MATH 601: Abstract Algebra II (Spring 2001)

Course web site: http://www.math.umd.edu/~jmr/600/
Meeting times: MWF, 12:00pm-12:50pm (MTH 0102)
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 mornings 10-11 and Friday afternoons 1-2.
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.
Recommended Extra Reading on Group Representations: J.-P. Serre, Linear Representations of Finite Groups (will be placed on reserve in the library)
Prerequisite: MATH 600 or equivalent
Catalog description: Field theory, Galois theory, multilinear algebra. Further topics from: Dedekind domains, Noetherian domains, rings with minimum condition, homological 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:

the tensor product, first concepts of homological algebra
field theory and Galois theory
linear representations of finite groups
basics of commutative Noetherian rings

Course Requirements:

Homework will be collected and graded regularly. In addition, there will be a mid-term exam on Monday, March 12 (the week before Spring Break) and a final exam on Wednesday, May 23, 8-10 AM. 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 the following sections in Hungerford:

Chapter IV, sections 3-5 (tensor product, projective and injective modules)
Chapters V and VI (Galois theory, more field theory such as transcendence bases)
much of Chapter VIII (commutative Noetherian rings)

In addition, we will cover some material on linear representations of finite groups. You are responsible for reading the text in pace with the lectures.