Geometry and Discrete Mathematics: A Selection of Highlights

Benjamin Fine; Anthony Gaglione; Anja Moldenhauer; Gerhard Rosenberger; Dennis Spellman

Book

Geometry and Discrete Mathematics

A Selection of Highlights

Benjamin Fine , Anthony Gaglione , Anja Moldenhauer , Gerhard Rosenberger and Dennis Spellman

Language: English

Published/Copyright: 2018

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This book is in the series

De Gruyter Textbook

About this book

This two-volume set collects and presents many fundamentals of mathematics in an enjoyable and elaborating fashion. The idea behind the two books is to provide substantials for assessing more modern developments in mathematics and to present impressions which indicate that mathematics is a fascinating subject with many ties between the diverse mathematical disciplines. The present volume examines many of the most important basic results in geometry and discrete mathematics, along with their proofs, and also their history.

Contents
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 platonic solids
Linear fractional transformation and planar hyperbolic geometry
Combinatorics and combinatorial problems
Finite probability theory and Bayesian analysis
Boolean lattices, Boolean algebras and Stone’s theorem

An exciting collection of fundamental results in geometry and discrete mathematics
Covers geometry, combinatorics, and probability theory
Aimed at lecturers, teachers, and students of mathematics, and at all mathematically interested

Author / Editor information

B. Fine, A. Gaglione, A. Moldenhauer, G. Rosenberger, D. Spellman.

Supplementary Materials

Errata

Topics

Publicly Available

Frontmatter
I

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Preface
V

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Contents
IX

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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
17

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3. The conic sections in the Euclidean plane
51

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4. Special groups of planar isometries
67

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5. Graph theory and platonic solids
101

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6. Linear fractional transformation and planar hyperbolic geometry
135

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7. Combinatorics and combinatorial problems
161

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8. Finite probability theory and Bayesian analysis
213

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9. Boolean lattices, Boolean algebras and Stone’s theorem
245

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Bibliography
279

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Index
281

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Publishing information

Pages and Images/Illustrations in book

eBook published on:

September 24, 2018

eBook ISBN:

9783110521504

Edition:

Please note this is a second edition

Pages and Images/Illustrations in book

Front matter:

15

Main content:

435

Illustrations:

20

https://doi.org/10.1515/9783110521504

eBook ISBN: 9783110521504

Keywords for this book

Analytische Geometrie; Euklidische Geometrie; Kombinatorik; Nichteuklidische Geometrie; Wahrscheinlichkeitstheorie

Audience(s) for this book

Lecturers, teachers, and students of mathematics, and the mathematically interested.

Geometry and Discrete Mathematics

Overview

About this book

Author / Editor information

Supplementary Materials

Topics

Table of contents

Frontmatter

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 platonic solids

6. Linear fractional transformation and planar hyperbolic geometry

7. Combinatorics and combinatorial problems

8. Finite probability theory and Bayesian analysis

9. Boolean lattices, Boolean algebras and Stone’s theorem

Bibliography

Index

Bibliographic data

2. Isometries in Euclidean vector spaces and their classification in ℝⁿ