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Problems of Number Theory in Mathematical Competitions

Author: Hong-Bing Yu

Publisher: World Scientific

Published: 2010

Total Pages: 115

ISBN-13: 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.

Number Theory

Author: Titu Andreescu

Publisher:

Published: 2017-07-15

Total Pages: 686

ISBN-13: 9780988562202

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Challenge your problem-solving aptitude in number theory with powerful problems that have concrete examples which reflect the potential and impact of theoretical results. Each chapter focuses on a fundamental concept or result, reinforced by each of the subsections, with scores of challenging problems that allow you to comprehend number theory like never before. All students and coaches wishing to excel in math competitions will benefit from this book as will mathematicians and adults who enjoy interesting mathematics.

Combinatorial Problems in Mathematical Competitions

Author: Yao Zhang

Publisher: World Scientific

Published: 2011

Total Pages: 303

ISBN-13: 9812839496

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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.

Problem-Solving and Selected Topics in Number Theory

Author: Michael Th. Rassias

Publisher: Springer Science & Business Media

Published: 2010-12-02

Total Pages: 336

ISBN-13: 1441904948

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The book provides a self-contained introduction to classical Number Theory. All the proofs of the individual theorems and the solutions of the exercises are being presented step by step. Some historical remarks are also presented. The book will be directed to advanced undergraduate, beginning graduate students as well as to students who prepare for mathematical competitions (ex. Mathematical Olympiads and Putnam Mathematical competition).

Mathematical Olympiad Challenges

Author: Titu Andreescu

Publisher: Springer Science & Business Media

Published: 2000-04-26

Total Pages: 296

ISBN-13: 9780817641900

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A collection of problems put together by coaches of the U.S. International Mathematical Olympiad Team.

104 Number Theory Problems

Author: Titu Andreescu

Publisher: Springer Science & Business Media

Published: 2007-04-05

Total Pages: 204

ISBN-13: 0817645616

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This challenging problem book by renowned US Olympiad coaches, mathematics teachers, and researchers develops a multitude of problem-solving skills needed to excel in mathematical contests and in mathematical research in number theory. Offering inspiration and intellectual delight, the problems throughout the book encourage students to express their ideas in writing to explain how they conceive problems, what conjectures they make, and what conclusions they reach. Applying specific techniques and strategies, readers will acquire a solid understanding of the fundamental concepts and ideas of number theory.

Concepts and Problems for Mathematical Competitors

Author: Alexander Sarana

Publisher: Courier Dover Publications

Published: 2020-08-12

Total Pages: 430

ISBN-13: 0486842533

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This original work discusses mathematical methods needed by undergraduates in the United States and Canada preparing for competitions at the level of the International Mathematical Olympiad (IMO) and the Putnam Competition. The six-part treatment covers counting methods, number theory, inequalities and the theory of equations, metrical geometry, analysis, and number representations and logic. Includes problems with solutions plus 1,000 problems for students to finish themselves.

Number Theory

Author: Titu Andreescu

Publisher: Springer Science & Business Media

Published: 2009-06-12

Total Pages: 383

ISBN-13: 0817646450

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This introductory textbook takes a problem-solving approach to number theory, situating each concept within the framework of an example or a problem for solving. Starting with the essentials, the text covers divisibility, unique factorization, modular arithmetic and the Chinese Remainder Theorem, Diophantine equations, binomial coefficients, Fermat and Mersenne primes and other special numbers, and special sequences. Included are sections on mathematical induction and the pigeonhole principle, as well as a discussion of other number systems. By emphasizing examples and applications the authors motivate and engage readers.

Problems And Solutions In Mathematical Olympiad (High School 3)

Author: Hong-bing Yu

Publisher: World Scientific

Published: 2022-03-16

Total Pages: 378

ISBN-13: 9811229937

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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.

Contests in Higher Mathematics

Author: Gabor J. Szekely

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 576

ISBN-13: 1461207339

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One of the most effective ways to stimulate students to enjoy intellectual efforts is the scientific competition. In 1894 the Hungarian Mathematical and Physical Society introduced a mathematical competition for high school students. The success of high school competitions led the Mathematical Society to found a college level contest, named after Miklós Schweitzer. The problems of the Schweitzer Contests are proposed and selected by the most prominent Hungarian mathematicians. This book collects the problems posed in the contests between 1962 and 1991 which range from algebra, combinatorics, theory of functions, geometry, measure theory, number theory, operator theory, probability theory, topology, to set theory. The second part contains the solutions. The Schweitzer competition is one of the most unique in the world. The experience shows that this competition helps to identify research talents. This collection of problems and solutions in several fields in mathematics can serve as a guide for many undergraduates and young mathematicians. The large variety of research level problems might be of interest for more mature mathematicians and historians of mathematics as well.