Problem-Solving Methods in Combinatorics

Problem-Solving Methods in Combinatorics

Author: Pablo Soberón

Publisher: Springer Science & Business Media

Published: 2013-03-20

Total Pages: 174

ISBN-13: 3034805977

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Every year there is at least one combinatorics problem in each of the major international mathematical olympiads. These problems can only be solved with a very high level of wit and creativity. This book explains all the problem-solving techniques necessary to tackle these problems, with clear examples from recent contests. It also includes a large problem section for each topic, including hints and full solutions so that the reader can practice the material covered in the book.​ The material will be useful not only to participants in the olympiads and their coaches but also in university courses on combinatorics.


Book Synopsis Problem-Solving Methods in Combinatorics by : Pablo Soberón

Download or read book Problem-Solving Methods in Combinatorics written by Pablo Soberón and published by Springer Science & Business Media. This book was released on 2013-03-20 with total page 174 pages. Available in PDF, EPUB and Kindle. Book excerpt: Every year there is at least one combinatorics problem in each of the major international mathematical olympiads. These problems can only be solved with a very high level of wit and creativity. This book explains all the problem-solving techniques necessary to tackle these problems, with clear examples from recent contests. It also includes a large problem section for each topic, including hints and full solutions so that the reader can practice the material covered in the book.​ The material will be useful not only to participants in the olympiads and their coaches but also in university courses on combinatorics.

Combinatorics

Combinatorics

Author: Daniel A. Marcus

Publisher: American Mathematical Soc.

Published: 1998-12-31

Total Pages: 148

ISBN-13: 0883857103

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The format of this book is unique in that it combines features of a traditional text with those of a problem book. The material is presented through a series of problems, about 250 in all, with connecting text; this is supplemented by 250 additional problems suitable for homework assignment. The problems are structured in order to introduce concepts in a logical order and in a thought-provoking way. The first four sections of the book deal with basic combinatorial entities; the last four cover special counting methods. Many applications to probability are included along the way. Students from a wide range of backgrounds--mathematics, computer science, or engineering--will appreciate this appealing introduction.


Book Synopsis Combinatorics by : Daniel A. Marcus

Download or read book Combinatorics written by Daniel A. Marcus and published by American Mathematical Soc.. This book was released on 1998-12-31 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: The format of this book is unique in that it combines features of a traditional text with those of a problem book. The material is presented through a series of problems, about 250 in all, with connecting text; this is supplemented by 250 additional problems suitable for homework assignment. The problems are structured in order to introduce concepts in a logical order and in a thought-provoking way. The first four sections of the book deal with basic combinatorial entities; the last four cover special counting methods. Many applications to probability are included along the way. Students from a wide range of backgrounds--mathematics, computer science, or engineering--will appreciate this appealing introduction.

Counting and Configurations

Counting and Configurations

Author: Jiri Herman

Publisher: Springer Science & Business Media

Published: 2013-03-14

Total Pages: 402

ISBN-13: 1475739257

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This book presents methods of solving problems in three areas of elementary combinatorial mathematics: classical combinatorics, combinatorial arithmetic, and combinatorial geometry. Brief theoretical discussions are immediately followed by carefully worked-out examples of increasing degrees of difficulty and by exercises that range from routine to rather challenging. The book features approximately 310 examples and 650 exercises.


Book Synopsis Counting and Configurations by : Jiri Herman

Download or read book Counting and Configurations written by Jiri Herman and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents methods of solving problems in three areas of elementary combinatorial mathematics: classical combinatorics, combinatorial arithmetic, and combinatorial geometry. Brief theoretical discussions are immediately followed by carefully worked-out examples of increasing degrees of difficulty and by exercises that range from routine to rather challenging. The book features approximately 310 examples and 650 exercises.

Combinatorics

Combinatorics

Author: Pavle Mladenović

Publisher: Springer

Published: 2019-03-13

Total Pages: 365

ISBN-13: 3030008312

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This text provides a theoretical background for several topics in combinatorial mathematics, such as enumerative combinatorics (including partitions and Burnside's lemma), magic and Latin squares, graph theory, extremal combinatorics, mathematical games and elementary probability. A number of examples are given with explanations while the book also provides more than 300 exercises of different levels of difficulty that are arranged at the end of each chapter, and more than 130 additional challenging problems, including problems from mathematical olympiads. Solutions or hints to all exercises and problems are included. The book can be used by secondary school students preparing for mathematical competitions, by their instructors, and by undergraduate students. The book may also be useful for graduate students and for researchers that apply combinatorial methods in different areas.


Book Synopsis Combinatorics by : Pavle Mladenović

Download or read book Combinatorics written by Pavle Mladenović and published by Springer. This book was released on 2019-03-13 with total page 365 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text provides a theoretical background for several topics in combinatorial mathematics, such as enumerative combinatorics (including partitions and Burnside's lemma), magic and Latin squares, graph theory, extremal combinatorics, mathematical games and elementary probability. A number of examples are given with explanations while the book also provides more than 300 exercises of different levels of difficulty that are arranged at the end of each chapter, and more than 130 additional challenging problems, including problems from mathematical olympiads. Solutions or hints to all exercises and problems are included. The book can be used by secondary school students preparing for mathematical competitions, by their instructors, and by undergraduate students. The book may also be useful for graduate students and for researchers that apply combinatorial methods in different areas.

102 Combinatorial Problems

102 Combinatorial Problems

Author: Titu Andreescu

Publisher: Springer Science & Business Media

Published: 2013-11-27

Total Pages: 125

ISBN-13: 0817682228

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"102 Combinatorial Problems" consists of carefully selected problems that have been used in the training and testing of the USA International Mathematical Olympiad (IMO) team. Key features: * Provides in-depth enrichment in the important areas of combinatorics by reorganizing and enhancing problem-solving tactics and strategies * Topics include: combinatorial arguments and identities, generating functions, graph theory, recursive relations, sums and products, probability, number theory, polynomials, theory of equations, complex numbers in geometry, algorithmic proofs, combinatorial and advanced geometry, functional equations and classical inequalities The book is systematically organized, gradually building combinatorial skills and techniques and broadening the student's view of mathematics. Aside from its practical use in training teachers and students engaged in mathematical competitions, it is a source of enrichment that is bound to stimulate interest in a variety of mathematical areas that are tangential to combinatorics.


Book Synopsis 102 Combinatorial Problems by : Titu Andreescu

Download or read book 102 Combinatorial Problems written by Titu Andreescu and published by Springer Science & Business Media. This book was released on 2013-11-27 with total page 125 pages. Available in PDF, EPUB and Kindle. Book excerpt: "102 Combinatorial Problems" consists of carefully selected problems that have been used in the training and testing of the USA International Mathematical Olympiad (IMO) team. Key features: * Provides in-depth enrichment in the important areas of combinatorics by reorganizing and enhancing problem-solving tactics and strategies * Topics include: combinatorial arguments and identities, generating functions, graph theory, recursive relations, sums and products, probability, number theory, polynomials, theory of equations, complex numbers in geometry, algorithmic proofs, combinatorial and advanced geometry, functional equations and classical inequalities The book is systematically organized, gradually building combinatorial skills and techniques and broadening the student's view of mathematics. Aside from its practical use in training teachers and students engaged in mathematical competitions, it is a source of enrichment that is bound to stimulate interest in a variety of mathematical areas that are tangential to combinatorics.

Combinatorics

Combinatorics

Author: Robin J. Wilson

Publisher: Oxford University Press

Published: 2016

Total Pages: 177

ISBN-13: 0198723490

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How many possible sudoku puzzles are there? In the lottery, what is the chance that two winning balls have consecutive numbers? Who invented Pascal's triangle? (it was not Pascal) Combinatorics, the branch of mathematics concerned with selecting, arranging, and listing or counting collections of objects, works to answer all these questions. Dating back some 3000 years, and initially consisting mainly of the study of permutations and combinations, its scope has broadened to include topics such as graph theory, partitions of numbers, block designs, design of codes, and latin squares. In this Very Short Introduction Robin Wilson gives an overview of the field and its applications in mathematics and computer theory, considering problems from the shortest routes covering certain stops to the minimum number of colours needed to colour a map with different colours for neighbouring countries. ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.


Book Synopsis Combinatorics by : Robin J. Wilson

Download or read book Combinatorics written by Robin J. Wilson and published by Oxford University Press. This book was released on 2016 with total page 177 pages. Available in PDF, EPUB and Kindle. Book excerpt: How many possible sudoku puzzles are there? In the lottery, what is the chance that two winning balls have consecutive numbers? Who invented Pascal's triangle? (it was not Pascal) Combinatorics, the branch of mathematics concerned with selecting, arranging, and listing or counting collections of objects, works to answer all these questions. Dating back some 3000 years, and initially consisting mainly of the study of permutations and combinations, its scope has broadened to include topics such as graph theory, partitions of numbers, block designs, design of codes, and latin squares. In this Very Short Introduction Robin Wilson gives an overview of the field and its applications in mathematics and computer theory, considering problems from the shortest routes covering certain stops to the minimum number of colours needed to colour a map with different colours for neighbouring countries. ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.

Combinatorial Methods with Computer Applications

Combinatorial Methods with Computer Applications

Author: Jonathan L. Gross

Publisher: CRC Press

Published: 2016-04-19

Total Pages: 664

ISBN-13: 1584887443

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Combinatorial Methods with Computer Applications provides in-depth coverage of recurrences, generating functions, partitions, and permutations, along with some of the most interesting graph and network topics, design constructions, and finite geometries. Requiring only a foundation in discrete mathematics, it can serve as the textbook in a combinat


Book Synopsis Combinatorial Methods with Computer Applications by : Jonathan L. Gross

Download or read book Combinatorial Methods with Computer Applications written by Jonathan L. Gross and published by CRC Press. This book was released on 2016-04-19 with total page 664 pages. Available in PDF, EPUB and Kindle. Book excerpt: Combinatorial Methods with Computer Applications provides in-depth coverage of recurrences, generating functions, partitions, and permutations, along with some of the most interesting graph and network topics, design constructions, and finite geometries. Requiring only a foundation in discrete mathematics, it can serve as the textbook in a combinat

Problem-Solving Strategies

Problem-Solving Strategies

Author: Arthur Engel

Publisher: Springer Science & Business Media

Published: 2008-01-19

Total Pages: 404

ISBN-13: 0387226419

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A unique collection of competition problems from over twenty major national and international mathematical competitions for high school students. Written for trainers and participants of contests of all levels up to the highest level, this will appeal to high school teachers conducting a mathematics club who need a range of simple to complex problems and to those instructors wishing to pose a "problem of the week", thus bringing a creative atmosphere into the classrooms. Equally, this is a must-have for individuals interested in solving difficult and challenging problems. Each chapter starts with typical examples illustrating the central concepts and is followed by a number of carefully selected problems and their solutions. Most of the solutions are complete, but some merely point to the road leading to the final solution. In addition to being a valuable resource of mathematical problems and solution strategies, this is the most complete training book on the market.


Book Synopsis Problem-Solving Strategies by : Arthur Engel

Download or read book Problem-Solving Strategies written by Arthur Engel and published by Springer Science & Business Media. This book was released on 2008-01-19 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: A unique collection of competition problems from over twenty major national and international mathematical competitions for high school students. Written for trainers and participants of contests of all levels up to the highest level, this will appeal to high school teachers conducting a mathematics club who need a range of simple to complex problems and to those instructors wishing to pose a "problem of the week", thus bringing a creative atmosphere into the classrooms. Equally, this is a must-have for individuals interested in solving difficult and challenging problems. Each chapter starts with typical examples illustrating the central concepts and is followed by a number of carefully selected problems and their solutions. Most of the solutions are complete, but some merely point to the road leading to the final solution. In addition to being a valuable resource of mathematical problems and solution strategies, this is the most complete training book on the market.

Introduction to Combinatorics

Introduction to Combinatorics

Author: Martin J. Erickson

Publisher: John Wiley & Sons

Published: 2011-10-24

Total Pages: 210

ISBN-13: 1118030893

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This gradual, systematic introduction to the main concepts of combinatorics is the ideal text for advanced undergraduate and early graduate courses in this subject. Each of the book's three sections--Existence, Enumeration, and Construction--begins with a simply stated first principle, which is then developed step by step until it leads to one of the three major achievements of combinatorics: Van der Waerden's theorem on arithmetic progressions, Polya's graph enumeration formula, and Leech's 24-dimensional lattice. Along the way, Professor Martin J. Erickson introduces fundamental results, discusses interconnection and problem-solving techniques, and collects and disseminates open problems that raise new and innovative questions and observations. His carefully chosen end-of-chapter exercises demonstrate the applicability of combinatorial methods to a wide variety of problems, including many drawn from the William Lowell Putnam Mathematical Competition. Many important combinatorial methods are revisited several times in the course of the text--in exercises and examples as well as theorems and proofs. This repetition enables students to build confidence and reinforce their understanding of complex material. Mathematicians, statisticians, and computer scientists profit greatly from a solid foundation in combinatorics. Introduction to Combinatorics builds that foundation in an orderly, methodical, and highly accessible manner.


Book Synopsis Introduction to Combinatorics by : Martin J. Erickson

Download or read book Introduction to Combinatorics written by Martin J. Erickson and published by John Wiley & Sons. This book was released on 2011-10-24 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: This gradual, systematic introduction to the main concepts of combinatorics is the ideal text for advanced undergraduate and early graduate courses in this subject. Each of the book's three sections--Existence, Enumeration, and Construction--begins with a simply stated first principle, which is then developed step by step until it leads to one of the three major achievements of combinatorics: Van der Waerden's theorem on arithmetic progressions, Polya's graph enumeration formula, and Leech's 24-dimensional lattice. Along the way, Professor Martin J. Erickson introduces fundamental results, discusses interconnection and problem-solving techniques, and collects and disseminates open problems that raise new and innovative questions and observations. His carefully chosen end-of-chapter exercises demonstrate the applicability of combinatorial methods to a wide variety of problems, including many drawn from the William Lowell Putnam Mathematical Competition. Many important combinatorial methods are revisited several times in the course of the text--in exercises and examples as well as theorems and proofs. This repetition enables students to build confidence and reinforce their understanding of complex material. Mathematicians, statisticians, and computer scientists profit greatly from a solid foundation in combinatorics. Introduction to Combinatorics builds that foundation in an orderly, methodical, and highly accessible manner.

Probabilistic and Combinatorial Techniques: Advanced Problem Solving

Probabilistic and Combinatorial Techniques: Advanced Problem Solving

Author: Carson Graves

Publisher: States Academic Press

Published: 2021-11-16

Total Pages: 248

ISBN-13: 9781639894444

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Probabilistic technique is a nonconstructive method used to prove the existence of a specified type of mathematical object. It works by showing that if one randomly selects objects from a specified class, the probability that the result is of the given kind is strictly greater than zero. The probabilistic method is applied in various areas of mathematics such as number theory, linear algebra and real analysis, as well as computer science and information theory. It is mainly used in combinatorics, which deals primarily with counting, both as a means and an end in obtaining results. It also deals with some properties of finite structures. It is used in various areas like logic, statistical physics, evolutionary biology, computer science, etc. Different approaches, evaluations, methodologies and advanced studies on probabilistic and combinatorial techniques have been included in this book. It traces the progress of this field and highlights some of its key concepts and applications. This book aims to equip students and experts with the advanced topics and upcoming models in this area.


Book Synopsis Probabilistic and Combinatorial Techniques: Advanced Problem Solving by : Carson Graves

Download or read book Probabilistic and Combinatorial Techniques: Advanced Problem Solving written by Carson Graves and published by States Academic Press. This book was released on 2021-11-16 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: Probabilistic technique is a nonconstructive method used to prove the existence of a specified type of mathematical object. It works by showing that if one randomly selects objects from a specified class, the probability that the result is of the given kind is strictly greater than zero. The probabilistic method is applied in various areas of mathematics such as number theory, linear algebra and real analysis, as well as computer science and information theory. It is mainly used in combinatorics, which deals primarily with counting, both as a means and an end in obtaining results. It also deals with some properties of finite structures. It is used in various areas like logic, statistical physics, evolutionary biology, computer science, etc. Different approaches, evaluations, methodologies and advanced studies on probabilistic and combinatorial techniques have been included in this book. It traces the progress of this field and highlights some of its key concepts and applications. This book aims to equip students and experts with the advanced topics and upcoming models in this area.