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Netlib is a collection of mission-critical software components for linear algebra systems (i.e. working with vectors or matrices). Netlib libraries are written in C, Fortran or optimised assembly code. A Java translation has been provided by the F2J project but it does not take advantage of optimised system libraries.

If two numbers b and c have the property that their difference b-c is integrally divisible by a number m (i.e., (b-c)/m is an integer), then b and c are said to be "congruent modulo m."

In mathematical logic, Gödel's incompleteness theorems, proved by Kurt Gödel in 1931, are two theorems stating inherent limitations of all but the most trivial formal systems for arithmetic of mathematical interest. The theorems are of considerable importance to the philosophy of mathematics. They are widely regarded as showing that Hilbert's program to find a complete and consistent set of axioms for all of mathematics is impossible, thus giving a negative answer to Hilbert's second problem.

We've all heard of 'six degrees of separation', the idea that everyone in the world can be connected in just a few steps. But what if those steps don't just relate to people but also to viruses, neurons, proteins and even to fashion trends? What if this 'six degrees of separation' allowed us an insight into something at the core of Nature?

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.

Statistical Theory and Method Abstracts (STMA) is now available as a component of Zentralblatt MATH, referred to as STMA-Z. Zentralblatt MATH is the one of the world’s most complete and longest running abstracting and reviewing services in pure and applied mathematics, containing more than 2 million entries drawn from more than 2,300 serials and journals, covering the period from 1868 to the present. STMA-Z contains all entries of ZMATH pertaining to statistics. Former entries of STMA are included to avoid duplication. Entries of Zentralblatt are classified since 1972 according to the Mathematics Subject Classification Scheme. STMA-Z will provide subscribers with specific access to statistical references and related fields.

The last few years have witnessed a growing recognition of the educational potential of computer games. However, it is generally agreed that the process of designing and deploying technology enhanced learning resources generally and games for mathematical learning specifically is a difficult task. The Kaleidoscope project Learning patterns for the design and deployment of mathematical games aims to investigate this problem. We work from the premise that designing and deploying games for mathematical learning requires the assimilation and integration of deep knowledge from diverse domains of expertise including mathematics, games development, software engineering, learning and teaching. We promote the use of a design patterns approach to address this problem. Our latest outcome is a draft pattern language, which addresses both the process of designing and deployning games for learning and the structure of such games. Our pattern language is suggested as an enabling tool for good practice, by facilitating pattern-specific communication and knowledge sharing between participants. We provide a set of trails as a 'way-in' to using the learning pattern language. In this talk we review the theoretical foundations of our work, demonstrate the language by following one of the 'trails' through it, and illustrate how this language could be used in a participatory design methodology. We also direct participants to our on-line interactive tools, which allow them to engage with our work beyound the scope of the talk.