The subject might be advanced mathematics of a kind only studied after a student has already taken a number of calculus courses but, the presentation is meant to be extremely approachable and easy to understand. One thing I have seen with many of the advanced undergraduate and post-graduate textbooks is that the authors seem more intent on showing off their vocabulary than ensuring the students can understand the material. Charles Wells, Professor Emeritus of Mathematics at Case Western Reserve University, refers to that type of writing as “heavy handed academic writing.”

Providing abstract math instruction in plain language has been a goal of Wells’ for some time. For over 32 years he kept notes on situations where students were having difficulty due to the language, or words, being used to explain concepts. He published *A Handbook of Mathematical Discourse* to be used like a dictionary where students could look up the “difficult words” while learning how to do abstract mathematics. A limited HTML version of the book is available on his site (click on his name at the top of the page) and a complete, printed version can be purchased on Amazon.

The website abstractmath.org is an extension of that book. On it, Wells continues to approach the material by making careful choices of the words he uses to describe things. He calls the material a “covert curriculum” in abstract math.

## Topics Covered on Abstractmath.org

- Attitude
- Diagnostic Examples
- The languages of math
- Glossary
- Proofs
- Understanding math
- Doing math
- Numbers
- Sets
- Functions
- Relations
- The unreliability of numerical evidence
- Finding factors, or not
- Sizes of infinity

I took a quick look at the glossary and I would strongly suggest anyone considering working with students at any level of mathematics to spend some time reviewing it.

View this Free Online Material at the source:

abstractmath.org