| title |
code |
books |
prereqs |
Algebraic Number Theory |
MA 313 |
| author |
title |
publ |
Artin, E. |
Galois Theory |
University of Notre Dame Press, 1944 |
|
| author |
title |
publ |
Borevich, Z. and Shafarevich, I. |
Number Theory |
Academic Press, New York, 1966 |
|
| author |
title |
publ |
Cassels, J.W. and Frohlich, A. |
Algebraic Number Theory |
Academic Press, New York, 1948 |
|
| author |
title |
publ |
Hasse, H. |
Zahlentheorie |
Akademie Verlag, Berlin, 1949 |
|
| author |
title |
publ |
Hecke, E. |
Vorlesungen uber die Theorie der algebraischen Zahlen |
Chelsea, New York, 1948 |
|
| author |
title |
publ |
Samuel, P. |
Algebraic Theory of Numbers |
Hermann, 1970 |
|
|
Linear algebra (MA 219 or equivalent) |
Basic algebra : Groups, rings, modules (MA 212 or equivalent), and algebraic field extensions |
|
Algebraic preliminaries: Algebraic field extensions: Normal, separable and
Galois extensions. Euclidean rings, principal ideal domains and factorial
rings. Quadratic number fields. Cyclotomic number fields.
Algebraic integers:
Integral extensions: Algebraic number fields and algebraic integers. Norms and
traces. Resultants and discriminants. Integral bases.
Class numbers:Lattices and Minkowski theory. Finiteness of class number.
Dirichlet's unit theorem.
Ramification Theory: Discriminants.
Applications to cryptography.
