Problem Solving Methods In Combinatorics

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Problem Solving Methods In Combinatorics

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Author : Pablo Soberón
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-20

Problem Solving Methods In Combinatorics written by Pablo Soberón and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-20 with Mathematics categories.

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.

A Path To Combinatorics For Undergraduates

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Author : Titu Andreescu
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-01

A Path To Combinatorics For Undergraduates written by Titu Andreescu and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-01 with Mathematics categories.

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.

Probabilistic And Combinatorial Techniques Advanced Problem Solving

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Author : Carson Graves
language : en
Publisher: States Academic Press
Release Date : 2021-11-16

Probabilistic And Combinatorial Techniques Advanced Problem Solving written by Carson Graves and has been published by States Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-11-16 with Mathematics categories.

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.

102 Combinatorial Problems

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Author : Titu Andreescu
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-27

102 Combinatorial Problems written by Titu Andreescu and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-27 with Mathematics categories.

"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.

Mathematics As Problem Solving

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Author : Alexander Soifer
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-04-28

Mathematics As Problem Solving written by Alexander Soifer and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-04-28 with Education categories.

Various elementary techniques for solving problems in algebra, geometry, and combinatorics are explored in this second edition of Mathematics as Problem Solving. Each new chapter builds on the previous one, allowing the reader to uncover new methods for using logic to solve problems. Topics are presented in self-contained chapters, with classical solutions as well as Soifer's own discoveries. With roughly 200 different problems, the reader is challenged to approach problems from different angles. Mathematics as Problem Solving is aimed at students from high school through undergraduate levels and beyond, educators, and the general reader interested in the methods of mathematical problem solving.

Combinatorics

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Author : Daniel A. Marcus
language : en
Publisher: American Mathematical Soc.
Release Date : 1998-12-31

Combinatorics written by Daniel A. Marcus and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-12-31 with Mathematics categories.

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.

How To Count

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Author : R.B.J.T. Allenby
language : en
Publisher: CRC Press
Release Date : 2011-07-01

How To Count written by R.B.J.T. Allenby and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-07-01 with Mathematics categories.

Emphasizes a Problem Solving Approach A first course in combinatorics Completely revised, How to Count: An Introduction to Combinatorics, Second Edition shows how to solve numerous classic and other interesting combinatorial problems. The authors take an easily accessible approach that introduces problems before leading into the theory involved. Although the authors present most of the topics through concrete problems, they also emphasize the importance of proofs in mathematics. New to the Second Edition This second edition incorporates 50 percent more material. It includes seven new chapters that cover occupancy problems, Stirling and Catalan numbers, graph theory, trees, Dirichlet’s pigeonhole principle, Ramsey theory, and rook polynomials. This edition also contains more than 450 exercises. Ideal for both classroom teaching and self-study, this text requires only a modest amount of mathematical background. In an engaging way, it covers many combinatorial tools, such as the inclusion-exclusion principle, generating functions, recurrence relations, and Pólya’s counting theorem.

Problem Solving Methods Programming And Future Concepts

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Author : O.V. German
language : en
Publisher: Elsevier
Release Date : 1995-11-28

Problem Solving Methods Programming And Future Concepts written by O.V. German and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-11-28 with Mathematics categories.

Problem solving is the very area of articifical intelligence AI which, probably, will never result in a complete set of formalized theories, in a pragmatic philosphy, or in a "universal" applied discipline. Studying questions concerning this area, encompasses different concepts, models and theories. This volume of the series looks at classifying problems, interpreting them, and the methods of solving them. The final chapter covers future concepts such as universal problem solving approach restoration, weak methods becoming strong, the role of formal logic in future developments, human factors and other paradigms. Different groups of readers such as mathematicians, specialists in computer sciences, and programmers will find this title of interest. Post-graduates and the students specializing in AI and applied mathematics will also find the work useful.

Solutions Manual To Accompany Combinatorial Reasoning An Introduction To The Art Of Counting

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Author : Duane DeTemple
language : en
Publisher: John Wiley & Sons
Release Date : 2014-08-19

Solutions Manual To Accompany Combinatorial Reasoning An Introduction To The Art Of Counting written by Duane DeTemple and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-08-19 with Mathematics categories.

COMBINATORIAL REASONING Showcases the interdisciplinary aspects of combinatorics and illustrates how to problem solve with a multitude of exercises 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.

Global Methods For Combinatorial Isoperimetric Problems

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Author : L. H. Harper
language : en
Publisher: Cambridge University Press
Release Date : 2004-02-09

Global Methods For Combinatorial Isoperimetric Problems written by L. H. Harper and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-02-09 with Mathematics categories.

Certain constrained combinatorial optimization problems have a natural analogue in the continuous setting of the classical isoperimetric problem. The study of so called combinatorial isoperimetric problems exploits similarities between these two, seemingly disparate, settings. This text focuses on global methods. This means that morphisms, typically arising from symmetry or direct product decomposition, are employed to transform new problems into more restricted and easily solvable settings whilst preserving essential structure. This book is based on Professor Harper's many years' experience in teaching this subject and is ideal for graduate students entering the field. The author has increased the utility of the text for teaching by including worked examples, exercises and material about applications to computer science. Applied systematically, the global point of view can lead to surprising insights and results, and established researchers will find this to be a valuable reference work on an innovative method for problem solving.