Posted on Wed 10 October 2018 in Data Science • Tagged with data science, python, NY Times
This is the second post in my ongoing series analyzing the restaurant reviews in the New York Times. In the previous post, we described how to use an API provided by the New York Times to download copies of that paper's recent restaurant reviews. In this post, we'll discuss how …
Posted on Wed 03 October 2018 in Data Science • Tagged with data science, python, NY Times
As a person who lives in New York City and is interested in food, I generally enjoy reading the restaurant reviews published by the New York Times. There is a new review of a restaurant in NYC roughly every week that includes a written review of the restaurant and, most …
Posted on Mon 01 October 2018 in Thesis • Tagged with thesis, quaternions, linear algebra
We're nearly ready to give the geometric interpretation of quaternionic multiplication that we've been working toward ever since we first defined the quaternions. Instead of considering the four-dimensional quaternions, we've spent the last few posts considering three-dimensional vectors, specifically discussing a product operation called the dot product that we can …
Posted on Wed 12 September 2018 in Thesis • Tagged with thesis, quaternions, linear algebra
Before the hiatus, we began discussing the geometry of vectors in three dimensions. At the end of that post, we discussed why it was impossible to define a multiplication operation on \(\mathbb{R}^3\) that also has an inverse (division) operation. However, there are still two useful "product" operations involving …
Posted on Tue 21 August 2018 in Misc
This blog has been on a long (and heretofore unannounced) hiatus as I completed my Ph.D. dissertation over the summer. But good news! Now that my dissertation has been defended, I'm ready to start posting again. Regular updates will resume soon.
Posted on Mon 30 April 2018 in Thesis • Tagged with thesis, quaternions, linear algebra
The previous posts in this series discussed two-dimensional vector geometry and how that geometry can be connected to the algebra of complex numbers. The main result is that the multiplication of complex numbers corresponds geometrically to rotations and dilations of the 2-dimensional plane.
As mentioned in an earlier post, this …
Posted on Thu 29 March 2018 in Finance • Tagged with finance, binomial-model, python
This post will be the last post, at least for the time being, in the series discussing the binomial model for pricing options. In the previous post we implemented this model in Python in order to find prices for basic European call options. In this post, we'll expand the implementation …
Posted on Fri 23 March 2018 in Thesis • Tagged with thesis, quaternions, complex numbers
In the previous post in this series, we introduced a geometrical interpretation of the complex numbers as vectors in the 2-dimensional plane. That post also explained the geometrical significance of the addition of complex numbers as vector addition. In this post, we'll see how to interpret the multiplication of complex …
Posted on Thu 15 March 2018 in Finance • Tagged with finance, binomial-model, python
In the previous posts in this series, we've described a model for stock price movements that can be used to find prices of simple European call and put options. The model works by dividing the life of the option into some number of discrete intervals, and assuming that the stock …
Posted on Wed 14 March 2018 in Thesis • Tagged with thesis, quaternions, complex numbers
In the previous post, we first encountered the quaternions, giving an essentially algebraic definition by defining a quaternion as a set of four real numbers and defining operations to add, subtract, multiply, and divide these quadruplets. But my thesis work is in geometry, not algebra, and so it still remains …