Problem-Solving Methods in Combinatorics

Problem-Solving Methods in Combinatorics
Author: Pablo Soberón
Publisher: Springer Science & Business Media
Total Pages: 178
Release: 2013-03-20
Genre: Mathematics
ISBN: 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.

Problem-Solving Strategies

Problem-Solving Strategies
Author: Arthur Engel
Publisher: Springer Science & Business Media
Total Pages: 404
Release: 2008-01-19
Genre: Mathematics
ISBN: 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.

Counting and Configurations

Counting and Configurations
Author: Jiri Herman
Publisher: Springer Science & Business Media
Total Pages: 402
Release: 2013-03-14
Genre: Mathematics
ISBN: 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.

Combinatorics

Combinatorics
Author: Pavle Mladenović
Publisher: Springer
Total Pages: 365
Release: 2019-03-13
Genre: Mathematics
ISBN: 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.

102 Combinatorial Problems

102 Combinatorial Problems
Author: Titu Andreescu
Publisher: Springer Science & Business Media
Total Pages: 125
Release: 2013-11-27
Genre: Mathematics
ISBN: 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.

Problem-Solving Through Problems

Problem-Solving Through Problems
Author: Loren C. Larson
Publisher: Springer Science & Business Media
Total Pages: 322
Release: 2012-12-06
Genre: Mathematics
ISBN: 1461254981

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This is a practical anthology of some of the best elementary problems in different branches of mathematics. Arranged by subject, the problems highlight the most common problem-solving techniques encountered in undergraduate mathematics. This book teaches the important principles and broad strategies for coping with the experience of solving problems. It has been found very helpful for students preparing for the Putnam exam.

A Path to Combinatorics for Undergraduates

A Path to Combinatorics for Undergraduates
Author: Titu Andreescu
Publisher: Springer Science & Business Media
Total Pages: 235
Release: 2013-12-01
Genre: Mathematics
ISBN: 081768154X

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This unique approach to combinatorics is centered around unconventional, essay-type combinatorial examples, followed by a number of carefully selected, challenging problems and extensive discussions of their solutions. Topics encompass permutations and combinations, binomial coefficients and their applications, bijections, inclusions and exclusions, and generating functions. Each chapter features fully-worked problems, including many from Olympiads and other competitions, as well as a number of problems original to the authors; at the end of each chapter are further exercises to reinforce understanding, encourage creativity, and build a repertory of problem-solving techniques. The authors' previous text, "102 Combinatorial Problems," makes a fine companion volume to the present work, which is ideal for Olympiad participants and coaches, advanced high school students, undergraduates, and college instructors. The book's unusual problems and examples will interest seasoned mathematicians as well. "A Path to Combinatorics for Undergraduates" is a lively introduction not only to combinatorics, but to mathematical ingenuity, rigor, and the joy of solving puzzles.

Combinatorics

Combinatorics
Author: Daniel A. Marcus
Publisher: American Mathematical Soc.
Total Pages: 136
Release: 1998-12-31
Genre: Mathematics
ISBN: 0883859815

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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.

Stochastic Local Search

Stochastic Local Search
Author: Holger H. Hoos
Publisher: Morgan Kaufmann
Total Pages: 678
Release: 2005
Genre: Business & Economics
ISBN: 1558608729

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Stochastic local search (SLS) algorithms are among the most prominent and successful techniques for solving computationally difficult problems. Offering a systematic treatment of SLS algorithms, this book examines the general concepts and specific instances of SLS algorithms and considers their development, analysis and application.

Combinatorial Methods with Computer Applications

Combinatorial Methods with Computer Applications
Author: Jonathan L. Gross
Publisher: CRC Press
Total Pages: 664
Release: 2016-04-19
Genre: Computers
ISBN: 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