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Combinatorics A Guided Tour 1st Edition by David Mazur 9780883857625 0883857626

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Combinatorics A Guided Tour 1st Edition David R. Mazur Digital Instant Download

Author(s): David R. Mazur
ISBN(s): 9780883857625, 0883857626
Edition: 1st
File Details: PDF, 5.55 MB
Year: 2009
Language: english
SKU: EB-4691016 Category: Tag:

Combinatorics A Guided Tour 1st Edition by David Mazur – Ebook PDF Instant Download/Delivery: 9780883857625, 0883857626

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Product details:

ISBN 10: 0883857626

ISBN 13: 9780883857625

Author: David R. Mazur

Combinatorics is mathematics of enumeration, existence, construction, and optimization questions concerning finite sets. This text focuses on the first three types of questions and covers basic counting and existence principles, distributions, generating functions, recurrence relations, Pólya theory, combinatorial designs, error correcting codes, partially ordered sets, and selected applications to graph theory including the enumeration of trees, the chromatic polynomial, and introductory Ramsey theory. The only prerequisites are single-variable calculus and familiarity with sets and basic proof techniques. It is flexible enough to be used for undergraduate courses in combinatorics, second courses in discrete mathematics, introductory graduate courses in applied mathematics programs, as well as for independent study or reading courses. It also features approximately 350 reading questions spread throughout its eight chapters. These questions provide checkpoints for learning and prepare the reader for the end-of-section exercises of which there are over 470.

Table of contents:

Part I. Principles of Combinatorics:

1. Typical counting questions, the product principle

2. Counting, overcounting, the sum principle

3. Functions and the bijection principle

4. Relations and the equivalence principle

5. Existence and the pigeonhole principle

Part II. Distributions and Combinatorial Proofs:

6. Counting functions

7. Counting subsets and multisets

8. Counting set partitions

9. Counting integer partitions

Part III. Algebraic Tools:

10. Inclusion-exclusion

11. Mathematical induction

12. Using generating functions, part I

13. Using generating functions, part II

14. techniques for solving recurrence relations

15. Solving linear recurrence relations

Part IV. Famous Number Families:

16. Binomial and multinomial coefficients

17. Fibonacci and Lucas numbers

18. Stirling numbers

19. Integer partition numbers

Part V. Counting Under Equivalence:

20. Two examples

21. Permutation groups

22. Orbits and fixed point sets

23. Using the CFB theorem

24. Proving the CFB theorem

25. The cycle index and Pólya’s theorem

Part VI. Combinatorics on Graphs:

26. Basic graph theory

27. Counting trees

28. Colouring and the chromatic polynomial

29. Ramsey theory

Part VII. Designs and Codes:

30. Construction methods for designs

31. The incidence matrix, symmetric designs

32. Fisher’s inequality, Steiner systems

33. Perfect binary codes

34. Codes from designs, designs from codes

Part VIII. Partially Ordered Sets:

35. Poset examples and vocabulary

36. Isomorphism and Sperner’s theorem

37. Dilworth’s theorem

38. Dimension

39. Möbius inversion, part I

40. Möbius inversion, part II

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Tags: David Mazur, Combinatorics, Guided, Tour