A Path to Combinatorics for Undergraduates: Counting Strategies

by Titu Andreescu, Zuming Feng

This unique approach to combinatorics is centered around challenging examples, fully-worked solutions, and hundreds of problems---many from Olympiads and other competitions, and many original to the authors. Each chapter highlights a particular aspect of the subject and casts combinatorial concepts in the guise of questions, illustrations, and exercises that are designed to encourage creativity, improve problem-solving techniques, and widen the reader's mathematical horizons.Topics encompass permutations and combinations, binomial coefficients and their applications, recursion, bijections, inclusions and exclusions, and generating functions. The work is replete with a broad range of useful methods and results, such as Sperner's Theorem, Catalan paths, integer partitions and Young's diagrams, and Lucas' and Kummer's Theorems on divisibility. Strong emphasis is placed on connections between combinatorial and graph-theoretic reasoning and on links between algebra and geometry.The authors' previous text, 102 Combinatorial Problems, makes a fine companion volume to the present work, which is ideal for Olympiad participants and coaches, advanced high school students, undergraduates, and

Genres: Mathematics, Textbooks

247 pages, Paperback

First published November 11, 2003

About the author

Titu Andreescu is an associate professor of mathematics at the University of Texas at Dallas. He is also firmly involved in mathematics contests and Olympiads, being the Director of AMC (as appointed by the Mathematical Association of America), Director of MOP, Head Coach of the USA IMO Team and Chairman of the USAMO. He has also authored a large number of books on the topic of problem solving and Olympiad-style mathematics.

Reviews

[Md Shohag · Rating 5 out of 5]

Very Effective book.

[Chris · Rating 5 out of 5]

Mind boggling descriptions of counting and its methods. The problems are way too good and beautifully handpicked. Would not recommend as a first book of the course tho. Helps to advance your mind.

[Abdullah Noman]

this is a good book