The Annual Boole Lecture was established and is sponsored by the Boole Centre for Research in Informatics, the Cork Constraint Computation Centre, the Department of Computer Science, and the School of Mathematics, Applied Mathematics and Statistics at University College Cork. The series is named in honour of George Boole, the first professor of Mathematics at UCC, whose seminal work on logic in...

The Annual Boole Lecture was established and is sponsored by the Boole Centre for Research in Informatics, the Cork Constraint Computation Centre, the Department of Computer Science, and the School of Mathematics, Applied Mathematics and Statistics at University College Cork. The series is named in honour of George Boole, the first professor of Mathematics at UCC, whose seminal work on logic in...

Department of Informatic and Automatic, E.P.S. de Zamora, Universidad de Salamanca. Avda. Cardenal Requejo 34, 49022-Zamora, Spain; Department of Applied Mathematics, E.P.S. de Ávila, Universidad de Salamanca. C/ Hornos Caleros 50,05003-Ávila, Spain; Department of Applied Mathematics, E.P.S. de Zamora, Universidad de Salamanca. Avda. Cardenal Requejo 34, 49022-Zamora, Spain; Department of Appli...

The need for curricular reform in K-4 mathematics is clear. Such reform must address both the content and emphasis of the curriculum as well as approaches to instruction. A longstanding preoccupation with computation and other traditional skills has dominated both what mathematics is taught and the way mathematics is taught at this level. As a result, the present K-4 curriculum is narrow in sco...

Mathematical fluency is important for academic and mathematical success. Fluency training programs have typically focused on fostering retrieval, which leads to math performance that does not reliably transfer to non-trained problems. More recent studies have focused on training number understanding and representational precision, but few have directly investigated whether training improvements...

Intuitionistic mathematics perceives subtle variations in meaning where classical mathematics asserts equivalence, and permits geometrically and computationally motivated axioms that classical mathematics prohibits. It is therefore wellsuited as a logical foundation on which questions about computability in the real world are studied. The realizability interpretation explains the computational ...

Mathematics is a process of creating, exploring, and connecting mathematical models. This paper presents an overview of a formal framework for managing the mathematics process as well as the mathematical knowledge produced by the process. The central idea of the framework is the notion of a biform theory which is simultaneously an axiomatic theory and an algorithmic theory. Representing a colle...

www.JCE.DivCHED.org • Vol. 84 No. 5 May 2007 • Journal of Chemical Education 889 Students of chemistry find mathematics difficult: some students entering a post-secondary institution even select chemistry rather than physics because they think that they might thereby avoid much mathematics. Even while chemistry has become more mathematical during the past half century, largely because of an inc...

Two-dimensional topological states of matter offer a route to quantum computation that would be topologically protected against the nemesis of the quantum circuit model: decoherence. Research groups in industry, government and academic institutions are pursuing this approach. We give a mathematicians perspective on some of the advantages and challenges of this model, highlighting some recent ad...