Math 333: Topics in Abstract Algebra: Computational Algebraic Geometry
Grades and Expectations
Grades will be based on- daily homework (worth 40%),
- one 30-minute in-class presentation (worth 40%),
- a TeXed write-up of your presentation and handouts (worth 20%).
Like basketball and violin, math is learned by doing not by watching. Class participation is critical: I expect that you'll do your part to keep the energy level of the class high. I also expect that you attend class every day; if illness or another serious problem prevents you from coming, let me know.
Math is also a creative endeavor: this class is a place to explore the boundaries of your knowledge and your abilities, to stretch yourself and your imagination. I do not expect you to complete every problem set or to solve every problem "perfectly"; I like to see how you think. Many students will receive an A with far less than perfect scores. If you are concerned with how your problem sets translate into a final letter grade for the course, please ask me.
Homework
Roughly two problems will be due each class. The four lowest homework scores will be dropped. Collaboration is encouraged, but each student is responsible for- writing her own solutions,
- knowing how to solve the problems, and
- listing all collaborators or other resources used.
- Late homework is a bad idea. If you're behind, it's hard for you to learn new stuff and to participate in class.
- Homework that is unreadable may not be graded.
- Problems for the second week (September 11-13).
- Problems for the third week (September 18-20).
- Problems for the fourth week (September 25-27).
- Problems for the fifth week (October 2-4).
- Problems for the sixth week (October 11).
- Problems for the seventh week (October 16-18).
- Problems for the eighth week (October 23-25).
- Problems for the ninth week (October 30-November 1).
- Problems for the tenth week (November 6-8).
- Problems for the eleventh week (November 13-15).
- Problems for the twelfth week (November 20).
- Problems for the thirteenth week (November 27-29).
Presentation
Being able to give a clear and compelling presentation is a critical and transferable skill you will bring out of college to the rest of your life. We will develop and hone this skill in this class.In the last two weeks of class, every student will give a 30-minute in-class presentation. Students can pick from a list of topics or choose a topic of their own (with instructor permission). Students may also cooperate with other students to explore one topic in an hour-long presentation; see me to discuss logistics. Some possible topics include: algebraic curves, hypersurfaces, Grassmannians, toric varieties, flag varieties, line bundles, Picard varieties, Hilbert scheme of points in a plane, moduli spaces.
The presentation will be a large part of your work for the semester. Parts of it will be due throughout the fall. On the syllabus, you can find dates for choosing the topic, writing an outline, discussing a draft of your presentation with me, and giving a practice presentation for a classmate.
Write-up
You know the importance of writing, both as an essential capability in itself and as a tool for honing your thoughts. We will gain one other tool: LaTeX, thepreeminent word-processing software for mathematical expressions. Anybody using mathematics professionally needs to know at least basic LaTeX. LaTeX is a document markup language, like HTML, so you will also be learning one of a family of useful programming languages.At the end of reading period, a LaTeXed write-up of your presentation, together with any handouts and suggested problems, will be due. Diagrams can be drawn freehand, unless you have (or wish to gain) particular expertise. An introduction to LaTeX can be found here, and a template document for you to work from is here.