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17 posts tagged with Math *and* probability.

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## Calculus without limits

Hyperreal numbers: infinities and infinitesimals - "In 1976, Jerome Keisler, a student of the famous logician Tarski, published this elementary textbook that teaches calculus using hyperreal numbers. Now it's free, with a Creative Commons copyright!" (pdf—25mb :) [more inside]

## John Baez on the maths of connecting everyone (and everything) on earth

Network Theory Overview - "The idea: nature and the world of human technology are full of networks! People like to draw diagrams of networks. Mathematical physicists know that in principle these diagrams can be understood using category theory. But why should physicists have all the fun? This is the century of

*understanding living systems and adapting to life on a finite planet*. Math isn't the main thing we need, but it's got to be part of the solution... so one thing we should do is develop a unified and powerful theory of networks." (via ;)## Math with Bad Drawings

## When To Start Caring About the Powerball Jackpot

Walter Hickey at Business Insider looks at when you should buy a Powerball ticket and whether to take the lump sum or annuity if you win.

## direct realism

The Nature of Computation - Intellects Vast and Warm and Sympathetic: "I hand you a network or graph, and ask whether there is a path through the network that crosses each edge exactly once, returning to its starting point. (That is, I ask whether there is a 'Eulerian' cycle.) Then I hand you another network, and ask whether there is a path which visits each node exactly once. (That is, I ask whether there is a 'Hamiltonian' cycle.) How hard is it to answer me?" (via) [more inside]

## The mathematical modelling of popular games by Nick Berry

H _ _ _ m _ n, Y a _ _ _ e e, _ _ t t _ _ _ h i p, _ h u t _ s & L a _ _ e r _ , R _ _ k , _ _ n d y _ _ _ _ , and _ _ r t s.

## Monte Carlo

Conceptually talked about on MeFi previously, some basic Monte Carlo methods include the Inverse Transform Method (PDF) mentioned in the quoted paper, Acceptance-Rejection Sampling (PDFs 1,2), and integration with and without importance sampling (PDF).The year was 1945. Two earthshaking events took place: the successful test at Alamogordo and the building of the first electronic computer. Their combined impact was to modify qualitatively the nature of global interactions between Russia and the West. No less perturbative were the changes wrought in all of academic research and in applied science. On a less grand scale these events brought about a [renaissance] of a mathematical technique known to the old guard as statistical sampling; in its new surroundings and owing to its nature, there was no denying its new name of the Monte Carlo method (PDF).-N. Metropolis

## Two PDFs about PDFs

An "Exciting Guide to Probability Distributions" from the University of Oxford: part 1, part 2. (Two links to PDFs)

## Never tell me the odds.

Measure-theoretic probability: Why it should be learnt and how to get started. The clickable chart of distribution relationships. Just two of the interesting and informative probability resources I've learned about, along with countless other tidbits of information, from statistician John D. Cook's blog and his probability fact-of-the-day Twitter feed ProbFact. John also has daily tip and fact Twitter feeds for Windows keyboard shortcuts, regular expressions, TeX and LaTeX, algebra and number theory, topology and geometry, real and complex analysis, and beginning tomorrow, computer science and statistics.

## from complexity, universality

## Nontransitive dice

Nontransitive dice are sets of dice (A, B, C, etc.) with counterintuitive properties: die A beats die B and die B beats die C, but die C beats die A. [more inside]

## How reliable is DNA in identifying suspects?

A discovery leads to questions about whether the odds of people sharing genetic profiles are sometimes higher than portrayed. Calling the finding meaningless, the FBI has sought to block such inquiry.

## 15 bits of crypto should be enough for anybody

On May 13, security advisories published by Debian and Ubuntu revealed that, for over a year, their OpenSSL libraries have had a major flaw in their CSPRNG, which is used by key generation functions in many widely-used applications, which caused the "random" numbers produced to be extremely predictable. [lolcat summary] [more inside]

## Behind Door Number One...

The Monty Hall Problem has struck again, and this time it’s not merely embarrassing mathematicians. If the calculations of a Yale economist are correct, there’s a sneaky logical fallacy in some of the most famous experiments in psychology." The NY Times' John Tierney reports on new research into cognitive dissonance as examined through the famous Monty Hall Problem. [A previous MetaFilter thread about the Monty Hall Problem: Let's Make A Deal!]

## Cut The Knot

Interactive mathematics miscellany and puzzles, including 75 proofs of the Pythagorean Theorem, an interactive column using Java applets, and eye-opening demonstrations. (Actually, much more.)

## The Complexity of a Controversial Concept

The Logic of Diversity "A new book,

*The Wisdom of Crowds*[..:] by The New Yorker columnist James Surowiecki, has recently popularized the idea that groups can, in some ways, be smarter than their members, which is superficially similar to Page's results. While Surowiecki gives many examples of what one might call collective cognition, where groups out-perform isolated individuals, he really has only one explanation for this phenomenon, based on one of his examples: jelly beans [...] averaging together many independent, unbiased guesses gives a result that is probably closer to the truth than any one guess. While true — it's the central limit theorem of statistics — it's far from being the only way in which diversity can be beneficial in problem solving." (Three-Toed Sloth)## Let's Make a Deal!

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