A Classical Introduction to Modern Number Theory

A CLASSICAL INTRODUCTION TO MODERN NUMBER THEORY is a well-developed and accessible text that requires only a familiarity with basic abstract algebra. Historical developement is stressed throughout, along with wide-ranging coverage of significant results with comparitively elementary proofs, some of them new. This second edition has been corrected and contains two new chapters which provide a complete proof of the Mordel-Weil theorem for elliptic curves over the rational numbers, and an overview of recent progress on the arithmetic of elliptic curves.

Autorentext
Kenneth Ireland [1937-1991] was Professor of Mathematics at the University of New Brunswick, Canada. Before UNB, he held positions at Johns Hopkins, Brandeis, Brown, Bowdoin, and a visiting membership in the Institute for Advanced Study. Known for his broad interests and active involvement in all areas of departmental life, he had a lasting impact on generations of students as a teacher and mentor. His widely acclaimed book with Michael Rosen, A Classical Introduction to Modern Number Theory, appears in the series Graduate Texts in Mathematics. Al Cuoco is a Distinguished Scholar at Education Development Center in Massachusetts. Before EDC, he taught high school mathematics for 24 years to a wide range of students in the Woburn, Massachusetts public schools. At EDC, he works in curriculum development, professional development, and education policy, and for over three decades, he has worked with Glenn Stevens in the PROMYS for Teachers program atBoston University. His mathematical interests and research publications lie in algebraic number theory.

Inhalt
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.

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