I wrote my Masters Thesis on Probability inequalities. This short gist is some notes I wrote up to help me remember the basics of probability inequalities. You may find it useful.

# Tag: mathematics

## Interview with a Data Scientist: Peadar Coyle

Peadar Coyle is a Data Analytics professional based in Luxembourg. His intellectual background is in Mathematics and Physics, and he currently works for Vodafone in one of their Supply Chain teams. He is passionate about data science and the lead author of this project. He also contributes to Open Source projects and speaks at EuroSciPy,… Continue reading Interview with a Data Scientist: Peadar Coyle

## Book Review: Analytics in a Big Data World

So this is a quick review of a book that ended up in my mailbox a few months ago. Firstly the good: this is a good academic introduction to a variety of techniques all in one reference book. I particularly liked the discussion of Process mining and survival analysis as I feel these are techniques… Continue reading Book Review: Analytics in a Big Data World

## Markov Chains and Monte Carlo Algorithms

1. General state space Markov chains Most applications of Markov Chain Monte Carlo algorithms (MCMC) are concerned with continuous random variables, i.e the corresponding Markov chain has a continuous state space S. In this section we will give a brief overview of the theory underlying Markov chains with general state spaces. Although the basic principles… Continue reading Markov Chains and Monte Carlo Algorithms

## Transfinite Induction

\maketitle 1. Introduction This is supposed to be a primer inspired by a piece by Hilbert Levitz. The theory of transfinite ordinals is a part of set theory. While the concept is tied up with the completed infinite and high cardinalities, we’ll emphasize more constructive aspects of the theory. There have been applicatons of constructive… Continue reading Transfinite Induction

## Information Retrieval

Attention conservation notice: 680 words about Information Retrieval, and highly unoriginal. The following is very much inspired by a course by Cosma Shalizi but I felt it was worth rewriting to get to grips with the concepts. This is the first of what is hopefully a series of posts on ‘Information Retrieval’, and applications of… Continue reading Information Retrieval

## Category theory and information

I often think about information. http://math.mit.edu/~dspivak/informatics/pure/ is a fascinating research project by the excellent David Spivak. Who I believe was a student of Jacob Lurie. I wonder how important Category theory will be.

## Yang Mills

To define the Yang-Mills Lagrangian, we need to define the ‘Trace’ of an End(E) valued form. Recall that the Trace of a matrix is the sum of its diagonal enTries. The Trace is independent of the choice of basis – an invariant notion that is independent of the choice of basis. A definition of the… Continue reading Yang Mills

## On Academic talks

Cosma Shalizi, has an excellent talk on Academic talks.

I suggest one reads it.

I merely quote my favourite part:

- The point of the talk is not to please
*you*, by reminding yourself of what a badass you are, but to tell your audience something useful and interesting. (Note to graduate students: It is important that you internalize that you are, in fact, a badass, but it is also important that then you move on. Needing to have your ego stroked by random academics listening to talks is a sign that you have not yet reached this stage.) Unless something matters to your actual message, it really doesn’t belong in the main body of the talk. - You can stick an arbitrary amount of detail in the “I’m glad you asked that” slides, which go
*after*the one which says “Thank you for your attention! Any questions?”. - You also can and should put all these details in your paper, and the people who really care, to whom it really matters, will go read your paper. Once again, think of an academic talk as an extended oral abstract.

Internalise that you are in fact a bad ass. I wish more Professors gave advice like that.

## Notebooks: Generalized Functions and PDE

In the style of Cosma Shalizi’s notebooks I’m including some links to things that I’ve read recently. This little one is written about PDE, Generalized Functions and Differential Equations. Historically generalized functions were first used in Physics by Heaviside and Dirac. Schwartz the great analyst came along and added rigour. Introduction to Generalized Functions with… Continue reading Notebooks: Generalized Functions and PDE