Transition to Advanced Mathematics, Math 300H
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:
- Be able to read, write, understand, and critique mathematical proofs.
- Learn the foundations of formal logic and set theory.
- Thoroughly understand the notion of a function, and be able to describe when one is injective, surjective, and bijective.
- 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.
- Be prepared to take more advanced (e.g. 500-level) math classes.
Text :
Ted Sundstrom, Mathematical Reasoning: Writing and Proof
(direct pdf link), Version 3. This is OER, available freely and legally.
You don't need a printed copy, but you can buy one here if you want.
The tentative plan is to cover the following chapters: 1, 2, 3 (except 3.5), 4, 5.1-5.3, 6 (6.4-6.5 briefly), 7.2 (briefly), 9 (briefly).
Lectures : MWF 10:50-11:40, LeConte 315.
The class will mostly be in a lecture format, but will also include some classroom discussion and in-class group work. Participation is required and is part of your grade.
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 given Monday, April 29, 9:00-11:30 as
scheduled by the registrar.
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.
Grading :
Please note. You will be graded both on correctness and on quality of exposition. Indeed, a major
focus of Math 300 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 exam: |
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.