Background notes: background.dvi (posted September 22, 2001).
These notes recall basic notions concerning rings and
fields, including PID's, UFD's, field extensions,
Galois theory, cyclotomic polynomials, and finite fields.
Proofs are included.
First day handout .
Introductory lectures: intro.dvi (posted September 22, 2001).
These notes discuss the arithmetic of the Gaussian
integers and the irreducibility of the cyclotomic
polynomials over the field of rational numbers.
Continuation of introductory lectures: moreintro.dvi (posted September 29, 2001).
These notes discuss the possibility of representing a
prime as the sum of a square and five times a
square, and serve as motivation for developing some general theory
of rings of algebraic integers.
Lectures on Dedekind domains: normalisation.dvi (posted October 5, 2001).
These notes begin the development of the theory of
Dedekind domains, by studying integral extensions
of domains, the properties of normal domains, and
the process of normalisation. They also include a
definition of Dedekind domains.
Coninuation of the lecures on Dedekind domains: localisation.dvi (posted October 10, 2001).
These notes develop the technique of localising a domain
(or module over the domain) at a prime ideal, and also
introduce the notion of discrete valuation rings.
Homework assignments: one.dvi (posted September 22 2001) two.dvi (posted October 5 2001) three.dvi (posted October 23 2001).