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| Author | : Yao Zhang |
| Publisher | : World Scientific |
| Total Pages | : 303 |
| Release | : 2011 |
| Genre | : Mathematics |
| ISBN | : 9812839496 |
Annotation. This text provides basic knowledge on how to solve combinatorial problems in mathematical competitions, and also introduces important solutions to combinatorial problems and some typical problems with often-used solutions.
| Author | : Titu Andreescu |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 125 |
| Release | : 2013-11-27 |
| Genre | : Mathematics |
| ISBN | : 0817682228 |
"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.
| Author | : Hong-Bing Yu |
| Publisher | : World Scientific |
| Total Pages | : 115 |
| Release | : 2010 |
| Genre | : Mathematics |
| ISBN | : 9814271144 |
Number theory is an important research field of mathematics. In mathematical competitions, problems of elementary number theory occur frequently. These problems use little knowledge and have many variations. They are flexible and diverse. In this book, the author introduces some basic concepts and methods in elementary number theory via problems in mathematical competitions. Readers are encouraged to try to solve the problems by themselves before they read the given solutions of examples. Only in this way can they truly appreciate the tricks of problem-solving.
| Author | : Titu Andreescu |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 235 |
| Release | : 2013-12-01 |
| Genre | : Mathematics |
| ISBN | : 081768154X |
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.
| Author | : Jiri Herman |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 402 |
| Release | : 2013-03-14 |
| Genre | : Mathematics |
| ISBN | : 1475739257 |
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.
| Author | : Titu Andreescu |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 296 |
| Release | : 2000-04-26 |
| Genre | : Mathematics |
| ISBN | : 9780817641900 |
A collection of problems put together by coaches of the U.S. International Mathematical Olympiad Team.
| Author | : Pavle Mladenović |
| Publisher | : Springer |
| Total Pages | : 365 |
| Release | : 2019-03-13 |
| Genre | : Mathematics |
| ISBN | : 3030008312 |
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.
| Author | : Chuan-Chong Chen |
| Publisher | : World Scientific |
| Total Pages | : 314 |
| Release | : 1992 |
| Genre | : Mathematics |
| ISBN | : 9789810211394 |
A textbook suitable for undergraduate courses. The materials are presented very explicitly so that students will find it very easy to read. A wide range of examples, about 500 combinatorial problems taken from various mathematical competitions and exercises are also included.
| Author | : Derek Allan Holton |
| Publisher | : World Scientific Publishing Company |
| Total Pages | : 292 |
| Release | : 2009-07-30 |
| Genre | : Mathematics |
| ISBN | : 9814365254 |
See also A SECOND STEP TO MATHEMATICAL OLYMPIAD PROBLEMS The International Mathematical Olympiad (IMO) is an annual international mathematics competition held for pre-collegiate students. It is also the oldest of the international science olympiads, and competition for places is particularly fierce. This book is an amalgamation of the first 8 of 15 booklets originally produced to guide students intending to contend for placement on their country's IMO team. The material contained in this book provides an introduction to the main mathematical topics covered in the IMO, which are: Combinatorics, Geometry and Number Theory. In addition, there is a special emphasis on how to approach unseen questions in Mathematics, and model the writing of proofs. Full answers are given to all questions. Though A First Step to Mathematical Olympiad Problems is written from the perspective of a mathematician, it is written in a way that makes it easily comprehensible to adolescents. This book is also a must-read for coaches and instructors of mathematical competitions.
| Author | : Hong-bing Yu |
| Publisher | : World Scientific |
| Total Pages | : 378 |
| Release | : 2022-03-16 |
| Genre | : Mathematics |
| ISBN | : 9811229937 |
The series is edited by the head coaches of China's IMO National Team. Each volume, catering to different grades, is contributed by the senior coaches of the IMO National Team. The Chinese edition has won the award of Top 50 Most Influential Educational Brands in China.The series is created in line with the mathematics cognition and intellectual development levels of the students in the corresponding grades. All hot mathematics topics of the competition are included in the volumes and are organized into chapters where concepts and methods are gradually introduced to equip the students with necessary knowledge until they can finally reach the competition level.In each chapter, well-designed problems including those collected from real competitions are provided so that the students can apply the skills and strategies they have learned to solve these problems. Detailed solutions are provided selectively. As a feature of the series, we also include some solutions generously offered by the members of Chinese national team and national training team.
