A First Course in Enumerative Combinatorics
eBook - PDF

A First Course in Enumerative Combinatorics

  1. 293 pages
  2. English
  3. PDF
  4. Available on iOS & Android
eBook - PDF

A First Course in Enumerative Combinatorics

About this book

A First Course in Enumerative Combinatorics provides an introduction to the fundamentals of enumeration for advanced undergraduates and beginning graduate students in the mathematical sciences. The book offers a careful and comprehensive account of the standard tools of enumeration—recursion, generating functions, sieve and inversion formulas, enumeration under group actions—and their application to counting problems for the fundamental structures of discrete mathematics, including sets and multisets, words and permutations, partitions of sets and integers, and graphs and trees. The author's exposition has been strongly influenced by the work of Rota and Stanley, highlighting bijective proofs, partially ordered sets, and an emphasis on organizing the subject under various unifying themes, including the theory of incidence algebras. In addition, there are distinctive chapters on the combinatorics of finite vector spaces, a detailed account of formal power series, and combinatorial number theory. The reader is assumed to have a knowledge of basic linear algebra and some familiarity with power series. There are over 200 well-designed exercises ranging in difficulty from straightforward to challenging. There are also sixteen large-scale honors projects on special topics appearing throughout the text. The author is a distinguished combinatorialist and award-winning teacher, and he is currently Professor Emeritus of Mathematics and Adjunct Professor of Philosophy at the University of Tennessee. He has published widely in number theory, combinatorics, probability, decision theory, and formal epistemology. His Erd?s number is 2. Ancillaries: Instructor's Manual

Information

Publisher
American Mathematical Society
Year
2020
Topic
Mathematics
eBook ISBN
9781470462628
Subtopic
Mathematics General
Index
Mathematics

Table of contents

  1. Cover
  2. Title page
  3. Copyright
  4. Contents
  5. Preface
  6. Notation
  7. Chapter 1. Prologue: Compositions of an integer
  8. Chapter 2. Sets, functions, and relations
  9. Chapter 3. Binomial coefficients
  10. Chapter 4. Multinomial coefficients and ordered partitions
  11. Chapter 5. Graphs and trees
  12. Chapter 6. Partitions: Stirling, Lah, and cycle numbers
  13. Chapter 7. Intermission: Some unifying themes
  14. Chapter 8. Combinatorics and number theory
  15. Chapter 9. Differences and sums
  16. Chapter 10. Enumeration under group action
  17. Chapter 11. Finite vector spaces
  18. Chapter 12. Ordered sets
  19. Chapter 13. Formal power series
  20. Chapter 14. Incidence algebra: The grand unified theory of enumerative combinatorics
  21. Appendix A. Analysis review
  22. Appendix B. Topology review
  23. Appendix C. Abstract algebra review
  24. Index
  25. Back Cover

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Yes, you can access A First Course in Enumerative Combinatorics by Carl G. Wagner in PDF and/or ePUB format, as well as other popular books in Mathematics & Mathematics General. We have over 1.5 million books available in our catalogue for you to explore.