Friday, April 19, 2013

Introductory Combinatorics 5th Edition, Richard Brualdi

Introductory Combinatorics 5th Edition PDF Download Ebook. Richard A. Brualdi emphasizes combinatorial ideas, including the pigeon-hole principle, counting techniques, permutations and combinations, Polya counting, binomial coefficients, inclusion-exclusion principle, generating functions and recurrence relations, and combinatortial structures (matchings, designs, graphs).

Written to be entertaining and readable, this book's lively style reflects the author's joy for teaching the subject. It presents an excellent treatment of Polya's Counting Theorem that doesn't assume the student is familiar with group theory. It also includes problems that offer good practice of the principles it presents.

The book has been updated to include new material on partially ordered sets, Dilworth's Theorem, partitions of integers and generating functions. In addition, the chapters on graph theory have been completely revised. It is valuable book for any reader interested in learning more about combinatorics. It clarifies the exposition throughout and adds a wealth of new exercises, appropriate for one- or two-semester, junior- to senior-level combinatorics courses.

A clear and accessible presentation, written from the student's perspective, facilitates understanding of basic concepts and principles. An excellent treatment of Polya's Counting Theorem that does not assume students have studied group theory. Use of the term “combination” as it applies to a set has been de-emphasized; the author now uses the essentially equivalent term of “subset” for clarity.

A new section (Section 1.6) on mutually overlapping circles has been moved from Chapter 7 to illustrate some of the counting techniques covered in later chapters. Chapter 2 now contains a short section (Section 3.6) on finite probability. Chapter 3 now contains a proof of Ramsey’s theorem in the case of pairs as well as Pascal’s formula.

An extensively revised Chapter 7 moves up generating functions and exponential generating functions to Sections 7.2 and 7.3, giving them a more central treatment. Coverage of more topics of graph theory and digraphs and networks has been reversed. Chapter 12 now covers more topics of graph theory and Chapter 13 now covers digraphs and networks.

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