# Tertiary Catalogue

## Mathematics

### Test Statistics for One- And Two-Tailed Tests

Hypothesis Testing

When we run a hypothesis test, we can choose an upper-tail test, a lower-tail test, or a two-tail test, but it's really important that we make a conservative decision about the type of test we'll run. Once we pick our test type, then we'll...Show More

### Confidence Interval for the Difference of Means

Hypothesis Testing

We've done hypothesis testing around point estimates, like the mean or the proportion, but now we want to work a hypothesis test around the difference of two means. In this video we'll talk about how to build a confidence interval around the...Show More

### Matched-Pair Hypothesis Testing

Hypothesis Testing

Normally when we're looking at the difference of means, we're dealing with independent samples, samples that don't impact each other. But sometimes we'll want to do hypothesis testing with dependent samples. When this is the case, we can run a...Show More

### Hypothesis Testing for the Difference of Means

Hypothesis Testing

We've done hypothesis testing around point estimates, like the mean or the proportion, but now we want to work a hypothesis test around the difference of two means. In other words, sometimes we'll want to look at the difference between the means...Show More

### Hypothesis Testing for the Difference of Proportions

Hypothesis Testing

We've done hypothesis testing around point estimates, like the mean or the proportion, but now we want to work a hypothesis test around the difference of two means. In other words, sometimes we'll want to look at the difference between the...Show More

### Confidence Interval for the Difference of Proportions

Hypothesis Testing

We've done hypothesis testing around point estimates, like the mean or the proportion, but now we want to work a hypothesis test around the difference of two proportions. In this video we'll talk about how to build a confidence interval around...Show More

### Hypothesis Testing for the Population Proportion

Hypothesis Testing

In this video we'll look at how to run a full hypothesis test, from beginning to end, or a proportion, instead of a mean. We'll also consider what it looks like to run this as a one-tail test and as a two-tail test.

### Imaginary Interest Rates

Lockdown Math

Compound interest, e, and how it relates to circles.

### The Medical Test Paradox: Can Redesigning Bayes' Rule Help?

This video uses the medical test paradox to discuss likelihood ratios, which are also sometimes known as Bayes factors.

### What Makes the Natural Logarithm "Natural"?

Lockdown Math

A video all about the natural logarithm, ln(x).

### Trigonometry Fundamentals

Lockdown Math

Intro to trig with a lurking mystery about cos(x)^2.

### What Is Euler's Formula Actually Saying?

Lockdown Math

What does it mean to compute e^{pi i}?

Lockdown Math

Another view on the quadratic formula.

### Binomial Distributions

The binomial distribution, introduced as setup to talk about the beta distribution

### Logarithm Fundamentals

Lockdown Math

Back to the basics with logarithms.

### Complex Number Fundamentals

Lockdown Math

An introduction to the geometry of complex numbers.

### Doing Mathematics

Mathematician Ian Stewart, University of Warwick, describes his unexpected trajectory from abstract mathematical calculations in the back of an Austin Mini to developing a deeper understanding of how animals move, illustrating the breadth of...Show More

### Mathematics and the Real World

University of Warwick mathematician and bestselling author Ian Stewart describes how pure and applied mathematics can be combined to solve problems of the world around us.

### Mathematical Musings

Famed scientist and writer Freeman Dyson, Institute for Advanced Study, muses on Mathematical Platonism, choosing the analogy of Daniel Hillis' Songs of Eden to speculate that mathematics might have played a similar role for science that Hillis...Show More

### Altitude of a Triangle

Triangles and Their Properties

An example of a substitution reaction is halogenation in which alkanes such as methane react with halogens such as chlorine in the presence of heat or light to form chloromethane and hydrogen chloride.

### Equilateral and Isosceles Triangles

Triangles and Their Properties

A triangle in which all sides are of equal length and the measure of each angle is 60° is called an equilateral triangle. A triangle in which two sides are of equal length and the base angles are of equal measure is called an isosceles triangle.

### Sum of the Length of Two Sides of the Triangle

Triangles and Their Properties

The sum of the lengths of any two sides of a triangle is greater than the length of its third side.

### Medians of Triangle

Triangles and Their Properties

The medians of a triangle are the line segments that join each vertex of the triangle to the midpoint of its opposite side.