# Probability Spaces: An Illustrated Introduction

Using pictures to explain the idea of Probability Spaces in Rigorous Probability Theory

# Measure Theory for Probability: A Very Brief Introduction

In this post we discuss an intuitive, high level view of measure theory and why it is important to the study of rigorous probability.

# The Riemann Integral

The Fundamental Theorem of Calculus is a beautiful thing, but it fails to describe some very simple integrals. In this post we look at how the Riemann Integral can solve some of these problems.

# Programming the Fundamental Theorem of Calculus

In this post we build an intuition for the Fundamental Theorem of Calculus by using computation rather than analytical models of the problem.

# How Big is the Difference Between Being 90% and 99% Certain?

People often discuss the idea of being "90% certain" or "99% sure that this is true", but how big is the difference between these two values? It turns out that the difference between these values is similiar to the difference between having $10 and$100 in your wallet.

# Rejection Sampling and Tricky Priors

We have looked at working with a variety of analytical priors, but how can you sample from a prior probability that is not so mathematically pleasant to work with? In this post we learn about Rejection Sampling as one method of solving this problem.