Homework 1

Please remember to include your name and the homework number (this is Homework 1) within the document. Some additional formatting instructions are in the syllabus. To summarize:

• Turn in your homework as a PDF with a filename like 584-Homework-<number>-<your last name>.pdf, e.g., 584-Homework-03-Smith.pdf
• Use a new page (\newpage) for each problem
• State which question you are answering and the actual question. Then, start your answer in a new paragraph
• Use environments such as proof and theorem (via \begin{proof}…\end{proof})
• Use 12pt option \documentclass[12pt]{amsart} and \linespread{2.4}.

Please find and use the LaTeX template uploaded to BlackBoard and/or course website.

This homework involves exercises from the Hassett textbook.

1. A.6 (Appendix A, page 244)
2. One of 1.2 or 1.3 (Chapter 1, page 8)
3. One problem from the list: 1.1, 1.4, 1.5, 1.6 (Most of them are about connections between ideal membership problems and solving linear systems in linear algebra, ranging from 1.1 which is fairly concrete to 1.5-1.6 that are a little more abstract. 1.5 uses the notation $V(f)$ which we haven’t talked about in class yet, but is explained in the textbook’s Chapter 1. 1.4 is also about a linear algebra connection, but it’s vector space dimension instead of solving linear systems.)

(I hope that you will at least think a little about all 7 of these problems and solve as many as possible. Turn in the best and/or most interesting ones you are able to solve.)

You are encouraged to work together on the homework!