Algebraic Structures -- Mathematics 546
Frank Thorne - Spring 2024
University of South Carolina
Instructor: Frank Thorne, thorne [at] math [dot] sc [dot] edu
Office Hours: Tue 9:30-11:00 and Wed 3:30-5:00, in LeConte 447.
Course objectives/learning outcomes:
Successful students will:
- Master the foundations of abstract group theory.
- Be able to
describe typical examples of groups and explain their properties.
- Be able to understand and provide
descriptions of groups given in both abstract or visual formats.
In addition, as with any 500-level pure math class, students will also:
- Thoroughly understand what definitions and theorems are. The student will be able to precisely state definitions and theorems and understand how they are applied.
- Practice writing proofs. It is expected that the student will have some, but not a lot, of experience writing proofs.
The student will gain more practice.
- Practice good mathematical writing. In mathematics, as indeed in everything else, it is important not only to be correct but to explain yourself clearly and as simply as possible.
Text :
Nathan Carter, Visual Group Theory, MAA Press. You can buy it
from the publisher, from the campus bookstore, or from your
favorite online bookseller.
I will also present some material not from the text, or in a different way from the text.
For this, I will write up supplementary
notes and make them freely available to you.
We will also use the Group Explorer web app, also by Nathan Carter, designed
to accompany the book.
Lectures : MWF 12:00-12:50, LeConte 315.
The class will mostly be in a lecture format, but will also include some classroom discussion and in-class group work.
Microsoft Teams :
We will use Microsoft Teams for announcements, discussion, and (if I get sick) livestreaming. You are responsible for checking for announcements there.
Exams : There will be two midterms of two hours each -- take home, closed book, and pledged.
Dates will be announced later in the term.
After they are handed out you will have at least a 72-hour period in which to finish them.
The final exam will be Wednesday, April 24 from 12:30-3:00, as scheduled by the registrar. I will not present any new material
which will appear on the final after Wednesday, April 17.
Homework :
The homework is intended to take 5-8 hours a week. That is a lot. Please
count on making a consistent effort to do well in this class! Starting the night before is a bad idea.
If homework takes you more than 10 hours on any given week, then that is more than I intended;
please let me know.
There might be a bonus problem on some of the homeworks (not guaranteed!), good for extra credit.
Some of the homework will involve the Group Explorer web app: you will be expected to
use the app, create, view, and describe diagrams, and take screenshots and send them to me over Microsoft Teams. Make sure you have
access to a computer!
Color :
In this course you will read, interpret, and produce Cayley diagrams of groups, where
color is used in a critical way. You are expected to obtain a variety of colored
pens or pencils and use them to take notes and to write homeworks and exams.
If you are colorblind (partially or fully) you are required to contact me on the first day of classes
so that appropriate accommodations can be made.
Grading :
Please note. You will be graded both on correctness and on quality of exposition. Indeed, a major
focus of Math 546 is the ability to communicate mathematical ideas clearly.
The standard is that someone who doesn't know the answer should be able to easily follow your work.
In particular, please write in complete English sentences and draw clear diagrams where appropriate.
Any work that is confusing, ambiguous, or poorly explained will not receive full credit.
Grading scale: You are guaranteed at least the following: A = 88+, B+ = 83+, B = 75+, C+ = 70+, C = 60+, D = 50+.
Please note that my grading scale is more generous than the usual 10-point scale. However,
I am a (slightly) stricter grader than most.
This is intended
to balance out.
| Grade component |
% of grade |
| Homework: |
40% |
| Two take-home midterm exams |
15% x 2 |
| Participation |
5% |
| Final project: |
25% |
Contacting me :
Please contact me if you have any questions about the course, about my expectations, about my lectures,
about the homeworks, about the reading, or about anything else. The syllabus is demanding and it is my
job to help you succeed.
The best ways to get help are to come to office hours (no appointment necessary) or to e-mail me (during the week, I will
almost always reply within 24 hours). If neither of these work for you then please e-mail me to set up an
appointment.
Other Policies :
-
Late homeworks and makeup exams:
In case of illness or emergency, please let me know immediately and before; alternative arrangements will be made.
In other cases, for homeworks extensions may be granted occasionally at the discretion of the instructor.
- Academic honesty and attendance are expected of all students. Roll will not be taken, but participation
is part of your grade and excessive unexcused absenteeism will hurt this. In case of excused absences, you may either go through
formal channels or simply let me know the circumstances.
- If you have difficulty seeing the board or hearing the lectures, or
a related problem, let me know ASAP, and I will do something
about it. Similarly if anyone is engaged in harassing or bullying behavior.
- If you require disability-related accommodations, please talk to the
Student Disability
Resource Center as soon as possible. It is your responsibility to advise me of any needed accomodations
a week in advance.