Math 171 - Fundamental Concepts of Analysis - Spring 2013

Writing in the Major The assignment is to present a short (4-7 pages) readable and complete account of the normed vector spaces and the operator norm. You should first read and understand sections 69, 80 and 81 in the book, and also do problem 82.6. Then you should read these suggestions for content.

Target audience You should write your text for someone at a similar stage in a similar class (for example, someone in class who have not yet read this section. Ideally by someone in a similar class using a different textbook). For example, the target audience will already know what a group is, and your paper should not define that. The emphasis in this assignment is on the exposition (so don't think of this as "solving an exercise", or "finding the solution").

Typesetting: It is required that you typeset your WIM text, and it is strongly encouraged that you use LaTeX. If you have not yet learned how to use Latex, now is a good time (but in that case it would be a good idea to start right away, for example by typesetting your homework in Latex). Shotaro Makisumi has kindly prepared a template tex file to get you started.

Do: Write whole sentences in proper English. Make sure you define your notation ("Let G be a group and H a subgroup"...). Begin your text with a less technical introduction, with the purpose of giving the reader an idea of what is going to happen in the rest of the paper. Here you could explain what the construction is good foor, why is it interesting, how does it fit into the rest of the mathematics, etc. Proofread! (and maybe ask someone else to proofread too). When you proofread, try to imagine you're someone else who didn't just write the text (can be difficult), and notice which parts which are difficult to comprehend.

Don't: Use abbreviations or unnecessary symbols (you won't need symbols for "for all", "exists", "implies", "therefore").

Deadlines Submit a draft for comments May 17th Final text due May 30th.