Combinatorics: A Problem Oriented Approach

(Classroom Resource Materials)
Daniel A. Marcus

The Mathematical Association of America | 1999 | 152 páginas | rar-PDF | 451 kb

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Descrição: The format of this book is unique in that it combines features of a traditional text with those of a problem book. The material is presented through a series of problems, about 250 in all, with connecting text; this is supplemented by a further 250 problems suitable for homework assignment. The problems are structured in order to introduce concepts in a logical order, and in a thought-provoking way. The first four sections of the book deal with basic combinatorial entities; the last four cover special counting methods. Many applications to probability are included along the way. Students from a wide range of backgrounds, mathematics, computer science or engineering will appreciate this appealing introduction.


Contents
Part I. Basics 1
Section A: Strings . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
Section B: Combinations . . . . . . . . . . . . . . . . . . . . . . . . 13
Section C: Distributions . . . . . . . . . . . . . . . . . . . . . . . . . 31
Section D: Partitions . . . . . . . . . . . . . . . . . . . . . . . . . . 47
Part II. Special Counting Methods 61
Section E: Inclusion and Exclusion . . . . . . . . . . . . . . . . . . . 63
Section F: Recurrence Relations . . . . . . . . . . . . . . . . . . . . 73
Section G: Generating Functions . . . . . . . . . . . . . . . . . . . . 87
Section H: The P´olya-Redfield Method . . . . . . . . . . . . . . . . . 97
List of Standard Problems . . . . . . . . . . . . . . . . . . . . . . . . . 119
Dependence of Problems . . . . . . . . . . . . . . . . . . . . . . . . . 123
Answers to Selected Problems . . . . . . . . . . . . . . . . . . . . . . 127
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135