Counting and Configurations: Problems in Combinatorics, Arithmetic, and Geometry

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Springer Science & Business Media, Jan 14, 2003 - Mathematics - 392 pages
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This book can be seen as a continuation of Equations and Inequalities: El ementary Problems and Theorems in Algebra and Number Theory by the same authors, and published as the first volume in this book series. How ever, it can be independently read or used as a textbook in its own right. This book is intended as a text for a problem-solving course at the first or second-year university level, as a text for enrichment classes for talented high-school students, or for mathematics competition training. It can also be used as a source of supplementary material for any course dealing with combinatorics, graph theory, number theory, or geometry, or for any of the discrete mathematics courses that are offered at most American and Canadian universities. The underlying "philosophy" of this book is the same as that of Equations and Inequalities. The following paragraphs are therefore taken from the preface of that book.
 

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Contents

Combinatorics
1
1 Fundamental Rules
2
2 Standard Concepts
6
3 Problems with Boundary Conditions
24
4 Distributions into Bins
41
5 Proving Identities
55
6 The InclusionExclusion Principle
66
7 Basics of Polyas Theory of Enumeration
95
4 Unordered Configurations
168
5 Iterations
192
Combinatorial Geometry
217
1 Systems of Points and Curves
219
2 Systems of Curves and Regions
241
3 Coverings and Packings
256
4 Colorings
273
Hints and Answers
287

8 Recursive Methods
103
Combinatorial Arithmetic
107
1 Arrangements
109
2 Sequences
121
3 Arrays
143
2 Hints and Answers to Chapter 2
311
3 Hints and Answers to Chapter 3
362
Bibliography
385
Index
389
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