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Math 7751. Algebra-I.
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Algebra-I. Math 7751. Fall 2009.

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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

** 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. In the spring semester (Math 752) we will study
module theory (including advanced linear algebra), field theory and Galois theory.

** 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. If you feel that your linear
algebra preparation is not sufficient, you are strongly encouraged to attend Math 551 in the Fall
(taught by Brian Parshall, TuTh 9:30-10:45) and do some homework for that class.

** Schedule: ** The plan for the fall semester is to cover the first 9 chapters
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 2-3 weeks. On average, we will
spend about 3.5-4 classes on each of the chapters 4-9. Additional topics not covered by Dummit and Foote
will 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 by Thursday, October 1st.
- Second midterm exam: due by Thursday, November 5th.
- Final exam: due on Tuesday, December 8th (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.