You've heard of E=mc2... but you probably haven't heard the whole story.

What is the derivative of a^x? Why is e^x its own derivative? This video shows how to think about the rule for differentiating exponential functions.

In the card game SET, what is the maximum number of cards you can deal that might not contain a SET?

How to think about implicit differentiation in terms of functions with multiple inputs, and tiny nudges to those inputs.

How do you think about the column space and null space of a matrix visually? How do you think about the inverse of a matrix?

The enigmatic equation e^{pi i} = -1 is usually explained using Taylor's formula during a calculus class. This video offers a different perspective, which involves thinking about numbers as actions, and about e^x as something which turns...

What is the derivative of a^x? Why is e^x its own derivative? This video shows how to think about the rule for differentiating exponential functions.

How do you think about the column space and null space of a matrix visually? How do you think about the inverse of a matrix?

In this video Paul Andersen explains that the angular momentum of a system will be conserved as long as there is no net external torque. Both point objects and extended objects are covered along with several examples.

Logarithms are confusing, but perhaps some alternate notation could make them more intuitive.

There is a proof for Brouwer's Fixed Point Theorem that uses a bridge - or portal - between geometry and algebra.

You've heard of E=mc2... but you probably haven't heard the whole story.

If you needed to tell someone what numbers are and how they work, without using the notion of number in your answer, could you do it?

In this video Paul Andersen explains how the angular momentum of an object if a product of the rotational inertia and the angular velocity. The rotational inertia depends on the mass, radius and shape of the rotating objects. A sample...

In this video Paul Andersen explains how thermodynamic and equilibrium reasoning can be related through changes in free energy and the equilibrium constant. When the delta G is negative the reaction shifts to the right or favors...

Using the harmonic series we can build an infinitely long bridge. It takes a very long time though. A faster method was discovered in 2009.

In this tutorial I show how I synthesized the sound of hydrogen for the "Sound of Hydrogen" video using mathematica - it's a little technical, but you've been requesting it!

Can folding a piece of paper 45 times get you to the moon? By seeing what happens when folding just one piece of paper, we see the unbelievable potential of exponential growth. This lesson will leave you wanting to grab a piece of paper...

How do you think about the column space and null space of a matrix visually? How do you think about the inverse of a matrix?

In this video Paul Andersen explains how the wave speed measure the speed of a wave through a medium. The medium determines the speed of the wave. The velocity of the wave is equal to the product of the wavelength and the frequency of...

Psyche was born so beautiful that she was worshipped as a new incarnation of Venus, the goddess of love. But human lovers were too intimidated to approach her, and Apollo recommended her father abandon her on a crag where she would marry...

In this video Paul Andersen explains how the continuity equation is an application of conservation of matter in a fluid. The continuity equation may apply to either mass or volumetric flow. Example problem and examples are included.

In this video Paul Andersen explains how light that is perfectly reflected creates specular reflection. The angle of the incident ray is equal to the angle of the reflected ray. Specular reflection is also known as mirror-like...

In this video Paul Andersen explains how light can be refracted, or bent, as it moves from one medium to another. The amount of refraction is determined by the angle of incidence and the index of refraction. Snell's Law can be used to...