Number Theory: Structures, Examples, and Problems

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9780817632458: Number Theory: Structures, Examples, and Problems

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.

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From the Back Cover:

Number theory, an ongoing rich area of mathematical exploration, is noted for its theoretical depth, with connections and applications to other fields from representation theory, to physics, cryptography, and more. While the forefront of number theory is replete with sophisticated and famous open problems, at its foundation are basic, elementary ideas that can stimulate and challenge beginning students. This lively introductory text focuses on a problem-solving approach to the subject.

Key features of Number Theory: Structures, Examples, and Problems:

* A rigorous exposition starts with the natural numbers and the basics.

* Important concepts are presented with an example, which may also emphasize an application. The exposition moves systematically and intuitively to uncover deeper properties.

* Topics include divisibility, unique factorization, modular arithmetic and the Chinese Remainder Theorem, Diophantine equations, quadratic residues, binomial coefficients, Fermat and Mersenne primes and other special numbers, and special sequences. Sections on mathematical induction and the pigeonhole principle, as well as a discussion of other number systems are covered.

* Unique exercises reinforce and motivate the reader, with selected solutions to some of the problems.

* Glossary, bibliography, and comprehensive index round out the text.

Written by distinguished research mathematicians and renowned teachers, this text is a clear, accessible introduction to the subject and a source of fascinating problems and puzzles, from advanced high school students to undergraduates, their instructors, and general readers at all levels.

About the Author:

Titu Andreescu received his Ph.D. from the West University of Timisoara, Romania. The topic of his dissertation was "Research on Diophantine Analysis and Applications." Professor Andreescu currently teaches at The University of Texas at Dallas. He is past chairman of the USA Mathematical Olympiad, served as director of the MAA American Mathematics Competitions (1998–2003), coach of the USA International Mathematical Olympiad Team (IMO) for 10 years (1993–2002), director of the Mathematical Olympiad Summer Program (1995–2002), and leader of the USA IMO Team (1995–2002). In 2002 Titu was elected member of the IMO Advisory Board, the governing body of the world’s most prestigious mathematics competition. Titu co-founded in 2006 and continues as director of the AwesomeMath Summer Program (AMSP). He received the Edyth May Sliffe Award for Distinguished High School Mathematics Teaching from the MAA in 1994 and a "Certificate of Appreciation" from the president of the MAA in 1995 for his outstanding service as coach of the Mathematical Olympiad Summer Program in preparing the US team for its perfect performance in Hong Kong at the 1994 IMO. Titu’s contributions to numerous textbooks and problem books are recognized worldwide.

Dorin Andrica received his Ph.D in 1992 from "Babes¸-Bolyai" University in Cluj-Napoca, Romania; his thesis treated critical points and applications to the geometry of differentiable submanifolds. Professor Andrica has been chairman of the Department of Geometry at "Babes¸-Bolyai" since 1995. He has written and contributed to numerous mathematics textbooks, problem books, articles and scientific papers at various levels. He is an invited lecturer at university conferences around the world: Austria, Bulgaria, Czech Republic, Egypt, France, Germany, Greece, Italy, the Netherlands, Portugal, Serbia, Turkey, and the USA. Dorin is a member of the Romanian Committee for the Mathematics Olympiad and is a member on the editorial boards of several international journals. Also, he is well known for his conjecture about consecutive primes called "Andrica’s Conjecture." He has been a regular faculty member at the Canada–USA Mathcamps between 2001–2005 and at the AwesomeMath Summer Program (AMSP) since 2006.

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Titu Andreescu, Dorin Andrica
Editore: Birkhäuser Boston 2009-03-11, Boston (2009)
ISBN 10: 081763245X ISBN 13: 9780817632458
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Descrizione libro Birkhäuser Boston 2009-03-11, Boston, 2009. hardback. Condizione libro: New. Codice libro della libreria 9780817632458

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Descrizione libro Birkhauser Boston Inc. Hardback. Condizione libro: new. BRAND NEW, Number Theory: Structures, Examples, and Problems, Titu Andreescu, Andrica Dorin, 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. Codice libro della libreria B9780817632458

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Descrizione libro BIRKHAUSER BOSTON INC, United States, 2009. Hardback. Condizione libro: New. Language: English . Brand New Book. 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. Codice libro della libreria AAZ9780817632458

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Titu Andreescu, Dorin Andrica
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Descrizione libro BIRKHAUSER BOSTON INC, United States, 2009. Hardback. Condizione libro: New. Language: English . Brand New Book. 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. Codice libro della libreria AAZ9780817632458

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Descrizione libro Birkhäuser Boston, 2009. Hardcover. Condizione libro: Brand New. 1st edition. 384 pages. 9.40x6.10x1.00 inches. This item is printed on demand. Codice libro della libreria zk081763245X

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Andreescu, Titu, Andrica, Dorin
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Descrizione libro Birkh?user, 2009. Condizione libro: New. 2009. 2009th Edition. Hardcover. This introductory textbook takes a problem-solving approach to number theory, situating each concept within the framework of an example for readers to solve. By introducing and reinforcing every idea with an exercise, the authors motivate and engage readers. Num Pages: 384 pages, black & white illustrations. BIC Classification: PBH. Category: (P) Professional & Vocational. Dimension: 235 x 166 x 29. Weight in Grams: 736. . . . . . . Codice libro della libreria V9780817632458

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