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# Mathematics Research Paper Topics

### Good Topics for Mathematics Research Papers

A mathematics research paper is an extremely intricate task that requires immense concentration, planning and naturally clear basic knowledge of mathematics, but what is essential for a  higher level research is the successful choice of a topic, matching your personal interests and level of competence.

You may be given a list of possible topics or to be allowed to choose yourself, but nevertheless consider your interest in the research field and if it is possible, try to choose a topic relevant to your previous and future research papers and tasks. In this case, you’ll be able to use your background knowledge acquired while writing one paper for your next projects. Try to search for something that will allow you not to fall out of the general research work and to have a basis for your current task.

To give a broad perspective of some mathematics research paper topics the custom essay writers of  ProfEssays.com have sorted some areas of this subject and enlisted some popular topics pertaining to this.

### Quick Navigation through the Mathematics Research Paper Topics Page:

#### Research paper topics pertaining to Algebra:

1. Homology Theories
Homologies are one of the basic notions of the algebraic topology. The homology theory provides a possibility to construct an algebraic object such as a group or a ring that is a topological variant of space. A closed line on a surface is homologous to nought, if a surface breaks up into parts while the scission of a surface. For example, on a sphere any closed line is as such, but on a torus, though there exist the closed lines that are homologous to nought, the section along a meridian or a parallel will not lead to the separation of a surface part.

The topics that deal with Homology Theories are the following:

• K – Theories
• Bordism and Cobordism Theories
• Basic group and Structure Operations

2. Unary and Binary Operations

#### Research paper topics pertaining to Geometry:

1. Geometry – methodology, terminologies and types:

• Euclidean Geometry

Euclidean or elementary geometry is a geometric theory based on the system of axioms that was first stated by Euclid in the 3rd century BC.  This is a geometry that is generally defined by a group of displacements and a group of similarities. But the content of the elementary geometry is not formed by the mentioned transformations, it includes also the inversion transformation, the problems of spherical geometry, the elements of geometric constructions, the theory of the measurement of geometric magnitudes etc.

• Stereometry

Stereometry is a branch of geometry that deals with the solid figures in space. When the main figures in space there are a point, a line and a plane, in the stereometry there appears a new kind of the relationship of lines, that is the skew lines. This is one of the few considerable differences of stereometry from planimetry, as in many cases the stereometric problems are solved by the consideration of different planes where the planimetric laws are satisfied.

• Computational Geometry

Computational Geometry is a branch of the discrete mathematics that deals with the algorithms for the solving of the geometric problems.  It deals with such problems as triangulation, construction of a convex hull, the defining of the belonging of one object to another one, the search of their intersection etc. It operates with such geometric objects as a point, a segment, a polygon and a circle. The computational geometry is used in the image recognition, computer graphics, engineering design etc.

2. Geometry algorithms

#### Research paper topics on Calculus:

1. Calculus theorems:

• Foundation and history of Calculus

Calculus is a branch of mathematics that deals with the research of functions and their generalization by the methods of the differential and integral calculus. Calculus has the resources for solving such problems for which only algebra is insufficient and has application in various spheres pf science. The history of calculus springs from the Ancient Greece, but many of the important ideas were developed in the 17th century, and the most prominent step in the development of calculus was made in the studies of Isaac Newton and Gottfried Leibniz who nowadays are considered to be the founders of calculus.

• Vector Spaces

A vector space is a structure formed by vectors. Vectors may be added together and scaled by numbers (“scaled” vectors are called scalars). Vector spaces are used in mathematical analysis, generally as the infinite-dimensional spaces where vectors are functions, however, this still create a number of analytical problems. In addition, vector spaces are applied in various spheres of science and engineering.

• Multivariate Calculus

Multivariate calculus is differentiated and integrated calculus involving multiple variables.

2. Construction of real numbers
The real numbers are constructed basing on the predetermined rational numbers. The rational numbers are taken as a basis, and the new objects are constructed, that are called the irrational numbers. As a result of their addition to the set of rational numbers, there is a set of real numbers.

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#### Research paper topics on Mathematical Logic:

Boolean functions, theorems and technical application:

• Model Theory

Model theory is a branch of mathematical logics that deals with study of relations between the formal languages and their interpretations, or models. A model is a structure that gives meaning to the formal language sentences, and if it satisfies also a particular theory it is called a model of the theory. Model theory has strong relations with algebra.

• Set Theory

Set theory is the branch of mathematics that deals with the general behavior of sets. The set theory lies in basis of the most of the mathematical disciplines, it has deeply influenced on the understanding of the subject of mathematics.

• Recursion Theory

Recursion theory, also called computability theory, is a branch of mathematical logic that is in close relation with computer science and deals with the study of computable functions and Turing degrees, including also the study of generalized computability and definability.

• Proof Theory

Proof theory is a branch of mathematical logics where the phenomenon of mathematical proof becomes an object of algebra or arithmetic. The proof is usually presented as the structure of data, such as plain lists or trees, up to the hypothetic extremely complicated structures or machines which are constructed according to the axioms and rules of the logical systems. The proof theory can be viewed as a branch of philosophic logic where the main interest is in the proof-theoretic semantics.

#### Probability and Statistics Topics:

1. Foundations of probability theory
Probability theory is the branch of mathematics dealing with analysis of random variables, processes and events. The sequence of repeated random events may keep within certain statistical patterns, in such way becoming predictable. Probability theory is applicable to many activities for which it is essential to consider the results of quantitative analysis of large sets of data.

The topics that deal with the probability theory are the following:
• Conditional probability
• Probability distribution function

2. Statistical package comparison

#### Research paper topics on Differential Equations:

1. Ordinary differential equations
Differential equation is an equation that connects the meaning of a certain unknown function in a certain points with the meaning of its various derivatives in the same point. A differential equation contains in its form an unknown function, its derivatives and independent variables, but not any equation that contains the derivatives of an unknown function is a differential equation. It is also worth noting that a differential equation may not contain an unknown function, some of its derivatives and free variables at all, but it must contain at least one variable.

The topics that deal with the differential equations are the following:

• Linear differential equations
• Rotating systems
• Differential equations in mathematics physics

2. Usage of Differential equations

#### Research Paper Topics on the Popular Theorems in Mathematics:

1. Fundamental theorems of algebra, calculus, curves and projective geometry
The topics that deal with the fundamental theorems are the following:

• Fishers Fundamental Theorem of Natural selection
• Fundamental Equations

2. Fundamental Theorem of Poker.
Fundamental theorem of poker is a principle explaining the nature of poker and its main regularity, basing on that the right decision in this game is the decision that has the largest expected value, so a player should act as if they see all the cards of their opponents.

#### Mathematics Research Paper Tips

However, to write a flawless research paper on any of the above mentioned topics a writer requires to:

1.  Conduct an extensive research on the chosen topic.

2.  Give a history and background regarding the development of the particular topic or theorem being discussed.

3.  Break the topics into sub topics to simplify the explanation of the topic and to help the readers understand it better.

4.  Clearly and comprehensively elucidate the conclusion of the theorem or topic that is being discussed.

#### Mathematics Research Paper Format (click the image to enlarge)

Generally, the paper format for the mathematics research papers is more flexible than for other scientific fields, so you have a possibility to develop the outline of your work in a way you need for your topic in general. However, there are several standard sections that must be included to ease the perception of your work: Background, Introduction, Body and Future Work or Conclusion, where you first give the description of the problem history, including its key notions, then present the specific results of your study and then providing the possible direction of the future research in your field.

#### Mathematics Research Paper Methodology

The methodology of mathematics in not a subject that is widely studied, but still there exist several issues that could help to develop the methodology of your own research. The first issue is the necessity to express complicated relations symbolically, which could help to master the notions that could hardly be expressed in words. The essential part of mathematics is abstraction that gives the possibility to codify out knowledge about several examples and thus to learn their common features. The same importance has the rigorous notion of proof which makes mathematics applicable and essential in physics, engineering, computer science etc. Considering these several key points of a research, each writer should himself define the own research strategy.