Introduction to Combinatorics (Discrete Mathematics and Its Applications) - Softcover

Wallis, Walter D.; George, John C.

Softcover

ISBN 10: 1032476990 ISBN 13: 9781032476995

Publisher: Chapman and Hall/CRC, 2023

Synopsis

What Is Combinatorics Anyway?

Broadly speaking, combinatorics is the branch of mathematics dealing

with different ways of selecting objects from a set or arranging objects. It

tries to answer two major kinds of questions, namely, counting questions: how many ways can a selection or arrangement be chosen with a particular set of properties; and structural

questions: does there exist a selection or arrangement of objects with a

particular set of properties?

The authors have presented a text for students at all levels of preparation.

For some, this will be the first course where the students see several real proofs.

Others will have a good background in linear algebra, will have completed the calculus

stream, and will have started abstract algebra.

The text starts by briefly discussing several examples of typical combinatorial problems

to give the reader a better idea of what the subject covers. The next

chapters explore enumerative ideas and also probability. It then moves on to

enumerative functions and the relations between them, and generating functions and recurrences.,

Important families of functions, or numbers and then theorems are presented.

Brief introductions to computer algebra and group theory come next. Structures of particular

interest in combinatorics: posets, graphs, codes, Latin squares, and experimental designs follow. The

authors conclude with further discussion of the interaction between linear algebra

and combinatorics.

Features

• Two new chapters on probability and posets.





• Numerous new illustrations, exercises, and problems.





• More examples on current technology use





• A thorough focus on accuracy





• Three appendices: sets, induction and proof techniques, vectors and matrices, and biographies with historical notes,





• Flexible use of MapleTM and MathematicaTM

About this title

About the Author

W.D. Wallis is Professor Emeritus of Southern Illiniois University. John C George is Asscoiate Professor at Gordon State College.

Edition details

• Publisher: Chapman and Hall/CRC
• Publication date: 2023
• Language: English
• ISBN 10: 1032476990
• ISBN 13: 9781032476995
• Binding: Paperback
• Edition number: 2
• Number of pages: 444