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).

"GNU Octave is a high-level interpreted language, primarily intended for numerical computations. It provides capabilities for the numerical solution of linear and nonlinear problems, and for performing other numerical experiments. It also provides extensive graphics capabilities for data visualization and manipulation. Octave is normally used through its interactive command line interface, but it can also be used to write non-interactive programs. The Octave language is quite similar to Matlab so that most programs are easily portable."

What are the common mistakes people make in trying to read mathematics?  How can these mistakes be corrected?

MathJax is an open source JavaScript display engine for mathematics that works in all modern browsers.

"Steven Strogatz, an award-winning professor, takes readers from the basics to the baffling in a 15-part series on mathematics. Beginning with a column on why numbers are helpful, he goes on to investigate topics including negative numbers, calculus and group theory, finishing with the mysteries of infinity."

All of elementary and high school mathematics is building up toward calculus. In this brief video, Mathemagician Arthur Benjamin proposes replacing this pinnacle of pre-secondary math education with statistics, which he suggest would be much more relevant and useful in the daily lives of most people.

"CVC3 is an automatic theorem prover for Satisfiability Modulo Theories (SMT) problems. It can be used to prove the validity (or, dually, the satisfiability) of first-order formulas in a large number of built-in logical theories and their combination. CVC3 is the last offspring of a series of popular SMT provers, which originated at Stanford University with the SVC system."

Claude Shannon's creation in the 1940's of the subject of information theory is arguably one of the great intellectual achievements of the twentieth century. Information theory has had an important and significant influence on mathematics, particularly on probability theory and ergodic theory, and Shannon's mathematics is in its own right a considerable and profound contribution to pure mathematics.

The prolific mathematician Paul Erdos died on 20 September 1996. His Washington Post obituary ends with the sentence "He left no immediate survivors." Charles Krauthammer disputes this dismal summary by pointing out Erdos's vast intellectual legacy, and exploring the unique traits that lead to this legacy. "No survivors, indeed."

This is the famous "HAKMEM" memo published at MIT in 1972. It includes an eclectic selection of problems in computer science, number theory, algebra, bit hacking, and so on, sometimes with equally eclectic solutions.

"Project Euler is a series of challenging mathematical/computer programming problems that will require more than just mathematical insights to solve. Although mathematics will help you arrive at elegant and efficient methods, the use of a computer and programming skills will be required to solve most problems. The motivation for starting Project Euler, and its continuation, is to provide a platform for the inquiring mind to delve into unfamiliar areas and learn new concepts in a fun and recreational context. The intended audience include students for whom the basic curriculum is not feeding their hunger to learn, adults whose background was not primarily mathematics but had an interest in things mathematical, and professionals who want to keep their problem solving and mathematics on the edge."