MAT 534 (Algebra I) - Fall 2021

Time and Place : TuTh 1:15-2:35; Physics P130

Instructor : Radu Laza

Office : Math Tower 4-121
Email :  radu.laza@stonybrook.edu

Office Hours: Tue 2:45-3:45; Thr 11:30-12:30; by appointment

Grader Alexandra Viktorova

Overview

Textbook : David S. Dummitt and Richard M. Foote, Abstract algebra, 3rd ed.

We will cover roughly the following topics: Groups: normal subgroups, quotient groups, Lagrange's theorem, class formula, finite p-groups and solvable groups, Sylow's theorems, finitely generated abelian groups. Rings and modules: subrings, fields, prime and maximal ideals, quotient rings, ID's, PID's, UFD's, polynomial rings, field of fractions, the Wedderburn theorem, Hilbert basis theorem, finitely generated modules over a PID. Vector spaces: basis, linear maps and matrices, dual spaces, determinants, eigenvalues and eigenvectors, inner products, spectral theorem for normal operators. (See also official course description)

Quick Links

• Schedule
• HW6 (due Dec 2)
• HW7 (due Dec 14, by e-mail to the TA)
• HW8 (not collected)

Announcements

• Welcome!
• Please check this webpage frequently for HW assignments and updated schedule.
• We will have the first exam in class on Sept 23. HW3 is what used as Midterm 1 in 2017. You can use that as a sample exam. The exam will cover groups (esp. Ch 3-5 of the textbook).
• Some old review materials: Review 1, Review 2
• The format of the final exam will be discussed in class. E-mail me if you have any questions.

Grading

• There will be 2 midterms and a final. We will have approximately 10 homework assignments.
• The exams count for 75% of the final grade. The division is roughly: 35% for the final and 20% for each midterm. The remaining 25% will be for the homework assignments.
• No late HWs, and no make-up exams.

Schedule