000			01808nam a22001697a 4500
008			210717b2017 ||||| |||| 00| 0 eng d
020			_a9781470454890
082			_a512.74 POL-AP
100			_aPollack, Paul
245			_aA conversational introduction to algebraic number theory : _bArithmetic Beyond Z / _cPaul Pollack
260			_aUSA _bAmerican Mathematical Society _c2017
300			_a316 p.
365			_aINR _b1160.00.
440			_aStudent Mathematical Library / _vVolume 84
500			_aGauss famously referred to mathematics as the “queen of the sciences” and to number theory as the “queen of mathematics”. This book is an introduction to algebraic number theory, meaning the study of arithmetic in finite extensions of the rational number field Q. Originating in the work of Gauss, the foundations of modern algebraic number theory are due to Dirichlet, Dedekind, Kronecker, Kummer, and others. This book lays out basic results, including the three “fundamental theorems”: unique factorization of ideals, finiteness of the class number, and Dirichlet’s unit theorem. While these theorems are by now quite classical, both the text and the exercises allude frequently to more recent developments. In addition to traversing the main highways, the book reveals some remarkable vistas by exploring scenic side roads. Several topics appear that are not present in the usual introductory texts. One example is the inclusion of an extensive discussion of the theory of elasticity, which provides a precise way of measuring the failure of unique factorization. The book is based on the author’s notes from a course delivered at the University of Georgia; pains have been taken to preserve the conversational style of the original lectures.
650			_aAlgebraic number theory
999			_c66761 _d66761