000			02191nam a2200181 4500
001			15063313
010			_a 2007060578
020			_a9781470454814
082	0	0	_a512.7 _bEDW/H
100	1		_aEdwards, Harold M
245	1	0	_aHigher arithmetic : _ban algorithmic introduction to number theory
260			_aProvidence, R.I. _bAmerican Mathematical Society _c2008
300			_axii, 210 p. _bill. ;
490	0		_aStudent mathematical library,
520			_aAlthough number theorists have sometimes shunned and even disparaged computation in the past, today's applications of number theory to cryptography and computer security demand vast arithmetical computations. These demands have shifted the focus of studies in number theory and have changed attitudes toward computation itself. The important new applications have attracted a great many students to number theory, but the best reason for studying the subject remains what it was when Gauss published his classicDisquisitiones Arithmeticae in 1801: Number theory is the equal of Euclidean geometry—some would say it is superior to Euclidean geometry—as a model of pure, logical, deductive thinking. An arithmetical computation, after all, is the purest form of deductive argument. Higher Arithmetic explains number theory in a way that gives deductive reasoning, including algorithms and computations, the central role. Hands-on experience with the application of algorithms to computational examples enables students to master the fundamental ideas of basic number theory. This is a worthwhile goal for any student of mathematics and an essential one for students interested in the modern applications of number theory. Harold M. Edwards is Emeritus Professor of Mathematics at New York University. His previous books are Advanced Calculus (1969, 1980, 1993), Riemann's Zeta Function (1974, 2001),Fermat's Last Theorem (1977), Galois Theory (1984), Divisor Theory (1990), Linear Algebra (1995), and Essays in Constructive Mathematics (2005). For his masterly mathematical exposition he was awarded a Steele Prize as well as a Whiteman Prize by the American Mathematical Society.
650		0	_aNumber theory
942			_cBK
999			_c67051 _d67051