03796nam a22004815i 4500
978-0-8176-4645-5
DE-He213
20180115171437.0
cr nn 008mamaa
100301s2009 xxu| s |||| 0|eng d
9780817646455
978-0-8176-4645-5
10.1007/b11856
doi
QA241-247.5
PBH
bicssc
MAT022000
bisacsh
512.7
23
Andrica, Dorin.
author.
Number Theory
[electronic resource] :
Structures, Examples, and Problems /
by Dorin Andrica, Titu Andreescu.
Boston :
Birkhäuser Boston,
2009.
XVIII, 384 p. 2 illus.
online resource.
text
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rdacontent
computer
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rdamedia
online resource
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rda
Fundamentals -- Divisibility -- Powers of Integers -- Floor Function and Fractional Part -- Digits of Numbers -- Basic Principles in Number Theory -- Arithmetic Functions -- More on Divisibility -- Diophantine Equations -- Some Special Problems in Number Theory -- Problems Involving Binomial Coefficients -- Miscellaneous Problems -- Solutions to Additional Problems -- Divisibility -- Powers of Integers -- Floor Function and Fractional Part -- Digits of Numbers -- Basic Principles in Number Theory -- Arithmetic Functions -- More on Divisibility -- Diophantine Equations -- Some Special Problems in Number Theory -- Problems Involving Binomial Coefficients -- Miscellaneous 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.
Mathematics.
Algebra.
Number theory.
Combinatorics.
Mathematics.
Number Theory.
Mathematics, general.
Algebra.
Combinatorics.
Andreescu, Titu.
author.
SpringerLink (Online service)
Springer eBooks
Printed edition:
9780817632458
http://dx.doi.org/10.1007/b11856
ZDB-2-SMA
369962
369962
0
0
0
0
EBook
elib
elib
2018-01-15
2018-01-15
2018-01-15
EBOOK