Geometry and Discrete Mathematics
Description
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.
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Persons
Ben Fine
is Professor of Mathematics and Statistics at Fairfield University. He received his Ph.D. from Courant Institute in 1973. He has had visiting positions at Yale University, University of California, NYU and TU Dortmund.
Anja Moldenhauer
received her Ph.D. from the University of Hamburg. Her research focus lies on Mathematical Cryptology using Combinatorial Group Theory. Since 2017 she is working as a data scientist.
Gerhard Rosenberger
did his doctorate in Analytic Number Theory and habilitated in Combinatorial Group Theory. Worldwide he has worked for longer terms at nine universities. At present he is at the University of Hamburg.
Annika Schürenberg
studied Mathematics, Physics and German and received her teaching degree from the University of Hamburg. Since 2020 she is working as a teacher at an elementary school.
Leonard Wienke
received his master degree from the University of Hamburg and is currently a Ph.D. student at the University of Bremen. His research focus lies on Combinatorial Algebraic Topology.
Content
- Intro
- Preface
- Contents
- 1 Geometry and Geometric Ideas
- 2 Isometries in Euclidean Vector Spaces and their Classification in R⊃&n&/sup&
- 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
