This, therefore, is mathematics:
she reminds you of the invisible form of the soul;
she gives light to her own discoveries;
she awakens the mind and purifies the intellect;
she brings light to our intrinsic ideas;
she abolishes oblivion and ignorance which are ours by birth.
- Proclus (quoted in Morris Kline, Mathematical Thought from Ancient to Modern Times)
Mathematics can be broadly subdivided into the study of:

• Quantity (Arithmetic)
• Structure (Algebra)
• Space (Geometry)
• Change (Analysis)

Recently added pages for numbers and the Greek Alphabet. Other recent found things include Philosophy of Mathematics (also see below for other interesting things at plato.stanford.edu).

Now at MAA: The Euler Archive.

Some easy/interesting things to do are:

• Prove the irrationality of the square root of two ( √ 2  or 2^½)
• Derive the Pythagorean theorem using similar triangles
• Derive the law of sines
• Derive the trigonometric identity sin² + cos² = 1

Out in the blogosphere are Devlin's Angle, Bill the Lizard, Division by Zero and Math^(blog). Those blogs contain links to many others.

Mathematics Books Online

There is a site at http://www.cut-the-knot.org/ that the author calls "... for teachers, parents and students who seek engaging mathematics"; it has many interesting articles on math-related topics.The author has book recommendations, including a bookstore on Amazon; some of his favorite books are listed in the section titled Mathematical Delights.

A site called Question Corner was put together by the Math department of the University of Toronto, and answers questions such as "Why is e^πi = -1?" and "What is the Square Root of i?". Another site with a large amount of useful info is the blog Resonances, Waves and Fields, which has a fantastic set of pages on Eulers equation and complex numbers; it provides a detailed description on that topic and related things on following pages.

Some other items of interest:

• Mathematics Pronunciation Guide
• Descartes - day kahRt
• Euler - 'oy ler (rhymes with toiler)
• Galois - gal 'wah
• Gamow - ga muhf
• Fermat - fehr 'mah
• Lavoisier - lah vwahz 'yay
• Legendre - luh 'zhahn druh
• 50 Best Blogs for Math Majors
• Plus is an internet magazine which aims to introduce readers to the beauty and the practical applications of mathematics
• Math Pages
• The MacTutor History of Mathematics archive
• The History of the Calculus and the Development of Computer Algebra Systems
• An Elementary Introduction to Logic and Set Theory
• Cantor's Diagonal Proof
• Prime Numbers? Sacks Spiral (or Sacks Number Spiral) is quite intriging.
• The above link uncovered Natural Numbers: exploring the undesigned intelligence of the numberverse, and eventually led to NumberSpiral.com.
• Introduction to Group Theory
• The Feynman Lectures on Physics

There is also TONS of information on Wikipedia about math-related things, including discussion of injective, surjective and bijective functions. Some things are categorized, like the category page for large cardinals, and some things are just interesting (like E8) and can lead to interesting places.

Society-type links:

• American Institute of Mathematics (AIM)
• AIM Problem List
• American Mathematical Society (AMS)
• AMS Books Online
• AMS Bookstore
• AMS Math on the Web
• Mathematical Association of America (MAA)
• MAA Bookstore
• MAA Mathematical Sciences Digital Library

Ars longa, vita brevis, occasio praeceps, experimentum periculosum, iudicium difficile.

[The] art is long, life is short, opportunity fleeting, experiment dangerous, judgment difficult.

- Hippocrates
Not math, but I had to put these somewhere: Richard Feynman: The Messenger Series (on video) and Three Lectures by Hans Bethe. There are some interesting articles on the Stanford Encycolpedia of Philospohy, such as Information Processing and Thermodynamic Entropy, Philosophy of Statistical Mechanics and Boltzmann's Work in Statistical Physics.

Go to the home page of Dave, Donna Marie and Marissa Haskell

---

Last updated Monday September 1^st 2014