Kevin Milans : Teaching : Fall 2013 Math545

Homework

General Guidelines and Advice

• All solutions require justification. When a formula is requested, it is not enough to provide the correct formula; you must also prove that your formula is correct.
• You may work on these problems with others in class, but the written solutions must be your own and you must understand everything you write under your own name.
• Using the course text is permitted. Using other resources (such as the internet, scholarly articles, and other texts) is not permitted, because this defeats the purpose of the assignment.
• Proofs must use complete sentences and proper punctuation, and they must be unambiguous. (If you, the author, do not completely understand every sentence and claim in your proof, then I won't either.)
• After finishing the first draft of your proof, read it back to yourself. Does it say exactly what you mean to say?
• Play with small examples to build your intuition; small examples are also great for checking whether a solution is potentially correct. Don't get discouraged if you have some difficulty solving these problems: the struggle is a necessary evil.
• If you would like to typeset your homework in LaTeX (highly recommended), you can add our solutions directly to the homework assignment source code (provided below). In addition to standard packages and tikz/pgf, you will need these home-grown style files: jeffe.sty, handout.sty, and kgm.sty.

Sage

• The recommended programming environment for computational questions is Sage.
• You may download sage to your computer, or you may establish a free account at http://www.sagenb.org/. Log in with your Google/Yahoo/etc ID using the Open ID system. (Your password is not shared with sagenb.org; see http://openid.net/get-an-openid/what-is-openid/ for more information.)