This paper describes a 25‐year project in which we defined problem solving, identified effective methods for developing students' skill in problem solving, implemented a series of four required courses to develop the skill, and evaluated the effectiveness of the program. Four research projects are summarized in which we identified which teaching methods failed to develop problem solving skill and which methods were successful in developing the skills. We found that students need both comprehension of Chemical Engineering and what we call general problem solving skill to solve problems successfully. We identified 37 general problem solving skills. We use 120 hours of workshops spread over four required courses to develop the skills. Each skill is built (using content‐independent activities), bridged (to apply the skill in the content‐specific domain of Chemical Engineering) and extended (to use the skill in other contexts and contents and in everyday life). The tests and examinations of process skills, TEPS, that assess the degree to which the students can apply the skills are described. We illustrate how self‐assessment was used.

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Stone Duality is a new paradigm for general topology in which computable continuous functions are described directly, without using set theory, infinitary lattice theory or a prior theory of discrete computation. Every expression in the calculus denotes both a continuous function and a program, and the reasoning looks remarkably like a sanitised form of that in classical topology. This is an introduction to ASD for the general mathematician, with application to elementary real analysis.This language is applied to the Intermediate Value Theorem: the solution of equations for continuous functions on the real line. As is well known from both numerical and constructive considerations, the equation cannot be solved if the function "hovers" near 0, whilst tangential solutions will never be found.In ASD, both of these failures, and the general method of finding solutions of the equation when they exist, are explained by the new concept of overtness. The zeroes are captured, not as a set, but by higher-type modal operators. Unlike the Brouwer degree of a mapping, these are naturally defined and (Scott) continuous across singularities of a parametric equation.Expressing topology in terms of continuous functions rather than using sets of points leads to treatments of open and closed concepts that are very closely lattice-(or de Morgan-) dual, without the double negations that are found in intuitionistic approaches. In this, the dual of compactness is overtness. Whereas meets and joins in locale theory are asymmetrically finite and infinite, they have overt and compact indices in ASD.Overtness replaces metrical properties such as total boundedness, and cardinality conditions such as having a countable dense subset. It is also related to locatedness in constructive analysis and recursive enumerability in recursion theory.2000 Mathematics Subject Classification 03F60 (primary); 54D05 03D45 68N18 68Q55 (secondary)

Transitive extensional well founded relations provide an intuitionistic notion of ordinals which admits transfinite induction. However these ordinals are not directed and their successor operation is poorly behaved, leading to problems of functoriality.We show how to make the successor monotone by introducing plumpness, which strengthens transitivity. This clarifes the traditional development of successors and unions, making it intuitionistic; even the (classical) proof of trichotomy is made simpler. The definition is, however, recursive, and, as their name suggests, the plump ordinals grow very rapidly.Directedness must be defined hereditarily. It is orthogonal to the other four conditions, and the lower powerdomain construction is shown to be the universal way of imposing it.We treat ordinals as order-types, and develop a corresponding set theory similar to Osius' transitive set objects. This presents Mostowski's theorem as a reflection of categories, and set-theoretic union is a corollary of the adjoint functor theorem. Mostowski's theorem and the rank for some of the notions of ordinal are formulated and proved without the axiom of replacement, but this seems to be unavoidable for the plump rank.The comparison between sets and toposes is developed as far as the identification of replacement with completeness and there are some suggestions for further work in this area.Each notion of set or ordinal defines a free algebra for one of the theories discussed by Joyal and Moerdijk, namely joins of a family of arities together with an operation s satisfying conditions such as x ≤ sx, monotonicity or s(x ∨ y) ≤ sx ∨ sy.Finally we discuss the fixed point theorem for a monotone endofunction s of a poset with least element and directed joins. This may be proved under each of a variety of additional hypotheses. We explain why it is unlikely that any notion of ordinal obeying the induction scheme for arbitrary predicates will prove the pure result.

This article traces the emergence of the new social movement of hacktivism from hacking and questions its potential as a source of technologically-mediated radical political action. It assesses hacktivism in the light of critical theories of technology that question the feasibility of re-engineering technical systems to more humane ends. The predecessor of hacktivism, hacking, is shown to contain certain parasitical elements that provide a barrier to more politically-orientated goals. Examples are provided of how such goals are much more in evidence within hacktivism. Its alternative conceptualization of the human-technology relationship is examined in terms of a purported development from conceptualizations of networks to webs that incorporate new ways of producing online solidarity and oppositional practices to global capital.

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XeF2.WOF4, M=445.2, monoclinic, space group P2Jc, a=5.44 (1), b=9.97 (1), c=12.17 (2) A, fl=92.0 (2) °, U= 659.4 A 3, z=4, D~=4.50 g cm -3. The atomic positions have been determined by blockdiagonal least-squares refinement of counter intensities, the final R being 0.081 for 817 reflexions. Mean bond lengths are W-F(terminal) 1.79, W-F(bridging) 2.18, W-O 1.65, Xe-F(terminal) 1.89 and Xe-F(bridging) 2.04 A. The geometry of the fluorine bridge is related to the degree of covalency of the adduct.