Introduction and recurrence relations -- The pigeonhole principle and Ramsey theory -- Counting, probability, balls and boxes -- Permutations and combinations -- Binomial and multinomial coefficients -- Stirling numbers -- Integer partitions -- The inclusion-Exclusion principle -- Generating functions.
Summary:
"Combinatorics is a fun, difficult, broad, and very active area of mathematics. Counting, deciding whether certain configurations exist, and elementary graph theory is where the subject begins. There are myriad of connections to other areas of mathematics and computer science, and, in fact, combinatorial problems can be found almost everywhere. To learn combinatorics is partly to become familiar with combinatorial topics, problems, and techniques, and partly to develop a can-do attitude toward discrete problem solving. This textbook is meant for a student who has completed an introductory college calculus sequence (a few sections require some knowledge of linear algebra but you can get quite a bit out of this text without a thorough understanding of linear algebra), has some familiarity with proofs, and desires to not only become acquainted with the main topics of introductory combinatorics, but also to become a better problem solver"-- Provided by publisher.
This resource is supported by the Institute of Museum and Library Services under the provisions of the Library Services and Technology Act as administered by State Library of Iowa.