Introduction

This course provides an introduction to groups and rings. Moreover, it affords an introduction to abstract reasoning and the careful construction of proofs. The basic project of abstract algebra is to strip away irrelevant details from apparently disparate problems and reveal the common structures which unite them.

Syllabus

Roughly speaking, our current plan is:

Introductory material (sets; induction; the arithmetic of Z)
Rings (fundamental examples; ideals and quotient rings)
Groups (definitions and properties; cosets, homomorphisms and quotients)
Applications

More details will be given as the semester unfolds.

Prerequisites

The only official prerequisite is Math 161. In practice, you'll need a flexible mind and a willingness to work hard.

Logistics:

Textbook Abstract Algebra: Theory and Applications, by Thomas W. Judson; freely available at http://abstract.ups.edu.

Lectures MWF 2:00-2:50PM, ENGRG E104.

Office hours TBA.

Requirements and other expectations

This may be one of the first non-calculus mathematics classes you take. You'll find the rhythm and demands of this class significantly different from those of the calculus sequence. Both in class and outside it, you'll be expected to generate and explore patterns. As a second step, you'll need to write down clear statements (and proofs!) or your assertions.

Homework 30% Homework will be assigned weekly, and due on Fridays at the beginning of class. No late homework will ever be accepted. Your work must be neat, and the pages stapled, in order to be graded. While you are encouraged to work in groups, the written work you hand in must be your own. On each assignment indicate who, if anybody you consulted with.
Mid-semester exams 40%. There will be two in-class exams, on Wednesday, March 6 and Monday, April 8. No makeup exam will be given.
Final exam 30% The final exam will be on Wednesday, May 15, 9:40AM-11:40AM. Again, no makeup exam will be given. You must pass the exam in order to pass the course.

University expectations for class behavior in general, and academic integrity in particular, are detailed here.

Help

This is challenging material; it's fully expected that sometimes you'll need a little help.

Questions directed to j.achter@colostate.edu will be answered swiftly. However, some questions are best answered in person. You can come by office hours or schedule an appointment.

This page is available at http://www.math.colostate.edu/~achter/366/