Feb 17, 2019

## Numerical Algorithms for Computing Eigenvectors

The eigenvalues and eigenvectors of a matrix are essential accross the sciences. In this post I describe several simple iterative algorithms for computing eigenvector eigenvalue pairs, packed with as much geometric intuition as possible.

Mar 3, 2018

## Counterintuitive Properties of High Dimensional Space

Our geometric intuition developed in our three-dimensional world often fails us in higher dimensions. In this post I describe just a few phenomena of high dimensions, including escaping spheres, concentration of measure, and kissing numbers. All of these properties can be illustrated using basic mathematics.

May 17, 2013

## On Computable Functions

What does it mean for a function to be computable? This question captured the imagination of several incredible mathematicians in the early 20th century, and laid the foundation for the field of computer science. In this post I recall a bit of the history surrounding this question.