• Homework Assignments

• Project Information

• Exam Dates

  • Exam 1: Fri Oct 9 (in class).
  • Exam 2: Self-scheduled, Nov 16 - Nov 19 (in science library).
  • Final Exam: Self-scheduled during Smith's final exam period. Visit the registar's webpage for more information.

Instructor: Michael Bush
Office: Burton 316
Phone: (413) 585-3644
e-mail: mbush[AT]smith.edu

Class Times: MWF 2:40 - 4:00 pm, Burton 307.
Office Hours: M 4:00 - 5:00 pm; W 11:00 - noon; F 10:30 - noon (or by appointment).
Textbook: Contemporary Abstract Algebra, 6th edition (*not* the 7th edition which has just come out), by Joseph A. Gallian.
On reserve in the Science library and available at the bookstore. Most of the homework problems will come from this book.

The course will follow on from Math 233 but will move at a slightly faster pace. The first part will be an introduction to ring theory. Rings are algebraic structures that appear throughout mathematics. After giving some definitions and results that parallel those for groups, we will move on to discuss unique factorization. Along the way we'll study the properties of polynomial rings in detail.

In the second part of the course we will see how the results and constructions from the first part can be applied to the theory of fields and their extensions. In particular we will study the Fundamental Theorem of Galois Theory together with its application to the problem of determining when the zeros of a polynomial can be expressed in terms of radicals.

We will cover Parts 3 and 4 in the textbook along with bits of chapter 33 and 34 (and possibly some supplementary material that I will supply).

Prerequisites: Math 211 (Linear Algebra) and Math 233 (Introduction to Abstract Algebra) - In particular I'll assume everyone knows some group theory and basic facts about vector spaces. If you're not sure you satisfy the prerequisites and want to take this course then please come and talk to me.

You grade will be based on HW, a project, two mid-term exams and a final exam. These will be weighted as follows: HW 20%, Project 10%, mid-terms 20% (each), Final Exam 30%.

Project: This will include a short written paper and talk at the end of semester. More details will be available in a few weeks.

Homework: Several problems will be assigned each week of which a random selection will be graded. The problems will range from routine exercises that involve practice in the use of some newly introduced tool/technique, to open ended problems requiring investigation and conjecture. In the latter case you should keep in mind that there may not be a correct answer! I will allow some class time (especially on Wednesday) for discussion of the HW problems. You can also get help by coming to see me in office hours or sending me email. Doing the homework exercises and reading the relevant sections of the text is the only way to master the material in this course! In general you should expect to spend 4-5 hours a week outside of class working on the material. If you find yourself doing a lot less or more than this on a regular basis then you should come and talk to me about it.

Late Homework: Homework will be collected in class (usually on Friday). Homework turned in later than this will not be graded for credit except under exceptional circumstances. I will however drop the two lowest homework set scores when working out your homework grade. This policy gives you some leeway but please be careful as not turning in HW may cause you to fall behind.