Combinatorics Through Guided Discovery

by Kenneth P. Bogart

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This book is an introduction to combinatorial mathematics, also known as combinatorics. The book focuses especially but not exclusively on the part of combinatorics that mathematicians refer to as “counting.” The book consists almost entirely of problems. Some of the problems are designed to lead you to think about a concept, others are designed to help you figure out a concept and state a theorem about it, while still others ask you to prove the theorem.

Description from LibreTexts.

Publisher
Dartmouth University
Subjects
Mathematics, Combinatorics and Discrete Mathematics
Licence
GNU Free Documentation License, as LibreTexts states it
Who can read
Tweens profiles and older, judged from its title and subjects

Contents

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  1. Front Matter
  2. TitlePage
  3. InfoPage
  4. About the Author
  5. Table of Contents
  6. Licensing
  7. Preface
  8. 1: What is Combinatorics?
  9. 1.1: About These Notes
  10. 1.2: Basic Counting Principles
  11. 1.3: Some Applications of Basic Counting Principles
  12. 1.4: What is Combinatorics? (Exercises)
  13. 2: Induction and Recursion
  14. 2.1: Some Examples of Mathematical Introduction
  15. 2.2: Recurrence Relations
  16. 2.3: Graph and Trees
  17. 2.4: Applications of Induction and Recursion in Combinatorics and Graph Theory (Exercises)
  18. 3: Distribution Problems
  19. 3.1: The Idea of Distribution
  20. 3.2: Partitions and Stirling Numbers
  21. 3.3: Partitions of Integers
  22. 3.4: Distribution Problems (Exercises)
  23. 4: Generating Functions
  24. 4.1: The Idea of Generating Functions
  25. 4.2: Generating Functions for Integer Partitions
  26. 4.3: Generating Functions and Recurrence Relations
  27. 4.4: Generating Functions (Exercises)
  28. 5: The Principle of Inclusion and Exclusion
  29. 5.1: The Size of a Union of Sets
  30. 5.2: Applications of Inclusion and Exclusion
  31. 5.3: Deletion-Contraction and the Chromatic Polynomial
  32. 5.4: The Principle of Inclusion and Exclusion (Exercises)
  33. 6: Groups Acting on Sets
  34. 6.1: Permutation Groups
  35. 6.2: Groups Acting on Sets
  36. 6.3: Pólya-Redfield Enumeration Theory
  37. 6.4: Groups Acting on Sets (Exercises)
  38. Back Matter
  39. Index
  40. Appendix A: Relations
  41. Appendix B: Mathematical Induction
  42. Appendix C: Exponential Generating Functions
  43. Appendix D: Hints to Selected Problems
  44. Appendix E: GNU Free Documentation License
  45. Detailed Licensing