Math 602, Fall
2015
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: After class, by appointment, and as scheduled.
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, eigenvalues and
eigenvectors, canonical forms, inner product spaces, adjoints, principal
axis theorem.
Class
schedule: Mon and Fri, 1:30-3pm in DRL 4N30, starting Monday, Aug. 31.
There will be no class on Mon., Sept. 7; Mon., Sept. 14; Fri., Sept. 25; Fri., Oct. 2; Fri., Oct. 9; Fri., Nov. 27.
There will also be some classes on Wednesdays at 1:30 or 2 in DRL 4E19. Details will be announced; tentative dates
are Sept. 16 (1:30), Sept. 30 (2:00), Oct. 7 (2:00), Oct. 14 (1:30), Nov. 25 (1:30).
The last class is on Mon., Dec. 8.
- Textbook: Thomas W. Hungerford, Algebra, Graduate Texts in Mathematics, vol. 73, Springer-Verlag, 1974.
- Course structure: The class will meet from 1:30-3pm on Mondays and Fridays, and occasionally on Wednesdays,
to supplement Monday/Friday classes. The dates of the Wednesday classes will be announced in advance.
There will be weekly problem sets, which will be key to the course. There will also be one exam, which will take
place in class on Mon., Dec. 8.
Homework assignments for Math
602
Sample exam. Exam scores: The distribution of scores on the exam was as follows (out of 75):
Median: 66. Quartiles: 63 and 69. Scores are available on Canvas.
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