Math 584, Fall 2020 Syllabus

Subsection 4.1 Components of course grade

Graded student work will consist of a short paper and a term paper, midterm and final exams, and written homework. Course grades will be based primarily on term papers and exams, and to a lesser extent on homework.

Subsection 4.2 Papers

Each student will write two papers for this class. Each paper is intended to provide:

• an opportunity to explore the mathematical research literature and seek a personally appealing research topic
• an authentic experience of working with the published mathematical literature
• an authentic experience of writing a substantial mathematical text, well beyond typical homework solutions
• preparation for writing even an larger text, such as a thesis
• an authentic experience of receiving feedback on a draft manuscript and responding to that feedback through multiple rounds of revision
• an authentic experience of writing mathematical exposition at a high level

The details of the two papers are as follows.

1. A short paper about an open question, unsolved problem, or currently studied research area within algebra, algebraic geometry, or computational algebra, or an application of one of those areas.
2. A term paper about a topic of the student's choice within algebra, algebraic geometry, or computational algebra, or an application of one of those areas (but emphasizing the algebraic aspect).

Lengths and deadlines of the papers are as follows:

1. The short paper will be 2–3 pages long, with the following deadlines:

   • A topic and source are due by the end of week 3.
   • A first draft is due by the end of week 4.
   • The short paper is due by the end of week 5.

2. The term paper will be 6–15 pages long (it can be shorter or longer if needed; please discuss with me), with the following deadlines:

   • A topic (1–2 pages) is due by the end of week 7.
   • An outline plus one section are due by the end of week 10.
   • A first draft is due by the end of week 13.
   • The term paper is due by the end of week 15.

For both papers, highly recommended sources are the recommended additional texts listed above. They contain numerous examples, applications of algebraic geometry, and links to other books and articles. If you find a topic that interests you in one of those texts, you can use it as a starting point for your paper.

Additional recommended sources include:

• MAA Writing Awards¹
• American Mathematical Monthly²
• College Mathematics Journal³
• Mathematics Magazine⁴
• Math Horizons⁵
• What's Happening in the Mathematical Sciences⁶

You should use high-quality published sources. For simplicity, this means the recommended sources listed above, or any publication listed in MathSciNet⁷. If you have questions or wish to use other sources, talk to me.

Papers for this class may not be about your own research.

Subsection 4.3 Midterm and final exams

A midterm exam in the 8th week of the semester, and the final exam, will be individual oral exams. The exams are intended to gauge mastery of course material, but also reflection on the course and its place in a larger context.

Subsection 4.4 Written homework