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A receiver operating characteristic (ROC) is a graph that illustrates the performance of a binary classifier as its discrimination threshold (cutoff) is changed.

The curve is created by plotting the true positive rate (TPR) against the false positive rate (FPR) at various cutoff settings. The true-positive rate is known as sensitivity, the false-positive rate is known as the fall-out and is calculated as (1 - specificity).

The ROC curve is thus a plot of the true positives (TPR) versus the false positives (FPR). The ROC curve can be generated by plotting the cumulative distribution function (area under the probability distribution from - ∞ to + ∞ ) of the correct detection probability in the y-axis versus the cumulative distribution function of the false-alarm probability in x-axis.

Mathematics is all around us, and it has shaped our understanding of the world in countless ways.

In 2013, mathematician and science author Ian Stewart published a book on 17 Equations That Changed The World. We recently came across this convenient table on Dr. Paul Coxon’s twitter account by mathematics tutor and blogger Larry Phillips that summarizes the equations.

A collection of functions for shaping and tweening signals in the range 0 to 1.

Beautiful math in all browsers.

A JavaScript display engine for mathematics that works in all browsers.

No more setup for readers. It just works.

This page points to a collection of mathematical quotations culled from many sources.