In the two-volume set ‘A Selection of Highlights’ we present basics of mathematics in an exciting and pedagogically sound way. This volume examines many fundamental results in Geometry and Discrete Mathematics along with their proofs and their history. In the second edition we include a new chapter on Topological Data Analysis and enhanced the chapter on Graph Theory for solving further classical problems such as the Traveling Salesman Problem.
A true collection of mathematical gems in Geometry, Graph Theory, Combinatorics, Probability Theory, Data Analysis and Boolean Lattices.
Valuable for lecturers, teachers and students of mathematics as well as for all who are mathematically interested.
Author(s): Benjamin Fine, Anja Moldenhauer, Gerhard Rosenberger, Annika Schürenberg, Leonard Wienke
Edition: 2
Publisher: De Gruyter
Year: 2022
Language: English
Pages: 363
City: Berlin
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 Graph Theoretical Problems
6 Spherical Geometry and Platonic Solids
7 Linear Fractional Transformation and Planar Hyperbolic Geometry
8 Simplicial Complexes and Topological Data Analysis
9 Combinatorics and Combinatorial Problems
10 Finite Probability Theory and Bayesian Analysis
11 Boolean Lattices, Boolean Algebras and Stone’s Theorem
Bibliography
Index
