417 - Fall 2018
Intro to Abstract Algebra
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
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
Abstract and Concrete (edition 2.6) by Goodman. This book is
available freely here.
engaging with the course material, both in and outside of class, is
crucial to your success in this class. Part of in-class engagement
means being present,
and not just in the sense
of being physically in the classroom.
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!
Your course grade is determined by the following:
- (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.
There will be three midterms and a final exam on the material covered
in the lectures. The midterms will occur during class. Our final
exam will be scheduled by the registrar's office and I will
let you know once it is scheduled. If you make travel arrangements
before the final exam is scheduled, you should assume that the final
will be held
on the last day of the final exam period.
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
Mathematics (and problem solving in general) is a collaborative
discipline. You are strongly encouraged to work and discuss together to
solve the homework problems. However, and this is important, you
write-up the solution on
your own and it must
in your own words. Anything else is plagiarism and will be treated as
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
Homework 1 (due 9/7):
1.4.2, 1.5.1, 1.5.2, 1.5.3, 1.5.5, 1.5.8
Appendix A, Appendix B,
1.6, 1.7, 1.10
Homework 2 (due 9/14):
1.6.3, 1.6.4, 1.6.8, 1.7.1, 1.7.5, 1.7.11Read:
Homework 3 (due 9/21):
2.1.3, 2.1.5, 2.1.7, 2.2.3, 2.2.12, 2.2.20Read:
Homework 4 (due 10/3):
2.3.1, 2.3.7, 2.4.5, 2.4.7, 2.4.14
Homework 5 (due 10/10):
2.5.7, 2.5.8, 2.5.12, 2.5.13, 2.6.2, 2.6.3Read:
Homework 6 (due 10/24):
2.7.4, 2.7.7, 2.7.10, 3.1.2, 3.1.3Read:
Homework 7 (due 10/31):
3.1.9, 3.1.10, 3.1.13, 3.2.1, 3.2.2, 3.2.6
Homework 8 (due 11/7):
5.1.1, 5.1.5, 5.1.6, 5.1.7, 5.1.10 (G is assumed to be finite)Read:
Homework 9 (due 11/16):
5.4.1, 5.4.3, 5.4.5, 5.4.8, 5.4.9, 5.4.18Optional Homework (due 11/26):
5.4.4, 5.4.6, 5.4.11, 5.4.12 Read:
1.8, 6.1-6.3Homework 10 (due 12/12):
6.1.4, 6.2.4, 6.2.18, 1.8.7, 1.8.17, 6.3.2
Course intro, First examples. Lecture
More examples: symmetry. Lecture
Dvisibility properties of integers. Lecture
Modular arithmetic. Lecture
First properties of groups. Lecture
.[9/14] Worksheet 1
Cyclic groups. Lecture
Dihedral groups. Lecture
Exam 1. Solutions here
Cosets, Lagrange's theorem. Lecture
More cosets. Lecture
Equivalence relations. Lecture
Quotient groups. Lecture
Exam 2. Solutions here
More quotient groups, direct products. Lecture
.[10/19] Worksheet 2
Direct products, semi-direct products. Lecture
Semi-direct products. Lecture
Finish semi-direct products, Group actions. Lecture
. [10/29] Worksheet 3
More group actions. Lecture
Orbit Stabilizer and counting. Lecture
More counting. Lecture
A little more counting. The class equation. Lecture
Sylow Theorems. Lecture
.[11/14] Worksheet 4
Sylow Theorems, proofs. Lecture
Rings and fields. Lecture
Polynomial rings. Lecture
Exam 3. Solutions here
Quotient Rings. Lecture
Field extensions. Lecture