Math 584, Fall 2020 Syllabus

Subsection 1.1 Instructor

Instructor:

Zach Teitler [he/him/his]

Email:

zteitler@boisestate.edu

Website:

https://sites.google.com/site/zteitler/home

Office:

MB 233A

Office Phone:

208-426-1086

Subsection 1.2 Section

Section Number:

001

Meeting Times:

MoWe 12:00-1:15

Meeting Remotely:

We will meet remotely using Zoom. Zoom sessions may be recorded for students who are not able to attend.

Zoom meeting ID:

Posted in BlackBoard¹

Subsection 3.1 Required Textbook

1. Brendan Hassett, Introduction to Algebraic Geometry. Cambridge University Press, 2007.

   ebook:

   978-0-511-28529-5

   hardback:

   978-0-521-87094-8

   paperback:

   978-0-521-69141-3

We will cover material from the chapters of the textbook listed above the dividing line in the following table; additional material from chapters listed after the dividing line may be covered if time permits:

Subsection 3.2 Recommended Optional Textbooks

1. Mateusz Michałek and Bernd Sturmfels, Invitation to Nonlinear Algebra¹ (pdf).
2. Cox, Little, O'Shea, Ideals, Varieties, and Algorithms

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

Subsection 5.1 Allowed resources

In this 500 level class, I expect you to use the full array of resources at your disposal to learn the material “by any means possible.” For homework assignments, you are encouraged (in fact, expected) to collaborate with your classmates and to ask me questions. Other resources (books, online sources, people outside the class) are highly recommended for clarifying class topics or for enrichment (but not for getting solutions to problems).

You are allowed to use things that you learn from a book, online source, or person outside the class that help you and your classmates to find your own solution for a problem. However, if you read a full solution, so that there's little or nothing left for you and your classmates to figure out, then you may not turn in that solution for credit.

The Mathematics Stack Exchange¹ is a very useful question-and-answer site for undergraduate/graduate level mathematics. You are welcome to browse the Mathematics Stack Exchange and even post questions there. Hopefully it will help you learn and understand the material! However please remember that if you use that site to get a solution to a problem, then you can't turn that solution in for credit. Other helpful websites for basic information include Wikipedia and MathWorld².

Subsection 5.2 A note on collaboration

Solving mathematical problems has three parts:

The discovery phase:

This is the time you spent trying to figure out how to solve the problems, and it often takes most of the time. You are welcome and encouraged to collaborate with other students in this phase. Collaboration is a healthy practice, and this is how mathematics is done in real life.

This phase starts with working to understand what a problem or question is asking for. That might include reviewing material from previous textbook sections.

The write-up phase:

This consists of writing your solutions once you have an idea of how the problem can be solved. You should do this entirely by yourself. Be alone when you write your solutions. If you collaborate on this part, or you copy part of your solutions from somebody else, or you have notes written by somebody else in front of you when you write your solutions, you are hurting yourself by depriving yourself of an opportunity to learn and practice.

If you need help in the write-up phase, talk to me! I can help you.

The editing phase:

This consists of editing and revising your write-up for clarity, organization, and presentation. At this stage it can be very helpful to get feedback and suggestions from other students.

Subsection 5.3 Expectations of lectures

Please read “Mathematics Professors and Mathematics Majors' Expectations of Lectures in Advanced Mathematics”³.

Subsection 5.4 How to read mathematics

Please read the following, especially the first:

1. https://www.lboro.ac.uk/media/media/schoolanddepartments/mathematics-education-centre/downloads/research/SE-booklet.pdf
2. https://web.stonehill.edu/compsci/History_Math/math-read.htm
3. https://brownmath.com/stfa/read.htm

Subsection 5.5 University Resources

Boise State University's The Basics⁴ web page has links to many forms of support, ranging from academic resources to family, living, and food resources.

You may reach out to me at any time if there's anything I can help with or if there's anything you think I should know.