An Invitation to Combinatorics
eBook - PDF

An Invitation to Combinatorics

  1. English
  2. PDF
  3. Available on iOS & Android
eBook - PDF

An Invitation to Combinatorics

About this book

Active student engagement is key to this classroom-tested combinatorics text, boasting 1200+ carefully designed problems, ten mini-projects, section warm-up problems, and chapter opening problems. The author – an award-winning teacher – writes in a conversational style, keeping the reader in mind on every page. Students will stay motivated through glimpses into current research trends and open problems as well as the history and global origins of the subject. All essential topics are covered, including Ramsey theory, enumerative combinatorics including Stirling numbers, partitions of integers, the inclusion-exclusion principle, generating functions, introductory graph theory, and partially ordered sets. Some significant results are presented as sets of guided problems, leading readers to discover them on their own. More than 140 problems have complete solutions and over 250 have hints in the back, making this book ideal for self-study. Ideal for a one semester upper undergraduate course, prerequisites include the calculus sequence and familiarity with proofs.

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Yes, you can access An Invitation to Combinatorics by Shahriar Shahriari in PDF and/or ePUB format, as well as other popular books in Mathematics & Discrete Mathematics. We have over one million books available in our catalogue for you to explore.

Table of contents

  1. Cover
  2. Half-title
  3. Series information
  4. Title page
  5. Copyright information
  6. Dedication
  7. Contents
  8. Preface
  9. Acknowledgments
  10. Introduction
  11. 1 Induction and Recurrence Relations
  12. 2 The Pigeonhole Principle and Ramsey Theory
  13. 3 Counting, Probability, Balls and Boxes
  14. Collaborative Mini-project 1: Counting Monochromatic Triangles
  15. Collaborative Mini-project 2: Binomial Coefficients
  16. Collaborative Mini-project 3: Stirling Numbers
  17. 4 Permutations and Combinations
  18. 5 Binomial and Multinomial Coefficients
  19. 6 Stirling Numbers
  20. 7 Integer Partitions
  21. Collaborative Mini-project 4: Generating Functions
  22. Collaborative Mini-project 5: Graphic Sequences and Planar Graphs
  23. Collaborative Mini-project 6: Connectivity of Graphs
  24. 8 The Inclusion–Exclusion Principle
  25. 9 Generating Functions
  26. Interregnum: Counting Table Completed
  27. Collaborative Mini-project 7: Ming–Catalan Numbers
  28. Collaborative Mini-project 8: Sperner's Theorem
  29. 10 Graph Theory
  30. Collaborative Mini-project 9: Cayley's Tree Formula
  31. Collaborative Mini-project 10: Incidence Matrices and Bipartite Graphs
  32. 11 Posets, Matchings, and Boolean Lattices
  33. Appendix A Short Answers for Warm-Up Problems
  34. Appendix B Hints for Selected Problems
  35. Appendix C Short Answers for Selected Problems
  36. Appendix D Complete Solutions for Selected Problems
  37. Bibliography
  38. Index