Overview
- Offers an accessible introduction to combinatorics, infused with Solomon Golomb’s insights and illuminating examples
- Features a conversational style that suits the classroom or independent study
- Includes numerous exercises, examples, and solutions that will serve as a valuable resource for instructors
Access this book
Tax calculation will be finalised at checkout
Other ways to access
Table of contents (7 chapters)
Keywords
- Solomon Golomb
- Solomon Golomb combinatorics
- Combinations with repetition
- Combinations without repetition
- Combining permutations
- Binomial theorem
- Generating functions
- Permutations with or without repetitions
- Exponential generating functions
- Fibonacci numbers
- Catalan numbers
- Stirling numbers
- Ramsay numbers
- Combinatorial structures
- Combinatorics
About this book
This textbook offers an accessible introduction to combinatorics, infused with Solomon Golomb’s insights and illustrative examples. Core concepts in combinatorics are presented with an engaging narrative that suits undergraduate study at any level. Featuring early coverage of the Principle of Inclusion-Exclusion and a unified treatment of permutations later on, the structure emphasizes the cohesive development of ideas. Combined with the conversational style, this approach is especially well suited to independent study.
Falling naturally into three parts, the book begins with a flexible Chapter Zero that can be used to cover essential background topics, or as a standalone problem-solving course. The following three chapters cover core topics in combinatorics, such as combinations, generating functions, and permutations. The final three chapters present additional topics, such as Fibonacci numbers, finite groups, and combinatorial structures. Numerous illuminating examples are included throughout, along with exercises of all levels. Three appendices include additional exercises, examples, and solutions to a selection of problems.
Solomon Golomb’s Course on Undergraduate Combinatorics is ideal for introducing mathematics students to combinatorics at any stage in their program. There are no formal prerequisites, but readers will benefit from mathematical curiosity and a willingness to engage in the book’s many entertaining challenges.
Authors and Affiliations
About the authors
Solomon Golomb (1932–2016) was a world leader in the development and application of mathematics for communications and coding theory. He received the National Medal of Science in 2011 in recognition of his pioneering work in shift register sequences. His remarkable career encompassed not only research contributions across a wide spectrum of science and technology, but also a gift and enthusiasm for recreational mathematics. He popularized polyominoes and published various long-running puzzle columns. In all areas of mathematics, Golomb was known for his enthusiasm and deep insight, which he shared generously through his teaching and mentoring.
Andy Liu is Professor Emeritus of the Department of Mathematical and Statistical Sciences at the University of Alberta, Canada. He has won numerous international awards in mathematics teaching and outreach, with a career-long involvement in mathematics competitions and math circles. His previous titles include an array ofengaging, problem-oriented books.
Bibliographic Information
Book Title: Solomon Golomb’s Course on Undergraduate Combinatorics
Authors: Solomon W. Golomb, Andy Liu
DOI: https://doi.org/10.1007/978-3-030-72228-9
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
Hardcover ISBN: 978-3-030-72227-2Published: 14 September 2021
Softcover ISBN: 978-3-030-72230-2Published: 15 September 2022
eBook ISBN: 978-3-030-72228-9Published: 13 September 2021
Edition Number: 1
Number of Pages: XVIII, 458
Topics: Combinatorics