Math 611: Algebra I
Fall 2015

Instructor: Paul Hacking, LGRT 1235H,


Classes: Mondays, Wednesdays, and Fridays, 9:05AM--9:55AM in LGRT 219.

Office hours: Mondays 3:00PM--4:00PM and Tuesdays 5:00--6:00PM, in my office LGRT 1235H.

Course text: Abstract Algebra, by D. Dummit and R. Foote, 3rd ed., Wiley 2004. googlebooks.

Other useful references:

Algebra by M. Artin. googlebooks.

Algebra by S. Lang. googlebooks.

Introduction to commutative algebra by M. Atiyah and I. MacDonald. googlebooks.

Prerequisites: Undergraduate abstract algebra at the level of UMass Math 411--412.


Homeworks will be assigned every 1--2 weeks and posted on this page.

HW1. Due Wednesday 9/23/15. Solutions.

HW2. Due Wednesday 9/30/15. Solutions.

HW3. Due Wednesday 10/7/15. Solutions.

HW4. Due Wednesday 10/21/15. Solutions. SolutionQ11b

Midterm review problems. (Will not be graded.) Solutions. CorrectionQ8.

HW5. Due Wednesday 11/4/15. Solutions.

HW6. Due Friday 11/13/15. Solutions. SolutionQ1b

HW7. Due Wednesday 12/2/15. Solutions.

HW8. (Will not be graded.) Solutions.


There will be one midterm exam and one final exam.

The midterm exam will be held on Wednesday 10/28/15, 7:00PM---8:30PM, in LGRT 219. Please try the midterm review problems here. Review problem solutions here. CorrectionQ8.

The midterm exam is here. Solutions are here.

The final exam will be a take home exam distributed on Friday 12/11/15 and due on Friday 12/18/15. The final exam is here.

The algebra sequence 611--612 is also assessed via the algebra qualifying exam. General information. Syllabus.


Your course grade will be computed as follows: Homework 30%, Midterm 30%, Final 40%.

Overview of course:

Here is the syllabus for 611. Roughly speaking it correponds to Chapters 1--12 of Dummit and Foote. The full syllabus for the Graduate algebra sequence 611--612 is here.

(1) Group Theory.

Group actions. Counting with groups. p-groups and Sylow theorems. Composition series. Jordan-Holder theorem. Solvable groups. Automorphisms. Semi-direct products. Finitely generated Abelian groups.

(2) Rings.

Euclidean domain is a principal ideal domain (PID). PID is a unique factorization domain (UFD). Gauss Lemma. Eisenstein's Criterion.

(3) Modules.

Exact sequences. First and second isomorphism theorems for R-modules. Free R-modules. Hom. Structure Theorem for finitely generated modules over a PID. Rational canonical form. Jordan canonical form. Bilinear forms. Tensor product of vector spaces, Abelian groups, and R-modules. Right-exactness of the tensor product. Restriction and extension of scalars. Symmetric and exterior algebras.

This page is maintained by Paul Hacking