Calculus has provided humanity a window into the inner workings of the world around us since the fateful day Isaac Newton got conked by a falling apple. But we've only ever really applied these ...

In the Idea of Limits video, we introduce the idea of limits and discuss how it underpins all of the major concepts in calculus. In the Limit Laws video, we introduce the limit laws and discuss how to ...

Calculus is a branch of mathematics that explores variables and how they change by looking at them in infinitely small pieces called infinitesimals. Calculus, as it is practiced today, was invented in ...

THIS little book deserves hearty welcome from those who are engaged in leading forward students to the higher mathematics; not so much as a substitute for any other work at present in use, but as ...

Graphs of Sine and Cosine 1.2 An applet illustrating how the graphs of sine and cosine are related to the unit circle. Transformations of Functions 1.3 An applet illustrating how transformations ...

In the late 19th century, Karl Weierstrass invented a fractal-like function that was decried as nothing less than a “deplorable evil.” In time, it would transform the foundations of mathematics.

The earliest known examples of mathematical and geometric astronomy have been identified in a series of ancient Babylonian cuneiform tablets. Five ancient Babylonian clay cuneiform tablets calculate ...

How the ultra-cooperative behavior of ants, bees and other social insects could have evolved continues to challenge formal analysis. But a new theory that includes hedging bets against nature’s ...