Revised 2013-06-05 website TOC website index blog
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”.
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.
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
Abmath also has articles on certain mathematical topics:
Many of the important ideas about mathematics in this site are summarized in
Slogans in Purple Prose Displayed Like This
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.
new system consists of combining the use of several well-known applications and is only new to me, not to the world.
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.
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, particularly Math on the Web.
Intute math site
Gödel's Lost Letter and P=NP
E. Kowalski’s blog
The Math Less Traveled
Mathematics under the Microsope
News from the World of Maths
Richard Elwes' Blog
The Unapologetic Mathematician
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
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.
to Prove It: A Structured Approach.
Wells, Charles, Discrete
Mathematics Class Notes.
Wells, Charles, The Handbook of Mathematical Discourse. Infinity Publishing Company, 2003.
Zakon, Elias, Basic Concepts of Mathematics. Trillia Group, 2003. (This is an e-book based on a book written in 1973.)
Bagchi, Atish and Charles Wells, Varieties of Mathematical Prose(1997).
Bagchi, Atish and Charles Wells, Communicating Logical Reasoning PRIMUS (1998).
Charles Wells, Representations III: Rigor and Rigor Mortis (blog post).
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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