"Some infinities are bigger than other infinities" - Hazel Grace Lancaster, in "The Fault in Our Stars," by John Green

What is a vector space? Even though they are initial taught in the context of arrows in space, or with vectors being lists of numbers, the idea is much more general and far-reaching.

Exponentiating matrices, and the kinds of linear differential equations this solves.

What is a vector space? Even though they are initial taught in the context of arrows in space, or with vectors being lists of numbers, the idea is much more general and far-reaching.

Infinities come in different sizes. There's a whole tower of progressively larger "sizes of infinity". So what's the right way to describe the size of the whole tower?

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

This is an absolutely beautiful piece of math. It shows how certain ideas from topology, such as the mobius strip, can be used to solve a slightly softer form of an unsolved problem in geometry.

This is an absolutely beautiful piece of math. It shows how certain ideas from topology, such as the mobius strip, can be used to solve a slightly softer form of an unsolved problem in geometry.

What is a vector space? Even though they are initial taught in the context of arrows in space, or with vectors being lists of numbers, the idea is much more general and far-reaching.

How one of the introductory ideas in a field called "measure theory" can be thought of in terms of musical harnomy and dissonance.

Here's a talk that could literally change your life. Which career should I pursue? Should I break up -- or get married?! Where should I live? Big decisions like these can be agonizingly difficult. But that's because we think about them...

What happens when you multiply shapes?

This is an absolutely beautiful piece of math. It shows how certain ideas from topology, such as the mobius strip, can be used to solve a slightly softer form of an unsolved problem in geometry.

Imagine a workplace where people of all colors and races are able to climb every rung of the corporate ladder -- and where the lessons we learn about diversity at work actually transform the things we do, think and say outside the...

Can you produce a rational number by exchanging infinitely many digits of pi and e?

There are different sizes of infinity. It turns out that some are larger than others. Mathematician Kelsey Houston-Edwards breaks down what these different sizes are and where they belong in The Hierarchy of Infinities.

"Some infinities are bigger than other infinities" - Hazel Grace Lancaster, in "The Fault in Our Stars," by John Green

Using the fundamentals of set theory, explore the mind-bending concept of the "infinity of infinities" -- and how it led mathematicians to conclude that math itself contains unanswerable questions.

What happens if you multiply things that aren't numbers? And what happens if that multiplication is not associative?

In this math video lesson, students learn how to determine the approximate location of irrational square roots on a number line through a clearly modeled exemplar problem. The lesson begins by labeling the number line with perfect...

In this video I am going to highlight the top ten types of functions that students make mistakes with when finding the domain and range

In this video, we will define imaginary numbers and examine the complex number system.

In this video, we define rational expression, and find the domain of rational expressions.

In this video, we solve three absolute value inequalities. The first example is pretty standard, the second example are what I would call "exceptions," meaning that one has no solutions, and the other has all real numbers as its solutions