
Preliminary Definitions and Theorems Two points in $E \impropersubset \R$ are rationally equivalent provided their difference belongs to $\Q$; this...

Preliminary Definitions and Theorems A countable collection of sets is ascending provided each set is a subset of the following...

Now that we’re familiar with what measurability is, there are couple other characterizations of measurability that we’ll be going over...

To remedy the predicament we found ourselves in the last post with the outer measure over the real numbers lacking...

To remedy the predicament we found ourselves in the last post with the outer measure over the real numbers lacking...

Now that we’re familiar with what measurability is, there are couple other characterizations of measurability that we’ll be going over...

I recently switched to an Android phone and have been immensely pleased so far, except with the new way Chrome...

Ideally we’d like to have these Lebesgue measurable sets with a Lebesgue measure set function, but it’s actually not possible...

In measure theory, we study ways of generalizing the idea of length, area, and volume. For example, certain functions aren’t...

Ideally we’d like to have these Lebesgue measurable sets with a Lebesgue measure set function, but it’s actually not possible...

In measure theory, we study ways of generalizing the idea of length, area, and volume. For example, certain functions aren’t...

Stationary distribution As stated in the introduction, a Markov chain is useful for representing stochastic systems because we can infer...

Stationary distribution As stated in the introduction, a Markov chain is useful for representing stochastic systems because we can infer...

Stochastic models have a variety of applications including Google’s Page Rank algorithm and reinforcement learning algorithms. These models can be...

Stochastic models have a variety of applications including Google’s Page Rank algorithm and reinforcement learning algorithms. These models can be...

An eigenvector of a transformation is a non-zero vector where its transformation is a scalar multiple of itself. This associated...

The inner product, denoted <>, on a vector space is a rule that accepts any two vectors and returns a...

The inner product, denoted <>, on a vector space is a rule that accepts any two vectors and returns a...

An eigenvector of a transformation is a non-zero vector where its transformation is a scalar multiple of itself. This associated...

Orthogonal vectors and sets Any two vectors are orthogonal if their inner product is equal to 0 and a matrix...

Coordinates and changing bases The coordinates of x relative to a basis B is the vector [x]B = c such...

Properties of a Basis A set of vectors, B, is a basis for a vector space is B is linearly...

Orthogonal vectors and sets Any two vectors are orthogonal if their inner product is equal to 0 and a matrix...

Coordinates and changing bases The coordinates of x relative to a basis B is the vector [x]B = c such...

Properties of a Basis A set of vectors, B, is a basis for a vector space is B is linearly...

The below is a review of linear systems, linear transformations, and the Rank Nullity Theorem. Linear transformations Let V and...

The below is a review of linear systems, linear transformations, and the Rank Nullity Theorem. Linear transformations Let V and...

Although linear models tend to be considered as a classical form of statistical modeling, it still remains to be widely...

The following is a review of linear dependence, the square matrix theorem, the rank nullity theorem, and the invertible matrix...

In the post, we talk about fields, vector spaces, and subspaces. Fields and vector spaces Suppose F is a nonempty...

The following is a review of linear dependence, the square matrix theorem, the rank nullity theorem, and the invertible matrix...

In the post, we talk about fields, vector spaces, and subspaces. Fields and vector spaces Suppose F is a nonempty...

For those who haven’t heard of LaTeX, it’s an awesome typesetting language typically used when writing mathematics. As I study...

For those who haven’t heard of LaTeX, it’s an awesome typesetting language typically used when writing mathematics. As I study...

This post contains links to Data Science related material that I wanted to keep track of. As such, this post...

Awhile ago, I had AWS set up to provide me a unique URL that I could navigate to and use...

Principal Components Analysis (PCA for short) is a technique used to reduce the dimensions of a data set. There are...

Vim is an amazing text editor and over the years has allowed me to be far more efficient when writing...

I needed to be able to add songs from my Spotify playlist to my Google Play Music playlist but since...

I know, trying to set up a deep learning environment on Windows isn’t exactly the first thought you have when...

Markov models are remarkably suited to mimicking the structure of a phenomenon and as a result, I thought it would...

Markov models are remarkably suited to mimicking the structure of a phenomenon and as a result, I thought it would...

Millions of Americans play the lotto each year as an innocent way to gamble their savings on winning some money...

Hypothesis testing is one of the most important tools in the sciences. It allows you to investigate a thing you’re...

Millions of Americans play the lotto each year as an innocent way to gamble their savings on winning some money...

Below is a collection of keyboard shortcuts using The ultimate vim configuration with these custom settings. As this is a...

Below is a collection of links that might be useful for a developer. It’s in its infancy at the moment...

Below is a compilation of command line tips that have helped me over the years. As this is a cheat...

Ok, we’re not dummies here, but dummy variables can be a tricky business for some. As a data scientist, you’re...