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Math 7752. Algebra-II. Syllabus
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Algebra-II. Math 7752. Spring 2012.

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TuTh 11am-12:15 pm, Kerchof 317.

- Instructor: Mikhail Ershov
- Office: Kerchof 302
- e-mail: ershov
*at* virginia *dot* edu
- phone: 924-4131
- Office hours: Tue 1:30-2 and Wed 2-3
- Problem session: Tue 2-3, lounge

#### Main Text:
*Abstract Algebra*, David Dummit and Richard Foote.

### Course outline

** Prerequisites: ** Math 7751 and an undergraduate course in linear algebra
comparable in level to UVA 5651.

** Course content: ** The first third of the semester (about 5 weeks) will be devoted
to modules and multilinear algebra. The material we will cover is mostly contained
in Chapters 10-12 of Dummit and Foote. I will assume familiarity with the content of
Sections 11.1-11.4 as they contain material covered in standard undergraduate linear algebra
courses. Next we will study fields and Galois theory (about 5.5 weeks).
The material we will cover is mostly discussed in Chapters 13-14 of Dummit and Foote,
though the order of my exposition will be quite different and closer to Lang's
book ``Algebra''. We will finish with a brief introduction to commutative algebra
covering all or parts of (depending on time) Chapters 15 of Dummit and Foote.

** Exams and homework: ** There will be weekly homework and three exams -- two midterms
and the final. The dates and format of the exams will be announced by February 9th.
### Evaluation:

- Final exam: 30%
- Midterm exams: 20% each
- Homework: 30%

** Homework ** will be assigned weekly and will usually be due on Thursdays.
Each assignment will contain 6-8 problems, and your lowest score
(on each assignment) will be dropped. If we have mandatory problem sessions,
part of your homework grade will be based on participation in those problems
sessions.

** Collaboration policy. **
- On homework: you are welcome (and even encouraged)
to work on homework together, but you
*must* write
up solutions independently, in your own words. In particular,
you should not be consulting others during the process of
writing down your solution.
- On exams: you may not discuss exam problems with others.