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Wikipedia on Mathematics

Mathematics , is the body of knowledge centered on concepts such as quantity, structure, space, and change, and also the academic discipline that studies them. Benjamin Peirce called it "the science that draws necessary conclusions". Other practitioners of mathematics maintain that mathematics is the science of pattern, that mathematicians seek out patterns whether found in numbers, space, science, computers, imaginary abstractions, or elsewhere. Mathematicians explore such concepts, aiming to formulate new conjectures and establish their truth by rigorous deduction from appropriately chosen axioms and definitions. Through the use of abstraction and logical reasoning, mathematics evolved from counting, calculation, measurement, and the systematic study of the shapes and motions of physical objects. Knowledge and use of basic mathematics have always been an inherent and integral part of individual and group life. Refinements of the basic ideas are visible in mathematical texts ori More »
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Mathematics
Mathematics , is the body of knowledge centered on concepts such as quantity, structure, space, and change, and also the academic discipline that studies them. Benjamin Peirce called it "the science that draws necessary conclusions". Other practitioners of mathematics maintain that mathematics is the science of pattern, that mathematicians seek out patterns whether found in numbers, space, science, computers, imaginary abstractions, or elsewhere. More »
Mathematician
A mathematician is a person whose primary area of study and research is the field of mathematics. More »
Real number
In mathematics, the real numbers may be described informally as numbers that can be given by an infinite decimal representation, such as 2.4871773339…. The real numbers include both rational numbers, such as 42 and −23/129, and irrational numbers, such as π and the square root of 2, and can be represented as points on an infinitely long number line. A more rigorous definition of the real numbers was one of the most important developments of 19th century mathematics. More »
Function (mathematics)
The mathematical concept of a function expresses the intuitive idea of deterministic dependence between two quantities, one of which is viewed as primary and the other as secondary . A function then is a way to associate a unique output for each input of a specified type, for example, a real number or an element of a given set. This definition covers most elementary functions, maps between algebraic structures, such as groups, and between geometric objects, such as manifolds. More »
Statistics
Statistics is a mathematical science pertaining to the collection, analysis, interpretation or explanation, and presentation of data. It is applicable to a wide variety of academic disciplines, from the physical and social sciences to the humanities. Statistics are also used for making informed decisions – and misused for other reasons – in all areas of business and government. Statistical methods can be used to summarize or describe a collection of data; this is called... More »
Geometry
Geometry is a part of mathematics concerned with questions of size, shape, and relative position of figures and with properties of space. Geometry is one of the oldest sciences. Initially a body of practical knowledge concerning lengths, areas, and volumes, in the third century B.C. geometry was put into an axiomatic form by Euclid, whose treatment set a standard for many centuries to follow. Astronomy served as an important source of geometric problems during the next one and a half... More »
Natural number
In mathematics, a natural number can mean either an element of the set , , , ...} or an element of the set , 1, 2, 3, ...} . The former is generally used in number theory, while the latter is preferred in mathematical logic, set theory and computer science. See below for a formal definition. Natural numbers have two main purposes: they can be used for counting , and they can be used for ordering . Properties of the natural numbers related to divisibility, such as the distribution of prime... More »
Set
In mathematics, a set can be thought of as any collection of distinct objects considered as a whole. Although this appears to be a simple idea, sets are one of the most important and fundamental concepts in modern mathematics. The study of the structure of possible sets, ''set theory'', is rich and ongoing. Having only been invented at the end of the 19th century, set theory is now a ubiquitous part of mathematics education, being introduced from primary school in many countries. More »
Topological space
:''This article is technical. For a general overview of the subject, see the article on topology.'' Topological spaces are mathematical structures that allow the formalization of concepts such as convergence, connectedness and continuity. They appear in virtually every branch of modern mathematics and are a central unifying notion. The branch of mathematics that studies topological spaces in their own right is called topology. More »
Cryptography
Cryptography is the study of message secrecy. In modern times, it has become a branch of information theory, as the mathematical study of information and especially its transmission from place to place. The noted cryptographer Ron Rivest has observed that "cryptography is about communication in the presence of adversaries", which neatly captures one of its unique aspects as a branch of engineering, and differences from, for instance, pure mathematics. More »
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