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portada Number Theory: Structures, Examples, and Problems
Number Theory: Structures, Examples, and ProblemsNumber Theory: Structures, Examples, and Problems
Type
Physical Book
Publisher
Author
Year
2009
Language
English
Pages
402
Format
Hardcover
Dimensions
23.9x16.5x3 cm
ISBN
081763245X
ISBN13
9780817632458
Categories

Number Theory: Structures, Examples, and Problems

Titu Andreescu; Dorin Andrica (Author) · Birkhäuser · Hardcover

Number Theory: Structures, Examples, and Problems - Titu Andreescu; Dorin Andrica

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Synopsis "Number Theory: Structures, Examples, and Problems"

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.

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