## Forster: Algorithmic Number Theory

Course (4 hours weekly + 2 hours Problem sessions) by
O. Forster

Summer Semester 2002,
Department of Mathematics, LMU München
**Time and Room:** Tue, Fri 9-11, E 6

Starts on Tuesday, April 18, 2002, at 9:15h

**Problem sessions:** Tue 14-16, HS 138

**Example Code**

** Contents:** In this course we will give an
introduction to number theory from the elements
up to the quadratic reciprocity law with an
emphasis on algorithmic methods. Important
problems (which have applications in modern
cryptography) are the factorization of integers,
recognition of primes and calculation of
discrete logarithms.
Algorithmic number theory has a long history
(Eucidean algorithm, sieve of Eratosthenes).
With the advent of computers, new and
efficient algorithms have been found.
Some of them use interesting algebraic and
geometric methods, like the theory of Elliptic Curves.
Besides algorithms for integers, we will study in the
course also algorithms for polynomials, in particular
over finite fields.

**Detailed Contents**

** Prerequisites:** Familiarity with basic concepts
of algebra (groups, rings, ideals, fields, polynomials)
is assumed. Some programming experience is useful.

** For:** Students of the International Master Program
in Mathematics,

StudentInnen mit Studienziel
Mathematik-Diplom und Lehramt nach Vordiplom
bzw. Zwischenprüfung

** Literature **

- E. Bach and J. Shallit: Algorithmic Number Theory, Vol. I.
MIT Press
- H. Cohen: A Course in Computational Algebraic Number Theory.
Springer-Verlag
- O. Forster:
Algorithmische Zahlentheorie, Vieweg-Verlag
- P. Giblin: Primes and Programming. An Introduction
to Number Theory with Computing. Cambridge UP
- D. Knuth: The Art of Computer Programming, Vol 2.
Seminumerical algorithms. Addison-Wiley
- H. Riesel: Prime Numbers and Computer Methods for
Factorization. Birkhäuser

This course will be followed in WS 2002/03 by a course in
**Cryptography** and a Seminar
on **Algorithmic Number Theory and Cryptography**

Topics for master theses (and diploma theses) will
be available from these subjects.

Otto Forster (),
2002-01-28/2002-05-02