Research papers in mathematics usually have a set of basic requirements that apply to all students. As a rule, they relate to the format of the research work and the requirements for it. Students need to adhere to a specific font, spacing, and writing format. It is necessary to have a title page of the research paper and the project, as well as the correct text formatting with recommendations and pagination.

Students must adhere to a clear heading hierarchy in research work and adhere to the correct abbreviations and formulas in the design of the entire project. As a rule, research work associated with the use of certain drawings, tables, diagrams, and graphs. Also, there may be charts which must also be marked following the requirements.

Students must reveal the topic given to them and bring clear arguments in favor of their statements. It should be a full-fledged mathematics research topic that fully reveals the theme and provides the reader with real evidence of opinion. It's important to choose an interesting math research topic.

The main task for each student is to relate everything they plan to write with one Topic. It will allow the teacher not to waste time looking for information and get the opportunity to see holistic work that fully meets all the established requirements. Students should also check the practical part as mathematics is an exact science that does not tolerate assumptions. So, let's take a look at the math research topics for middle schools.

## Algebra & Algebraic Geometry

Algebra and algebraic geometry are the oldest branches of this science. This section arose as a result of the need to solve arithmetic problems of the same type. Now, this is a huge branch of science, which is extremely important because of its ability to make accurate calculations and definitions in various areas of our life. Choose any research topic for mathematics that suits you well.

- Formality in Deformation Theory
- The World of P-adic Numbers
- Toric Geometry and Mirror Symmetry
- Algebraic Geometry and Singularity Theory
- P-adic Dynamics and Applications of P-adic Numbers in Other Sciences
- Algebraic Geometry New Trends: The height Functions in Modern Science
- Theory of Height Functions & in Math

## Algebraic Topology

This section of typology studies topological spaces using the juxtaposition of algebraic objects. At the moment, it is one of the more popular offshoots that uses homotopy groups and homomorphism. Any research topic in mathematics is a chance to create a good paper. This area of mathematics is popular thanks to several scientific studies. Here is a list of paper themes, but you can also find math education research topics by yourself.

- Main Calculus Functions and How to Use it in Real Life
- The Calculus of Functors and Applications
- How to Use the Algebraic Models for Spaces in Real Life
- New Wave of Automorphisms in Math
- The Asymptotic Properties of Polynomials in Higher Dimensions
- Moduli Spaces Geometry: Main Features
- The Lefschetz Properties and Main Parameters
- The Group Theory in Mathematics: Main Benefits
- Automorphisms of Manifolds and Related Options
- Modern Trends in Algebraic Topology and How to Use it Properly

## Analysis & PDEs

This list of topics can be especially interesting for those who want to develop methods for solving equations of mathematical physics. Let's proceed to researchable topics in mathematics. In particular, students can create their work based on the approximation of the differential operator and use numerical methods to solve the tasks and open the topic of scientific research.

- Regularity Theory for Linear, Semilinear, and Fully Nonlinear Elliptic and Parabolic Equation
- New Theory for Linear, Semilinear, and Nonlinear Functions
- Qualitative Properties of Solutions to Reaction-diffusion Equations
- The Analysis of Problems in Mathematical Physics and Mathematical Modeling
- Delay Equations Formulation of Structured Population Dynamics
- Fractional differential equations and Fractals
- Mathematical Modeling of Ecological Systems and Epidemic Systems
- Delay Differential Equations is One Best Research Area in Mathematics.

## Geometry

According to many historians, the foundations of geometry were laid by the ancient Greeks, who took over from the Egyptians some mathematical calculations and general principles. This section received such a name in 1822. Nevertheless, all the foundations and important stages of this science branch were laid many centuries ago. Here are the applied mathematics research topics.

- The Bending Active Approach In Lightweight Design
- The Need Of Geometry In Orthodontics
- Archimedes Theory of a Circle ABCD and a Triangle K
- Applications of Toric Geometry to Geometric Representation Theory
- Geometry and Conservation Laws for a Class of Second-Order Parabolic Equations
- Geometric Constructions of Mapping Cones in the Fukaya Category
- Euclidean and Non-Euclidean Geometries. Going Beyond the Space, We Used to know

## Mathematical Logic & Foundations

This branch of mathematics may be of interest to those who want to study the nature of mathematical proof in general and various mathematical judgments as a branch of informal logic. In many respects, the foundation of this science was laid by Aristotle. Nevertheless, mathematical logic is developing in our time. Therefore, this is a good basis for scientific work.

- Deductive Parsing of Visual Languages
- Reduction of the Yablo paradox
- Gödel's: Minds are not Machines
- Ways to use the Mathematical logic in data science
- Applied Propositional Logic and digital circuit design
- Category Theory and Model Theory of Constructive Systems
- Constructive Mathematics and Point-free Methods in Topology and Analysis
- Ways to Use Martin-Löf type Theory and Univalent Foundations in Real Life

## Number Theory

This is one of the popular branches of mathematics, consisting of many areas such as the Euclidean algorithm, continued fractions, Diophantine equations, and farm theory. At the moment, this industry has a lot of interesting topics to write a research paper. That's why you can find interesting mathematical topics.

- Writing Pi As the Sum of Arctangents With Recurring Linear Sequences, the Golden Mean and Lucas Numbers
- Binary Options Winning Formula: Make Consistent Wins Every Time
- A Theory of Numbers and New Operations
- The Twin Prime Conjecture in a Number Theory
- Pythagorean Triplets (Alternative Approach, Algebraic Operations, Dual of Given Triplets, and New Observations)
- A New Theory of Numbers: The Latest Discoveries in Mathematics
- Alternative Formula for the Series of Consecutive m-Squares under Alternating Signs
- A Clever Way To Factor One Less A Perfect Square
- How to use Number Theory to fight with gender stereotypes
- Goldbachs Twin Prime Conjecture

## Probability & Statistics

By choosing this direction of mathematics, you can write a lot of interesting materials on modeling and data distribution and the study of two-dimensional numerical data. This is a particularly popular area of mathematics that will allow you to choose interesting topics for yourself with experiments and proofs. Let's check the research topics for mathematic paper.

- Highlighting Probability Issues in Simulated Annealing and Tabu Search
- Estimation of the Probability of Non-Response in Sampling Surveys Using Kernel Density Estimation Methods
- Importance of Statistical Tools and Methods in Data Science
- A Statistical Approach on Experimental Study for Determining Switching Frequency of Retro Reflector Sensor Using PLC
- The Statistics Analysis on Gender: Ain't ia Woman
- Quantitative Data Management, Statistical Analysis, and Graphics Using Stata
- The Data Science and Modern Statistics: the Symbiotic Connection
- Sei Shonagon's Pillow Book as an Example of Probability & Statistics Processes
- The Weibull Length Biased Exponential Distribution: Statistical Properties and Applications
- Univariate and Bivariate Transformations

## Representation Theory

This branch of mathematics is especially interesting due to algebraic structures and linear transformations of vector spaces. Students can use Number Theory and Differential Geometry to describe certain nuances of Fourier theory or use topological groups to prove new theories. Here you can choose an undergraduate math research topic.

- Computing Modular Forms for the Weil Representation
- Combinatorics of the Asymmetric Simple Exclusion Process
- The Representation Theory & Asymmetric Simple Exclusion
- Applications of Toric Geometry to Geometric Representation Theory
- The Weil Representation in Tropical Mathematics
- Combinatorics of the Asymmetric Simple Exclusion Process
- Camel and Cactus Test in Representation Theory
- Combinatorics and Computations in Tropical Mathematics
- Quaternionic Representation and Its Use in Real Life
- The Modern Trends in Representation Theory of Diffeomorphism Groups

## How to Write a Research Paper on Mathematics?

As we wrote earlier, teachers are very scrupulous about the correct design and writing of research papers. And interesting math research paper topics are a must. First of all, you need to write a clear introduction and structure of all your work. It is worth noting that you need formal and informal exposure, as well as bringing evidence of your work. One of the sections there will be special recommendations that depend on a particular educational institution.

You should understand that any such work requires a clear technical design and the ghost of the necessary graphs, tables, formulas, and calculations. The most important task of such research papers is to provide clear and evidence of your point of view to argue for each point and paragraph of your work. This is the key aspect, without which you do not get good grades.

That is why you should turn to professionals if you are not confident in your abilities or want to save a little time. Our company can help you write a research paper in mathematics and accompany you until you receive your final grade. It's important to choose good research topics in mathematics education, and we are ready to help you.