*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.

- Problem Set 1
- Problem Set 2
- Problem Set 3
- Problem Set 4
- Problem Set 5
- Problem Set 6
- Problem Set 7
- Problem Set 8
- Problem Set 9
- Problem Set 10
- Problem Set 11
- Problem Set 12

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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