Introductory Combinatorics, 5/e (Paperback)
暫譯: 初級組合數學，第5版（平裝本）

Richard A. Brualdi

Introductory Combinatorics, 5/e (Paperback)

商品描述

本書序言

●A wealth of new exercises has been added to this revision.
●Use of the term “combination” as it applies to a set has been de-emphasized; the author now uses the essentially equivalent term of “subset” for clarity. (In the case of multisets, the text continues to use “combination” versus the more cumbersome term “submultiset.”)
●A new section (Section 1.6) on mutually overlapping circles has been moved from Chapter 7 to illustrate some of the counting techniques covered in later chapters.
●Coverage of the pigeonhole principle and permutations and combinations has been reversed; Chapter 2 now covers permutations and combinations, with Chapter 3 covering the pigeonhole principle.
●An extensively revised Chapter 7 moves up generating functions and exponential generating functions to Sections 7.2 and 7.3, giving them a more central treatment.
●Section 8.3 on partition numbers has been expanded; and much more.

本書特色

●Comprehensive, accessible coverage of main topics in combinatorics:
。Provides students with accessible coverage of basic concepts and principles.
。Covers a wide range of topics: Dilworth's Theorem, partitions of integers, counting sequences and generating functions, and extensive graph theory coverage.
●A clear and accessible presentation, written from the student's perspective, facilitates understanding of basic concepts and principles.
●An excellent treatment of Polya's Counting Theorem does not assume students have studied group theory.
●Many worked examples illustrate methods used.

商品描述(中文翻譯)

本書序言

●本次修訂新增了大量練習題。

●對於集合的術語「組合」的使用已被弱化；作者現在為了清晰起見，使用了本質上等同的術語「子集」。(在多重集合的情況下，文本仍然使用「組合」，而不是較為繁瑣的術語「子多重集合」。)

●關於互相重疊圓的全新部分（第1.6節）已從第7章移至此處，以說明後面章節中涵蓋的一些計數技術。

●鴿巢原理及排列組合的內容順序已調整；第2章現在涵蓋排列和組合，第3章則涵蓋鴿巢原理。

●第7章經過大幅修訂，將生成函數和指數生成函數移至第7.2節和第7.3節，給予它們更中心的處理。

●第8.3節關於分割數的內容已擴展；還有更多內容。

本書特色

●對組合數學主要主題的全面且易於理解的涵蓋：

。為學生提供基本概念和原則的易懂介紹。

。涵蓋廣泛的主題：迪爾沃斯定理、整數的分割、計數序列和生成函數，以及廣泛的圖論內容。

●從學生的角度出發，清晰且易於理解的呈現方式，促進對基本概念和原則的理解。

●對波利亞計數定理的優秀處理不假設學生已學習群論。

●許多範例展示了所使用的方法。

作者簡介

Richard A. Brualdi is Bascom Professor of Mathematics, Emeritus at the University of Wisconsin - Madison. He served as Chair of the Department of Mathematics from 1993-1999. His research interests lie in matrix theory and combinatorics/graph theory. Professor Brualdi is the author or co-author of 6 books, and has published extensively. He is one of the editors-in-chief of the journal "Linear Algebra and its Applications" and of the journal "Electronic Journal of Combinatorics." He is a member of the American Mathematical Society, the Mathematical Association of America, the International Linear Algebra Society, and the Institute for Combinatorics and its Applications. He is also a Fellow of the Society for Industrial and Applied Mathematics.

作者簡介(中文翻譯)

理查德·A·布魯阿爾迪是威斯康辛大學麥迪遜分校的數學榮譽巴斯科姆教授。他於1993年至1999年擔任數學系主任。他的研究興趣包括矩陣理論和組合數學/圖論。布魯阿爾迪教授是6本書的作者或合著者，並且發表了大量的研究成果。他是期刊《線性代數及其應用》（"Linear Algebra and its Applications"）和期刊《電子組合數學期刊》（"Electronic Journal of Combinatorics"）的主編之一。他是美國數學學會、數學協會、美國國際線性代數學會以及組合數學及其應用研究所的成員。他也是工業與應用數學學會的會士。

目錄大綱

1. What is Combinatorics?
2. Permutations and Combinations
3. The Pigeonhole Principle
4. Generating Permutations and Combinations
5. The Binomial Coefficients
6. The Inclusion-Exclusion Principle and Applications
7. Recurrence Relations and Generating Functions
8. Special Counting Sequences
9. Systems of Distinct Representatives
10. Combinatorial Designs
11. Introduction to Graph Theory
12. More on Graph Theory
13. Digraphs and Networks
14. Pólya Counting

目錄大綱(中文翻譯)

1. What is Combinatorics?

2. Permutations and Combinations

3. The Pigeonhole Principle

4. Generating Permutations and Combinations

5. The Binomial Coefficients

6. The Inclusion-Exclusion Principle and Applications

7. Recurrence Relations and Generating Functions

8. Special Counting Sequences

9. Systems of Distinct Representatives

10. Combinatorial Designs

11. Introduction to Graph Theory

12. More on Graph Theory

13. Digraphs and Networks

14. Pólya Counting

類似商品