How to Read Math Texts

Even so much as a glance at page of a math textbook will immediately suggest that mathematical text is something quite different from most other kinds of text.

Read the article How to Read Mathematics by Shai Simonson and Fernando Gouvea. Take time (as per the instructions!) to read this very carefully and apply what you are learning. An hour or two spend at this will greatly increase the learning you'll be able to achieve with your textbook, and save you a good deal of frustration, too.

Of course, as you are doing this you will be writing mathematics. This should be considered as part of your note-taking; see the page on How to Take Notes

Hints

Here are some specific tips on how to implement some of the suggested reading protocols.

Whenever you see a definition

Pull it apart into its logical propositions and clearly identify the way in which these are combined.

What is being defined? What is it defined in terms of? How are these related to things you already know about?

Identify the main grammatical parts of speech (nouns, verbs, adjectives, adverbs)

Ask yourself why each condition in the definition is there. What would change if you were to omit one?

Construct examples of the thing that is being defined.

Construct non-examples

For example, if the definition tells us what a "fneefnek" is, then look for things that are not fneefneks. This will generally involve negating the proposition.

Whenever you see a theorem

Pull it apart into its logical propositions and clearly identify the way in which these are combined.

Identify the hypotheses (pre-conditions) and the conclusion(s).

Determine why each hypothesis is necessary

Find (construct) several different examples of situations for which the theorem is true, and others for which it is false.