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Math 7752. Algebra-II.
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Algebra-II. Math 7752. Spring 2010.

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

- Instructor: Mikhail Ershov
- Office: Kerchof 302
- Office hours: 2 hrs 30 min TBA and by APPOINTMENT

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

### Course outline

** Prerequisites: ** Math 751 and an undergraduate courses in linear algebra comparable in level to
UVa 551.

** Course content: ** The first half of the semester (up to the spring break) will be devoted
to modules and multilinear algebra. The material we will cover is mostly contained
in Chapters 10-12 of Dummit and Foote. Sections 11.1-11.3 will only be briefly
reviewed as they contain material covered in standard undergraduate linear algebra
courses. In the second half of the course we will study fields and Galois theory.
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''. Time permitting, at the end of the course (the last two or three classes)
we will discuss an additional topic, e.g. the proof of Hilbert's Nullstellensatz.

** Exams and homework: ** There will be weekly homework and three exams -- two midterms
(both take-home) and the final (format TBD). Tentative dates for exams are as follows:
### Exams

- First midterm exam: take-home, due on Thursday, February 25th.
- Second midterm exam: take-home, due on Thursday, April 8th.
- Final exam: take-home part will be due on Tuesday, May 4th.
There may also be an in-class part on Friday, May 14th, 9-12pm.

### 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. You are allowed and encouraged to
submit your homework electronically (as a .tex file) or orally to
get a more efficient feedback.

** 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.