Algebraic Number Theory Notes

Lectures on Topics in Algebraic Number Theory

2 Preface During December 2000, I gave a course of ten lectures on Algebraic Number Theory at the University of Kiel in Germany. These lectures were aimed at giving a rapid introduction to some basic aspects of Algebraic Number Theory with as few prerequisites as possible. I had also hoped to cover some parts of Algebraic Geometry based on the idea, which goes back to Dedekind, that algebraic n...

18 . 785 : Algebraic Number Theory ( lecture notes )

Notes for second semester algebraic topology

These are some notes for a second-semester algebraic topology course at UC Berkeley which I taught in 2004 and 2005. The topics of the course are: higher homotopy groups and obstruction theory, bundles and characteristic classes, spectral sequences, and Morse theory and applications to differential topology. Disclaimers: These notes are intended as an elementary introduction to selected core id...

Math 538: Algebraic Number Theory Lecture Notes

These are rough notes for the Spring 2013 course. Problem sets and solutions were posted on an internal website.

Notes on Algebraic Number Theory

1 Number Fields 2 1.1 Norm, Trace, and Discriminant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2 Algebraic Integers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2 Dedekind Rings 7 2.1 Fractional Ideals and Unique Factorization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.2 The Ideal Class Group ...

Algebraic Topology Notes: Homotopy Theory

Notes on homotopy theory, the first part of a trilogy on algebraic topology. Any typos, errors, mistakes, gaffes, etc., are entirely my folly.