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.
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 of engaging, problem-oriented books.
0. Basic Tools.- 1. Combinations.- 2. Recurrence Relations and Generating Functions.- 3. Permutations.- 4. Special Numbers.- 5. Counting Under Symmetries.- 6. Combinatorial Structures.- A. Additional Exercises.- B. Additional Examples.- C. Solutions to Odd-numbered Exercises.- Bibliography.- Index.