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Combinatorics: A Guided Tour (MAA Textbooks) - Hardcover
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Bevindt zich in: Decatur, Georgia, Verenigde Staten
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Specificaties
- Objectstaat
- Brand
- Unbranded
- Book Title
- Combinatorics: A Guided Tour (MAA Textbooks)
- MPN
- Does not apply
- ISBN
- 9780883857625
- Publication Name
- Combinatorics : a Guided Tour
- Item Length
- 10.3in
- Publisher
- American Mathematical Society
- Publication Year
- 2010
- Series
- Maa Textbooks Ser.
- Type
- Textbook
- Format
- Hardcover
- Language
- English
- Item Height
- 1in
- Item Width
- 7.2in
- Item Weight
- 30.8 Oz
- Number of Pages
- 410 Pages
Over dit product
Product Information
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, Polya 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."
Product Identifiers
Publisher
American Mathematical Society
ISBN-10
0883857626
ISBN-13
9780883857625
eBay Product ID (ePID)
80063318
Product Key Features
Publication Name
Combinatorics : a Guided Tour
Format
Hardcover
Language
English
Publication Year
2010
Series
Maa Textbooks Ser.
Type
Textbook
Number of Pages
410 Pages
Dimensions
Item Length
10.3in
Item Height
1in
Item Width
7.2in
Item Weight
30.8 Oz
Additional Product Features
Series Volume Number
17
Lc Classification Number
Qa164 .M398 2010
Reviews
This is a well-written, reader-friendly, and self-contained undergraduate course on combinatorics, focusing on enumeration. The book includes plenty of exercises, and about hal of them come with hints."" - M. Bona, Choice Magazine ""The delineation of the topics is first rate-better than I have ever seen in any other book. Their presentation is generally thorough, with much of it in the form of worked problems. The book is very much designed as a textbook; there are plenty of problems at the end of each section. ... CAGT has both good breadth and great presentation; it is in fact a new standard in presentation for combinatorics, essential as a resource for any instructor, including those teaching out of a different text. For the student: If you are just starting to build a library in combinatorics, this should be your first book."" - The UMAP Journal ""Combinatorics is an excellent candidate for a special topics course for mathematics majors; with the broad spectrum of applications that course can simultaneously be an advanced and a capstone course. This book would be an excellent selection for the textbook of such a course. The explanations are at an appropriate level for the audience and there are exercises at the end of each section...The coverage is also sufficient of breadth; all of the major areas of combinatorics are covered...This book is the best candidate for a textbook in combinatorics that I have encountered."" - Charles Ashbacher
Table of Content
Preface; Before you go; Notation; 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; Bibliography; Hints and answers to selected exercises.
Copyright Date
2010
Target Audience
Scholarly & Professional
Topic
Combinatorics, Discrete Mathematics
Lccn
2009-937059
Dewey Decimal
511.6
Dewey Edition
22
Illustrated
Yes
Genre
Mathematics
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