Teaching / Fundamental Concepts of Modern Algebra
Disclaimer: In-person lectures. No recordings, solutions, or make-up tests.
Asterisks indicate short weeks or weeks I am away. Exclamation marks indicate test weeks.
|1||Rings, integral domains, order (MB 1.1-1.4)||1.2#1,3,5,7,8b; 1.3#1-4,7; 1.4#1,2||1.4#3-5, 1.5#6,8|
|2*||W.o.p., induction (MB 1.5-1.8)||1.5#1,2,5(a,b, or c),11-12,14; 1.7#1,3,5,6,10,14||1.4#3-5, 1.5#6,8|
|3||Euclidean algorithm, FTA, valuation, congruences (MB 1.9-1.12)||1.8#1,5,8; 1.9#6,11,16|
|4||Maps of sets, fields (MB 1.11-1.12, 2.1-2.4)||1.11#2, 1.12 #3, 4, 2.1 #2, 6, 9||1.10#7|
|5||Detour on p-adic integers (Cuoco, Koblitz Ch 1)||2.3#3, 2.4#2, 3.1#7; 2.5-2.6 in Perusall|
|6!||Polynomials (MB 3)||Test 1 on Ch 1 & 2 Feb 13|
|7*||UFDs (MB 3)||3.1#3, Prove the corollary of 3.2 theorem 4. 3. 3.2#1, 3.2#2, 3.3 # 1(c), 3.3#4||3.2#9|
|8||Extension fields and their automorphism groups (MB 6, 15)||3.3 #3,7; 3.5 #2,3,4,5||3.5#6 or 7|
|9||Groups (MB 6)||6.1#3, 6.2#3,4||Dihedral groups|
|March||Break March Break ...||March Break March ...||Break|
|15||Death by a thousand cuts||TODO||TODO|
|11*||Actions and the orbit-stabilizer theorem||TODO||TODO|
|12*||Normal subgroups and quotient groups||TODO||TODO|
|13||Symmetric and alternating groups, and the platonic solids||TODO||TODO|
|14!||Center, centralizers, conjugation, simplicity of
||TODO||Test 2 on TBA Apr 17|
|15||Automorphisms (inner, outer)||TODO||TODO|
Instructor: Anne Dranowski (email@example.com)
- Office: KAP 444C or my zoom room
- Office hour windows: Tuesdays 3:45-5 in Zoom and Fridays 2:30-4:30 in person (as much as possible, please email to confirm your attendance)
TA: Kayla Orlinsky (firstname.lastname@example.org)
All ~five hours of weekly classes are equally important. As much as possible we will spend class time motivating difficult concepts or elaborating on harder examples or walking through a proof together (as opposed to, say, regurgitating the details of an easy proof that can be found in the book and that you can reconstruct on your own)
- Lectures: Mondays, Wednesdays, and Fridays 1:00-1:50pm in CPA 211
- Discussion: Tuesdays 2:00-3:50pm in GFS 222
- Test 1: approx. February 13th, in class
- Test 2: approx. April 17th, in class
- Project: Sign up for 1-2 5-30 minute planning meeting(s) here
- Final exam: Wednesday, May 3rd, 2:00-4:00 p.m. Please review USC Policy here: https://classes.usc.edu/term-20231/finals/.
- The Textbook: A Survey of Modern Algebra by Garrett Birkhoff & Saunders Mac Lane (4th Ed.)
- Lectures & Discussions: Some of the material we may uncover (e.g. Sylow's theorems) will be outside the scope of the book. If it is significant, I will let you know
- Math Center: The math department hosts a math help center. See their website for details
- Accessibility: Please contact OSAS as soon as possible should you require accommodation
- Calendar: Session dates are summarized here https://classes.usc.edu/term-20223/calendar/
- Course material will be posted to the course webpage and communicated thru Blackboard announcements, therefore please check Blackboard announcements regularly.
- Homework assignments and other assessments will be administered in Gradescope, which can be accessed through Blackboard.
This course will provide a detailed introduction to modern abstract algebra, which is a basic part of the language of much of modern math.
Time permitting we aim to cover parts of Chapters 1-3, 6, 9-11, and 13-15.
Beyond classroom time and the textbook, the course will involve:
Reading: Weekly readings will be assigned from the textbook, corresponding to the material that we are uncovering. You are expected to read the entirety of a chapter to understand it, in addition to class notes, even if we do not complete all the details in class.
Homework: There will be roughly weekly homework assignments. Late assignments will not be accepted: this course is unforgiving if you fall behind, so I do not want to encourage it. The three lowest scores will be dropped for every student.
Project: You will select one of the starred problems from the textbook and write up a detailed solution in the form of a short math article, preferably in LaTeX. Collaboration is welcome.
The final grade will consist of
- homework (13%)
- project (18%)
- two tests (18% each)
- cumulative final exam (33%)