Introduction to Combinatorics

Combinatorics is the branch of mathematics that deals with selecting and arranging objects. It answers counting and structural questions, such as how many ways can a selection or arrangement be chosen with a particular set of properties? This text is for students at all levels of preparation and covers enumerative ideas, probability, enumerative functions, generating functions, recurrences, computer algebra, group theory, posets, graphs, codes, Latin squares, and experimental designs. It also includes two new chapters on probability and posets, numerous new illustrations, exercises, and problems, and a thorough focus on accuracy.

Format: Paperback / softback
Length: 444 pages
Publication date: 21 January 2023
Publisher: Taylor & Francis Ltd

Combinatorics is a branch of mathematics that deals with selecting and arranging objects in various ways. It encompasses two main areas of inquiry: counting questions, which involve determining the number of ways a selection or arrangement can be made with specific properties, and structural questions, which explore whether a particular selection or arrangement exists with those properties. The authors of this text have designed it to cater to students at different levels of preparation, including those who may be encountering combinatorics for the first time, those with a strong background in linear algebra and calculus, and those who have begun studying abstract algebra.

The text begins by providing examples of typical combinatorial problems to give the reader a clearer understanding of the subject matter. It then delves into enumerative ideas, probability, enumerative functions, generating functions, and recurrences. Important families of functions, such as permutations, combinations, and power sets, are presented, along with theorems and concepts related to them. Brief introductions to computer algebra and group theory are included to provide additional context.

Structures of particular interest in combinatorics, such as posets, graphs, codes, Latin squares, and experimental designs, are discussed. The authors conclude by further exploring the interplay between linear algebra and combinatorics.

This updated edition of the text includes two new chapters on probability and posets, along with numerous new illustrations, exercises, and problems. It also emphasizes the importance of accuracy in solving combinatorial problems, with three appendices providing additional information on sets, induction, and proofs.

Overall, this text is an excellent resource for students seeking to gain a deeper understanding of combinatorics and its applications in mathematics and other fields.

Weight: 820g
Dimension: 229 x 152 (mm)
ISBN-13: 9781032476995
Edition number: 2 ed