| Lecture 1 |
Introduction |
| Lecture 2 |
Fast Fourier Transform |
| Lecture 3 |
Z-modules 1 (HNF/LLL) |
| Lecture 4 |
Z-modules 2, applications: algebraicity test, factoring over
Q[X] and C[X] (Schönhage's algorithm) |
| Lecture 5 | Polynomials 1 (over finite fields) |
| Lecture 6 |
Polynomials 2 (over Qp, Q, Z:
Hensel, Zassenhaus) |
| Lecture 7 |
Polynomials 3 (LLL) |
| Lecture 8 |
Algebraic number theory 1 (maximal order, splitting of primes) |
| Lecture 9 |
Algebraic number theory 2 (class group, S-unit group, class field
theory) |
| Lecture 10 |
Algebraic number theory 3 (generators of the ideal class group and
the Riemann Hypothesis) |
| Lecture 11 |
Integers (ECPP and ECM) |
