algebraic geometry a problem solving approach

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Posting one question a week to the Piazza discussion board is a baseline. 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. Please try to make your discussion board question as specific as you can.

#Algebraic geometry a problem solving approach how to

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. Furthermore, you should post (at least) one question a week to the Piazza discussion board. To help develop these skills, I strongly encourage you to participate in class and also to bring questions to office hours. 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. I will provide more information once we have developed the basic mathematical tools of the course.

Performing some calculations using a computer algebra system in order to make conjectures.

#Algebraic geometry a problem solving approach code

Writing code to implement some of the algorithms that we will discuss.

Developing a detailed but approachable exposition of some known results that we will not cover in class.

The final product will be a project that can take on several forms:

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. 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.

#Algebraic geometry a problem solving approach free

LaTeX is a wonderful free typesetting system which produces high-quality documents at the cost of only a small amount of additional work. I strongly recommend that you learn to type your solutions. 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. If you choose to extend the deadline of an assignment, you should send me an email by the usual due date. Throughout the semester, you may extend the deadline of at most two homework assignments by (up to) two days.Solutions to the homework will be posted to the course webpage.Homework will be graded using a basic check-plus, check, and check-minus system, but I will provide substantive comments.

#Algebraic geometry a problem solving approach pdf

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 is due at 5:00pm Grinnell time.Homework assignments will be due on most Tuesdays and Fridays, and will be posted to the course webpage. Continue to hone your perseverance in problem solving.Learn some important concepts of algebraic geometry, including polynomial rings (in several variables), Noetherian rings, ideals, varieties, Gröbner bases, and the Nullstellensatz.Develop an appreciation for how penetrating theoretical insights can lead to important computational tools.Continue to learn how to read mathematics with a critical and inquisitive mind, and articulate relevant questions during your study.Develop technical writing skills, including the ability to communicate abstract mathematical ideas clearly and elegantly.Abstract Algebra: Theory and Applications by Thomas Judson.Abstract Algebra by David Dummit and Richard Foote.A First Course in Abstract Algebra by John Fraleigh.If you do not have such a book, you can refer to my Course Notes from Fall 2020, or any of the following: In addition, I recommend keeping a general Abstract Algebra textbook nearby. Moreover, it provides some additional motivation for several of the topics we will study, and fills in many other connections between algebra and geometry that we will not have time to cover. We will not cover most of the material in this book (with the exception of Chapter 4, which overlaps with Chapter 4 of the above book), but it is well-organized, accessible to undergraduates, and has many nice problems. I also recommend the book Algebraic Geometry: A Problem Solving Approach by Garrity et al.

You can obtain a free electronic version through the Grinnell Library. We will mostly follow the book Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry by David A. Computational Algebraic Geometry Math 322 Computational Algebraic Geometry General Information