A Classical Introduction to Modern Number Theory

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. Language: English