How to Read a Math Text

(Applicable to lower-division mathematics classes)

Art Duval

This is the transcription of a handout I made for my Calculus III class, Spring 2004. (I have used a similar handout in several calculus classes for several years now.) The "in-class reading exercise" is specific to how we used this in class one day. The "General Rules" are generally applicable to lower-division mathematics classes, say, pre-calculus through differential equations and matrix algebra (applied linear algebra).

Further background: A quick search on "How to read a math text" on Google turns up several promising pages. In the future, I plan to look through them to make recommendations.

General Rules

Make sure you have paper and a pen or pencil (and, if necessary, an appropriate calculator) handy! Then:
  1. Read one subsection at a time. Skim first, and then read it more seriously.
  2. For examples, cover up the solution, and try it yourself first. When you get stuck, try to uncover a little at a time, and then think about it more. Afterwards, make your own example.
  3. For displayed and boxed equations, ask what does each variable mean?
  4. For displayed and boxed definitions, try to construct an example.

Procedure for the in-class reading exercise

First, get a reading partner sitting near you. Now, for each subsection:
  1. Read silently for a minute or so (skim the material).
  2. Then, with your partner, take it about one paragraph at a time:
    1. Take turns asking each other what this paragraph means.
    2. At the examples, try to construct your own examples. (I will suggest restrictions and modifications, as necessary.)
    3. For each paragraph (or block of several paragraphs), agree what the most important point is, and take notes (as you would for a lecture) or highlight the text.
  3. Every five minutes or so, I'll pick random people to explain the part you've been reading.