Combinatorics: A Guided Tour

By David R. Mazur

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, P?lya 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.

• Format: Hardcover
• Language: English
• ISBN: 0883857626
• ISBN13: 9780883857625
• Release Date: March 2010
• Publisher: Mathematical Association of America (MAA)
• Length: 410 Pages
• Weight: 2.00 lbs.
• Dimensions: 1.2" x 7.2" x 9.9"

Customer Reviews

Mazur’s A Guided Tour: Where Mathematical Rigor Meets Reader Delight

Professor Mazur’s Combinatorics – A Guided Tour stands out for several compelling reasons. One of its most distinctive features is the seamless integration of questions throughout the main text. Rather than relegating all exercises to the end of each chapter, Mazur embeds thought-provoking prompts directly into the narrative. This encourages readers to pause, reflect, and actively engage with the material as they progress—something rarely seen in traditional mathematics textbooks. It’s a refreshing and effective approach that transforms passive reading into an interactive learning experience. True to the spirit of the book’s title, “A Guided Tour,” Professor Mazur also includes sections called Travel Notes. These add a conversational tone, historical context, and delightful anecdotes that enhance the sense of an intellectual journey. They invite the reader not just to learn, but to appreciate the broader landscape and development of combinatorial ideas. Finally, it's worth applauding the accuracy and reliability of the content. In a field where even well-regarded resources sometimes falter—requiring errata or future revisions—Mazur’s meticulous care shines through. It’s a relief and a joy to study from a text where the solutions and reasoning can be trusted from the outset. All in all, Combinatorics – A Guided Tour is a thoughtfully crafted and engaging textbook. Hats off to Professor Mazur for creating such an exceptional resource—one that both informs and inspires.