MAT 313 Abstract Algebra

Fall 2014

SUNY at Stony Brook

This course is an introduction to the main ideas of abstract algebra. The focal points are the concepts of groups, rings and fields. The course emphasizes abstract reasoning which is at the core of modern mathematics and many of its applications to the real world. Proofs - understanding them and developing them on your own - play a central role.

It will benefit you a lot to read the corresponding sections of the text before each lecture. There is a lot of material in the text that can't be covered in class, and you will need to read and understand this on your own, starting with Chapters 0 and 1. Always feel free to ask questions to your instructor and grader.


Final Exam, Wednesday, Dec 10, 5:30-8:00pm, in Library E4315

The Final is cumulative, covering the full semester of material roughly equally. There are 10 problems on the exam, with 4-5 on group theory, 5-6 on rings and fields. The exam covers material up to and including Ch. 22. (This is a change from an earlier statement if you saw that).
As before, prepare by doing many problems to test your understanding. In addition to previous exercises below and HW problems, try some of the following. One of them will be on the exam.
Supplementary Exercises, p 341-: 1, 2, 8, 23, 31
(to be continued - maybe)

Midterm II, Tuesday, Nov 18, in class.

Material on Midterm II:
Rings: Chapters 12 - 17
Fields: Chapter 20

Topics you may skip:
Ch. 17, statement only of Thms. 17.2, 3, 4, skip Corollary p. 310, and p.313 on, but know statement of Theorem 17.6
Ch. 18 - all
Ch. 20, p.360-366, but know statement of uniqueness of splitting fields, p.362.

Topics to read, not covered in class
Ch. 19

There is no formal practice midterm exam, but have a look at the midterms for MAT 313 for Fall 13 and Fall 09; these are indicative for this exam. As before, in general do as many problems/exercises as you can: below are some concrete suggestions.

Supplementary Exercises, p. 276-: 8, 19, 24, 31, 39
Supplementary Exercises, p. 341-: 7, 11, 19, 21, 23

Midterm I: Tuesday, Oct 7, in class.

Material: Group theory, Chapters 1-11
Topics to read, not covered in class:
Ch. 0 and Ch. 1
Ch. 5, even and odd permuations, alternating group
Ch. 6, automorphisms and inner automorphisms
Ch. 9, internal direct products
Topics you can skip:
Ch.4, Theorem 4.4 and Corollary, p.80
p. 107-113
p. 144-149
p. 159-167
p. 185(bottom) - p. 188 (top)
p. 209

Practice Exam Look at the Midterm I exams for MAT 313, Fall 13 and Fall 09. (Find the link for the websites for these courses via the undergrad course webpages on the math dept site). Some of the problems for Fall 13 are too hard, but most are at the level of this exam; all of the Fall 09 exam is fine.
In general, do as many problems as you can to practice for the Midterm. Here are some concrete suggestions:
Supplemental Problems, Ch.9-11, p.230: 7, 18, 19, 22
Supplemental Problems, Ch.5-8, p.174: 10, 24, 25, 29
Supplemental Problems, Ch.1-4, p.91: 2, 16, 33, 34

MAT 313


Final Exam: Wednesday Dec 10, 5:30-8:00pm, Library E4315



11:30am - 12:50pm

Physics P123

Michael Anderson