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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 .
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.
The types of finite geometry covered by the book include partial linear spaces, linear spaces, affine spaces and affine planes, projective spaces and projective planes, polar spaces, generalized quadrangles, and partial geometries. [1]
A finite projective space defined over such a finite field has q + 1 points on a line, so the two concepts of order coincide. Such a finite projective space is denoted by PG( n , q ) , where PG stands for projective geometry, n is the geometric dimension of the geometry and q is the size (order) of the finite field used to construct the geometry.
The ATLAS of Finite Groups, often simply known as the ATLAS, is a group theory book by John Horton Conway, Robert Turner Curtis, Simon Phillips Norton, Richard Alan Parker and Robert Arnott Wilson (with computational assistance from J. G. Thackray), published in December 1985 by Oxford University Press and reprinted with corrections in 2003 (ISBN 978-0-19-853199-9).
Negatively curved groups (hyperbolic or CAT(0) groups) are always of type F ∞. [7] Such a group is of type F if and only if it is torsion-free. As an example, cocompact S-arithmetic groups in algebraic groups over number fields are of type F ∞. The Borel–Serre compactification shows that this is also the case for non-cocompact arithmetic ...
A Cayley graph of the symmetric group S 4. The symmetric group S n on a finite set of n symbols is the group whose elements are all the permutations of the n symbols, and whose group operation is the composition of such permutations, which are treated as bijective functions from the set of symbols to itself. [4]
The theory of finite fields, whose origins can be traced back to the works of Gauss and Galois, has played a part in various branches of mathematics.Due to the applicability of the concept in other topics of mathematics and sciences like computer science there has been a resurgence of interest in finite fields and this is partly due to important applications in coding theory and cryptography.