Problems of Number Theory in Mathematical Competitions

Problems of Number Theory in Mathematical Competitions

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  • Author: Hong-Bing Yu
  • Publisher: World Scientific
  • ISBN: 9814271144
  • Category : Mathematics
  • Languages : en
  • Pages : 115

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.


Problems Of Number Theory In Mathematical Competitions

Problems Of Number Theory In Mathematical Competitions

PDF Problems Of Number Theory In Mathematical Competitions Download

  • Author: Hong-bing Yu
  • Publisher: World Scientific Publishing Company
  • ISBN: 9813101083
  • Category : Mathematics
  • Languages : en
  • Pages : 115

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.


Combinatorial Problems in Mathematical Competitions

Combinatorial Problems in Mathematical Competitions

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  • Author: Yao Zhang
  • Publisher: World Scientific
  • ISBN: 9812839496
  • Category : Mathematics
  • Languages : en
  • Pages : 303

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.


Number Theory

Number Theory

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  • Author: Titu Andreescu
  • Publisher:
  • ISBN: 9780988562202
  • Category : Number theory
  • Languages : en
  • Pages : 686

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.


A Primer for Mathematics Competitions

A Primer for Mathematics Competitions

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  • Author: Alexander Zawaira
  • Publisher: OUP Oxford
  • ISBN: 0191561703
  • Category : Mathematics
  • Languages : en
  • Pages : 368

The importance of mathematics competitions has been widely recognised for three reasons: they help to develop imaginative capacity and thinking skills whose value far transcends mathematics; they constitute the most effective way of discovering and nurturing mathematical talent; and they provide a means to combat the prevalent false image of mathematics held by high school students, as either a fearsomely difficult or a dull and uncreative subject. This book provides a comprehensive training resource for competitions from local and provincial to national Olympiad level, containing hundreds of diagrams, and graced by many light-hearted cartoons. It features a large collection of what mathematicians call "beautiful" problems - non-routine, provocative, fascinating, and challenging problems, often with elegant solutions. It features careful, systematic exposition of a selection of the most important topics encountered in mathematics competitions, assuming little prior knowledge. Geometry, trigonometry, mathematical induction, inequalities, Diophantine equations, number theory, sequences and series, the binomial theorem, and combinatorics - are all developed in a gentle but lively manner, liberally illustrated with examples, and consistently motivated by attractive "appetiser" problems, whose solution appears after the relevant theory has been expounded. Each chapter is presented as a "toolchest" of instruments designed for cracking the problems collected at the end of the chapter. Other topics, such as algebra, co-ordinate geometry, functional equations and probability, are introduced and elucidated in the posing and solving of the large collection of miscellaneous problems in the final toolchest. An unusual feature of this book is the attention paid throughout to the history of mathematics - the origins of the ideas, the terminology and some of the problems, and the celebration of mathematics as a multicultural, cooperative human achievement. As a bonus the aspiring "mathlete" may encounter, in the most enjoyable way possible, many of the topics that form the core of the standard school curriculum.


Concepts and Problems for Mathematical Competitors

Concepts and Problems for Mathematical Competitors

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  • Author: Alexander Sarana
  • Publisher: Courier Dover Publications
  • ISBN: 0486842533
  • Category : Mathematics
  • Languages : en
  • Pages : 430

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.


104 Number Theory Problems

104 Number Theory Problems

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  • Author: Titu Andreescu
  • Publisher: Springer Science & Business Media
  • ISBN: 0817645616
  • Category : Mathematics
  • Languages : en
  • Pages : 214

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.


Number Theory

Number Theory

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  • Author: Titu Andreescu
  • Publisher: Springer Science & Business Media
  • ISBN: 0817646450
  • Category : Mathematics
  • Languages : en
  • Pages : 383

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.


Mathematical Olympiad Challenges

Mathematical Olympiad Challenges

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  • Author: Titu Andreescu
  • Publisher: Springer Science & Business Media
  • ISBN: 9780817641900
  • Category : Mathematics
  • Languages : en
  • Pages : 296

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


A First Step To Mathematical Olympiad Problems

A First Step To Mathematical Olympiad Problems

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  • Author: Derek Allan Holton
  • Publisher: World Scientific Publishing Company
  • ISBN: 9814365254
  • Category : Mathematics
  • Languages : en
  • Pages : 292

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.