Office hours: Tuesday 10-11am, Friday 2-3pm

Section B13 at MWF 9:00-9:50am in 447 ALTGELD

Section D13 at MWF 11:00-11:50am in 343 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 to 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!

- (20%) Homework.
- (10%) Quizzes
- (40%) Midterm exams
- (30%) Final exam

- Extra office hours: Thursday 5/3 12:30-1:30pm.
- Final exam info. Practice problem solutions here.
- Midterm 2 solutions.
- Exam revisions due by Friday, 4/13.
- Extra office hours: Tuesday 4/3, 3-4pm
- Midterm 2 info. Practice problem solutions here.
- Midterm 1 solutions.
- Extra office hours: Monday 2/19 2-3pm, Tuesday 2/20 1-2pm
- Midterm 1 info. Practice problem solutions here.
- You can check your grades here.

**Exam 1:** Wednesday, February 21.

**Exam 2:** Wednesday, April 4.

**Final Exam:** Friday, May 4, 1:30-4:30pm, 103 Transportation Building.

There will be regular short quizzes (5-10 minutes) which will occur every week or so. These are meant to serve as a regular "reality check", to be sure the basics are being understood.

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

Homework 2 (due 2/5): 1.6.3, 1.6.4, 1.6.8, 1.7.1, 1.7.5, 1.7.11

Read: 2.1, 2.2

Homework 3 (due 2/12): 2.1.3, 2.1.5, 2.1.7, 2.2.3, 2.2.12, 2.2.16

Read: 2.4, 2.5

Homework 4 (due 2/28): 2.4.5, 2.4.7, 2.4.14, 2.5.7, 2.5.8, 2.5.12

Read: 2.6, 2.7

Homework 5 (due 3/7): 2.6.1, 2.6.2, 2.6.3, 2.7.1, 2.7.2, 2.7.7

Read: 3.1, 3.2

Homework 6 (due 3/14): 3.1.2, 3.1.10, 3.1.3, 3.1.13, 3.2.2, 3.2.6

Read: 5.1, 5.2

Homework 7 (due 3/28): 5.1.1, 5.1.5, 5.1.6, 5.1.7, 5.1.10 (G is assumed to be finite)

Read: 5.4

Homework 8 (due 4/18): 5.4.1, 5.4.3, 5.4.5, 5.4.8, 5.4.9, 5.4.18

Read: 1.8, 6.1, 6.2

Homework 9 (due 4/25): 6.1.5, 6.1.12, 6.2.4, 6.2.18, 1.8.7, 1.8.17

Homework 10 (due 5/2): Homework 10

[1/19] More examples, symmetry. Lecture notes.

[1/22] Permutation groups. Lecture notes.

[1/24-26] Divisibility properties of integers. Lecture notes.

[1/29-31] Modular arithmetic. Lecture notes.

[2/2] First properties of groups. Lecture notes

[2/5] Subgroups. Lecture notes

[2/7-12] Cyclic groups and their subgroups. Lecture notes

[2/14] Dihedral groups. Lecture notes

[2/16] Homomorphisms. Lecture notes

[2/19] Cosets, Lagrange's theorem. Lecture notes

[2/21] Midterm Exam 1

[2/23] More cosets. Lecture notes

[2/26-28] Equivalence relations. Lecture notes

[3/2-3/5] Quotient groups. Lecture notes

[3/7] More quotient groups. Lecture notes

[3/9-12] Direct products, Semi-direct products. Lecture notes

[3/14] Finish semi-direct products. Group actions. Lecture notes

[3/16] Group actions, more examples. Lecture notes

[3/26] Orbit-stabilizer theorem, basic counting. Lecture notes

[3/28] Burnside lemma, more counting. Lecture notes

[4/6] Class Equation. Lecture notes

[4/9] Sylow's Theorems. Lecture notes

[4/11-13] Proofs of Sylow's Theorems. Lecture notes

[4/16] Rings and fields. Lecture notes

[4/18] Polynomial rings. Lecture notes

[4/20] Ring homomorphisms. Lecture notes

[4/23] Ideals. Lecture notes

[4/23] Quotient rings. Lecture notes

[4/23] Field extensions. Lecture notes

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