Math 417: Abstract Algebra I
Instructor: Rebecca Tramel.
Office Hours: Illini Hall 241 Monday 3-5 and Tuesday 1-2, or by appointment.
Abstract and Concrete by Frederick M. Goodman.
The goal of this course is to introduce
important topics in the study of Algebra. We will devote most of the
course to the study of groups. We will also introduce rings and
fields in this course.
Weekly Homework: 25%
Midterm Exams (Sep 28, Nov 2): 35%
Final Exam: 40%
Homework assignments will be graded on a two-tier system:
- Most exercises will be graded out of 2 points, with full
credit awarded for a mostly correct solution.
- One exercise each week will be looked at in more detail, and
will usually be graded out of 4 points. For this exercise, a
perfect score will be reserved for a perfect solution.
- Another 2 points will be awarded to each assignment based on
its neatness and organization. In order to ensure you always
earn these points, make sure to staple your assignments, label
your exercises, and either type your solutions or write them out
There will be opportunities throughout the semester to earn up to
3 dropped homework grades.
The two midterm exams are scheduled for
Wednesday, September 28 and Wednesday, November 2. The
final exam is scheduled by the Registrar's office, and so the
date and time will be listed later in the semester. Keep these
dates in mind while scheduling holiday travel.
- Week 1 (Aug. 22, 24, 26): Sections 1.1-1.4 on
symmetries of polygons.
- HW1 Due Wed. Aug. 31: 1.3.1, 1.3.3, 1.4.2, B.4, E.1.
(The notation in the appendices may be different from what
you are used to, please let me know if you'd like some of it
- Aug. 22 Game: Breakout.
(For reference, the solutions were 253, 764, 861.)
- Week 2 (Aug. 29, 31, Sep 2): Sections 1.5-1.6 on
permutations and properties of the integers.
- HW2 Due Wed. Sep. 7: 1.5.3 a,b,g,h, 1.5.6, read
example 1.5.2 and do exercise 1.5.11, 1.6.3. You can do the
calculations in 1.5.3 and 1.5.11 without providing a complete
- Aug. 29 Game: Battleship.
- For Friday's class, please read section 1.6. We will go
through the highlights together, but you are responsible for
the full section.
- Week 3 (Sep. 7, 9): Sections 1.6 - 1.7 on prime numbers
and modular arithmetic.
- HW3 Due Wed. Sep. 14: 1.6.9, 1.7.4, 1.7.11, 1.7.14. Solutions.
- Week 4 (Sep. 12, 14, 16): Sections 1.7, 1.9-1.12 on
modular arithmetic, counting, groups, and rings.
- Week 5 (Sep. 19, 21, 23): Sections 2.1 and 2.2 on
groups and subgroups.
- Week 6 (Sep. 26, 28, 30): Midterm 1, Section 2.3 on the
- Week 7 (Oct. 3, 5, 7): Sections 2.4 and 2.5 on Group
Homomorphisms and Cosets.
- HW6 Due Wed. Oct 12: 2.3.6, 2.4.4, 2.4.8, 2.4.13,
- Week 8 (Oct. 10, 12, 14): Sections 2.5, 2.6, and 2.7
on Lagrange's Theorem, equivalence relations, and quotient
- Week 9 (Oct. 17, 19, 21): Sections 2.7 and 3.1 on
isomorphism theorems and direct products.
- HW8 Due Wed. Oct 26: 2.7.4, 2.7.6, 2.7.7, 2.7.11. Solutions.
- Week 10 (Oct. 24, 26, 28): Sections 3.1, 3.5, 3.6 on
direct product, the Chinese Remainder Theorem, and the
Fundamental Theorem of Finitely Generated Abelian Groups.
- Week 11 (Oct. 31, Nov 2, 4): Midterm 2, Section 5.1 on
- Week 12 (Nov 7, 9, 11): Sections
5.1-5.3 on group actions.
- Week 13 (Nov 14, 16, 18): Sections 5.4
and 6.1 on the Sylow theorems and an introduction to ring
- Week 14 (Nov 28, 30, Dec 2):
Sections 6.2-6.4 on ideals, quotient rings, and integral
- HW12 Due Wed. Dec 7: 6.2.17, 6.3.7, 6.3.8, 6.4.14. Solutions.
- Week 15 (Dec 5,7): Review.
This is our course page on Piazza. It is visible only to me and to
other students in this class. You can ask and answer course related
LaTeX template - You will
need to download a program to compile the document. There are many
options, for example TeXStudio
or MacTeX (Mac), and Kile (Linux).