Math – Alicia’s Side Projects

Julia: Strogatz Figure 8.1.6

Figure 8.1.6 of Strogatz is an exmaple of a supercritical pitchfork, wherein a bifurcation happens that splits a single fixed point into 3 fixed points depending on the…

Julia: Strogatz Example 7.1.2

This document builds on Strogatz’s Example 7.1.2 of the van der Pol equation.

Julia: Strogatz Chapter 06 Examples

The following Julia packages will be needed for this document:

Julia: Strogatz Ch. 05 Examples

Chapter 5 in Strogatz, 3rd edition has many great phase portraits! In this post, I seek to make similar phase portraits in Julia to enhance my understanding of the material.

Julia: Multivariate Normal Distribution

Plot of multivariate normal distribution.

Julia: Metropolis Algorithm

Draw random samples from a distribution with the classic Metropolis algorithm.

Julia: Positive and Negative Definite Matrices

These functions implement the expression, which can calculate scalar quantities when given x1 and x2 components of a 2-element vector.

Python: Simple Gradient Descent

This is a simple polynomial gradient descent. It is a naive implmentation that is not optimized or vectorized. It is meant to be a simple demo on how gradient descent can be…

R: FFT with fftpipe

fftpipe is a package of functions that wrap around the base R fft() function. The fftpipe package enables workflows around the fft() function that use the pipe (%>%)…