Combinatorics concerns the study of discrete and usually finite objects. Aspects include "counting" the objects satisfying certain criteria enumerative combinatorics , deciding when the criteria can be met, and constructing and analyzing objects meeting the criteria as in combinatorial designs and matroid theory , finding "largest", "smallest", or "optimal" objects extremal combinatorics and combinatorial optimization , and finding algebraic structures these objects may have algebraic combinatorics.
Logic is the foundation which underlies mathematical logic and the rest of mathematics. It tries to formalize valid reasoning. In particular, it attempts to define what constitutes a proof. Number theory studies the natural, or whole, numbers.
One of the central concepts in number theory is that of the prime number , and there are many questions about primes that appear simple but whose resolution continues to elude mathematicians. A differential equation is an equation involving an unknown function and its derivatives. In a dynamical system , a fixed rule describes the time dependence of a point in a geometrical space. The mathematical models used to describe the swinging of a clock pendulum, the flow of water in a pipe, or the number of fish each spring in a lake are examples of dynamical systems.
Mathematical physics is concerned with "the application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and for the formulation of physical theories". The fields of mathematics and computing intersect both in computer science , the study of algorithms and data structures, and in scientific computing , the study of algorithmic methods for solving problems in mathematics, science and engineering.
Information theory is a branch of applied mathematics and electrical engineering involving the quantification of information. Historically, information theory was developed to find fundamental limits on compressing and reliably communicating data.
Signal processing is the analysis, interpretation, and manipulation of signals. Signals of interest include sound , images , biological signals such as ECG , radar signals, and many others. Processing of such signals includes filtering , storage and reconstruction, separation of information from noise , compression , and feature extraction.
Probability theory is the formalization and study of the mathematics of uncertain events or knowledge. The related field of mathematical statistics develops statistical theory with mathematics. For that reason, it is unlikely that you will ever be called on to write a term paper on math. As such, you should bear the following in mind:. Those tips may not console you much but they can still be useful to you if you have no clue where to start in this process. To help you in coming up with your own topics you can look through this list of topics compiled for you below:.
These topics cover many different aspects of mathematics with hints of Early Childhood Education, History, Psychology and even Philosophy thrown in. You can make that time come back briefly for your reader. We will teach you how to write impeccable introductions and conclusions for your term papers as well as show you how to conduct research for your term papers. Ideas on picking a topic Picking an argument topic Cover page formatting hints A topic in Economics Writing an outline APA references format 3 hints on term paper writing Free term paper samples Term paper basic structure Term project biology topic Great college research paper topics Finding research paper help Education research paper topics Insights for a criminal justice paper College term paper topics on Math Writing a research project on breast cancer Example titles for a term paper Looking for free term paper samples Getting Archaeology term paper examples Coming up with IB research project topics Inventing Biology term project topics Finding research project outline in the APA.
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. 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:. Geometry — methodology, terminologies and types: 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 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 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. 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.
A vector space is a structure formed by vectors. 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 is differentiated and integrated calculus involving multiple variables. 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. If you encounter problems in writing your paper, the P rof E ssays.
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Math term papers are one of the rare kinds of term papers as many students don't have mathematics as a subject in their carrier run. So, it usually becomes.
A List Of Great Math Term Paper Topics For College. The first problem you are going to encounter is getting your head around writing about math, it may seem a little paradoxical but if you find a math term paper topic that inspires you, you will have no problem.
MATH HISTORY: POSSIBLE TOPICS FOR TERM PAPERS Some possible seeds for “historical developmental” topics are: • The Platonic Solids • Solution of . 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.
A Math term paper consists of many details to consider and a proper choice of a topic is one of those. Do not hesitate to use our guide to this sphere. 5 Good topics for a math research paper. The more research you invest into a math problem, the more rewarding it tends to be. Math research papers are fun to write, and explaining a logical analysis of something that is usually interpreted with numbers, makes for an interesting read.