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A finite geometry is any geometric system that has only a finite number of points. The familiar Euclidean geometry is not finite, because a Euclidean line contains infinitely many points. A geometry based on the graphics displayed on a computer screen, where the pixels are considered to be the points, would be a finite geometry.
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]
The second book addressed PG(3,q) and the third PG(n,q). Chapters are numbered sequentially through the trilogy: 14 in the first book, 15 to 21 in the second, and 22 to 27 in the third. Finite geometry has contributed to coding theory, such as algebraic geometry codes, so the field is supported by computer science.
A frequently studied problem in finite geometry is to identify ways in which an object can be covered by other simpler objects such as points, lines, and planes. In projective geometry, a specific instance of this problem that has numerous applications is determining whether, and how, a projective space can be covered by pairwise disjoint subspaces which have the same dimension; such a ...
92 Finite Group Theory, I. Martin Isaacs (2008, ISBN 978-0-8218-4344-4) 93 Topics in Differential Geometry , Peter W. Michor (2008, ISBN 978-0-8218-2003-2 ) 94 Representations of Semisimple Lie Algebras in the BGG Category O , James E. Humphreys (2008, ISBN 978-0-8218-4678-0 )
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.
Mirrors and Reflections: The Geometry of Finite Reflection Groups is an undergraduate-level textbook on the geometry of reflection groups.It was written by Alexandre V. Borovik and Anna Borovik and published in 2009 by Springer in their Universitext book series.
Combinatorics of Experimental Design is a textbook on the design of experiments, a subject that connects applications in statistics to the theory of combinatorial mathematics. It was written by mathematician Anne Penfold Street and her daughter, statistician Deborah Street , and published in 1987 by the Oxford University Press under their ...