Math 1530 Abstract Algebra, Spring 2013

Course Information

A printable pdf version of the syllabus is here.

Basic Information

Instructor: Chris Kottke

Office: 303 Kassar-Gould House


Office hours: Wed 11:15-12:00 (shared with Math 540), Fri 3:00-3:45 or by appointment.

Text: Abstract Algebra, by Dummit and Foote. 3rd Ed (ISBN 978-0-471-43334-7).



This class will introduce you to abstract algebra -- one of the three pillars of modern mathematics along with analysis and geometry/topology. Historically, this subject grew out of the observation that many structures which arise over and over again in the study of classical mathematics and algebra can be abstracted and studied using just a handful of their properties, taken as axioms. Thus, once one has a proof about, say, groups as abstract objects, that proof applies to all concrete groups which arise in applications no matter how different they appear, from the permutations of the roots of a polynomial, to the invertible matrices under matrix multiplication, to the symmetries of a geometric object. We will focus mostly on the theory of groups and rings, with some time spent towards the end of the course on polynomials and fields.

The class will be entirely rigorous and proof based, and will require quite a bit of time and effort. You will be expected to spend time studying the text and solving difficult homework problems, many of which you will not be able to solve right away. Working on such problems is an integral part of learning a subject such as this. As with speaking a new language or playing a musical instrument, learning to do modern mathematics is not something which can be done passively, but rather requires active practice, perseverance, and patience.

Approximate lecture schedule:

1-5Ch. 1: Introduction to groups.
4-8CH. 2: Subgroups.
9-13Ch. 3: Quotient groups and homomorphisms. Midterm 1.
14-18Ch. 4: Group actions.
19-21Ch. 5: Direct and semidirect products and abelian groups.
22-27Ch. 7: Introduction to rings. Midterm 2.
28-30Ch. 8: Euclidean domains, PIDs and UFDs.
31-36Selected topics from Ch. 9, 13.

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