Math 602, Fall
2021
Graduate Algebra
- Faculty: David Harbater
- E-mail:
harbater AT math.upenn.edu
- Telephone: (215) 898-9594; Department office: (215) 898-8178
- Office: DRL
4E2A; Department office: DRL 4W1-6.
- Office hours: By appointment.
- Grader: Ming Jing.
First semester graduate algebra.
Topics include:
- groups: symmetry groups, group
actions,
Sylow theorems, Jordan-Holder theorem, nilpotent and solvable
groups,
semi-direct products, group cohomology;
- rings: one and two sided ideals, prime
and maximal ideals, Noetherian rings, extension and contraction of ideals,
unique factorization domains, nilradical and Jacobson radical;
- linear algebra: dual spaces, tensor products, bilinear forms,
alternating forms, determinants, invariant subspaces, exactness, introduction to modules.
Class
schedule: Mon and Fri, 10:15-11:45am in DRL 2C2, starting Friday, Sept. 3.
There will be no class on Mon., Sept. 6; Fri., Oct. 15; Fri., Nov. 26.
There will a class on Wednesday, Nov. 24, at the usual time and place (replacing the
class that would have been held on Nov. 26).
The last class is on Friday., Dec. 10.
- Course structure: The class will meet twice weekly, as indicated above.
There will be weekly problem sets, which will be key to the course. They will be available on the course website
(when they are assigned) and are to be
submitted electronically to the course Canvas page.
Students are encouraged to work together on the problems, but should write up
their solutions individually. There will be one exam, which will take
place in class on Friday, Dec. 10.
- Textbook: Thomas W. Hungerford, Algebra, Graduate Texts in Mathematics, vol. 73, Springer-Verlag, 1974.
Available on reserve in the Math-Physics-Astronomy Library in DRL;
electronically on the course Canvas site and on
MathSciNet;
and for purchase at the campus bookstore and online.
Homework assignments for Math
602
Sample exam.
Back to
David Harbater's Home Page.