions; in some schools, the short word for it is BODMAS. This is known as the Bracket of Division, Multiplication, Addition, and Subtraction. Algebra This is where unknown quantities are represented by alphabets and used along with numbers. The letters these unknown quantities are represented by are usually A, B, X, and Y, and they could also be symbols. Geometry This is considered one of the practical branches of maths as it examines sizes, shapes, figures, and the features of these entities. The most common parts of geometry are lines, points, solids, surfaces, and angles.

There are many other types but the above are the most popular. Others are trigonometry, topology, mathematical analysis, calculus, probability, statistics, and a few others.

As many students find it hard to develop maths research topics on their own, this is a chance for you. It’s okay to be worked up when you can’t find undergraduate math research topics that fit your project, essay or paper choices. This article will provide custom maths education research topics for your use. Before that, how do you structure your math essay or paper?

How to Structure Your Math Essay or Paper

Structuring your essay or paper may require that you’ve been reading critical math journals. Reading them could have made it easy to understand how to structure your paper. However, you don’t have to worry if you haven’t. Structuring your paper as expected is an essential part of writing and you’ll know about it in this section. Before you learn that, how do you choose a topic?

Choosing a Topic to Discuss

One of the difficult yet significant parts of any math essay or paper is choosing your topic. This is because you need to solve a problem or engage in a subject that has got less attention. You also need to understand the background to the subject you want to discuss as you can’t write blindly.

You must also be able to articulate your thoughts well as you must show visible knowledge before you commence the research and writing. How do you go about this? You can consider reading existing research. You can even take notes during classes to see the areas you think more work needs to be done.

After choosing your topic, conduct your research to see if you can investigate the sphere. If you can, you need to structure your research thus:

The Background This includes the discussion on what the essay is about. Depending on what you’re writing about, you need to discuss the primary concepts, including the history of some terms, where essential, in this section. This section is more like general information about the subject you want to discuss with your paper. This helps your readers familiarize themselves with your intended discussion. The Introduction This is where the main ideas behind your essays (and the solutions you hope to proffer) are tended to the readers. This is where you also explain the symbols you’ll use and the principles which are required in your essay. Aside from this, you need to state the basic issues, the solutions you could offer, the laws which are essential to discuss to make your work comprehensible. The Main Body This is where you elaborate on your findings. You need to state the research problem, the formulas, the theories you’ll use in tackling the problem, and many other things. You also need to introduce different sections of maths into the main body which is divided by paragraphs and/or chapters as well as mathematical analysis where needed. Implications This is the last part of your essay or paper. This is where you share the insights of your research with your readers. You offer short explanations of the things you have discussed. If you have treated a subject in applied mathematics, this is where you give summaries of how math is connected to human life and the strategic importance of these to people.

By adhering to this structure, you would have crafted the best rated and high-quality maths paper. Furthermore, remember you always have an option to get help with dissertations and save your time. Since it is sometimes challenging to choose cool maths topics to research on your own, these are some for you:

Research Topics in Math

Math is a broad subject. There is a study of the history of math as well as its influence in education, amongst many other sub-sections. If you’d like to create stunning research, you may choose to discuss any of these research topics in math to fulfill one of your academic requirements:

What are the distinctions between commutative and noncommutative algebra?
Discuss the methods of factoring quadratics
Types of sequences and your understanding of them
Partial fractions: what are they and how do they work?
Logarithms: what are they and how do they work?
An overview of Gaussian elimination
An overview of Brun’s constant relevant
A description of the effect of dyscalculia on daily student lives
Describe Descartes’s Dukes of Signs and their application
Greeks and geometry: discuss
Describe Euler’s formula
The progression in the study of math
Congruence meaning and methods
Describe the correlation of CT scans to geometry
Hypercubes and how they work
The basis of Cramer’s rule
The examination of Archimedean solids
Projective geometry and why it’s studied
Types of Transformations and the available types
Picasso’s works and the application of geometry
Difference between the conventional and unconventional approaches to teaching
Math education and the process of Improvement in the US
Rhombicosidodecahedron and how it operates in real life
What are the STEM career fields and why are they important?
Why women are needed in STEM
The goals of teaching maths
How to teach maths to special students
The correlation between maths and accounting
The distinction between computer programming and applied maths
Applied maths and its dynamics
Processes of solving Heesch’s problem
Why should kids learn equations?
History of calculus
Why there is a need for math camps in schools
The need for more maths competition in the US
Methods of draining flight schedule for a country
Why are some math problems unsolved?
Discuss the consequences of the gender gap in math students
Encryption and prime numbers: how do they apply?
The significance of maths in day to day living.

Undergraduate Math Research Topics

As an undergraduate, you may also have a difficult time wrapping your head around math research topics. You may need to offer both practical and theoretical assessments while writing your paper or essay. The following are undergraduate math research topics:

Show the proofs of what F-algebras are used
Abstract algebra, what does it mean?
Algebra and geometry: discuss
Acute square triangulation: how it works
Right triangles: discuss their importance
Discuss number problems
Why every math student should study non-Euclidean geometry
Dirac manifolds and what it means
Influence of geometry in physics, chemistry, and others
The application of Riemannian manifolds in the Euclidean space
How to improve your mathematical thinking ability
Technology in maths: how is it used?
Studies of maths in Europe
Math anxiety and what it truly means
Standardized testing and the goals of such
Challenges of learning maths from public schools
The significance of circles in maths
The political and social significance of learning maths
Research into how to increase student interest in maths
How painting and drawing could help with maths
Relationship of culture and maths
History of algebra
Role of maths in everyday life
How math is used in Artificial intelligence
The transferable belief model and its application
An analysis of the Dempster-Shafer theory
The role of continuous stochastic process in mathematics
The major math theorems: discuss how they work
Understanding the Gauss-Markov: The Evolution of maths
Discrete random variable: an in-depth understanding of what it means in math and how to identify one.

Math Research Topics for High School Students

As a high school student writing a research paper, one way to get high grades is to write what you know. If you know any math research paper topics for high school, they are the topics you should pick. You can consider:

Hyperbola: what it is and how it’s used in math
When to use a calculator in class
How to find solutions to linear equations
The need for Pythagoras theorem in maths
The role of art in maths and vice versa
Role of philosophy in maths
An overview of numerical data
Egyptian mathematics explained
Binomial theorem and its importance
Probability, and how to solve a question on dice
Why is math made compulsory in schools?
Why do students hate maths?
Why do students hate math teachers?
How is math applied in the workplace?
What are imaginary numbers and why are they needed
How to calculate the interest rate and what is their importance in the banking sector?
Discount factor: how is it achieved and why is it important for students?
Types of techniques to be used while finding solutions to mathematical and finance gaps
Solving a matrix: what are the important formulas and principles to embrace?
How to create a chart on a company’s financial analysis for the past 5 years.

Interesting Math Research Topics

Writing a mathematical essay may seem complex to you if you can’t find simple topics to write about. There are many easy topics which are also general in maths. If you want to choose a relaxing topic for your math essay or paper, you can write about the following:

The basic elements of Boolean algebra
The life, time, and contribution of Isaac Newton to maths
Sphericon and what it means
Martingales and what they mean
Hyperboloid and importance in geometry
Describe the life, times, and contribution of Gauss to maths
The most famous work of Jakob Bernoulli
The most famous work of Jean d’Alembert
Meaning and application of calculus in the banking field
The meaning of congruence in math
Analysis of De Finetti theorem in probability and statistics
Describe Egyptian pyramids in concert with calculus
Describe the enclosing sphere technique as used in combinatorics
Tree automation meaning
Pushdown automaton and Buchi automaton: differences and similarities
What is the Markov algorithm?
Describe what a Turing machine is
What is the linear speedup theory in math?
The Boolean satisfiability problem and what it means for students
Why is the multiplication table important?
Computational maths and its classes
What does the post correspondence problem mean?
What does the Scholz conjecture mean?
How to calculate mean, median, and mode
A study of the most difficult equations in math.

Cool Math Topics to Research

As a student of any level, you may love to create math topics that are not exactly complex. These are topics that lean on the history of maths, math education research topics, and others. Consider these math research topics for college students for your next essay or paper:

Discuss what the Golden Ratio means in the paintings of the Renaissance period
How to learn math
An overview of the multiple ideas to probability
How chess and checkers is essential in understanding mathematics
How Pythagorean theorem is applied in real-life maths
How to measure infinity
The features of Mobius strip in geometry
Describe what is meant by the Pascal’s Triangle
Evaluate the Georg Cantor set theory
What is the history of the number types?
How does probability relate to card tricks?
Compare and contrast abstract and universal algebra
Describe Euclid’s role in the evolution of maths
Evaluate the role of Indians in maths
Explain the limits of calculus
Discuss what predictive and prescriptive statistical analysis means
What does chaos theory mean?
Explain how to solve the Rubik’s Cube
Why are some math equations so complex?
How is geometry used in contemporary architectural designs?

Math Research Topics for Middle School

It’s okay to be worried about math topics for your research as a middle school student. There are still different unique topics that are rebranded from existing ones. You can find some of the right math research paper topics for you here:

The role of statistics in business
Definition of economic lot scheduling
Why stock market crash
The contribution of many traders in the New York Stock Exchange
Revenue management and its history
What are the financial indicators of a good investment?
What are the odds of depreciation?
How can any country benefit from the poor currency?
Describe debt amortization and how math helps
How to calculate net worth
Distinctions in calculus, trigonometry, and algebra
How did calculus start?
How did trigonometry start?
Why is Ito stochastic important in math?
What do limits in math mean?
How to know critical points in graphs
What does nonstandard analysis in the probability theory mean?
Describe continuous function
The main principles of calculus
The main principles of Pythagoras theorem
Application of calculus in finance
Value theorem in math
Ratio and root test definition
Linear approximations and how they work
What is the Jacobson density theorem?
Similarities and differences between epimorphisms and monopolists
What does the Artin-Wedderburn theorem mean?
Commutative ring and its meaning in algebra
How difficult is it to teach maths?
How standards examination curriculum affects math education.

Applied Math Research Topics

Applied math is a branch which deals with the application of mathematical methods in real life. These are manifested by applications in finance, physics, engineering, biology, medicine, and others. Through specialized knowledge, applied math is made possible. These are some topics for you in this area:

How discovering genes can help determine healthy and unhealthy patients
Role of algorithms in probabilistic modeling
The need for mathematicians in developing robots
The role of mathematicians in crime data analysis and prevention
How did Isaac’s Laws of Motion help in real life?
How math helped with energy conservation
The role of math in quantum theory
Analyze the features of the Lorentz symmetry
Evaluate statistical signal processing in details
Discuss how Galilean Transformation was achieved
Examine nonlinear models
Elucidate on the importance of data mining in banking
The importance of step-stress modeling
The significance of computer tomography
What are the dimensions used in examining fingerprints?

Math Research Topics for College Students

As college students, you are at a critical level. You need maths topics for your essays and paper. You may also need them to prepare for your exams. These are some math research topics for you:

Evolution of mathematics
Explore the varieties of the Tower of Hanoi solutions
Discuss how to use Napier’s bones
Give examples of chaos theory and explain
Discuss the important mathematical equations of all times
Examine the nitty-gritty of barcodes
What is the Traveling Salesman Problem?
Natural selection and Fisher’s fundamental theorem of understanding it
The Influence of math in biology
The Influence of math in chemistry
What is quantum computing?
How to solve extremal problems in maths
Analyze the meaning of fractals
Discuss Einstein’s field equation theory
Who created computer vision and object recognition?
Five formulas and how they are applied
Give three approaches to understanding maths
Explain the origin and importance of algebra
What do you know about the Fibonacci sequence?
Trace the origin of math
How does math help in geography?
What does the operator spaces notion mean?

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Mathematical Problem-Posing Research: Thirty Years of Advances Building on the Publication of “On Mathematical Problem Posing”

First Online: 03 August 2023

Cite this chapter

Jinfa Cai 6 ,
Stephen Hwang 6 &
Matthew Melville 7

Part of the book series: Research in Mathematics Education ((RME))

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In 1994, Ed Silver published a seminal paper entitled “On Mathematical Problem Posing.” Silver both helped to lay a foundation for problem-posing research and pointed out key directions that problem-posing research could explore. This chapter provides a brief review of the problem-posing literature in the past three decades, showing that there have been marked advances in problem-posing research. We not only provide a review of the advances in problem-posing research, but also of the impact of Silver’s seminal paper on problem-posing research. The chapter ends with a discussion of three specific areas of research on mathematical problem posing (one of these areas is Problem-Posing-Based Learning [P-PBL]) that are ripe for progress and could significantly move the entire field forward.

During the preparation of this chapter, the authors were supported by a grant from the National Science Foundation (DRL 2101552). Any opinions expressed herein are those of the authors and do not necessarily represent the views of the National Science Foundation.

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Cai, J., Hwang, S., Melville, M. (2023). Mathematical Problem-Posing Research: Thirty Years of Advances Building on the Publication of “On Mathematical Problem Posing”. In: Cai, J., Stylianides, G.J., Kenney, P.A. (eds) Research Studies on Learning and Teaching of Mathematics. Research in Mathematics Education. Springer, Cham. https://doi.org/10.1007/978-3-031-35459-5_1

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100+ Amazing Algebra Topics for Research Papers

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.

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Make Math Instruction Better: 3 Tips on How From Researchers

$math research problems$

Education Week reporter and data journalist Sarah D. Sparks attended the American Educational Research Association’s annual conference in Philadelphia earlier this month. Here, she shares three of the key takeaways she heard from researchers studying some of the key challenges around math instruction.

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MATH Seminar: “Semi-periodic Problems for Nonlinear Integrable Evolution”, Petros Kalamvokas, 3:30PM April 29 2024 (EN)

You are cordially invited to the Analysis Seminar organized by the Department of Mathematics.

Speaker: Petros Kalamvokas (Bilkent University)

“Semi-periodic Problems for Nonlinear Integrable Evolution”

Abstract: In this talk we present the solvability of a semi-periodic problem for the well known Kadomtsev–Petviashvili (KP) equation. Specifically, we consider the Cauchy problem on the cylinder (C:=S1 × R) for the KPII equation, with one temporal (t) and two spatial (x, y) independent variables, with periodicity in the x-direction and decay in the y-direction. Since this equation posses a Lax pair, the method of the inverse spectral transform is being used. For initial data with small L1 and L2 norms (and assuming the zero mass constraint), the initial-value problem is reduced to a Riemann–Hilbert problem with shift on the boundary of certain infinite strips in the complex plane of the spectral parameter. Both the direct and inverse spectral problems are being rigorously solved and we prove that the initial-value problem has a unique solution for all non-negative time t, uniformly bounded for all t in L2(C), by assuming that the initial data have small derivatives up to 8th order in the space L1(C) ∩ L2(C).

Date: Monday, April 29, 2024 Time: 15:30 – 16:30 Place: Mathematics Seminar Room SA – 141

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251+ Math Research Topics [2024 Updated]
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.
181 Math Research Topics
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.
Harvard professor shares research-backed math lessons
With researchers from Vanderbilt University, Star found that teaching students multiple ways to solve math problems instead of using a single method improves teaching and learning. In an interview with the Gazette, Star, a former math teacher, outlined the research and explained how anyone, with the right instruction, can develop a knack for ...
Mathematics
math.MP is an alias for math-ph. Articles in this category focus on areas of research that illustrate the application of mathematics to problems in physics, develop mathematical methods for such applications, or provide mathematically rigorous formulations of existing physical theories.
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.
AIM Problem Lists
Welcome to AimPL: the American Institute of Mathematics Problem Lists.This website provides a mechanism for creating and maintaining up-to-date lists of unsolved problems in research mathematics. Users can read precise statements of open problems, along with accompanying remarks, as well as pose new problems and add new remarks.
Research Areas
Currently research in financial mathematics at Stanford is in two broad areas. One is on mathematical problems arising from the analysis of financial data; it involves... Geometry. Modern geometry takes many different guises, ranging from geometric topology and algebraic geometry and symplectic geometry to geometric analysis (which has a ...
Open Problems in Mathematics
"It presents a collection of open research problems in pure and applied mathematics, but each article is written by a different specialist. … certainly you may find some appealing and engaging presentations in this collection of problems that somehow got the attention of John Nash." (Felipe Zaldivar, MAA Reviews, maa.org, November, 2016)
Research Areas
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.
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Applied mathematics is the application of mathematical techniques to describe real-world systems and solve technologically relevant problems. This can include the mechanics of a moving body, the ...
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Explore a wide range of recent research in mathematics. From mathematical modeling to why some people have difficulty learning math, read all the math-related news here.
Posing Researchable Questions in Mathematics and Science ...
Research questions in science and mathematics education arise from multiple sources, including problems of practice, extensions of theory, and lacunae in existing areas of research. Therefore, through a research question's connections to prior research, it should be clear how answering the question extends the field's knowledge (Cai et al ...
What's the point of maths research? It's the abstract nonsense behind
Maths research, on the other hand, looks at the myriad problems for which we don't have such a method. It's about finding the tools and systems that other subject areas find so useful in ...
Exploring Best Math Research Topics That Push the Boundaries
Math research is the process of investigating new mathematical problems and developing new mathematical theories. It is a vital part of mathematics, as it helps to expand our understanding of the world and to develop new mathematical tools that can be used in other fields, such as science, engineering, and technology.
Making Mathematics: Mathematics Research Teacher Handbook
Mathematics research influences student learning in a number of ways: Research provides students with an understanding of what it means to do mathematics and of mathematics as a living, growing field. Writing mathematics and problem-solving become central to student's learning. Students develop mastery of mathematics topics.
home
if you really want to get inspired for your mathematical research, don't expect some dull list of open problems everyone knows about. Instead look at what has already been done by other mathematical minds and try to move one step forward. Try to generalize a concept, try to connect properties from different areas of mathematics, or try to ...
Finding math research problems
What is an efficient strategy to find fruitful research problems. So far the best advice I have heard about choosing a problem is to "talk to as many people as possible and go to as many talks as . ... Finding math research problems [closed] Ask Question Asked 8 years, 8 months ago. Modified 8 years, 8 months ago. Viewed 3k times 10 $\begingroup$
202 Math Research Topics To Impress Your College Professor
202 Math Research Topics: List To Vary Your Ideas. Mathematics is an exceptional field of study dealing primarily with numbers. It also deals with structures, formulas, shapes, spaces, and quantities of where they are contained. Maths encompasses different types of computations that are applied in the real world. Math requires a lot of analysis.
Mathematical Problem-Posing Research: Thirty Years of ...
Silver raised six themes in "On Mathematical Problem Posing."In this chapter, we describe these six themes and then examine the advances in problem-posing research from the perspectives of problem posing as a cognitive enterprise, as something to be taught, and as something to teach through (Stanic & Kilpatrick, 1988).We decided to use these three perspectives to identify the advances that ...
Research Problems in Mathematics Education: II
Communications. Research Problems in Mathematics Education - II. 6. Students hold conceptions of math which impede the development of processes; they focus on get- ting answers, manipulate blindly, and see mathe- matics as an alien, formal system on which they. have no claim.
100-Plus Exciting Algebra Topics for Research Papers
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.
How to solve for math anxiety? Studying the causes, consequences, and
Other researchers are coming at the challenge from the teacher's side. Research has shown that elementary education students have the highest math anxiety levels of all college majors (Hembree, R., Journal for Research in Mathematics Education, Vol. 21, No. 1, 1990). Jameson hopes to reduce teachers' anxiety before they step in to the ...
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Mathematics Research Skills. ... Problem Posing HTML | PDF Examples, Patterns, and Conjectures HTML | PDF Proof HTML | PDF Getting Information HTML | PDF : Proof : Conditional Statements Mathematical Induction Proof by Contradiction Parity Arguments ...
Make Math Instruction Better: 3 Tips on How From Researchers
Mathematics What the Research Says Ready or Not for an AI Economy: How U.S. Students Stack Up "Artificial intelligence has triggered a global talent race," an expert says, and American students ...
Improving students' mathematical complex problem solving using the
Solving complex problems is crucial for navigating the 21st century's development. The primary measure of academic accomplishment required in both educational and occupational settings and daily life is this competency. However, especially when learning mathematics, students still have relatively limited skills in addressing complex problems. Including students' experiences and knowledge from ...
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This article delves into the complexities of the three-body problem, exploring its historical background, mathematical approaches, practical implications, and the ongoing research efforts to shed ...
MATH Seminar: "Semi-periodic Problems for Nonlinear Integrable
Both the direct and inverse spectral problems are being rigorously solved and we prove that the initial-value problem has a unique solution for all non-negative time t, uniformly bounded for all t in L2(C), by assuming that the initial data have small derivatives up to 8th order in the space L1(C) ∩ L2(C). Date: Monday, April 29, 2024
Operations Research
MS students interested in operations research apply methods such as mathematical programming, stochastic modeling, and discrete-event simulation to the solution of problems in complex systems such as logistics, supply chain optimization, long-range planning, energy and environmental systems, urban and health systems, and manufacturing.

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