Syllabus - Geometry, Algebra, and Algorithms
MATH 548 - Spring 2022
General Information
- Course webpage
- https://duncan.math.sc.edu/s22/math548
- Instructor
- Alexander Duncan
- duncan@math.sc.edu
- Office
- Coliseum 1022B
- Office Hours
- Tuesday, Wednesday 12:30 PM - 1:30 PM
Thursday 1:30 PM - 2:30 PM - Lecture
- Tuesday, Thursday 8:30 AM-9:45 AM
Coliseum 3007 - Textbook
-
Ideals, Varieties, and Algorithms (Fourth Edition).
David A. Cox, John Little, Donal O'Shea. - Prerequisites
- C or better in MATH 300 and in one of MATH 344 or MATH 544.
- W Deadline
- January 18
- WF Deadline
- March 28
Learning outcomes
Upon successful completion of this course, students will be able to:
- Translate between the languages of geometry, algebra, and computation using the ideal-variety correspondence.
- Determine the solutions to systems of multivariate polynomial equations.
- Solve problems using computer algebra systems.
Computer Algebra Systems
A substantial fraction of the course deals with computer algebra. Consequently, computer algebra systems will be used in lecture and required for portions of the homework assignments.
The recommended computer algebra package is the free open-source software system SageMath. There are many different ways of using this software - some ways only require a modern web browser. Some suggested methods for using SageMath are listed on the course website.
Students are welcome to use a different computer algebra system to complete assignments or explore the topics of the course. However, the necessary functionality may not be present and the instructor will not help troubleshoot.
Assessment
Your raw numerical grade will be computed as follows:
| Assignments | 40% |
|---|---|
| Midterm 1 | 15% |
| Midterm 2 | 15% |
| Final Exam | 30% |
Your raw numerical score will be converted into a final letter grade, which should be interpreted as follows:
| A | Demonstrates the potential to apply the course material confidently and correctly with minimal supervision in undergraduate research, graduate school, or industrial applications. |
|---|---|
| B+/B | Can apply ideas from the course in situations requiring more than a superficial understanding of the material. |
| C+/C | Able to consistently solve routine problems. |
| D+/D | Demonstrates understanding of core course concepts. |
Assignments
There will be written homeworks due roughly every other week. It is your responsibility to check the course website regularly for new assignments. When a computer algebra system is used on an assignment, be sure to explicitly state the commands used and their output (for example, by including a printout of your session).
Unless explicitly told not to do so, you may use any resource you'd like for assignments (e.g., computer algebra systems, the textbook, your classmates, online videos, or the instructor). However, you must write up your assignment on your own using your own words and list any resources used to do the assignment. Failure to abide by these guidelines will be considered a breach of academic integrity.
Reading the textbook and doing the assignments is necessary, but not sufficient, to succeed in this course! Also, relying too much on external resources will negatively impact your performance on the exams.
Exams
There are two midterm exams and a final exam. The midterm exams will take place instead of lecture on the following dates:
| Midterm Exam 1 | February 10, during class |
|---|---|
| Midterm Exam 2 | March 24, during class |
The final exam is a take-home exam, which will be due on April 28.
Course Policies
There will be no credit for late assignments. There will be no make-up exams. If you expect to miss an exam for any reason, then let the instructor know at least two weeks in advance. In the case of an excused absence from a midterm exam, the other midterm exam grade will be used for the missed midterm (adjusted to account for differences in the difficulty of the exams).
It is not reasonable to expect to learn the material without regularly attending classes. However, no attendance policy will be enforced.
Academic Integrity
The University of South Carolina has clearly articulated its policies governing academic integrity and students are encouraged to carefully review the policy on the Honor Code in the Carolina Community. Any deviation from these expectations will result in academic penalties as well as disciplinary action.
Office of Student Disability Services
Any student with a documented disability should contact the Student Disability Resource Center to make arrangements for appropriate accommodations.