MATH601-0101: Abstract Algebra II-Spring 2014 jmr

MATH601-0101: Abstract Algebra II-Spring 2014 jmr

Course content: MATH 600-601 is the basic first graduate course in abstract algebra.  It begins at the same point as the undergraduate course MATH 403, but moves much faster and takes a more sophisticated point of view.  Math 601 will include Galois theory, basic commutative algebra (localization, completion, Hilbert Nullstellensatz), homological algebra (Ext and Tor), and representation theory of finite groups.  Together with MATH 600, this course gives you the algebra you need for all major branches of mathematics, including algebraic topology, algebraic geometry, algebraic number theory, and representation theory, and even many branches of applied mathematics, including coding theory and cryptography.  The course sequence 600-601 also redoes much of undergraduate linear algebra from a more advanced point of view.

Textbook: Abstract Algebra, 3rd Edition, by Dummit and Foote, Wiley, ISBN 978-0471433347.  You can get it from the bookstore or from online stores such as Amazon. The table of contents may be found here.

Teacher: Professor Jonathan Rosenberg, office MTH 2114, phone 301-405-5166.  Office hours M and W 11-12 or by appointment at other times.  The best way to reach me is by email to jmr@math.umd.edu.  The course TA is Sean Ballentine.

Grading and Homework: There will be two exams during the semester, each counting for 15% of the grade, one on Galois theory and commutative algebra (March 28) and one on homological algebra and representation theory (April 30), plus a final exam (May 19) counting 30% of the grade. If you must miss an exam for a legitimate reason (e.g., illness, religious observance, or an event such as an official university athletic meet), please contact Dr. Rosenberg as soon as possible, preferably in advance, and a make-up will be arranged. In addition, homework will be collected (usually once a week) and graded by the TA, and counts toward 35% of the grade.  Note: Every now and then, written homework will be replaced by a quick online quiz. The quizzes count for 5% of the grade. You can talk to fellow students and to the teacher about the homework, but the work you submit should be your own.  If you skip the homework or copy someone else's work, you are only cheating yourself.  If you haven't already done so, this might be a good opportunity to learn about latex for mathematical typesetting. Essentially all serious mathematics is now written in latex, so the sooner in your career that you learn how to use it, the better. Read the Wikiboook on latex or Lamport's classic book, which is very easy to read and well worth owning.

Accomodations: Accommodations will be made for students with disabilities, but students should inform Dr. Rosenberg of any special needs at the beginning of the semester. We will also make accommodations for absences for religious observances, such as for Passover on April 16 and 21 (in fact Dr. Rosenberg will be absent those days and another professor will substitute) and for Good Friday on April 18 and Easter on April 20.

Course evaluations: Please go to  https://CourseEvalUM.umd.edu to submit your course evaluation before the end of the semester (May 14).

Course Summary:

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