Geometry and Discrete Mathematics: A Selection of Highlights

Benjamin Fine; Anja Moldenhauer; Gerhard Rosenberger; Annika Schürenberg; Leonard Wienke

Published by De Gruyter 2022

Geometry and Discrete Mathematics

A Selection of Highlights

Benjamin Fine , Anja Moldenhauer , Gerhard Rosenberger , Annika Schürenberg and Leonard Wienke

In the series De Gruyter Textbook

https://doi.org/10.1515/9783110740783

Overview
Contents

About this book

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 / Editor information

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.

Topics

Frontmatter Publicly Available Download PDF	I
Preface Publicly Available Download PDF	V
Contents Publicly Available Download PDF	VII
1 Geometry and Geometric Ideas Requires Authentication Unlicensed Licensed Download PDF	1
2 Isometries in Euclidean Vector Spaces and their Classification in ℝⁿ Requires Authentication Unlicensed Licensed Download PDF	31
3 The Conic Sections in the Euclidean Plane Requires Authentication Unlicensed Licensed Download PDF	69
4 Special Groups of Planar Isometries Requires Authentication Unlicensed Licensed Download PDF	87
5 Graph Theory and Graph Theoretical Problems Requires Authentication Unlicensed Licensed Download PDF	127
6 Spherical Geometry and Platonic Solids Requires Authentication Unlicensed Licensed Download PDF	159
7 Linear Fractional Transformation and Planar Hyperbolic Geometry Requires Authentication Unlicensed Licensed Download PDF	177
8 Simplicial Complexes and Topological Data Analysis Requires Authentication Unlicensed Licensed Download PDF	205
9 Combinatorics and Combinatorial Problems Requires Authentication Unlicensed Licensed Download PDF	223
10 Finite Probability Theory and Bayesian Analysis Requires Authentication Unlicensed Licensed Download PDF	277
11 Boolean Lattices, Boolean Algebras and Stone’s Theorem Requires Authentication Unlicensed Licensed Download PDF	311
Bibliography Requires Authentication Unlicensed Licensed Download PDF	347
Index Requires Authentication Unlicensed Licensed Download PDF	349

(Deutsch)

Language: English
Publisher: De Gruyter
Edition: 2nd edition
Audience: Lecturers, teachers, and students of mathematics, and the mathematically interested.
Pages
- Front matter: 10
- Main content: 354
Illustrations
- Illustrations: 165
- Coloured Illustrations: 4
Keywords: Elementary number theory; Galois theory; Polynomial functions; Prime number; Numeral system

eBook

Published: August 22, 2022
ISBN: 9783110740783

Paperback

Published: August 22, 2022
ISBN: 9783110740776