# General information

*Where and when:* Monday, Wednesday and Friday
12:00-1:00pm in 241 Cory.
*Textbook:* D. Dummit and R. Foote, *Abstract
Algebra*, third edition.
*Office hours:* in Evans 1091:
- Wednesday 9:00-10:30am.
- Friday 2:00-3:30pm.

*GSI:* Justin Chen will be holding office hours in 959
Evans at the following times:
- Tuesday: 11 am - 3 pm
- Wednesday: 2 pm - 7 pm
- Friday: 11 am - 12 pm

*Piazza:* I encourage you to ask your
questions there.
*Grade:*
- 10% homeworks, 20% each midterm, 50% final.
- The final grade can replace one of the midterms.
- You can drop one homework.

# Broad syllabus

**Groups:** We will be covering Ch. 1, 2 and 3.
**Rings:** We will be covering Ch. 7, 8 and 9.
**Fields:** We will be covering parts of of
Ch. 13 and 14.

# Homework

- Homework 1,
due September 6th, and its solution.
- Homework 2,
due September 11th, and its solution.
- Homework 3,
due September 18th, and its solution.
- Homework 4,
due October 2nd, and its solution.
- Homework 5,
due October 9th, and its solution.
- Homework 6,
due October 16th, and its solution.
- Homework 7,
due October 23rd, and its solution.
- Homework 8,
due November 8th, and its solution.
- Homework 9, due
November 15th, and its solution.
- Homework 10, due
November 29th, and its solution.

# Exams

# Past exams

- Spring 17
- Fall 16
- Spring 16

# Syllabus

*August 23rd:* Preliminaries (DF 0.1).
*August 25th:* Arithmetic and equivalence relations (DF
0.1 and 0.2).
*August 28th:* Equivalence relations and modular
arithmetic (DF 0.1 and 0.3)
*August 30th: Groups (DF 1.1).**
**September 1st:* Order of an element (DF 1.1).
*September 6th:* Symmetric groups (DF 1.3).
*September 8th:* Dihedral groups (DF 1.2).
*September 11th:* Homomorphisms (DF 1.6).
*September 13th:* Subgroups (DF 2.1).
*September 15th:* Examples of subgroups (DF 2.2).
*September 18th:* Cyclic groups (DF 2.3).
*September 20th:* Generated subgroups and cosets (DF
2.4 and 3.2).
*September 22nd:* First midterm.
*September 25th:* Lagrange's theorem, normal subgroups
and quotient groups (DF 3.2 and 3.1).
*September 27th:* First and second isomorphism
theorems (DF 3.1 and 3.3).
*September 29th:* Third isomorphism
theorem and groups actions (DF 3.3 and 1.7).
*October 2nd:* Stablizers, orbits and the class
equation (DF 2.2, 4.1 and 4.3).
*October 4th:* Cauchy's theorem (DF 3.4 and 4.3).
*October 6th:* Signature of a permutation (DF 3.5).
*October 9th:* Rings, Definitions and examples (DF
7.1).
*October 11th:* Ring homomorphisms, ideals and
quotients (DF 7.3).
*October 13th:* Ring quotients and polynomial rings
(DF 7.3 and 7.2).
*October 16th:* Polynomial rings and generated ideals
(DF 7.3 and 7.4).
*October 18th:* Maximal ideals (DF 7.4).
*October 20th:* Prime ideals and Chines remainder
theorem (DF 7.4 and 7.6).
*October 23rd:* Chinese remainder theorem and
Euclidian domains (DF 7.6 and 8.1).
*October 25th:* Euclidian domains and principal ideal
domains (DF 8.1 and 8.2).
*October 27th:* Greatest common divisors and unique
factorization domain (DF 8.1 and 8.2).
*October 30th:* Second midterm
*November 1st:* Unique factorization domains and
fraction fields (DF 8.3 and 7.5).
*November 3rd:* Polynomial factorization (DF 9.3).
*November 6th:* Roots of polynomials (DF 9.5)
*November 8th:* Field extensions (DF 13.1).
*November 13th:* Algebraic extensions (DF 13.1 and 13.2).
*November 15th:* Algebraic extensions (DF 13.2).
*November 17th:* Algebraic extensions (DF 13.2).
*November 20th:* Spliting fields (DF 13.4).
*November 27th:* Algebraic closure dand finite fields
(DF 13.4 and 13.5).

*
*# Approximate syllabus of future classes

*November 29th:* Finite fields and introduction to
Galois theory (DF 13.5, 14.1 and 14.2).
*December 1st:* The fundamental theorem of algebra (DF
14.6).

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