Math 322 - Abstract Algebra II

Sections 1 & 2, Winter 2017

 



General Information

Instructor: Michael Bush
Office: Robinson 201
Phone: x8801
e-mail: bushm[AT]wlu [dot] edu

Class Times: Section 1 - MTRF 1:25 am - 2:20 pm in Robinson 107; Section 2 - MTRF 3:35 - 4:30 pm in Robinson 107.

Office Hours: MTRF 2:30 - 3:25 pm; TF 10:10 - 12:10 pm.
Feel free to stop by at other times if you have a quick question.

Textbook: Same as for Math 321 last semester. Abstract Algebra: Theory and Applications, *** 2015 edition ***, by Thomas Judson; ISBN-13: 978-0989897594.
A PDF version of this open source book can be downloaded for free. Nicely bound hardcopies can also be purchased through Amazon and other dealers. Links will be posted on Sakai.


Syllabus

This second course in abstract algebra will focus on rings. These are algebraic structures which have two operations satisfying various axioms. To begin, we will familiarize ourselves with various examples and build up notions and tools similar to those introduced for groups (subrings, homomorphisms, quotients etc.). However, there are also new phenomena to be investigated. In particular, the study of rings was historically motivated by various questions in number theory and we will spend a fair amount of time discussing the important notion of unique factorization and conditions under which this holds. In the latter part of the course, we will apply the theory developed earlier to study fields and their extensions and look at related applications. These may include showing the nonexistence of certain constructions related to classical geometric problems; Galois Theory and the existence/nonexistence of simple formulas for the roots of polynomials; and/or a proof of the Fundamental Theorem of Algebra.

Prerequisites: Math 321 (Abstract Algebra I).


Grading

Your grade will be based on HW, two midterm exams and a final exam. These will be weighted as follows: HW - 25%; Exam 1 - 20%; Exam 2 - 25%; Final Exam- 30%. The exam dates can be found above.

Homework: Problems will be assigned weekly. I will ask you to hand in written solutions to some of these problems. For the first five assignments (excluding the first which will be special), you may work individually or with a partner. For the remaining assignments, you will work individually. Use of the Latex typesetting package for HW assignments is required this semester. I will provide some materials to help you get started with Latex if you have not used it before. I would also suggest partnering up with someone who has used it previously.

Some time in class will be allowed for discussion of the 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 5-8 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: In weeks when it is assigned, homework will be collected in class (usually on Friday) although I will also accept submissions at my office by 4:30 pm on the same day. Work submitted after this deadline will not be graded for credit unless there are exceptional circumstances. The lowest HW score will be dropped when working out the HW component of your grade. This policy gives you some leeway but please try not to miss any assignments, as you (and I) will miss out on the feedback they provide.

Missed Exams: In general, make-ups for exams will not be given without good reason. If you believe you have some sort of conflict that will prevent you taking an exam at the designated time then you should contact me well in advance to discuss the matter. Occasionally, emergency situations may arise that preclude you from doing this. If this happens then you should contact me as soon as is reasonable to discuss things.


Honor Code

All students are expected to abide by Washington and Lee's Honor code. It's fine to discuss the assigned problems and course work outside of class. Obviously, Group HW assignments will be a collaborative effort. I only ask that you write up solutions in your own words and that you acknowledge any sources of help (beyond the textbook). All other work (exams) will be submitted individually and must be completed on your own without any external aids (including calculators/computers/web) or assistance from others.

Information about Accommodations

Washington and Lee University makes reasonable academic accommodations for qualified students with disabilities. All undergraduate accommodations must be approved through the Office of the Dean of the College. Students requesting accommodations for this course should present an official accommodation letter within the first two weeks of the term and schedule a meeting outside of class time to discuss accommodations. It is the student's responsibility to present this paperwork in a timely fashion and to follow up about accommodation arrangements. Accommodations for test-taking should be arranged with the professor at least a week before the date of the test or exam, including finals.
Please talk to me in class or email me if you have any questions about the policies above or the course work. Good luck this semester!