abstractmath.org 2.0
help with abstract math

Revised 2014-12-19           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:

What is abstract math?

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

This list contains links to the head page of each of the four main parts of abstractmath.org.  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

Abstractmath 2.0

Some of the articles on abstractmath, including this one, are headed Abstractmath 2.0. These articles are new or new revisions of old articles using a much more efficient system of presenting math on the web. This represents a new start on abstractmath after several years of very little change. The reasons for this and the new system are discussed in my post Writing math for the web.

This new system consists of combining the use of several well-known applications and is only new to me, not to the world.

Other things on this website

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

Diagnostic examples:  These 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:  Most new ideas I have about abstract math and language, some specifically related to abstractmath.org, are posted on this blog.

Astounding Math Stories  is a blog containing short articles that are designed to Astound you with the Weird Things that Happen in Math.  Sh!  They also have an educational purpose.

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


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.


Planet Math

n-Category Café

+plus magazine


Math Blogs

Gowers’s Weblog



E. Kowalski’s blog



What’s New

Books on beginning abstract math

The books listed below are written 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. The Mathematical Association of America, 2003.

Bloch, Ethan D., Proofs and Fundamentals : A First Course in Abstract Mathematics, Springer, 2011. 

Exner, G.R., An Accompaniment to Higher Mathematics. Springer-Verlag, 1996.

Hale, Margie, Essentials of Mathematics: Introduction to Theory, Proof and the Professional Culture.  The Mathematical Association of America, 2003.

Solow, Daniel, How to Read and Do Proofs : An Introduction to Mathematical Thought Processes.  Wiley, 2009.

Velleman, Daniel J.  How to Prove It: A Structured ApproachCambridge University Press, 1994.

Wells, Charles, Discrete Mathematics Class Notes.  Case Western Reserve University, 1999.

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

Articles and blog posts about beginning 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.

Charles Wells, Representations III: Rigor and Rigor Mortis (blog post).

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.

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