• Develop technical writing skills, including the ability to communicate abstract mathematical ideas clearly and elegantly.
• Continue to learn how to read mathematics with a critical and inquisitive mind, and articulate relevant questions during your study.
• Develop an appreciation for how penetrating theoretical insights can lead to important computational tools.
• Learn some important concepts of algebraic geometry, including polynomial rings (in several variables), Noetherian rings, ideals, varieties, Gröbner bases, and the Nullstellensatz.
• Continue to hone your perseverance in problem solving.

Homework assignments will be due on most Tuesdays and Fridays, and will be posted to the course webpage.

• Homework is due at 5:00pm Grinnell time.
• You should submit you solutions as one pdf file to the corresponding homework folder within your course OneDrive folder (that I will share with you).
• Homework will be graded using a basic check-plus, check, and check-minus system, but I will provide substantive comments.
• Solutions to the homework will be posted to the course webpage.
• Throughout the semester, you may extend the deadline of at most two homework assignments by (up to) two days. If you choose to extend the deadline of an assignment, you should send me an email by the usual due date. Beyond these two extensions, late homework will not be accepted for credit, unless there is an emergency that you bring to my attention before the due date.

I strongly recommend that you learn to type your solutions. LaTeX is a wonderful free typesetting system which produces high-quality documents at the cost of only a small amount of additional work. If you plan to do any kind of scientific writing in the future, you will most likely use LaTeX, so taking the time right now to familiarize yourself with it will pay off.

One of the goals of the course is to give you an opportunity to work through a topic of your choosing in depth, in order to experience some aspects of mathematical research. The final product will be a project that can take on several forms:

• Developing a detailed but approachable exposition of some known results that we will not cover in class.
• Writing code to implement some of the algorithms that we will discuss.
• Performing some calculations using a computer algebra system in order to make conjectures.
• Exploring an open problem.

In order to learn mathematics effectively, it is essential to constantly ask questions, to isolate which aspects of the material are unclear, and to make conjectures. To help develop these skills, I strongly encourage you to participate in class and also to bring questions to office hours. Furthermore, you should post (at least) one question a week to the Piazza discussion board. For example, you can ask whether a conjecture you have is true, how to overcome an obstacle in a proof, or why a definition takes the form it does. Please try to make your discussion board question as specific as you can. Instead of saying "I don't understand the proof of Theorem 2.4.3", try to explain why you are having difficulty with the proof, isolate where you are getting stuck, and ask a question that might help clarify your understanding. Posting one question a week to the Piazza discussion board is a baseline. The corresponding part of the grade will also incorporate participation in synchronous class sessions, answering questions on Piazza, and attending office hours.

Consult the general Grinnell College policy on Academic Honesty and the associated booklet for general information.

If you enjoy working in groups, I strongly encourage you to work with others in the class to solve the homework problems. If you do collaborative work or receive help form somebody in the course, you must acknowledge this on the corresponding problem(s). Writing "I worked with Sam on this problem" or "Mary helped me with this problem" suffices. You may ask students outside the course for help, but you need to make sure they understand the academic honesty policies for the course and you need to cite their assistance as well. Failing to acknowledge such collaboration or assistance is a violation of academic honesty.

If you work with others, your homework must be written up independently in your own words. You can not write a communal solution and all copy it down. You can not read one person's solution and alter it slightly in notation/exposition. Discussing ideas and/or writing parts of computations together on a shared document is perfectly fine, but you need to take those ideas and write the problem up on your own. Under no circumstances can you look at another student's completed written work.

You may look at other sources, but you must cite other books or online sources if they provide you with an idea that helps you solve a problem. However, you may not specifically look for solutions to homework problems, and you may not solicit help for homework problems from online forums.

I encourage students with documented disabilities to discuss appropriate accommodations with me. You will also need to have a conversation with, and provide documentation of your disability to, the Coordinator of Disability Resources, John Hirschman, located on the third floor of Goodnow Hall (x3089).

I encourage students who plan to observe holy days that coincide with class meetings or assignment due dates to consult with me as soon as possible so that we may reach a mutual understanding of how you can meet the terms of your religious observance and also the requirements for this course.