Geometry and Discrete Mathematics
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Benjamin Fine
, Anja Moldenhauer , Gerhard Rosenberger , Annika Schürenberg and Leonard Wienke
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
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Frontmatter
I -
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Preface
V -
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Contents
VII -
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1 Geometry and Geometric Ideas
1 -
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2 Isometries in Euclidean Vector Spaces and their Classification in ℝn
31 -
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3 The Conic Sections in the Euclidean Plane
69 -
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4 Special Groups of Planar Isometries
87 -
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5 Graph Theory and Graph Theoretical Problems
127 -
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6 Spherical Geometry and Platonic Solids
159 -
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7 Linear Fractional Transformation and Planar Hyperbolic Geometry
177 -
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8 Simplicial Complexes and Topological Data Analysis
205 -
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9 Combinatorics and Combinatorial Problems
223 -
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10 Finite Probability Theory and Bayesian Analysis
277 -
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11 Boolean Lattices, Boolean Algebras and Stone’s Theorem
311 -
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Bibliography
347 -
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Index
349
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