MAT 534 (Algebra I) - Fall 2017

Time and Place : TuTh 10-11:20; Earth&Space 181

Instructor : Radu Laza

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

Office Hours: Thr 4-6

Grader Lilya Lyubich

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.

Quick Links

• Schedule
• HW9 (due Nov 30)

Announcements

• Welcome!
• The first midterm will take place in class on Tuesday, Sept 26. It will cover all the material on groups (Chapters 1-5 in the textbook).
• The second midterm will take place in class on Tuesday, November 7. It will focus on Divisibility in Rings (Ch 8), Modules (Ch 10), and Modules over PIDs (Ch 12).
• The final exam will take place Monday (Dec 11). Details to follow.

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. (There will an extra make-up HW in case you missed one HW assignment).

Schedule