Jeromy Anglim's Blog: Psychology and Statistics

Thursday, January 14, 2010

Tips on Reading Mathematics for the Non-Mathematician

This post provides a few tips on reading a mathematics text book or other mathematical material such as a journal article that includes mathematics. In particular I wrote this post for social science researchers with less training in mathematics but who are otherwise motivated to learn mathematical material. It also offers useful links to other guides on reading mathematics.

Choosing a Text Book

Students studying a mathematics subjects are typically prescribed a text book. However, for independent social science researchers the required book is often less clear. Common scenarios include: (a) you are reading a journal article and it uses a mathematical or statistical technique and you want to learn more about it; (b) you are considering applying a technique in a research project and want to learn more; or (c)  you are doing a statistics course that smooths over some of the details on implementation and you want to understand these details. When choosing a text book, relevance, clarity, and an appropriate level of sophistication is required.


Does the chosen book align with your learning goals? Does it go into the appropriate degree of depth for your needs?

Clarity of presentation:

Some books are just better than others. Also, some may be written with your particular applications and concerns in mind. For example, there are many mathematics books written with the social scientist in mind. They often make fewer assumptions about background mathematical knowledge and present relevant applications.

The right level of sophistication:

This depends on your prior knowledge. Most mathematics textbooks will list the assumed knowledge in the preface or in an introduction. Failing that a look at the first few pages will tend to reveal whether the book is too sophisticated.

If a book is too sophisticated, you are confronted with the choice of whether it is worth acquiring the prerequisites to understand it. If you decide the book is worth reading, you must then ascertain what such prerequisites are and work out a means of acquiring them. This assumes some knowledge of the hierarchical dependencies between mathematical topics. I have previously posted on this in relation to a sequence of videos and textbooks related to learning statistics. A knowledgeable adviser can also assist in setting a sequence of self-study.

Once a textbook has been selected, there is the question of how to read the material in order to acquire the desired skills and knowledge.

Active Reading

Reading mathematics is different to reading other material. The following are a brief set of suggestions. The subsequent links should supplement this list.
  • read with a pen and paper
  • do provided problems
  • create problems and do them
  • work slowly monitoring comprehension
  • structure the material; identify core concepts and interrelationships
  • identify material that is not understood and devise methods to learn it
  • learn to read the symbols:
    Learn how to pronounce the symbols: I previously posted on links for looking up the pronunciation of mathematical symbols.
    Learn what the symbols means: Learn how to use them, manipulate them. Learn their conceptual importance.
  • learn key terminology

Additional Online Resources

The following links provide additional tips on reading mathematical material.

Additional Off line Resources

  • Section 1.2 of The Princeton Companion to Mathematics has an well-written and accessible discussion of the language and grammar of mathematics.

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