Titu Andreescu, Zuming Feng9780817642884, 0817642889
Topics encompass permutations and combinations, binomial coefficients and their applications, recursion, bijections, inclusions and exclusions, and generating functions. The work is replete with a broad range of useful methods and results, such as Sperner’s Theorem, Catalan paths, integer partitions and Young’s diagrams, and Lucas’ and Kummer’s Theorems on divisibility. Strong emphasis is placed on connections between combinatorial and graph-theoretic reasoning and on links between algebra and geometry.
The authors’ previous text, 102 Combinatorial Problems, makes a fine companion volume to the present work, which is ideal for Olympiad participants and coaches, advanced high school students, undergraduates, and college instructors. The book’s unusual problems and examples will stimulate seasoned mathematicians as well. A Path to Combinatorics for Undergraduates is a lively introduction not only to combinatorics, but to mathematical ingenuity, rigor, and the joy of solving puzzles.
Table of contents :
Front cover……Page 1
Title page……Page 3
Date-line……Page 4
Contents……Page 5
Preface……Page 7
Introduction……Page 9
Acknowledgements……Page 15
Abbreviations and Notation……Page 17
1. Addition or Multiplication?……Page 21
2. Combinations……Page 45
3. Properties of Binomial Coefficients……Page 63
4. Bijections……Page 89
5. Recursions……Page 111
6. Inclusion and Exclusion……Page 137
7. Calculating in Two Ways: Fubini’s Principle……Page 163
8. Generating Functions……Page 185
9. Review Exercises……Page 215
Glossary……Page 233
Index……Page 237
Further Reading……Page 241
Afterword……Page 247
Back cover……Page 249
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