Algebraic Number Theory

Credits	8 credit points
Instructors	Top, J. (Rijksuniversiteit Groningen), Smit, B. de (Universiteit Leiden)
E-mail	J.Top@math.rug.nl, desmit@math.leidenuniv.nl
Description	The course provides a thorough introduction to algebraic number theory. It treats the arithmetic of the number rings that occur in (algorithmic) practice. Topics: Introduction to algebraic numbers and number rings. Ideal factorization, finiteness results on class groups and units, explicit computation of these invariants. Special topic: the number field sieve. Each week, students have to hand in 4 exercises from the course notes out of those listed on the website of this course. Solving the more difficult problems will result in a higher grade. The final problem set of the course will be more substantial.
Organization	Mondays from September 11 - December 18, 2006, 10:15 - 13:00. The final hour (12:15-13:00) will be devoted to homework problems.
Examination	The final grade is exclusively based on the results obtained for the weekly homework assignments. The last problem set will be more substantial and determine one third of the final grade.
Literature	We will use the course notes and homework exercises of Peter Stevenhagen. Further recommended books: I.N. Stewart & D.A. Tall, Algebraic number theory; P. Samuel, Algebraic theory of numbers; D.A. Marcus, Number Fields
Prerequisites	Undergraduate algebra, i.e., the basic properties of groups, rings and fields. This material is covered in first and second year algebra courses in the bachelor program of most universities. The course notes used in Leiden (in Dutch) and those used in Groningen (also in Dutch) are available online.
Remarks	The teaching assistants (Stephen Meagher (Groningen) and Willem Jan Palenstijn (Leiden)) are always available by e-mail or in person if you require assistance.

Last changed: 18-01-2012 10:21