Course Information-632, Spring 2009

Course Information
Abstract Algebra, Math 632
Spring, 2009 - T, Th 11:00am-12:15pm, PS 327

Professor: Dr. Cathy Kriloff	Office/Phone: PS 316C / 282-3093	Math Dept. Phone: 282-3350
E-mail: krilcath@isu.edu	Web Page: www.isu.edu/~krilcath	Math Dept. Fax: 282-2636

Office Hours: M 12:00-2:00pm, Th,F 10:00-11:00am, and by appointment or e-mail, or feel free to just stop by.

Objectives: This year-long sequence will:

Deepen your ability to construct proofs of results on groups, rings, modules, and fields. (In general, these are distinguished from undergraduate proofs by going beyond basic verification of definitions toward deeper structural results and classifications of algebraic objects.)
Deepen your knowledge of substantial results in algebra at the graduate level.
Provide a foundation for your own studying for the written or oral Masters exam in algebra.
Improve your ability to communicate mathematics clearly, both orally and in writing.
Enhance your ability to learn mathematics independently.

Prerequisites: The prerequisite is Math 631.

Materials: The required text is Abstract Algebra, by D. Dummit and R. Foote, 3rd Edition, John Wiley & Sons, 2003. We will aim to cover most but not all of Chapters 9-14.

Some other graduate level texts in roughly recommended order (those by MacLane and Birkhoff, Lang, and Bourbaki are on reserve at the library):

Algebra, by S. MacLane and G. Birkhoff, AMS/Chelsea Publishing, 1988.
Algebra; A Graduate Course, by M. Isaacs, Brooks/Cole, 1994.
Advanced Modern Algebra, by J. Rotman, Prentice Hall, 2002.
Basic Algebra I & II, by Jacobson, Freeman, 1985.
Algebra, by S. Lang, Third revised edition. Springer-Verlag, 2002.
Algebra Chapters 1-7, by N. Bourbaki, Translated from the French, Springer-Verlag, 1990.
Algebra, by T.W. Hungerford, Graduate Texts in Mathematics, 73, Springer-Verlag, 1980.

Other books that are not so well-known to me, may be useful, but do not precisely fit the course:
Algebra: An Approach via Module Theory, by W. Adkins and S. Weintraub, Springer-Verlag, 1992.
Introduction to Abstract Algebra, by W. Nicholson, John Wiley & Sons, 2007.

There are many short books specifically focused on Galois theory. I have several of these checked out from our library in my office - feel free to come by and borrow them. Here are a couple I have read and can recommend:
Galois Theory, by I. Stewart, Chapman & Hall/CRC, 2003. (The 2nd edition is on reserve at the library.)
Galois Theory, by E. Artin, Dover, 1997. (Also available online at ProjectEuclid.org.)

Accommodations: Idaho State University is committed to equal opportunity in education for all students. If you have a diagnosed disability or if you believe that you have a disability that might require reasonable accommodation in this course, please contact the ADA & Disabilities Resource Center, Room 123, Graveley Hall, Phone No. 282-3599 as soon as possible.

Format and Evaluation
Class time will include a mixture of lectures, discussion, and student presentations. Material covered in class lectures and activities will assume that you have read and thought about the material ahead of time and begun to think about some exercises. You are encouraged to raise questions for discussion before or during class.

Homework written up in final form will be turned in for comments and a grade roughly once a week. You are encouraged to try additional problems from Dummit-Foote and from other texts and I will try to recommend other good problems which may be used for in-class discussion in place of lecture at times. The calendar, lists of problems, and due dates will be updated as the semester progresses on the class web page, http://www.isu.edu/~krilcath/m632Spr09.html. Late homework is an inconvenience and an obstacle to both me and your colleagues because it takes me longer to grade and it delays my circulating or discussing solutions with those who turned it in on time, so please avoid it as much as possible. As an aid in achieving correct, clear, complete proofs, I may occasionally allow improvement and resubmission of a homework assignment. Your lowest homework score will be dropped before calculating your grade.

Studying together and discussing problems are encouraged, after you have worked hard on the material or problem yourself, since this can be a very effective and rewarding way to learn mathematics. To be fair to your colleagues, to remain compliant with ISU's policy against plagiarism, and to guarantee your own understanding, you must write up solutions in your own words and acknowledge in writing any assistance you received.

Each student will give two presentations - one over material that is somewhat closely related to earlier experience and one that is more advanced. Guidelines for these and a grading rubric will be distributed in class in advance. The Midterm Exam will consist of a take-home and an oral portion.

Homework	20%
Presentations	20%
Midterm Exam	30%	Due Thursday, March 5	Chapters 9-12
Final	30%	Due Thursday, May 7, 10:00am-12:00pm	Cumulative

Overall percentages of 90%, 80%, 70%, 60% will guarantee the letter grades A, B, C, D. Cutoffs for +/- will be these values +/- 3 percentage points.

Philosophy: All of you have the potential to succeed in this course and hard work counts for a great deal. I continue to learn by expanding my knowledge of mathematics and its connections with other subjects, by doing original mathematical research, by understanding more about learning and teaching, and by working to teach in ever more effective ways. I expect that you will also deepen your knowledge of algebra and its connections to other fields of mathematics, will learn to formulate questions that lead you to construct your own understanding of mathematics, and will know more about learning, problem solving, and teaching after you complete this course. The most important skill you can gain from graduate school is the ability to learn and conduct research independently.