Areas of mathematics
en.wikipedia.org/wiki/Areas_of_mathematics"Mathematics encompasses a growing variety and depth of subjects over history, and comprehension requires a system to categorize and organize the many subjects into more general areas of mathematics. A number of different classification schemes have arisen, and though they share some similarities, there are differences due in part to the different purposes they serve. In addition, as mathematics continues to be developed, these classification schemes must change as well to account for newly created areas or newly discovered links between different areas. Classification is made more difficult by some subjects, often the most active, which straddle the boundary between different areas.
A traditional division of mathematics is into pure mathematics, mathematics studied for its intrinsic interest, and applied mathematics, mathematics which can be directly applied to real world problems.[1] This division is not always clear and many subjects have been developed as pure mathematics to find unexpected applications later on. Broad divisions, such as discrete mathematics and computational mathematics, have emerged more recently.
An ideal system of classification permits adding new areas into the organization of previous knowledge, and fitting surprising discoveries and unexpected interactions into the outline. For example, the Langlands program has found unexpected connections between areas previously thought unconnected, at least Galois groups, Riemann surfaces and number theory."
Lists of mathematics topics
en.wikipedia.org/wiki/Lists_of_mathematics_topics"This article itemizes the various lists of mathematics topics. Some of these lists link to hundreds of articles; some link only to a few. The template to the right includes links to alphabetical lists of all mathematical articles. This article brings together the same content organized in a manner better suited for browsing.
The purpose of this list is not similar to that of the Mathematics Subject Classification formulated by the American Mathematical Society. Many mathematics journals ask authors of research papers and expository articles to list subject codes from the Mathematics Subject Classification in their papers. The subject codes so listed are used by the two major reviewing databases, Mathematical Reviews and Zentralblatt MATH. This list has some items that would not fit in such a classification, such as list of exponential topics and list of factorial and binomial topics, which may surprise the reader with the diversity of their coverage."
What are all the branches of mathematics?
"Mathematics has been described as the Queen of Science.
There are so many different fields of Mathematics, from early number theory to the modern research areas of game theory, fractals, probability theories, spherical and spatial geometry etc.
Mathematics may broadly be divided into the following fields:
1. ALGEBRA
Algebra is a branch of Math most people who have gone through High School would have studied at some stage: it introduces symbols (your familiar x, y , z etc) and a series of mathematical operations like factorization, expansions, etc. It can be studied from a very elementary level ( like addition and simplifications of algebraic fractions, solving simple simultaneous linear equations involving 2 unknowns ) up to college and university levels and beyond where one studies complex linear systems, determinants, matrices, eigenvalues, vectors spaces, fractals, etc.
2. TRIGONOMETRY
This is the branch of Math studying angles; in fact, it generally forms part of what used to be called Plane Geometry. In trigonometry the angles are associated with certain defined ratios and thus are born the trigonometric concepts of sine, cosine, tangent, secant, cosecant and cotangent associated with an angle of any magnitude. One studies the various trigonometric ratios and trigonometric identities and various operations involving these.
3. GEOMETRY
In Geometry, various theorems and lemmas regarding plane figures ( straight lines, triangles, quadrilaterals, trapeziums, circles, ellipses etc ) are studies in detail. Geometry theorems are often associated with angles( see Trigonometry above ) . You probably have studied graphing, with horizontal axis (the x-axis ) and the vertical axis (y-axis ) with straight lines and methods of determining the slope of the straight line. This subdivision of Geometry is Cartesian Geometry or Co-ordinate Geometry, attributed to Rene Descartes . Again, the study of Geometry can progress from the very simple but can become highly complex as in Vector and Spherical Geometry, Topology etc.
4. CALCULUS
This is probably one of the most important branches of Mathematics, not least because it has many applications in other fields of knowledge – social science, physical sciences, biological sciences and all divisions of engineering. It introduces various important concepts ( e.g the derivative or differential coefficient of one variable with respect to another, the anti-derivative ) and provides powerful mathematical tools that allow mathematicians to determine accurately and efficiently quantities like rates of flow of water from a tunnel, rate of decay of a radioactive chemical, etc.
5. STATISTICS
This subject, usually studied together with Probability Theory ( which some regard as a branch of Algebra, or Boolean Algebra ) is the Math subject that examines the methods of collecting, representing, collating, comparing, analysing and interpreting data. In probability theory, the concept of a probability of an event is defined, followed by discussions of various probability theorems and probability distributions like the Normal Distribution, Binomial Distribution etc. It introduces terms like mean or average, median, mode, and discusses various ways of representing data – in ogives, histograms, etc . There are also statistical tests (chi-squared tests, the t-tests ) that are being used to co-relate sets of data to determine if there is some significant relationship between them."