Math 502, Fall 2017

Abstract Algebra

Course structure:
Description of course: This is a the first semester of a year-long masters level course in algebra, discussing groups, rings, fields, vector spaces, and modules. The fall semester will cover roughly the first half of the text, which emphasizes group theory and topics in linear algebra.

The course will be varied, involving theory, computations, and examples. It is open both to undergraduates and graduate students, from the Mathematics Department and elsewhere at Penn. The course is more in-depth than Math 370, but is less abstract and less general than Math 602. Students are not expected to have prior familiarity with groups, rings, fields or modules, but are expected to have seen and worked with vectors and matrices (e.g. knowing about eigenvectors, diagonalization of matrices, vector spaces, bases, and linear transformations), as covered in Math 240 or in Math 116 - 260. Those who need to brush up on their linear algebra background, or who would like an additional reference for this material during the semester, may wish to look at the paperback book "Linear Algebra" by Lipschutz and Lipson in the Schaum Outline series, or at a standard text like "Linear Algebra" by Hoffman and Kunze. (Note: Math 314/514 is a proof-based course on linear algebra that is offered every semester and is required for math majors.)

The first two meetings of the lecture are on Wednesday, August 30 and on Wednesday, Sept. 6. The labs begin during the week of August 28, with the first Tuesday lab held on the evening prior to the first lecture. In preparation for the first lab session, students are asked to think about the problems on the warm-up problem set. It may be helpful first to review the definition of a vector space (from a previous course, or Definition 3.3.1 in the textbook).

Homework assignments for Math 502