Stochastic Arithmetic Theory and Experiments

Stochastic arithmetic has been developed as a model for exact computing with imprecise data. Stochastic arithmetic provides confidence intervals for the numerical results and can be implemented in any existing numerical software by redefining types of the variables and overloading the operators on them. Here some properties of stochastic arithmetic are further investigated and applied to the computation of inner products and the solution to linear systems. Several numerical experiments are performed showing the efficiency of the proposed approach.

Interior Boundaries for Degenerate Elliptic Equations of Second Order Some Theory and Numerical Observations

2010 Mathematics Subject Classification: Primary 35J70; Secondary 35J15, 35D05.

Probabilistic Models in Cryptography, Coding Theory and Tests for PRNG

2000 Mathematics Subject Classification: 94A29, 94B70

Encouraging the intellectual craft of living research:tattoos, theory and time

This chapter contributes to the anthology on learning to research - researching to learn because it emphases a need to design curricula that enables living research, and on-going researcher development, rather than one that restricts student and staff activities, within a marketised approach towards time. In recent decades higher education (HE) has come to be valued for its contribution to the global economy. Referred to as the neo-liberal university, a strong prioritisation has been placed on meeting the needs of industry by providing a better workforce. This perspective emphasises the role of a degree in HE to secure future material affluence, rather than to study as an on-going investment in the self (Molesworth , Nixon & Scullion, 2009: 280). Students are treated primarily as consumers in this model, where through their tuition fees they purchase a product, rather than benefit from the transformative potential university education offers for the whole of life.Given that HE is now measured by the numbers of students it attracts, and later places into well-paid jobs, there is an intense pressure on time, which has led to a method where the learning experiences of students are broken down into discrete modules. Whilst this provides consistency, students can come to view research processes in a fragmented way within the modular system. Topics are presented chronologically, week-by-week and students simply complete a set of tasks to ‘have a degree’, rather than to ‘be learners’ (Molesworth , Nixon & Scullion, 2009: 277) who are living their research, in relation to their own past, present and future. The idea of living research in this context is my own adaptation of an approach suggested by C. Wright Mills (1959) in The Sociological Imagination. Mills advises that successful scholars do not split their work from the rest of their lives, but treat scholarship as a choice of how to live, as well as a choice of career. The marketised slant in HE thus creates a tension firstly, for students who are learning to research. Mills would encourage them to be creative, not instrumental, in their use of time, yet they are journeying through a system that is structured for a swift progression towards a high paid job, rather than crafted for reflexive inquiry, that transforms their understanding throughout life. Many universities are placing a strong focus on discrete skills for student employability, but I suggest that embedding the transformative skills emphasised by Mills empowers students and builds their confidence to help them make connections that aid their employability. Secondly, the marketised approach creates a problem for staff designing the curriculum, if students do not easily make links across time over their years of study and whole programmes. By researching to learn, staff can discover new methods to apply in their design of the curriculum, to help students make important and creative connections across their programmes of study.