Difference between revisions of "Mathematics"
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'''Mathematics''' is the [[science]] of [[number]]s, and the study of relationships that exist between them. It generally also is considered to contain [[geometry]] and [[topology]] as a subset, as they are related to <math>\mathbb{R}_2</math> and <math>\mathbb{R}_n</math> in general.  '''Mathematics''' is the [[science]] of [[number]]s, and the study of relationships that exist between them. It generally also is considered to contain [[geometry]] and [[topology]] as a subset, as they are related to <math>\mathbb{R}_2</math> and <math>\mathbb{R}_n</math> in general.  
Revision as of 16:42, 12 February 2008
Mathematics is the science of numbers, and the study of relationships that exist between them. It generally also is considered to contain geometry and topology as a subset, as they are related to and in general.
Contents
Overview

The ten digits making up the base ten number system. 
Modern mathematics is normally built around base 10, with ten digits. () Modern mathematics is separated into two categories: discrete mathematics and nondiscrete.
NonDiscrete Mathematics
Nondiscrete mathematics is study of mathematics that is generally applicable to the "real world", such as algebra, Euclidean geometry, statistics, and other such topics. (Note that the real world is actually only approximately Euclidean if one studies large areas of it, infinitesimal areas actually are nonEuclidean) There is some controversy over what varieties of algebra are nondiscrete, but it is generally agreed that elementary and superior algebra are nondiscrete, while abstract algebra and intermediate topics such as field and graph theory and Diophantine equations are discrete.
Discrete Mathematics
Combinatorics, number theory, and some of the algebraic fields mentioned above are examples of discrete mathematics. Topics of discrete mathematics are generally not directly applicable to the "real world", and if they are, it is only in an abstract fashion.
History of Mathematics
Mathematics was noted by the earliest humans. Over time, as humans evolved, the complexity of mathematics also evolved. There was an astounding discovery on how the numbers correlated with each other, as well as in nature, so well, as they created the concept of numbers. As a great 19th century thinker said,
"God created the integers. All the rest is the work of man." (Leopold Kronecker)