Capstone courses fulfills a writing requirement. When I wrote the syllabus for the course I put in a “final paper” as a way to include writing. As I tried to come up with reasonable topics to suggest for papers, I began to get the feeling that this assignment would turn into busy work that would not necessarily contribute to your mathematical education. So I have decided to alter the syllabus for the course. A final paper is no longer required.
In stead the writing component of the capstone will be fulfilled with homework. We will have two or three additional homework assignments, one of which will be an extended project homework like the one you have currently.
In view of this change, I will grade the remaining homework, including the outstanding project homework on a free particle in 1D, with an additional emphasis on mathematical writing. As you write up your proofs, remember that a proof is first of all an essay written in the English language. It is a technical essay that may employ mathematical symbols and equations, but all such should be surrounded by a wrapper of explanatory language.
Here are some more specific guidelines to help you:
- Adhere to standard rules of grammar and punctuation.
- Break each proof into paragraphs each of which has a limited number of ideas (preferably just one, though that is not always possible).
- Define non-standard symbols before you use them.
- Use words to explain an idea or a computation if doing so is clearer or easier than using symbols.
- Figure out what you want to write before you write it. Write a rough draft or an outline and then write up the assignment. Assemble the problems in the order assigned.
- Be neat. You may typeset the homework if that helps, but you do not have to. (Although I highly encourage you to learn the latex typesetting language if you plan a mathematical career).
Let me emphasize that this is not just so much busy work to fulfill a writing requirement. As you move on through a career in which you use your mathematics degree a challenging and difficult task that you will have over and over again will be to convey mathematical ideas to others. Your success may in fact be determined just as much by your ability to explain as your ability to come up with new ideas. So it behooves you to practice this skill now.