Julia Language

Here's an interesting language for mathematical endeavors
http://julialang.org/

hat'tip to Paul Snively@psnively


From the Julia blog:

Julia is a dynamic language in the tradition of Lisp, Perl, Python and Ruby. It aims to advance expressiveness and convenience for scientific and technical computing beyond that of environments like Matlab and NumPy, while simultaneously closing the performance gap with compiled languages like C, C++, Fortran and Java.
Most high-performance dynamic language implementations have taken an existing interpreted language and worked to accelerate its execution. In creating Julia, we have reconsidered the basic language design, taking into account the capabilities of modern JIT compilers and the specific needs of technical computing. Our design includes:

• Multiple dispatch as the core language paradigm.
• Exposing a sophisticated type system including parametric dependent types.
• Dynamic type inference to generate fast code from programs with no declarations.
• Aggressive specialization of generated code for types encountered at run-time.

Julia feels light and natural for data exploration and algorithm prototyping, but has performance that lets you deploy your prototypes.

Funny: If the IRS had discovered the quadratic formula . . .

http://www.cs.amherst.edu/~djv/irs.pdf

Allen Downey

Allen Downey is a professor of Computer Science at Olin College in Needham MA
http://sites.google.com/site/allendowney/

He writes an interesting blog focused on probability and statistics problems: 
http://allendowney.blogspot.com

He's also the author of a book:
Probability and Statistics for Programmers
which is published by O'Reilly
http://greenteapress.com/thinkstats/

and also available under the Creative Commons 3.0 license as a PDF: http://greenteapress.com/thinkstats/thinkstats.pdf

Sage: Open Source Mathematics Software

http://www.sagemath.org/

Sage is a free open-source mathematics software system licensed under the GPL. It combines the power of many existing open-source packages into a common Python-based interface.

Mission: Creating a viable free open source alternative to Magma, Maple, Mathematica and Matlab.

Monads

Today I'm reading some background on Monad theory - as it relates to computer programming.

http://en.wikipedia.org/wiki/Functor

http://en.wikipedia.org/wiki/Adjoint_functors

http://en.wikipedia.org/wiki/Closure_operator

http://en.wikipedia.org/wiki/Kleisli_category

http://en.wikipedia.org/wiki/Continuation

http://lambda-the-ultimate.org/node/86

http://sanjaypande.blogspot.com/2004/06/understanding-scheme-continuations.html


http://www.java.net/external?url=http://blog.tmorris.net/understanding-monads-using-scala-part-1/

http://www.java.net/external?url=http://blog.sigfpe.com/2006/08/you-could-have-invented-monads-and.html

http://www.java.net/external?url=http://byorgey.wordpress.com/2009/01/12/abstraction-intuition-and-the-monad-tutorial-fallacy/

http://stackoverflow.com/questions/1823731/can-somebody-please-explain-this-continuation-in-scheme

Mathematics Genealogy Project

http://genealogy.math.ndsu.nodak.edu/

List of Mathematical Symbols

http://en.wikipedia.org/wiki/List_of_mathematical_symbols