In the final two lectures of my differential equations class , I discussed how Dynamical Systems theory can be used to understand and describe the dynamics of cosmological solutions to Einstein’s field equations. Videos and lecture notes posted below: Lecture Notes:

# Category: Mathematics

By: Dr. Ikjyot Singh Kohli So, I came across this article today by Matt Moore on CBSSports, who basically once again has taken to the web to bash the Triangle Offense. Of course, much of what he claims (like much of the Knicks media) is flat-out wrong based on very primitive and simplistic analysis, and […]

It was pointed out to me recently that a few of the articles I have written describing the detailed geometric structure behind the triangle offense is scattered in various places around my blog, so here is a list of the articles in one convenient place: The Mathematics of Filling the Triangle (First article) Group Theory and […]

By: Dr. Ikjyot Singh Kohli As I write this post, the Knicks are currently 12th in the Eastern conference with a record of 22-32. A plethora of people are offering the opinions on what is wrong with the Knicks, and of course, most of it being from ESPN and the New York media, most of […]

I have now made a significant update to my applied machine learning paper on predicting patterns among NBA playoff and championship teams, which can be accessed here: arXiv Link .

Today, The Dow Jones Industrial Average (DJIA) surpassed the 20,000 mark for the first time in history. At the time of the writing of this posting (12:31 PM on January 25), it is actually 20,058.29, so, I am not sure if it will close above 20,000 points, but, nevertheless, a lot of people are crediting this […]

New #cosmology paper: https://arxiv.org/pdf/1609.01310.pdf Using a dynamical systems approach to provide a unifying framework for the AdS, Minkowski, and de Sitter universes. #physics #mathematics #science

In a previous post, I described the most optimal offensive strategy for the Knicks based on developing relevant joint probability density functions. In this post, I attempt a solution to the following problem: Given 5 players on the court, how can one determine (x,y) coordinates for each player such that the spacing / distance between each […]

In a previous article, I showed how one could use data in combination with advanced probability techniques to determine the optimal shot / court positions for LeBron James. I decided to use this algorithm on the Knicks’ starting 5, and obtained the following joint probability density contour plots: One sees that the Knicks offensive strategy […]

Where is Lebron James most effective on the court? Based on 2015-2016 data, we obtained from NBA.com the following data which tracks Lebron’s FG% based on defender distance: From Basketball-Reference.com, we then obtained data of Lebron’s FG% based on his shot distance from the basket: Based on this data, we generated tens of thousands of […]