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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.
Preface
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 Graph Theoretical Problems
Spherical Geometry and Platonic Solids
Linear Fractional Transformation and Planar Hyperbolic Geometry
Simplicial Complexes and Topological Data Analysis
Combinatorics and Combinatorial Problems
Finite Probability Theory and Bayesian Analysis
Boolean Lattices, Boolean Algebras and Stone’s Theorem
Bibliography
Index