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Month: November 2017

A Note on Russell’s Paradox

A Note on Russell’s Paradox

Topics in mathematics very frequently rely on set theory (I am hard-pressed to quickly think of one that doesn't). Set theory itself is a very abstract area of study. Even so, mathematicians built it on axioms (self-evident truths taken as fundamental starting points), and, of course, debate continues to this day as to which axioms…

Welcome to GF(4)

Welcome to GF(4)

Everyone has solved some version of a linear system in either high school or college mathematics. If you've been keeping up with some of my other posts on algebra, you know that I'm about to either take something familiar away, or twist it into a different form. This time is no different; we're going to…

On Permuted First-Kind Dependence of Categorical Random Variables

On Permuted First-Kind Dependence of Categorical Random Variables

  This paper discusses the notion of horizontal dependency in sequences of first-kind dependent categorical random variables. We examine the necessary and sufficient conditions for a sequence of first-kind dependent categorical random variables to be identically distributed when the conditional probability distribution of subsequent variables after the first are permuted from the identity permutation used…

A Partition by any Other Name

A Partition by any Other Name

I promise I'm actually a probability theorist, despite many of my posts being algebraic in nature. Algebra, as we've seen in several other posts, elegantly generalizes many things in basic arithmetic, leading to highly lucrative applications in coding theory and data protection.  Some definitions in mathematics may not have obvious "practical use", but turn out to yield theorems and results so…

Time Series Analysis Part 1: Regression with a Twist

Time Series Analysis Part 1: Regression with a Twist

We're surrounded by time series. It's one of the more common plots we see in day-to-day life. Finance and economics are full of them - stock prices, GDP over time, and 401K value over time to name a few. The plot looks deceptively simple; just a nice univariate squiggle. No crazy vectors, no surfaces, just…

Commentary: Infrastructure Considerations for Machine Learning

Commentary: Infrastructure Considerations for Machine Learning

Welcome to another brief commentary and departure from the heavier mathematics. I have been endeavoring to expand the breadth of my knowledge on the tech side of things, and chronicling some things I've learned and observed from speaking with different companies, both as an independent and as a Tech Field Day delegate. Many of these…