next up previous
Next: Bibliography

How to read a math book

W. Stephen Wilson

The usual way. Practice.

First, make sure you have the prerequisites. Usually a textbook will tell you what they are in the introduction. Anyway, you'll find out soon enough if you don't have them. When/if that happens, go back and read the prerequisite book. (If you find you have to go all the way back to TERC (which will happen if you took TERC) then you are in trouble since they don't have a book.)

Assuming you have the prerequisites, then read a section or chapter. Most texts have a lot of problems at the end of each section/chapter. Usually they have the answers to the odd numbered problems at the end of the book. Work all the odd numbered problems and compare your answers with the answers at the back of the book. If you get a wrong answer then go back and read the chapter/section over again and work the problem again. Repeat until you get the problem right. This is easier than it sounds since when you reread the section you'll do it with the problem in mind.

When you've worked through one chapter/section and done all the problems correctly, then move on to the next section. Since most books start off with the easy stuff then you learn how to do this on the easy stuff and will be good at it by the time you get to the harder stuff.

If you find you MUST get help, then the appropriate help to get is to ask someone which page of the chapter you should read that will help you with the problem.

One of the main difficulties students have is knowing when they are NOT understanding something. The problems make this a self correcting issue. If they think they understood the chapter but can't work the problems then they didn't understand the chapter. (And, to some extent, if they thought they didn't understand but they can work all the problems then maybe they did understand.) One thing that isn't self-correcting: pay particular attention to the definitions. Think about them. Memorize them. Some day you'll want to talk about the material with other people and if you don't know the definitions (and understand them) then you can't.

Probably best to start with a math book that you know a good portion of already or one that you don't expect to be too difficult. Say you learned algebra from a sub-standard text. You know some algebra, read a good algebra text now.



 
next up previous
Next: Bibliography
W. Stephen Wilson
2004-03-22