Winter Quarter 2006, Math 225A, Algebraic Number Theory I


Instructor:
A. Agboola
Lecture:
TuTh 2:00pm-3:15pm, HSSB 1215
Office:
6724 South Hall, (805) 893-3844
Office hours:
TuTh 11:15am-12:30pm
Textbooks:
D. A. Marcus, Number Fields, Springer, (1977) (required).
A. Frohlich, M. J. Taylor, Algebraic Number Theory, CUP, (1991) (required).


Homework:
The following link will take you to the homework assignments:

  • Homework Assignments


    • Examinations:
    There will be no examinations given in this course.
    Course Outline:
    We shall aim to cover the following topics. Additional topics will be covered if time permits.

    Basic commutative algebra: Noetherian properties, integrality, rings of integers.

    More commutative algebra: Dedekind domains, unique factorisation of ideals, localisation.

    Norms, traces and discriminants.

    Decomposition of prime ideals in an extension field.

    Class numbers and units. Finiteness of the class number: Minkowski bounds. Dirichlet's unit theorem. Explicit calculation of units.

    Decomposition of prime ideals revisited: the decomposition group and the inertia group associated to a prime ideal. A nice proof of quadratic reciprocity.