Notes on Reading and Writing Mathematics

Math 340

Spring 05

Notes on Reading and Writing Mathematics

Reading the Text:

Reading a mathematics text is an active process. Always read with a pencil or pen and paper. Continually ask yourself questions such as the following:

Try to anticipate where the text is going next. When you see an example, cover the text and spend a few minutes trying to solve the example yourself, and then read what the text has to say about it. Feel free to explore, “what would happen if…” questions, often you will anticipate what comes next in the text.
If you don’t understand something and can’t figure it out, move on. You might figure it out as you keep reading.
Feel free to email me questions you have reading the text or to bring them to class.
Do all practice problems. Answers to the practice problems are at the end of the section; in most cases, you’ll want to check the answers before you move on.

Writing Mathematics:

Make it clear what is the problem you solved or theorem you proved. You don’t have to copy the problem exactly from the book; you can incorporate it into your writing or use your own words, but five years from now, if you pick up your paper, it should be clear what you were doing or trying to do.
Use pictures, equations, tables, graphs, etc. to make your writing clearer.
Use complete sentences. Some of your verbs might be symbols, e.g. “Let x=3.”
If there’s a piece of your argument that is missing, admit it. It’s much better to turn in something that is partially solved, where you’re clear about what you have and have not done, than to turn in something partially solved, hoping I won’t notice what is missing.
You don’t have to type your assignments, but whether they are typed or hand-written, please double-space, so there is room for comments.