Math 7751. Algebra-I.

Algebra-I. Math 7751. Fall 2018.

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_Fall2018

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

Course outline

Course content:

Math 7751 is the first half of the standard graduate algebra sequence (the second half is Math 7752). In the fall semester we will study primarily group theory and ring theory. The main topics in the spring semester (Math 7752) 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. Also, if time allows, we will spend some time on basic representation theory or basic commutative algebra at the end of Math 7752.

Prerequisites:

Undergraduate courses in linear algebra and abstract algebra comparable in level to UVA 4651 and 4652, 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 7752, but a linear algebra assessment exam will be posted during the week before 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 Thu, October 4th.
Second midterm exam: due on Thu, November 9th.
Final exam: due on Fri, December 7th (last day of classes).

Evaluation:

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

Homework

Homework will be assigned weekly and will usually be due on Thursday.
Please STAPLE your homework.
No late homework will be accepted. However, the lowest homework score will be dropped; in addition, the lowest score on each assignment will be dropped
GRADING: it will not be possible to grade all homework problems.

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.

Announcements

Major announcements will be made in class and also posted on the course webpage. Some other announcements may only be made by e-mail, so check your e-mail account regularly.

Add/drop/withdrawal dates:

Tuesday, September 11 -- Last day to ADD a course, elect the audit option, change the grading option (grade or CR/NC), or establish an independent study
Wednesday, September 12 -- Last day to DROP a course (deletion from the transcript)
Tuesday, October 23 -- Last day to withdraw from a course

SDAC

All students with special needs requiring accommodations should present the appropriate paperwork from the Student Disability Access Center (SDAC). It is the student's responsibility to present this paperwork in a timely fashion and follow up with the instructor about the accommodations being offered. Accommodations for test-taking (e.g., extended time) should be arranged at least 5 business days before an exam.