Math 7752. Algebra-II.

Algebra-II. Math 7752. Spring 2019.

TuTh 12:30-1:45 pm, Kerchof 128.

Instructor: Mikhail Ershov
Office: Kerchof 302
e-mail: ershov at virginia dot edu
Office hours: Tue 3:30-4:30, Wed 2:30-3:15 and 4:45-5:30 and by APPOINTMENT
Course webpage: http://people.virginia.edu/~mve2x/7752_Spring2019

Main Text:

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

Prerequisites:

Math 7751 and an undergraduate course in linear algebra comparable in level to UVA 4651.

Course content:

The first part of the semester (5-6 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 (also 5-6 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''. If time allows, we will finish with a brief introduction to either commutative algebra (parts of Chapter 15 of Dummit and Foote) or representation theory (parts of Chapters 18 and/or 19 of Dummit and Foote).

Exams and homework:

There will be weekly homework and three exams (two midterms and the final). The format of the exams will be determined later; the current plan is that one of the midterms will be take-home while the other midterm and the final will be in-class. Tentative dates of the exams are as follows:

Exams

First midterm exam: Tue, February 26th
Second midterm exam: Fri, April 12th
Final exam: Thu, May 2nd, 9am-12pm

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:

Monday, January 28 -- Last day to ADD a course, elect the audit option, change the grading option (grade or CR/NC), or establish an independent study
Tuesday, January 29 -- Last day to DROP a course (deletion from the transcript)
Monday, March 18 -- 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.