A First Course in Enumerative Combinatorics 1st Edition by Carl G Wagner ISBN 1470459957 978-1470459956

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Product details:

ISBN 10: 1470459957  

ISBN 13: 978-1470459956 

Author:   Carl G. Wagner

 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.

Table of contents: 

1. Prologue: Compositions of an Integer

2. Sets, Functions, and Relations

3. Binomial Coefficients

4. Multinomial Coefficients and Ordered Partitions

5. Graphs and Trees

6. Partitions: Stirling, Lah, and Cycle Numbers

7. Intermission: Some Unifying Themes

8. Combinatorics and Number Theory

9. Differences and Sums

10. Enumeration Under Group Action

11. Finite Vector Spaces

12. Ordered Sets

13. Formal Power Series

14. Incidence Algebra: The Grand Unified Theory of Enumerative Combinatorics

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