Proving the triangle inequality for vectors in Rn

Let's get our feet (and probably the rest of our body) wet in thinking in terms of vectors and spaces.

Definitions of the vector dot product and vector length

Let's get our feet (and probably the rest of our body) wet in thinking in terms of vectors and spaces.

Proving the associative, distributive and commutative properties for vector dot products.

Let's get our feet (and probably the rest of our body) wet in thinking in terms of vectors and spaces.

Proof: Relationship between the cross product and sin of angle between vectors

Let's get our feet (and probably the rest of our body) wet in thinking in terms of vectors and spaces.

Proof of the Cauchy-Schwarz Inequality

Let's get our feet (and probably the rest of our body) wet in thinking in terms of vectors and spaces.

Distance between a point and a plane in three dimensions

Let's get our feet (and probably the rest of our body) wet in thinking in terms of vectors and spaces.

Figuring out a normal vector to a plane from its equation

Let's get our feet (and probably the rest of our body) wet in thinking in terms of vectors and spaces.

Dot and Cross Product Comparison/Intuition

Let's get our feet (and probably the rest of our body) wet in thinking in terms of vectors and spaces.

2010 IIT JEE Paper 1 Problem 51 Distance Between Planes

Let's get our feet (and probably the rest of our body) wet in thinking in terms of vectors and spaces.

Introducing the idea of an angle between two vectors

Let's get our feet (and probably the rest of our body) wet in thinking in terms of vectors and spaces.

Determining the equation for a plane in R3 using a point on the plane and a normal vector

Let's get our feet (and probably the rest of our body) wet in thinking in terms of vectors and spaces.

Introduction to the cross product

Let's get our feet (and probably the rest of our body) wet in thinking in terms of vectors and spaces.

Variance as a measure of, on average, how far the data points in a population are from the population mean

Measures of central tendency and dispersion. Mean, median, mode, variance, and standard deviation.

Review of what we've learned. Introduction to the standard deviation.

Measures of central tendency and dispersion. Mean, median, mode, variance, and standard deviation.

Playing with the formula for variance of a population.

Measures of central tendency and dispersion. Mean, median, mode, variance, and standard deviation.

Simulation by Peter Collingridge giving us a better understanding of why we divide by (n-1) when calculating the unbiased sample variance.

Measures of central tendency and dispersion. Mean, median, mode, variance, and standard deviation.

Simulation by KA user tetef showing that dividing by (n-1) gives us an unbiased estimate of population variance.

Measures of central tendency and dispersion. Mean, median, mode, variance, and standard deviation.

Thinking about how we can estimate the variance of a population by looking at the data in a sample.

Measures of central tendency and dispersion. Mean, median, mode, variance, and standard deviation.

Reviewing the population mean, sample mean, population variance, sample variance and building an intuition for why we divide by n-1 for the unbiased sample variance

Measures of central tendency and dispersion. Mean, median, mode, variance, and standard deviation.

Ben Eater and Sal Khan talk through the Khan Academy Standard Deviation 1 Module

Measures of central tendency and dispersion. Mean, median, mode, variance, and standard deviation.