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The Art of Proving Binomial Identities

Author : Michael Z. Spivey

Publisher : CRC Press

Page : 277 pages

File Size : 17,44 MB

Release : 2019-05-10

Category : Mathematics

ISBN : 1351215809

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Book Description

The book has two goals: (1) Provide a unified treatment of the binomial coefficients, and (2) Bring together much of the undergraduate mathematics curriculum via one theme (the binomial coefficients). The binomial coefficients arise in a variety of areas of mathematics: combinatorics, of course, but also basic algebra (binomial theorem), infinite series (Newton’s binomial series), differentiation (Leibniz’s generalized product rule), special functions (the beta and gamma functions), probability, statistics, number theory, finite difference calculus, algorithm analysis, and even statistical mechanics.



The Art of Proving Binomial Identities

Author : Michael Z. Spivey

Publisher : CRC Press

Page : 368 pages

File Size : 31,61 MB

Release : 2019

Category : Binomial coefficients

ISBN : 9780815379423

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Book Description

The book has two goals: (1) Provide a unified treatment of the binomial coefficients, and (2) Bring together much of the undergraduate mathematics curriculum via one theme (the binomial coefficients). The binomial coefficients arise in a variety of areas of mathematics: combinatorics, of course, but also basic algebra (binomial theorem), infinite series (Newton's binomial series), differentiation (Leibniz's generalized product rule), special functions (the beta and gamma functions), probability, statistics, number theory, finite difference calculus, algorithm analysis, and even statistical mechanics.



Proofs that Really Count

Author : Arthur T. Benjamin

Publisher : American Mathematical Society

Page : 210 pages

File Size : 38,44 MB

Release : 2022-09-21

Category : Mathematics

ISBN : 1470472597

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Book Description

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: The Art of Counting

Author : Bruce E. Sagan

Publisher : American Mathematical Soc.

Page : 304 pages

File Size : 48,8 MB

Release : 2020-10-16

Category : Education

ISBN : 1470460327

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Book Description

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.



Surveys in Combinatorics, 1989

Author : J. Siemons

Publisher : Cambridge University Press

Page : 232 pages

File Size : 13,15 MB

Release : 1989-08-03

Category : Mathematics

ISBN : 9780521378239

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Book Description

Many areas of current research activity in combinatorics and its applications, including graph theory, designs and probabilistic graphs, are surveyed in lectures presented at the 12th British Combinatorial Conference.



Book of Proof

Author : Richard H. Hammack

Publisher :

Page : 314 pages

File Size : 24,63 MB

Release : 2016-01-01

Category : Mathematics

ISBN : 9780989472111

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Book Description

This book is an introduction to the language and standard proof methods of mathematics. It is a bridge from the computational courses (such as calculus or differential equations) that students typically encounter in their first year of college to a more abstract outlook. It lays a foundation for more theoretical courses such as topology, analysis and abstract algebra. Although it may be more meaningful to the student who has had some calculus, there is really no prerequisite other than a measure of mathematical maturity.



Proofs from THE BOOK

Author : Martin Aigner

Publisher : Springer Science & Business Media

Page : 194 pages

File Size : 31,99 MB

Release : 2013-06-29

Category : Mathematics

ISBN : 3662223430

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Book Description

According to the great mathematician Paul Erdös, God maintains perfect mathematical proofs in The Book. This book presents the authors candidates for such "perfect proofs," those which contain brilliant ideas, clever connections, and wonderful observations, bringing new insight and surprising perspectives to problems from number theory, geometry, analysis, combinatorics, and graph theory. As a result, this book will be fun reading for anyone with an interest in mathematics.



Generatingfunctionology

Author : Herbert S. Wilf

Publisher : Elsevier

Page : 193 pages

File Size : 14,92 MB

Release : 2014-05-10

Category : Mathematics

ISBN : 1483276635

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Book Description

Generatingfunctionology provides information pertinent to generating functions and some of their uses in discrete mathematics. This book presents the power of the method by giving a number of examples of problems that can be profitably thought about from the point of view of generating functions. Organized into five chapters, this book begins with an overview of the basic concepts of a generating function. This text then discusses the different kinds of series that are widely used as generating functions. Other chapters explain how to make much more precise estimates of the sizes of the coefficients of power series based on the analyticity of the function that is represented by the series. This book discusses as well the applications of the theory of generating functions to counting problems. The final chapter deals with the formal aspects of the theory of generating functions. This book is a valuable resource for mathematicians and students.



A Book of Abstract Algebra

Author : Charles C Pinter

Publisher : Courier Corporation

Page : 402 pages

File Size : 15,56 MB

Release : 2010-01-14

Category : Mathematics

ISBN : 0486474178

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Book Description

Accessible but rigorous, this outstanding text encompasses all of the topics covered by a typical course in elementary abstract algebra. Its easy-to-read treatment offers an intuitive approach, featuring informal discussions followed by thematically arranged exercises. This second edition features additional exercises to improve student familiarity with applications. 1990 edition.



The Art and Craft of Problem Solving

Author : Paul Zeitz

Publisher : John Wiley & Sons

Page : 389 pages

File Size : 30,74 MB

Release : 2017

Category : Problem solving

ISBN : 1119239907

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Book Description

This text on mathematical problem solving provides a comprehensive outline of "problemsolving-ology," concentrating on strategy and tactics. It discusses a number of standard mathematical subjects such as combinatorics and calculus from a problem solver's perspective.