Office hours: Tuesday 13:00-14:00, Wednesday 14:00-15:00

Section B13 at MWF 9:00-9:50 in 345 ALTGELD

Section E13 at MWF 13:00-13:50 in 145 ALTGELD

Algebra is the branch of mathematics which studies equations, their solutions, and ways to manipulate them (the word algebra comes from Arabic and means "reunion of broken parts"). The abstraction and distillation of ideas over time has led us to the definition of a group, the basic object of study in modern abstract algebra. Other central objects which we will study are rings and fields. This course serves as an introduction to abstract algebra, its connections to other areas of mathematics, and to abstract mathematical thinking.

Text: Algebra: Abstract and Concrete (edition 2.6) by Goodman. This book is available freely here.

It is all too easy to be distracted by our electronic devices. Save your emails, texts, and posts for after class! Rather than listening passively, grapple with the material and ask questions!

- (22%) Homework
- (6%) Worksheets
- (42%) Midterm exams
- (30%) Final exam

- Extra Office hours: Thursday 12/13 at 2:00pm in 141 Altgeld.
- Final exam info and review here. Solutions to practice problems here.
- Revisions (optional) to be turned in by 12/10.
- Extra office hours before exam: Thursday 11/29 at 2:00pm.
- Midterm 3 info and review here. Solutions to practice problems here.
- Office hours on 10/30 moved to 3:00pm.
- Revisions (optional) to be turned in by 10/24.
- Extra office hours before exam: 10/14 at 1:00pm.
- Midterm 2 info and review here. Solutions to practice problems here.
- Extra office hours before exam: 9/23 at 1:00pm.
- Midterm 1 info and review here. Solutions to practice problems here.

**Exam 1: **September 24

**Exam 2: **October 15**Exam 3: **November 30**Final Exam:** December 14, 1:30 - 4:30pm in 1310 Digital Computer Laboratory

Your solution needs to be correct (of course!), complete, and legible (if it can't be read, it will not be graded). Homework is due in class.

Exercises come from the text (unless otherwise specified). Solutions to selected exercises can be found here.

Read: 1.1-1.5

Review: Appendix A, Appendix B, as needed

Read: 1.6, 1.7, 1.10

Read: 2.1,2.2

Read: 2.3,2.4

Read: 2.5,2.6

Read: 2.7,3.1

Read: 3.1,3.2

Read: 5.1,5.2

Read: 5.4

Read: 1.8, 6.1-6.3

Homework 10 (due 12/12): 6.1.4, 6.2.4, 6.2.18, 1.8.7, 1.8.17, 6.3.2

[8/29] More examples: symmetry. Lecture notes.

[8/31] Permutations. Lecture notes.

[9/5] Dvisibility properties of integers. Lecture notes.

[9/7-10] Modular arithmetic. Lecture notes.

[9/12] First properties of groups. Lecture notes.

[9/14] Worksheet 1.

[9/17] Subgroups. Lecture notes.

[9/19-21] Cyclic groups. Lecture notes.

[9/21,26] Dihedral groups. Lecture notes.

[9/24] Exam 1. Solutions here.

[9/26-28] Homomorphisms. Lecture notes.

[10/1] Cosets, Lagrange's theorem. Lecture notes.

[10/3] More cosets. Lecture notes.

[10/5-8] Equivalence relations. Lecture notes.

[10/8-12] Quotient groups. Lecture notes.

[10/15] Exam 2. Solutions here.

[10/17] More quotient groups, direct products. Lecture notes.

[10/19] Worksheet 2.

[10/22] Direct products, semi-direct products. Lecture notes.

[10/24] Semi-direct products. Lecture notes.

[10/26] Finish semi-direct products, Group actions. Lecture notes.

[10/29] Worksheet 3.

[10/31] More group actions. Lecture notes.

[11/2] Orbit Stabilizer and counting. Lecture notes.

[11/5] More counting. Lecture notes.

[11/7] A little more counting. The class equation. Lecture notes.

[11/9-12] Sylow Theorems. Lecture notes.

[11/14] Worksheet 4.

[11/16] Sylow Theorems, proofs. Lecture notes.

[11/26] Rings and fields. Lecture notes.

[11/28] Polynomial rings. Lecture notes.

[11/30] Exam 3. Solutions here.

[12/3] Homomorphisms. Lecture notes.

[12/5] Ideals. Lecture notes.

[12/7] Quotient Rings. Lecture notes.

[12/10] Field extensions. Lecture notes.

[12/13] Review

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