Reading mathematics

The following resources are about reading mathematics to understand it.

Resources for students

  • Terry Tao’s blog What’s New has a section On Writing with a subsection on reading writing.
  • Stewart, I., “How to Learn Math,” Letters to a Young Mathematician, Basic Books, 2006, pp. 62-70. (AMS Book Review)
    This letter is from a wonderful collection of letters from a mathematician to “Meg,” as she progresses from a high school student wondering whether higher levels of math are anything more than “bigger numbers and harder calculations,” to a tenured professor. The letters are unerringly encouraging while explaining myriad aspects of what it’s like to be a mathematician. The letter, “How to Learn Math,” is to Meg when she is a college student and explains what to do to get past sticking points when reading. The author also advises Meg to “read around the subject” to gain a sense of the larger picture within which any subject fits.
  • Gerver, R., “Reading and Keeping a Research Journal,” Writing Math Research Papers: A Guide for Students and Instructors Key Curriculum Press, 2004.
    This book chapter provides guidance for reading the literature relevant to a research project. Subsections include “Preparing to Read,” “Reading and Taking Notes,” and “Conquering Difficult Concepts.”
  • How to Read Mathematics” by Shai Simonson and Fernando Gouvea
    Provides advice such as “don’t miss the big picture” and “make the idea your own” and illustrates how this advice can be applied to an example of mathematical writing. From Rediscovering Mathematics by Shai Simonson.
  • See also the resources for teachers below, some of which include resources for students.

Resources for teachers

An assignment and class discussion

Encourage students to read critically: not all mathematics is written well. Students can learn much about how to write mathematics by noticing what does and doesn’t work well for them as readers.

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