Math

Academic researchers have improved wireless bandwidth by an order of magnitude”not by adding base stations, tapping more spectrum, or cranking up transmitter wattage, but by using algebra to eliminate the network-clogging task of resending dropped packets of data. By providing new ways for mobile devices to solve for missing data, the technology not only eliminates this wasteful process but also can seamlessly weave data streams from Wi-Fi and LTE”a leap forward from other approaches that toggle back and forth. ”Any IP network will benefit from this technology,” says Sheau Ng, vice president for research and development at NBC Universal. ...

The world of game theory is currently on fire. In May, Freeman Dyson at Princeton University and William Press at the University of Texas announced that they had discovered a previously unknown strategy for the game of prisoner’s dilemma which guarantees one player a better outcome than the other. That’s a monumental surprise. Theorists have studied Prisoner’s Dilemma for decades, using it as a model for the emergence of co-operation in nature. This work has had a profound impact on disciplines such as economics, evolutionary biology and, of course, game theory itself. The new result will have impact in all these areas and more. The game is this: imagine Alice and Bob have committed a crime and are arrested. The police offer each one a deal–snitch and you go free while your friend does 6 months in jail. If both Alice and Bob snitch, they both get 3 months in jail. If they both remain silent, they both get one month in jail for a lesser offence. What should Alice and Bob do? ...

Autism may be associated with mathematical skills. Autism researcher Simon Baron-Cohen has published studies that autism is more prevalent in the familes of physicists, engineers, and mathematicians. Unusual mathematical skills are reported in a small percentage of cases of ”classic autism.” Movies, television, and popular culture such as Rainman (1988), Mercury Rising (1998), and many other works often play up this rare association by presenting autistic characters with extreme mathematical abilities. It has frequently been suggested that various scientists and mathematicians including the Nobel Prize winning physicist Paul Dirac, the Russian mathematician and Fields Medal refuser Grigori Perelman, and Fields Medal winner Richard Borcherds have had or have Asperger’s Syndrome, now included in the autism spectrum. Vernon L. Smith who won the Nobel Prize for Economics in 2002 has stated that he has Asperger’s Syndrome. Wired Magazine popularized the notion of an association of Asperger’s syndrome and autism with computer technology and math in the article The Geek Syndrome by Steve Silberman. ...

In every decent programmer’s toolbox lies a strange weapon called a Radix Sort. Where does it come from ? Who invented it ? I don’t know. As far as I can remember it was there, fast, easy, effective. Really effective. So unbelievably useful I’ve never really understood why people would want to use something else. The reasons ? Most of the time, they tell me about floats, negative values, and why their new quick-sort code rocks. Enough, I’m tired. Although the standard Radix Sort doesn’t work very well with floating point values, this is something actually very easy to fix. In this little article I will review the standard Radix Sort algorithm, and enhance it so that : it sorts negative floats as well it has reduced complexity for bytes and words it uses temporal coherence it supports sorting on multiple keys ...

El algoritmo de Dios es un término que surgió en la búsqueda de aquel algoritmo que indicara los pasos mínimos que resuelven un cubo de Rubik cualquiera. El término se usa profusamente, no sólo para el cubo de Rubik. Mucho antes de conocer dicho término, cuando me encontraba con diversos tipos de problemas, ya me asaltaba recurrentemente una pregunta irrelevante (para el caso que me ocupaba), pero que espero te haga pensar un poco en la importancia de algunas cuestiones que quizás no conoces: ”¿Qué solución daría Dios si fuera él quien resolviera el problema?” Lo más sorprendente quizás, es que ”las soluciones de Dios” no sólo no están vedadas al intelecto humano, sino que son numerosas y prolíficas. Veamosló. ...

Maurits Cornelis Escher es un artista holandés nacido en la ciudad de Leeuwarden, Países Bajos, el 17 de junio de 1898, mejor conocido por sus grabados en madera, xilografías y litografías que tratan sobre figuras imposibles, teselados y mundos imaginarios. Su obra experimenta con diversos métodos de representar (en dibujos de 2 ó 3 dimensiones) espacios paradójicos que desafían a los modos habituales de representación. No fue precisamente un estudiante brillante, y sólo llegó a destacar en las clases de dibujo. En 1919, bajo presión paterna, empieza los estudios de arquitectura en la Escuela de Arquitectura y Artes Decorativas de Haarlem, estudios que abandonó poco después para pasar como discípulo de un profesor de artes gráficas, Jessurum de Mesquitas. Con él, adquirió unos buenos conocimientos básicos de dibujo, y destacó sobremanera en la técnica de grabado en madera, la cual llegó a dominar con gran maestría. ...

This document is a gentle introduction to computational number theory. The plan of the paper is to first give a quick overview of arithmetic in the modular integers. Throughout, we will emphasize computation and practical results rather than delving into the why. Simple programs, generally in JavaScript, are available for all of the algorithms mentioned. At the end of the paper we will introduce the Gaussian Integers and Galois Fields and compare them to the modular integers. Companion papers will examine number theory from a more advanced perspective. ...