MATH 600: Abstract Algebra I (Fall 2000)

Course web site: http://www.math.umd.edu/~jmr/600/
Meeting times: MWF, 12:00pm-12:50pm (MTH 0104)
Instructor: Professor Jonathan Rosenberg. His office is room 2114 of the Math Building, phone extension 55166, or you can contact him by email. His office hours are tentatively scheduled for Monday afternoons 1-2PM and Thursday mornings 11-12.
Teaching Assistant (and Homework Grader): Ruth Auerbach, room 4400, Math Building, phone extension 55101.
Text: T. Hungerford, Algebra, Springer, Graduate Texts in Mathematics, no. 73.
Prerequisite: Undergraduate-level abstract or linear algebra (MATH 403 or 405). The course will start from scratch, so it's not that you need to have remembered specific facts. Rather, the prerequisite is to make sure you have enough facility with algebraic proofs to keep up with the pace, which will be much faster than in undergraduate courses.
Catalog description: Groups with operators, homomorphism and isomorphism theorems, normal series, Sylow theorems, free groups, Abelian groups, rings, integral domains, fields, modules. If time permits, HOM (A,B), Tensor products, exterior algebra.

Course Description:

This course is a basic introduction to abstract algebra. Its three main functions are:

To prepare mathematics graduate students for the written qualifying exam in algebra.
To cover those topics in algebra which "every mathematician needs to know", regardless of specialty.
To prepare students for more advanced courses that use algebra heavily, such as courses in algebraic number theory (MATH 620), algebraic geometry (MATH 606), homological algebra (MATH 602), and algebraic topology (MATH 734).

The course will emphasize the following topics:

finite groups, including the Sylow theorems, Jordan-Hölder theorem, etc.
free groups, free abelian groups
basics of commutative rings, and in particular, PIDs and the structure theorem for finitely generated modules over PID's. applications to abelian groups and linear algebra
beginnings of field theory and Galois theory

The course continues with MATH 601 in the Spring semester.

Course Requirements:

Homework will be collected and graded regularly. In addition, there will be a mid-term exam on Monday, October 30 and a final exam on Wednesday, December 20. Grades will be based on homework (40%), the mid-term exam (20%), and the final exam (40%). You may wish also to see the web page for a previous year's course.

Plan of Classes:

I intend to cover Chapters I-IV of Hungerford, plus section 7 of the Introduction (on Zorn's Lemma), which we'll defer till the first time we need it, plus about the first half of Chapter V. That comes to about 35 sections in about 42 class periods, which means we will usually cover one section per class, with occasional exceptions for unusually long or difficult sections. You are responsible for reading the text in pace with the lectures.