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In mathematics education, Finite Mathematics is a syllabus in college and university mathematics that is independent of calculus. A course in precalculus may be a prerequisite for Finite Mathematics.
At Dartmouth College Snell became involved in a mathematics department project to develop a course on modern mathematics used in biological and social sciences. He worked with John G. Kemeny and Gerald L. Thompson to write Introduction to Finite Mathematics (1957) which described probability theory, linear algebra, and applications in sociology, genetics, psychology, anthropology, and economics.
Discrete mathematics, also called finite mathematics, is the study of mathematical structures that are fundamentally discrete, in the sense of not supporting or requiring the notion of continuity. Most, if not all, of the objects studied in finite mathematics are countable sets , such as integers , finite graphs , and formal languages .
Thompson's group is an example of a torsion-free group which is of type F ∞ but not of type F. [ 1 ] A reformulation of the F n property is that a group has it if and only if it acts properly discontinuously, freely and cocompactly on a CW-complex whose homotopy groups π 0 , … , π n − 1 {\displaystyle \pi _{0},\ldots ,\pi _{n-1}} vanish.
In mathematics, the classification of finite simple groups (popularly called the enormous theorem [1] [2]) is a result of group theory stating that every finite simple group is either cyclic, or alternating, or belongs to a broad infinite class called the groups of Lie type, or else it is one of twenty-six exceptions, called sporadic (the Tits group is sometimes regarded as a sporadic group ...
Discrete mathematics is the study of mathematical structures that can be considered "discrete" (in a way analogous to discrete variables, having a bijection with the set of natural numbers) rather than "continuous" (analogously to continuous functions). Objects studied in discrete mathematics include integers, graphs, and statements in logic.
A lattice in a locally compact topological group is a discrete subgroup with the property that the quotient space has finite invariant measure. In the special case of subgroups of R n , this amounts to the usual geometric notion of a lattice , and both the algebraic structure of lattices and the geometry of the totality of all lattices are ...
Discrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous.In contrast to real numbers that have the property of varying "smoothly", the objects studied in discrete mathematics – such as integers, graphs, and statements in logic [1] – do not vary smoothly in this way, but have distinct, separated values. [2]