Combinatorics: a guided tour
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 Ramse…
Read More ↓Title Statements
- Full title :Combinatorics : a guided tour / David R. Mazur.
Summary
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. The text emphasizes the brands of thinking that are characteristic of combinatorics: bijective and combinatorial proofs, recursive analysis, and counting problem classification.
Read More ↓Edition Statements
- Publication Date:©2010
Publication Statements
- Publisher(s):Mathematical Association of America
- Place of Publication:Washington, DC
- Language:eng
- Publication Date:©2010
The Physical Object
- Description:xviii, 391 pages : : illustrations ; : 27 cm.
Edition Identifiers
- ISBN:9780883857625, 0883857626
- oclc:ocn471794290
- LC Classification:QA164
- Dewey Decimal:511.6
Table of Contents
Ch. 1 . Principles of Combinatorics -- ch. 2. Distributions and Combinatorial Proofs -- ch. 3. Algebraic Tools -- ch. 4. Famous Number Families -- ch. 5. Counting Under Equivalence -- ch. 6. Combinatorics on Graphs -- ch. 7. Designs and Codes -- ch. 8. Partially Ordered Sets.
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