"The Most Important Noog of Our Time" - Gilbert Strang

Gilbert Strang described the Fast Fourier Transform as "the most important numerical algorithm of our time".

The FFT samples a signal over time and divides it into its frequency components.

Cooley and Tukey are credited with the development of the FFT in its modern form although Gauss had developed his own methods in an unpublished work from 1805 (using it to interpolate the orbit of asteroids).

John Tukey was an American statistician who coined the term "bit"(a short form for "binary digit"). He and Cooley developed the FFT algo in 1965 while working at IBM.

Manchester-born Frank Yates (graduate of St John's College Cambridge and one of the pioneers of 20th Century statistics, known to A-level students for Yates Continuity Correction) also created something similar in 1932 which he called the interaction algorithm.

Modern FFT was developed in the context of processing sensor data and has become a leading algorithm in the art of digital signal processing.

Mathematician Marcus du Sautoy (Fellow of New College Oxford) also talks about it in his podcast on Fourier, on the BBC's podcast series A Brief History of Mathematics.

Introduction to Classification - The Spam Filter

A spam filter is a simple example of statistical classification, putting data into known categories.

Classification is a case of supervised learning - where a training set is provided with correctly identified observations. An algorithm that performs classification is called a classifier.

A simple class of classification algorithms is called Naive Bayes, which has been studied extensively since the 1950s.

Naive Bayes (NB) is a popular choice for text classification e.g. is this a novel versus is this a poem or an essay. It is also used in word sense disambiguation.

Discriminative Models (aka Conditional Models)

Discriminative models are also known as conditional models.  They are used in Machine Learning to model the dependence of unobserved variables on observed variables, modeled probabilistically using P(y|x), where y is the unobserved variable vector, and x is the observed variable vector.

What is Nonparametric Statistics?

"Conventional" statistics uses distributions and parameters like mean and variance.

"Nonparametric" statistics relies on being "distribution free" or using unspecified distribution parameters.

"Support Vector Machines" are a form of nonparametric statistics useful in machine learning. It is a "discriminative" classifier. 

Analytic Number Theory

Ah, so you've heard of the Riemann zeta function, have you not, and no doubt you will want to start programming with it, yes?  If so, read on!

To know it in its contemporary form, you should have a basic knowledge of complex analysis, including Cauchy's theorem and contour integration.   (Note that Euler studied this function earlier without complex analysis but his analysis was limited to the R-z as a function of real variable, rather than a complex variable).

A flavour of the subject can be found here and here (the latter addresses analytic number theory under the headline of multiplicative number theory). Prepare to be dazzled by the spectral theory of automorphic forms.

The Los Alamos Background to the GSL

The GSL project was initiated in 1996 by Los Alamos physicists Mark Galassi and James Theiler. 

GNU Cim is Open Source Simula

Want to do some Simula? Try the GNU Cim compiler. It is written in C and produces C which is passed to a C compiler to be translated to machine code. (Simula was developed in the 1960s as a simulation language at the Norwegian Computing Center (Norsk Regnesentral) in Oslo. It had two incarnations, Simula I and Simula 67).