Combinatorial Reasoning : An Introduction to the Art of Counting （SOL）

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Combinatorial Reasoning : An Introduction to the Art of Counting （SOL）

Detemple, Duane/ Webb, William

ウェブストア価格 ¥7,541（本体¥6,856）
John Wiley & Sons Inc（2014/09発売）
外貨定価 US$ 35.95
ポイント 68pt

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製本 Paperback:紙装版/ペーパーバック版／ページ数 186 p.
言語 ENG
商品コード 9781118830789
DDC分類 511

Full Description

COMBINATORIAL REASONING Showcases the interdisciplinary aspects of combinatorics and illustrates how to problem solve with a multitude of exercises

Written by two well-known scholars in the field, Combinatorial Reasoning: An Introduction to the Art of Counting presents a clear and comprehensive introduction to the concepts and methodology of beginning combinatorics. Focusing on modern techniques and applications, the book develops a variety of effective approaches to solving counting problems.

Balancing abstract ideas with specific topical coverage, the book utilizes real-world examples with problems ranging from basic calculations that are designed to develop fundamental concepts to more challenging exercises that allow for a deeper exploration of complex combinatorial situations. Simple cases are treated first before moving on to general and more advanced cases. Additional features of the book include:

Approximately 700 carefully structured problems designed for readers at multiple levels, many with hints and/or short answers
Numerous examples that illustrate problem solving using both combinatorial reasoning and sophisticated algorithmic methods
A novel approach to the study of recurrence sequences, which simplifies many proofs and calculations
Concrete examples and diagrams interspersed throughout to further aid comprehension of abstract concepts
A chapter-by-chapter review to clarify the most crucial concepts covered

Combinatorial Reasoning: An Introduction to the Art of Counting is an excellent textbook for upper-undergraduate and beginning graduate-level courses on introductory combinatorics and discrete mathematics.

Preface vii

Part I The Basics of Enumerative Combinatorics

1 Initial EnCOUNTers with Combinatorial Reasoning 3

2 Selections, Arrangements, and Distributions 23

3 Binomial Series and Generating Functions 51

4 Alternating Sums, Inclusion-Exclusion Principle, Rook Polynomials, and Fibonacci Nim 77

5 Recurrence Relations 95

6 Special Numbers 129

Part II Two Additional Topics in Enumeration

7 Linear Spaces and Recurrence Sequences 161

8 Counting with Symmetries 175