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Math 7751. Algebra-I.
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Algebra-I. Math 7751. Fall 2011.

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11am-12:15 pm, Kerchof 317.

- Instructor: Mikhail Ershov
- Office: Kerchof 302
- e-mail: ershov
*at* virginia *dot* edu
- Office hours: 3 hrs TBA and by APPOINTMENT
- Course webpage:
*http://people.virginia.edu/~mve2x/7751_Fall2011 *

#### Main Text:
*Abstract Algebra*, David Dummit and Richard Foote, 3rd edition.

### Course outline

** Course content: ** Math 751 is the first half of the standard graduate algebra sequence
(the second half is Math 752). In the fall semester we will study primarily
group theory and ring theory. The main topics in the spring semester (Math 752) are
module theory (including advanced linear algebra), field theory and Galois theory.
If we stay on pace, I plan to start module theory in the last two weeks of Math 7751.

** Prerequisites: ** Undergraduate courses in linear algebra and abstract algebra
comparable in level to UVa 551 and 552, respectively. For more details on your
expected abstract algebra background consult the questionnaire distributed in class.
Linear algebra material will not be seriously used until 752, but a linear algebra
assessment exam will be given during the first week of the fall semester. If you feel that
your linear algebra preparation is not sufficient, you are strongly encouraged to review
the main linear algebra topics before the spring semester begins.

** Schedule: ** The plan for the fall semester is to cover the first 9 chapters
and the beginning of chapter 10 of Dummit and Foote. Most of the material in Chapters 1-3 is covered in standard undergraduate abstract algebra courses and will be briefly reviewed in the first 2 weeks. On average, we will
spend about 3.5 classes on each of the chapters 4-10. Additional topics not covered by Dummit and Foote
may be discussed, time permitting.

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

- First midterm exam: due on Thursday, October 6th.
- Second midterm exam: due by Thursday, November 9th.
- Final exam: due on Tuesday, December 6th (last day of classes).

### 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.

** 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.