MAT 355, Abstract Algebra I
Fall, 2011

Tue/Thu, 12:15-1:30 p.m.
Chambers 3234


Outline


Instructor:
Stephen L. Davis; click here for my weekly schedule.

Text:
text cover Ronald Solomon, Abstract Algebra, American Mathematical Society, 2003

Overview:
A survey of our projected progress through the text is given in the table below. Our goal is to develop your capacity for reading, writing, and speaking mathematics. The theories of groups and rings will serve as the principal objects of investigation in this course.

Class time will be divided between problem solving and lectures-on-demand. It is your responsibility to read the text and to engage in the struggle to achieve an understanding of the material before coming to class. I will attempt to illuminate those concepts that remain in the shadows in spite of your attempts to coax them out. Also, you may be asked to present problem solutions in class, and there will be regular written homework assignments for you to turn in for my inspection.

Note: Homework assignments and other course announcements will be posted on our class Moodle site, access this via http://moodle.davidson.edu/.

Evaluation:
There will be two reviews as indicated below. You will be tested on vocabulary, examples, and statements and proofs of major results, as well as on creative problem solving. Reviews will consist of two components: one to be completed on the designated day during class, and the other to "take home" and return at the start of the next class meeting. I anticipate that the final examination will be administered as a take home examination.

A culminating activity in the course (along with the final examination) will be the compilation of a problem portfolio. The portfolio will include at least a dozen examples of your proof-writing from homework, each showing your progression from initial effort to polished revision. Your choices for inclusion in the portfolio should provide a broad representation of topics from our course. (Tentative portfolio due dates: a "substantial" draft by 5 p.m., November 11; final version by 5 p.m., December 5.)

The major components of your grade are the two reviews, homework, the portfolio, and the final examination. A recipe for the relative contributions of these components toward your grade in this course is roughly

(An explanation of my grading system is available in a web-based memo.)

Class Policies:
The portfolio, writs, review and final examination are pledged events; you are expected to be vigilant in upholding the Honor Code.

Collaboration on homework is encouraged. However, anything you present or turn in should represent your understanding of the material. Homework is evaluated with letter grades. If you have any questions regarding ground rules for individual events, do not hesitate to ask for clarification.

You should come to class prepared to discuss the material of the day. Each member of the class is a valuable resource for others in the class. Absences and tardiness diminish the quality of the course; come to class and come on time. I monitor attendance; missing 20% of class meetings can trigger action to encourage more faithful attendance. In any event, you are responsible for all material discussed in class, whether you are present or absent.

Schedule Guesstimate: (volatile!)

Date Chapter Event/Topic
Aug 23, 25 1 .. What is Congruence?
Aug 30, Sep 1 2 .. Some 2-D Geometry
Sep 6, 8 3 .. Symmetry
Sep 13, 15 4 5 Root of it All; Renaissance of Algebra
Sep 20, 22 .. 6 Complex Numbers
Sep 27, 29 .. Review Review #1
Oct 4, 6 7 8 Symmetric Poly's & the FTA; Perms & Lagrange
Oct 11, 13 no class .. Fall Break; ..
Oct 18, 20 9 .. Orbits & Cauchy's Formula
Oct 25, 27 10 .. Back to Euclid
Nov 1, 3 11 .. Euclid's Lemma for Polynomials
Nov 8, 10 12 .. Fermat & Rebirth of Number Theory
Nov 15, 17 Review 13 Review #2; Lagrange Revisited
Nov 22, 24 14 no class Rings & Squares; Thanksgiving
Nov 29, Dec 1 .. 14A More Rings & More Squares
Dec 6, 8 debrief Reading Day ..
Dec 9--15 Final Examination