Course Information
Abstract Algebra, Math 632
Spring, 2003

Office Hours: W,F 10:00-11:00am, M 12:00-1:00pm.  Feel free to e-mail or stop by at other times.

Objectives: By the end of this year you should:

• Master a substantial amount of algebra at the graduate level, including work on groups, modules, rings, and fields.
• Be prepared to pass the written Masters exam in algebra and the algebra part of the oral exam.
• Improve your ability to communicate mathematics clearly, both orally and in writing.
• Enhance your ability to learn mathematics independently.

Materials: The required text is Algebra; A Graduate Course, by Isaacs.  We will use other texts for some material (for example Chapter 7 of Artin's Algebra).

Some other recommended texts:

Algebra, by M. Artin, Prentice Hall Inc., 1991.
Algebra Chaps 1-7, by N. Bourbaki, Translated from the French, Springer-Verlag, Berlin, 1990.
Abstract Algebra, by D. Dummit and R. Foote, John Wiley & Sons, 1999.
Basic Algebra I & II, by Jacobson, Freeman, 1985.
Algebra, by S. Lang, Second edition. Addison-Wesley Publishing Company, 1984.
Advanced Modern Algebra, by J. Rotman, Prentice Hall, 2002.
Algebra, by T.W. Hungerford, Graduate Texts in Mathematics, 73, Springer-Verlag, New York, 1980.

Accommodations: If you have a disability or think you have a disability (physical, learning disability, hearing, vision, psychiatric) which may need a reasonable accommodation, please contact the ADA Disabilities & Resource Center located in Graveley Hall, Room 123, 282-3599 as early as possible.

Format and Evaluation
Class time will include a mixture of lectures, discussion, and student presentations.  I expect you to come to class prepared and to bring questions to discuss in class.

Homework will be assigned and collected.  Organize and present complete, clear proofs neatly.

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 and to guarantee your own understanding, you must write up solutions in your own words and acknowledge in writing any assistance you received.
 

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

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 mathematics and its applications, 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 is the ability to learn independently.