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Cartesian Faith

Category Archives: mathematics

A primer on universal function approximation with deep learning (in Torch and R)

September 23, 2016

Arthur C. Clarke famously stated that “any sufficiently advanced technology is indistinguishable from magic.” No current technology embodies this statement …

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Using Occam’s Razor to solve genius math puzzles

March 4, 2016

Math puzzles always tickle the brain, and this one has tickled quite a few on LinkedIn. Why are these puzzles …

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Modeling data with functional programming – lists

December 8, 2015

UPDATE: This draft is obsolete. Please see latest draft at The latest update of my book includes a chapter on …

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The Data-Driven Weekly #1.2

November 17, 2015

Last week witnessed a number of exciting announcements from the big data and machine learning space. What it shows is …

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Understanding a basis in linear algebra

July 29, 2014

Chapter 7 of Cherney, Denton, and Waldron begins by introducing the concept of a basis. The essence of a basis …

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How to stay 29 forever (and other secrets of math)

July 17, 2014

It’s a fact of life that we age. As we age, the more we wish we didn’t. What if I …

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The secrets of a linear world exposed

July 15, 2014

Like many concepts in mathematics, linearity has multiple interpretations and meanings. What do we mean when we say something is …

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Deducing the mechanics of matrix multiplication

July 13, 2014

For question 1.4.6 of Cherney, Denton, and Waldron, there is a question about how matrix multiplication works. Indeed, part (b) …

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Probability and Monte Carlo methods

December 15, 2013

This is a lecture post for my students in the CUNY MS Data Analytics program. In this series of lectures …

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Matrix factorizations and social network graph analysis

December 9, 2013

This is a lecture post for my students in the CUNY MS Data Analytics program. In this series of lectures …

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