Math 120 - Modern algebra - Fall 2011

Homepage http://math.stanford.edu/~galatius/120F11/

Classes TTh 11:00 - 12:15 in 380F

Instructor Soren Galatius

Office 383-DD

e-mail galatius@stanford.edu

Office hours Wed 9:30 - 12

Course Assistant Jeremy Booher

Office 381-H

e-mail jbooher@math.stanford.edu

Office hours MW 1:30 - 3

Course Assistant Omid Hatami Varzaneh

Office 380-J

e-mail omidh@math.stanford.edu

Office hours TTh 12:45 - 2:15

Textbook Abstract algebra, 3rd edition, by Dummit and Foote.

About the class. This class will cover groups, fields, rings, and ideals. More explicitly: Groups acting on sets, examples of finite groups, Sylow theorems, solvable and simple groups. Fields, rings, and ideals; polynomial rings over a field; PID and non-PID. Unique factorization domains. Students more interested in applications of the theory should also consider math 109.

Writing in the Major. Writing is an important part of mathematics, and the WIM assignment is an important part of this class. A draft is due 11/8, final text (4-7 pages) due 11/29. More information.

Exams

Midterm 10/25, in-class. Open book, open notes. Sample solutions.

Final 12/12, 3:30PM - 6:30PM. Open book, open notes. Will be held in Meyer Forum (in the Meyer Library). Here's a practice final (actually an exam from a previous year, so there'll be some differences in what was covered and how the class was taught.)

Exams
Midterm	10/25, in-class. Open book, open notes. Sample solutions.
Final	12/12, 3:30PM - 6:30PM. Open book, open notes. Will be held in Meyer Forum (in the Meyer Library). Here's a practice final (actually an exam from a previous year, so there'll be some differences in what was covered and how the class was taught.)

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

Lecture plan. The class will cover roughly the first 8 chapters of the book, approximately a chapter a week. A more detailed lecture plan (updated after each lecture) is here.

Homework is due each week.

Due date Problems

10/6 1.1.9, 1.1.22, 1.1.32, 1.2.5, 1.2.9, 1.3.8, 1.3.13, 1.3.14, 1.4.3, 1.5.1, 1.6.4, 1.6.18, 1.6.20. Solutions: Part 1 Part 2.

10/13 1.7.16, 1.7.19, 1.7.20, 1.7.21, 2.1.(1d+2a+2b), 2.1.6, 2.2.7, 2.2.14, 2.3.2, 2.3.12, 2.4.8, 2.5.10 Solutions: Part 1 Part 2.

10/20 2.3.9, 2.3.11, 2.4.11, 2.4.14(c+d), 3.1.14, 3.1.25, 3.2.4, 3.2.6, 3.3.1, 3.3.8 Solutions: Part 1 Part 2

10/27 Practice problems, not due: 3.4.1, 3.5.2, 3.5.3, 3.5.12, 4.1.1, 4.2.2, 4.2.4, 4.2.7, 4.3.2, 4.3.22

11/3 3.3.4, 4.1.4, 4.2.4, 4.2.6, 4.3.2, 4.3.5, 4.3.11, 4.3.13, 4.3.22 Solutions: Part 1 Part 2

11/10 4.5.4, 4.5.17, 4.5.19, 4.5.30, 4.5.32, 4.5.45, 4.6.2, 4.6.5, 4.6.6 Solutions: Part 1 Part 2

11/17 5.1.4, 5.5.3, 7.1.1, 7.1.2, 7.1.3, 7.1.11, 7.1.12, 7.1.14 Solutions: Part 1 Part 2

12/1 7.1.15, 7.1.21, 7.3.1, 7.3.2, 7.3.13, 7.3.26, 7.4.7, 7.4.8, 7.4.15 Solutions: Part 1 Part 2

12/8 Practice problems on chapter 8 (not due): 8.1.8, 8.1.10, 8.2.3, 8.3.1, 8.3.2, 8.3.4, 8.3.6, 8.3.7.

Due date	Problems
10/6	1.1.9, 1.1.22, 1.1.32, 1.2.5, 1.2.9, 1.3.8, 1.3.13, 1.3.14, 1.4.3, 1.5.1, 1.6.4, 1.6.18, 1.6.20. Solutions: Part 1 Part 2.
10/13	1.7.16, 1.7.19, 1.7.20, 1.7.21, 2.1.(1d+2a+2b), 2.1.6, 2.2.7, 2.2.14, 2.3.2, 2.3.12, 2.4.8, 2.5.10 Solutions: Part 1 Part 2.
10/20	2.3.9, 2.3.11, 2.4.11, 2.4.14(c+d), 3.1.14, 3.1.25, 3.2.4, 3.2.6, 3.3.1, 3.3.8 Solutions: Part 1 Part 2
10/27	Practice problems, not due: 3.4.1, 3.5.2, 3.5.3, 3.5.12, 4.1.1, 4.2.2, 4.2.4, 4.2.7, 4.3.2, 4.3.22
11/3	3.3.4, 4.1.4, 4.2.4, 4.2.6, 4.3.2, 4.3.5, 4.3.11, 4.3.13, 4.3.22 Solutions: Part 1 Part 2
11/10	4.5.4, 4.5.17, 4.5.19, 4.5.30, 4.5.32, 4.5.45, 4.6.2, 4.6.5, 4.6.6 Solutions: Part 1 Part 2
11/17	5.1.4, 5.5.3, 7.1.1, 7.1.2, 7.1.3, 7.1.11, 7.1.12, 7.1.14 Solutions: Part 1 Part 2
12/1	7.1.15, 7.1.21, 7.3.1, 7.3.2, 7.3.13, 7.3.26, 7.4.7, 7.4.8, 7.4.15 Solutions: Part 1 Part 2
12/8	Practice problems on chapter 8 (not due): 8.1.8, 8.1.10, 8.2.3, 8.3.1, 8.3.2, 8.3.4, 8.3.6, 8.3.7.