abstractmath.org 2.0
help with abstract math

Revised 2015-05-10      website TOC      website index   blog	


Who is this website for?

What is abstract math?


Other sources for math


Who is this website for?

Abstractmath.org is designed for people who are beginning the study of some part of abstract math. This includes:

Abstract math is my name for what is often called “higher math” or “pure math”.

Overview of the site

This website is a multiple-entry site with many cross-links. This overview will give you a start on finding out what is on it.

The four main parts of the website

These head pages explain the ideas of that part in more detail:

The languages of math


Understanding math

Doing math

Abmath also has articles on certain mathematical topics:




Purple prose

Many of the important ideas about mathematics in this site are summarized in

Slogans in Purple Prose Displayed Like This

Other things on this website

Background and Attitude: This article describes some of the thinking behind this website.  

Diagnostic examples: These examples illustrate some of the many kinds of difficulty people meet with when studying and doing abstract math. Each example gives links to the relevant sections of the website.

Gyre&Gimble: A blog that discusses new ideas I have about abstract math and language, some specifically related to abstractmath.org.

Discrete Mathematics Class Notes: An introduction to abstract math for computing science students based on some of the ideas of abstractmath.org.

Mathematica notebooks and CDF files: These are the sources for most of the diagrams, including interactive diagrams, in abmath and in the Gyre&Gimble posts.

Expository articles.

Other sources for math

Math sites

I provide links to other treatments of a specific topic at the point where they are discussed. These general links are particularly useful for learning about various aspects of math:

Mathematical Association of America

American Mathematical Society.

Math Forum

Math on the Web.


MathOverflow A question and answer site for professional mathematicians

MathStackExchange A question and answer site for people studying math at any level and professionals in related fields

$n$-Category Cafe

Planet Math

+plus magazine


Wolfram Alpha

Math Blogs

Explaining Mathematics

Gowers’s Weblog


Pat’s Blog

Plus Magazine Blog

Roots of unity

Visual Insight

Books on beginning abstract math

The books listed below are suitable for people beginning abstract math.  Except for the Handbook, they emphasize different aspects of abstract math from what this website emphasizes. 

Ash, Robert, A Primer of Abstract Mathematics.

Eugenia Chang, How to Bake Pi: An Edible Exploration of the Mathematics of Mathematics.

Hale, Margie, Essentials of Mathematics: Introduction to Theory, Proof and the Professional Culture.

Solow, Daniel, How to Read and Do Proofs : An Introduction to Mathematical Thought Processes. 

Wells, Charles, The Handbook of Mathematical Discourse. Infinity Publishing Company, 2003.

Articles and blog posts about abstract math

Bagchi, Atish and Charles Wells, Varieties of Mathematical Prose (1997).

Bagchi, Atish and Charles Wells, Communicating Logical Reasoning PRIMUS (1998).

Tao, Terry, There is more to mathematics than rigour and proofs.

Wells, Charles, Communicating mathematics: useful ideas from computer science. American Mathematical Monthly 102, 1995.

University courses containing abstract math

Courses that math majors must take typically include some of these:

All of them may involve abstract definitions and require doing proofs.


I am grateful to Case Western Reserve University for providing software and library privileges.

Creative Commons License

This work is licensed under a Creative Commons Attribution-ShareAlike 2.5 License.