Combinatorics: The Art of Counting

2020-10-16 Education

Author : Bruce E. Sagan
Release : 2020-10-16
Genre : Education
Kind : eBook
Book Rating : 327/5 ( reviews)

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Book Synopsis Combinatorics: The Art of Counting by : Bruce E. Sagan

Download or read book Combinatorics: The Art of Counting written by Bruce E. Sagan. This book was released on 2020-10-16. Available in PDF, EPUB and Kindle. Book excerpt: This book is a gentle introduction to the enumerative part of combinatorics suitable for study at the advanced undergraduate or beginning graduate level. In addition to covering all the standard techniques for counting combinatorial objects, the text contains material from the research literature which has never before appeared in print, such as the use of quotient posets to study the Möbius function and characteristic polynomial of a partially ordered set, or the connection between quasisymmetric functions and pattern avoidance. The book assumes minimal background, and a first course in abstract algebra should suffice. The exposition is very reader friendly: keeping a moderate pace, using lots of examples, emphasizing recurring themes, and frankly expressing the delight the author takes in mathematics in general and combinatorics in particular.

Counting: The Art of Enumerative Combinatorics

2013-03-09 Mathematics

Author : George E. Martin
Release : 2013-03-09
Genre : Mathematics
Kind : eBook
Book Rating : 787/5 ( reviews)

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Book Synopsis Counting: The Art of Enumerative Combinatorics by : George E. Martin

Download or read book Counting: The Art of Enumerative Combinatorics written by George E. Martin. This book was released on 2013-03-09. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to discrete mathematics. At the end of the book the reader should be able to answer counting questions such as: How many ways are there to stack n poker chips, each of which can be red, white, blue, or green, such that each red chip is adjacent to at least 1 green chip? The book can be used as a textbook for a semester course at the sophomore level. The first five chapters can also serve as a basis for a graduate course for in-service teachers.

Combinatorial Reasoning

2014-04-08 Mathematics

Author : Duane DeTemple
Release : 2014-04-08
Genre : Mathematics
Kind : eBook
Book Rating : 134/5 ( reviews)

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Book Synopsis Combinatorial Reasoning by : Duane DeTemple

Download or read book Combinatorial Reasoning written by Duane DeTemple. This book was released on 2014-04-08. Available in PDF, EPUB and Kindle. Book excerpt: Written by two well-known scholars in the field, Combinatorial Reasoning: An Introduction to the Art of Counting presents a clear and comprehensive introduction to the concepts and methodology of beginning combinatorics. Focusing on modern techniques and applications, the book develops a variety of effective approaches to solving counting problems. Balancing abstract ideas with specific topical coverage, the book utilizes real world examples with problems ranging from basic calculations that are designed to develop fundamental concepts to more challenging exercises that allow for a deeper exploration of complex combinatorial situations. Simple cases are treated first before moving on to general and more advanced cases. Additional features of the book include: • Approximately 700 carefully structured problems designed for readers at multiple levels, many with hints and/or short answers • Numerous examples that illustrate problem solving using both combinatorial reasoning and sophisticated algorithmic methods • A novel approach to the study of recurrence sequences, which simplifies many proofs and calculations • Concrete examples and diagrams interspersed throughout to further aid comprehension of abstract concepts • A chapter-by-chapter review to clarify the most crucial concepts covered Combinatorial Reasoning: An Introduction to the Art of Counting is an excellent textbook for upper-undergraduate and beginning graduate-level courses on introductory combinatorics and discrete mathematics.

Proofs that Really Count

2022-09-21 Mathematics

Author : Arthur T. Benjamin
Release : 2022-09-21
Genre : Mathematics
Kind : eBook
Book Rating : 597/5 ( reviews)

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Book Synopsis Proofs that Really Count by : Arthur T. Benjamin

Download or read book Proofs that Really Count written by Arthur T. Benjamin. This book was released on 2022-09-21. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics is the science of patterns, and mathematicians attempt to understand these patterns and discover new ones using a variety of tools. In Proofs That Really Count, award-winning math professors Arthur Benjamin and Jennifer Quinn demonstrate that many number patterns, even very complex ones, can be understood by simple counting arguments. The book emphasizes numbers that are often not thought of as numbers that count: Fibonacci Numbers, Lucas Numbers, Continued Fractions, and Harmonic Numbers, to name a few. Numerous hints and references are given for all chapter exercises and many chapters end with a list of identities in need of combinatorial proof. The extensive appendix of identities will be a valuable resource. This book should appeal to readers of all levels, from high school math students to professional mathematicians.

Combinatorics

2020 Combinatorial analysis

Author : Bruce Eli Sagan
Release : 2020
Genre : Combinatorial analysis
Kind : eBook
Book Rating : 802/5 ( reviews)

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Book Synopsis Combinatorics by : Bruce Eli Sagan

Download or read book Combinatorics written by Bruce Eli Sagan. This book was released on 2020. Available in PDF, EPUB and Kindle. Book excerpt: This book is a gentle introduction to the enumerative part of combinatorics suitable for study at the advanced undergraduate or beginning graduate level. In addition to covering all the standard techniques for counting combinatorial objects, the text contains material from the research literature which has never before appeared in print, such as the use of quotient posets to study the Möbius function and characteristic polynomial of a partially ordered set, or the connection between quasisymmetric functions and pattern avoidance.The book assumes minimal background, and a first course in abstra

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