### About this course

**Lectures**: Tuesday and Thursday 11:00am-12:15pm, Herrin T-195

**Course assistant**:Daniel Alvarez-Gavela

**Text**:Dummit and Foote's Abstract Algebra, third edition

Spring 2014

**Lectures**: Tuesday and Thursday 11:00am-12:15pm, Herrin T-195

**Course assistant**:Daniel Alvarez-Gavela

**Text**:Dummit and Foote's Abstract Algebra, third edition

Clear writing is essential to mathematical communication, and the WIM
assignment is an important part of this class. This course will
emphasize both exposition in communciating mathematics and the
structure of proofs. Part of your grade on each assignment and on
the exams will be on your exposition of your solutions to
problems. Information about the Writing in the Major assignment is
** here **. The
first draft is due by **May
18** and final text is due by **May 30**.

Homework 25%, WIM assignment 15%, Midterm 25%, Final exam 35%

Midterm: **April 29**, open book, open notes, (covering chapter 0-3) **in
class**. **Old
midterms** and ** solutions**

Final: ** June 6, 3:30pm-6:30pm **,
open book, open notes, in ** Herrin Hall
T195**. **Old
final exam**

Zhiyuan Li

- Office:

Bldg 380-382B

- Email: zli2 at stanford.edu

- Office Hours:

MW 12pm-1:30pm (also available for most of the SUMO homework night)

Daniel Alvarez-Gavela

- Office:

Bldg 380-380T

- Email:dgavela at stanford.edu

- Office Hours:

Wed 5:30pm-8:30pm

Due every Thursday at 2pm. You are encouraged to work together to solve problems. Late homework will not be accepted, but the lowest scoring problem set will be dropped. You should give complete proofs. Please staple your homework, and write your name on each page.

- Problem Set 1 (due April.10). $1.1, #9, #14, #24, #27; $1.2, #5; $1.3, #11,#14; $1.6, #1, #5, #18; $1.7, #4, #17. Solutions.1
- Problem Set 2 (due April.17). $2.1, #6, #8, #13; $2.2, #2, #8, #10; $2.3, #3, #21, #23; $2.4, #14. Solutions.2
- Problem Set 3 (due April.24). $3.1, #14, #34, #36; $3.2, #10, #11, #23; $3.3 #3 Solutions.3
- Problem Set 4 (due May.2). $4.1, #2, #7; $4.2, #7, #11, #13; and also Extra problems Solutions.4
- Problem Set 5 (due May.8). $4.3, #5, #10(b), #17, #22, #25, #27, #30, #34; Solutions.5
- Problem Set 6 (due May.15). $4.4, #3, #11, #13, #18; $4.5, #5, #16, #24; Solutions.6
- Problem Set 7 (due May.22). $5.1 #2; $5.2, #1 (e), #2 (b), #9, #10; $7.1, #13, #14, #25, #26; Solutions.7
- Problem Set 8 (due May.29). $7.2 #3, #5; $7.3, #26, #29; $7.4, #15, #30, #32; Solutions.8
- Problem Set 9 (last set!! due June.5). $7.6 #1, #6; $8.1, #7, #8; $8.2, #5, #6 (optional with extra point), #8; $8.3 #5, #6; Solutions.9

- Tue.April.1: definition of group; example of groups. Words you should know: binary operation, associative, commutative, group, abelian, identity, inverse, cyclic group, dihedral group.
- Thur.April.3:more examples: symmetric (permutation) groups, cycle decomposition; homomorphism and of groups; group actions.
- Tue.April.8:Subgroups, cyclic and subgroups of cyclic groups.
- Thur.April.10: finitely generated subgroups, Center, Centralizer, Normalizer of the group, Stabilizer and kernel;
- Tue.April.15: Cosets, Lagrange theorem and applications, (Fermat's little theorem), Normal subgroups
- Thur.April.17: Quotient groups, Isomorphism theorem
- Tue.April.22: Simple groups, Alternating groups
- Thur.April.24: Group action, Cayley's theorem, Class equation
- Tue.April.29: Midterm
- Thur.May.1: Conjugate action and class equation, automorphism of groups
- Tue.May.6: Sylow theorems
- Thur.May.8:Direct product and fundamental theorem of finitely generated abelian groups
- Tue.May.13:Rings, ideals and ring homomorphism
- Thur.May.15:Quotieng rings and Isomorphism theorems
- Tue.May.20:Automorphism of rings, properties of ideals
- Thur.May.22:Chinese reminder theorem, Ring of fractions
- Tue.May.25:Euclidean domain, Principal ideal domain
- Thur.May.29: irreducible and prime elements, U.F.D,
- Friday.May.30:Deadline for WIM assignment
- Tue.June.3 (last class):Gaussian integers and Gaussian primes