Hyperreal numbers: infinities and infinitesimals - "In 1976, Jerome Keisler, a student of the famous logician Tarski, published this elementary textbook that teaches calculus using hyperreal numbers. Now it's free, with a Creative Commons copyright!" (pdf—25mb :) [more inside]
The power of math: 17 Equations That Changed the World - a one table summary of the book by Ian Stewart FRS. Business Insider gives its interpretation of the importance of each equation. Brain pickings (2012) on this book and equations, and another extract from the book. [more inside]
Why playing with algebraic and calculus concepts—rather than doing arithmetic drills—may be a better way to introduce children to math.
Geogebra is an interactive geometry tool which started as a free clone of Geometer's Sketchpad, but is now also an algebra, statistics and calculus tool. It is available for download for Windows, Mac, Linux, iOS and Android, or as a web app. [more inside]
"700 years ago, a monk needed parchment for a new prayer book. He pulled the copy of Archimedes' book off the shelf, cut the pages in half, rotated them 90 degrees, and scraped the surface to remove the ink, creating a palimpsest—fresh writing material made by clearing away older text. Then he wrote his prayers on the nearly-clean pages." - A Prayer for Archimedes
Neil Degrasse Tyson waxes eloquent about Isaac Newton [chopped YouTube link, full length video 'SciCafe: Life the Universe and Everything' here] [more inside]
How To Fold a Julia Fractal. A beautiful interactive introduction to complex numbers, fractals and waves. (Requires WebGL). To Infinity And Beyond is a similar introduction to calculus.
Every film Pixar has produced has landed in the top fifty highest-grossing animated films of all time. What's their secret? Mathematics. Oh, and 22 Rules of Storytelling. [more inside]
There were ways to find the tangent to a curve, and the area under one, in an ad hoc manner before the birth of calculus. It was even known that these two were inverses of each other.
Microsoft Mathematics is a free Computer Algebra System (CAS) available from Microsoft. A CAS is a program that can solve purely symbolic mathematical equations. For example, the program can tell you that the derivative of 6x^2 + 12x is 12x + 12. The program has functions for calculus, statistics, linear algebra, and graphing. One interesting feature of the program is that in some cases it can show and describe the intermediate steps involved in solving an equation. Here’s a 16 page tutorial (in MS Word docx format) showing how to use the program. The program can be downloaded from the Microsoft download page. Thirty-two and sixty-four bit versions are available. The program only works on XP/Vista/Windows 7.
'Stand and Deliver' teacher dies of cancer. Jaime Escalante, the math teacher portrayed in the 1988 film "Stand and Deliver," died Tuesday after a battle with cancer, according to the actor who played him. ... "Stand and Deliver" told the inspirational story of how Escalante turned the failing calculus program at Garfield High School in east Los Angeles into one of the top in the nation. (previously)
The Calculus Lifesaver lectures -- videos available here in streaming (Real Player), mp4 and wmv formats -- were originally given as "review sessions for the Princeton introductory calculus courses MAT103 and MAT104 during the 2006/7 academic year". Each lecture is about 2 hours.
Calculus of Averages - Newton and Archimedes did not possess this knowledge. No mathematics professor today can provide this knowledge and depth of understanding. Author John Gabriel maintains a blog, Friend of Wisdom, and contributes articles such as Are real numbers uncountable? to Google's Knol project.
MathTV is a real problem solver for many. It is also found on YouTube, and is free. Here is some background.
The Mechanical Universe...and Beyond is a critically-acclaimed series of 52 thirty-minute videotape programs covering the basic topics of an introductory university physics course. This well produced and highly informative 52 episode series, hosted by David Goodstein of Caltech, is available as Video on Demand (Note: simple registration required to view videos). [more inside]