This two-volume set collects and presents many fundamentals of mathematics in an enjoyable and elaborating fashion. The idea behind the two books is to provide substantials for assessing more modern developments in mathematics and to present impressions which indicate that mathematics is a fascinating subject with many ties between the diverse mathematical disciplines. The present volume examines many of the most important basic results in geometry and discrete mathematics, along with their proofs, and also their history.
Contents
Geometry and geometric ideas
Isometries in Euclidean vector spaces and their classification in ℝn
The conic sections in the Euclidean plane
Special groups of planar isometries
Graph theory and platonic solids
Linear fractional transformation and planar hyperbolic geometry
Combinatorics and combinatorial problems
Finite probability theory and Bayesian analysis
Boolean lattices, Boolean algebras and Stone’s theorem
An exciting collection of fundamental results in geometry and discrete mathematics
Covers geometry, combinatorics, and probability theory
Aimed at lecturers, teachers, and students of mathematics, and at all mathematically interested
Author(s): Benjamin Fine, Anthony Gaglione, Anja Moldenhauer, Gerhard Rosenberger and Dennis Spellman
Year: 2018
Language: English
Tags: Geometry, Discrete Mathematics
Frontmatter
Preface
Contents
1 Geometry and geometric ideas
2 Isometries in Euclidean vector spaces and their
classification in ℝn
3 The conic sections in the Euclidean plane
4 Special groups of planar isometries
5 Graph theory and platonic solids
6 Linear fractional transformation and planar
hyperbolic geometry
7 Combinatorics and combinatorial problems
8 Finite probability theory and Bayesian analysis
9 Boolean lattices, Boolean algebras and Stone’s
theorem
Bibliography
Index
