Carnegie Mellon University, Department of Philosophy,
Spring 2001

The Nature of Mathematical Reasoning

Dirk Schlimm

Related links

Here are some links to web-pages which contain material related to the course.
If you find other links that you think should appear here, too, just tell me!

Early history of mathematics:

The cave of Lascaux. About 30000 year old paintings and drawings. Great website!

More pictures from Lascaux. Also links.

Newgrange, Ireland. Built around 3,200 BC.

Newgrange, Ireland. More pictures.

Stone Pages. Pictures and descriptions of neolithic stone circles, dolmens, standing stones, cairns, barrows and hillforts in Europe.

Neolithic Carved Stone Polyhedra. Believed to date to around 2000 BC, found in Scotland.

Axiomatic systems:

Euclid's Elements, very fun, with moving diagrams!

Spinoza's Ethics. You don't believe it, unless you see it.

Biographies, etc:

For biographies of mathematicians, this is the best resource on the web, the MacTutor History of Mathematics archive

Information concering Frege can also be found here.

Jeff Miller's pages on the earliest known uses of

... some of the words of mathematics, and

... various mathematical symbols are very interesting.

A nice explanation of deductive validity using a

thermos.

If you're interested in the history of mathematics in general, see

David Wilkins' pages on the History of Mathematics. It has tons of links!

What is mathematics, anyway?

A Gentle Introduction to the Mathematics Subject Classification Scheme

2000 Mathematics Subject Classification

Proofs:

Keith Lynn's proof that Pi is irrational

Jim Morey's interactive proof of the Theorem of Pythagoras

More proofs of the Theorem of Pythagoras

If you are curious about Descartes' ontological argument for the existence of God (Question 8 in the midterm exam), follow these links:

To look for books in the Pittsburgh libraries:

CMU Libraries

University of Pittsburgh Libraries

References:

The Language of First-Order Logic. The official website of CSLI

Philosophy section of CMU Library

For some advice on how to write a paper or how to cope with math axiety, look at:

Advice to research and writing, with many very useful links

Coping with math anxiety, a good resource.

Here are some links of general interest:

AddAll.com, finds you the cheapest online store for a particular book.

FreeStuff, has coupons for online stores.