Julia is a high-level, high-performance dynamic programming language for technical computing, with syntax that is familiar to users of other technical computing environments. It provides a sophisticated compiler, distributed parallel execution, numerical accuracy, and an extensive mathematical function library. The library, mostly written in Julia itself, also integrates mature, best-of-breed C and Fortran libraries for linear algebra, random number generation, FFTs, and string processing. More libraries continue to be added over time. Julia programs are organized around defining functions, and overloading them for different combinations of argument types (which can also be user-defined).

Notes on the TrueSkill algorithm

These five Highlights of Calculus videos provide an overview of the key topics and ideas of calculus and how they apply to real-life situations and problems. In addition to the videos, there are summary slides and practice problems complete with an audio narration by Professor Strang. You can find these files under the Related Resources tab on each video page.

Awesome article about monoids and abstraction in cs

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A delightfully funny, yet effective, introduction to calculus book from 1914.

It starts by ranting about uppity mathematicians and academics while showing how simply you can get your head around basic calculus.

Lots of Project Euler solutions implemented in Clojure

Good documentary on the limits of knowledge.

Jump to: navigation, search

In logic, extensionality, or extensional equality refers to principles that judge objects to be equal if they have the same external properties. It is the opposite concept of intensionality, which is concerned with whether two descriptions are intended to be the same or not.

A SHORT MOVIE INSPIRED ON NUMBERS, GEOMETRY AND NATURE. (Fibonacci, Golden Ratio, Delaunay, Voronoi…), stills and screenshots showing the work in progress. There are lots of free training materials and 3D workshops, too ;-)

when adiabatic quantum computers are used to solve NP-complete problems, the energy gap between the lowest energy state and the next state up is not well behaved. Instead, it narrows faster than exponentially, meaning the adiabatic quantum computing cannot, even in principle, solve NP-complete problems faster than a classical computer.

when adiabatic quantum computers are used to solve NP-complete problems, the energy gap between the lowest energy state and the next state up is not well behaved. Instead, it narrows faster than exponentially, meaning the adiabatic quantum computing cannot, even in principle, solve NP-complete problems faster than a classical computer.

Coq is a formal proof management system. It provides a formal language to write mathematical definitions, executable algorithms and theorems together with an environment for semi-interactive development of machine-checked proofs.

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"Russell's Introduction to Mathematical Philosophy available free online."

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... Or foldl and foldr considered slightly harmful.

On the mathematical quantity, Entropy, which allows us to measure how close a fact comes to revealing somebody's identity uniquely.

How we have a tendency to underestimate the unknown...

Cute...

"It reflects a beautiful property of the quantum system – a hidden symmetry. Actually quite a special one called E8 by mathematicians, and this is its first observation in a material"

Awesome 15 minute lecture on Physics

The moral of the story is: "You can be fully lazy if and only if your condition is a stopping time!"

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Good reference of low level bit tweaking tricks.

The book aims to provide a modern approach to information retrieval from a computer science perspective. It is based on a course we have been teaching in various forms at Stanford University and at the University of Stuttgart.

"The usual way in which we plan today for tomorrow is in yesterday's vocabulary. We do so, because we try to get away with the concepts we are familiar with and that have acquired their meanings in our past experience. Of course, the words and the concepts don't quite fit because our future differs from our past, but then we stretch them a little bit..."

More from Feynman...

"The following links point to a set of tutorials on many aspects of statistical data mining, including the foundations of probability, the foundations of statistical data analysis, and most of the classic machine learning and data mining algorithms. "

Stephen Wolfram's new search engine... to be released in May.

“Wolfram|Alpha isn’t really a search engine, because we compute the answers, and we discover new truths. If anything, you might call it a platonic search engine, unearthing eternal truths that may never have been written down before.” The sceptic in me wonders if this is the new Cyc gravy-train! :-)

A working demonstration of Godel's incompleteness theorem

Welcome to the Colt Project. Colt provides a set of Open Source Libraries for High Performance Scientific and Technical Computing in Java.

Scientific and technical computing, as, for example, carried out at CERN, is characterized by demanding problem sizes and a need for high performance at reasonably small memory footprint. There is a perception by many that the Java language is unsuited for such work. However, recent trends in its evolution suggest that it may soon be a major player in performance sensitive scientific and technical computing. For example, IBM Watson's Ninja project showed that Java can indeed perform BLAS matrix computations up to 90% as fast as optimized Fortran.

An interesting Wired article about a guy applying psychological approaches to recommendation systems in order to win the netflix prize. He's currently near the top of the leaderboard against teams of academics and students

Mathematics problems requiring programming/algorithm design.