# 50 Best Math Research Topics To Explore

Mathematics is a broad discipline that finds interrelation with several other subjects and fields of study. It is also a subject that, in many ways, unifies different disciplines through its theories and concepts. As a result, mathematics is studied across different educational levels in varying degrees of complexity. It is, therefore, also common for students to come across a requirement of math research topics to work on at various juncture of their educational journey.

Whether the math research paper topics are needed for a PhD research or for a middle school assignment it is not uncommon to find students perplexed over which topic to choose. The decision is not easy as everyone wants to make a good impression with their work and of course score well.

Before you pick a topic for your research it is important to understand that the topic should be one that offers an appropriate and adequate scope of the study. Your topic should allow you to work in detail on the subject chosen and yet it must suit your time constraints as well. Often students who do not carry out a careful selection of their research topics in math end up fighting against time to meet the deadlines. This not only puts an additional burden on their routine but often affects their performance in other subjects as well, leading to undue stress. Therefore, time, complexity, and scope are three vital factors to consider before shortlisting a math topic.

Here is a list of topics that you can explore as per your educational level. Pick the one that suits you best and offers you an opportunity to score well.

## Math Research Topics for Middle School

At the middle school level, the scope and complexity of mathematics are far more accessible to students as compared to when they research math topics in higher education. Here are some easy math research topics that middle students can explore and attempt. Take a look:

- Exploring areas of shapes and the formulate for calculating them
- Significant mathematical applications in ancient Rome
- Euclid and his contributions to math
- Quick techniques for two-digit number multiplication
- How to count objects by sight through the fastest techniques
- Origin and logic of using Greek symbols in mathematics
- What were some major applications of mathematics in Ancient Rome?
- Roman and Greek Civilizations – a comparison of their contributions to mathematics
- Pascal’s triangle – How to find patterns
- Math in nature and around us
- Geometry as it exists in nature
- Easy ways to memorize algebraic expressions
- Early civilizations and their history with algebra
- Blaise Pascal and his study and contributions to probability
- The greatest mathematical invention in the history of mankind

### Math Research Topics for High School

If you are looking for some impressive math research paper topics for high school consider the following for your assignment:

- A comparison of imaginary and real numbers
- Study of the Fibonacci series
- Solving the simultaneous equations – Evaluation of the methods
- Pythagoras’ theorem – an analysis through real-world situations
- Proving trigonometry theorems
- Archimedes’ history and his contributions to mathematics
- Important Greek mathematicians and their contributions to mathematics
- The European Renaissance Era and Role of mathematics during the period
- Ancient Egyptian Mathematical applications and accomplishments
- How was Ancient Greek architecture influenced by mathematics?

### Math Research Topics for College Students

At the college level, you have to pick your applied math research topics very carefully. While your topic must help you make a lasting impression it must also offer ample depth and complexity for detailed study, which may even be interdisciplinary. Here are some effective undergraduate math research topics to consider:

- Mathematical Biology
- Understanding Euclidean and non-Euclidean geometries
- Major advancements in Topology over two decades
- High dimensional spaces – Analyzing geometry
- Kinematics of rolling – Analyzing a mathematical angle
- Application of symmetric functions in the field of combinatorics
- Periodicity and complexity
- Solving the inequalities of the linear matrix using rank constraints
- Algebra: an exposition on the invariants of matrices
- Symmetries of differential equations – A study

### Interesting Math Research Topics for PhD. Students

If you are a PhD student you must certainly be looking for some impressive and cool math topics to research on. Here are a few math education research topics that are sure to move you in the right direction:

- Studying systems with multiple time scales
- Exploring the double pendulum and chaos
- A detailed study of the Knot theory — what are its applications
- All about the geometry of singular spaces
- Exploring the different methods for solving inverse problems
- Weather forecasting and the role of advancements in predictive models
- Exploring the calculus of functors along with the application they have
- Group theory and its role in mathematics
- Complex analysis for higher dimensions — their complex analysis and exploration of the associated geometric aspects
- Studying the elementary mathematical foundations of Computational fluid dynamics
- Single polymer entanglements and the significance of mathematical modelling
- Exploring the continuous and discrete quantum graphs
- Study of Egyptian fractions
- Zero-sets of polynomials and their asymptotic properties in holonomic systems, currents, and higher dimensions of differential equations
- Analyzing Multilinear and Rough Linear Pseudodifferential Operators

Whether you are in school or college this list can surely be a good starting point if you are finding it difficult to pick a topic for your paper. However, there are many reasons because of which you may find it difficult to work on your math research paper. It could be due to ill health, pending deadlines of other subjects, increased work pressure, the burden of multitasking, upcoming examinations, too many commitments or a general inability to handle the pressure due to some personal issues.

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