Classical Introduction to Modern Number Theory

Häftad, Engelska, 2010

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Bridging the gap between elementary number theory and the systematic study of advanced topics, A Classical Introduction to Modern Number Theory is a well-developed and accessible text that requires only a familiarity with basic abstract algebra.

Produktinformation

Utgivningsdatum2010-12-01
Mått155 x 235 x 22 mm
Vikt590 g
FormatHäftad
SpråkEngelska
SerieGraduate Texts in Mathematics
Antal sidor394
Upplaga2
FörlagSpringer-Verlag New York Inc.
ISBN9781441930941

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Talteori inom Naturvetenskap och teknik

1 Unique Factorization.- 2 Applications of Unique Factorization.- 3 Congruence.- 4 The Structure of U(?/n?).- 5 Quadratic Reciprocity.- 6 Quadratic Gauss Sums.- 7 Finite Fields.- 8 Gauss and Jacobi Sums.- 9 Cubic and Biquadratic Reciprocity.- 10 Equations over Finite Fields.- 11 The Zeta Function.- 12 Algebraic Number Theory.- 13 Quadratic and Cyclotomic Fields.- 14 The Stickelberger Relation and the Eisenstein Reciprocity Law.- 15 Bernoulli Numbers.- 16 Dirichlet L-functions.- 17 Diophantine Equations.- 18 Elliptic Curves.- 19 The Mordell-Weil Theorem.- 20 New Progress in Arithmetic Geometry.- Selected Hints for the Exercises.

From the reviews of the second edition: K. Ireland and M. Rosen A Classical Introduction to Modern Number Theory "Many mathematicians of this generation have reached the frontiers of research without having a good sense of the history of their subject. In number theory this historical ignorance is being alleviated by a number of fine recent books. This work stands among them as a unique and valuable contribution." - MATHEMATICAL REVIEWS "This is a great book, one that does exactly what it proposes to do, and does it well. For me, this is the go-to book whenever a student wants to do an advanced independent study project in number theory. ... for a student who wants to get started on the subject and has taken a basic course on elementary number theory and the standard abstract algebra course, this is perfect." (Fernando Q. Gouvea, MathDL, January, 2006)