The 'what' and 'how' of learning in design, invited paper

Previous experiences hold a wealth of knowledge which we often take for granted and use unknowingly through our every day working lives. In design, those experiences can play a crucial role in the success or failure of a design project, having a great deal of influence on the quality, cost and development time of a product. But how can we empower computer based design systems to acquire this knowledge? How would we use such systems to support design? This paper outlines some of the work which has been carried out in applying and developing Machine Learning techniques to support the design activity; particularly in utilising previous designs and learning the design process

Aggregation theory and the relevance of some issues to others

I propose a general collective decision problem consisting in many issues that are interconnected in two ways: by mutual constraints and by connections of relevance. Aggregate decisions should respect the mutual constraints, and be based on relevant information only. This general informational constraint has many special cases, including premise-basedness and Arrow''s independence condition; they result from special notions of relevance. The existence and nature of (non-degenerate) aggregation rules depends on both types of connections. One result, if applied to the preference aggregation problem and adopting Arrow''s notion of (ir)relevance, becomes Arrow''s Theorem, without excluding indifferences unlike in earlier generalisations.mathematical economics;

Newton's Idea and Practice of Unification

In this paper I try to capture Newton's notion and practice of unification (I will mainly focus on the Principia). I will use contemporary theories on unification in philosophy of science as analytic tools (Kitcher, Schurz and Salmon). I will argue that Salmon's later work on the topic provides a good starting point to characterize Newton's notion and practice. However, in order to fully grasp Newton's idea and practice of unification, Salmon's model needs to be fleshed out and extended

Three themes in the work of Charles Ehresmann: Local-to-global; Groupoids; Higher dimensions

This paper illustrates the themes of the title in terms of: van Kampen type theorems for the fundamental groupoid; holonomy and monodromy groupoids; and higher homotopy groupoids. Interaction with work of the writer is explored.Comment: 13 pages; Expansion of an invited talk given to the 7th Conference on the Geometry and Topology of Manifolds: The Mathematical Legacy of Charles Ehresmann, Bedlewo 8.05.2005-15.05.2005 (Poland) Version 2: corrections of a date and some grammar, slight referencing changes, and a small comment added Version4. Theorem 2.2 got corrected and then uncorrected! It is now corrected. Version5. Reference added. Various minor improvements made in reaction to comment

Do bold shakeups of the learning-teaching agreement work? A commognitive perspective on a LUMOS low lecture innovation

Mathematics undergraduates, and their lecturers, often describe the transition into university mathematics as a process of enculturation into new mathematical practices and new ways of constructing and conveying mathematical meaning (Nardi, 1996). Whatcharacterises the breadth and intensity of this enculturation varies according to factors such as (Artigue, Kent & Batanero, 2007): student background and preparedness for university level studies of mathematics; the aims and scope of each of the courses that thestudents take in the early days of their arrival at university; how distant the pedagogical approaches taken in these courses are from those taken in the secondary schools that the students come from; the students’ affective dispositions towards the subject and their expectations for what role mathematics is expected to play in their professional life. On their part, lecturers’ views on their pedagogical role may also vary according to factors such as (Nardi, 2008): length of teaching experience; type of courses (pure, applied, optional, compulsory etc.) they teach; perceptions of the goals of university mathematics teaching (such as to facilitate access to the widest possible population of participants in mathematics or select those likely to push the frontiers of the discipline); and, crucially, institutional access to innovative practices, e.g. through funded, encouraged and acknowledged research into such practices.In this paper I draw on my experiences as a member of the International Advisory Board of the LUMOS project (Barton & Paterson, 2013) to comment on aspects of aforementioned student enculturation. Here I see this enculturation as the adaptation of different ways to act and communicate mathematically. I take a perspective on these ways to act and communicate as discourses and I treat the changes to the mathematical and pedagogical perspectives of those who act as discursive shifts. To this purpose, I deploythe approach introduced by Anna Sfard (2008) and known as the commognitive approach

Fusion Rings Related to Affine Weyl Groups

The construction of the fusion ring of a quasi-rational CFT based on $\hat{sl}(3)_k$ at generic level $k\not \in {\Bbb Q}$ is reviewed. It is a commutative ring generated by formal characters, elements in the group ring ${\Bbb Z}[\tilde{W}]$ of the extended affine Weyl group $\tilde{W}$ of $\hat{sl}(3)_k$. Some partial results towards the $\hat{sl}(4)_k$ generalisation of this character ring are presented.Comment: 13 pages; two figures. Talk at ``Lie Theory and Its Applications in Physics III'', Clausthal, 11-14 July, 1999, to appear in the Proceedings, eds. H.-D. Doebner et a

A non-moral critique of the norm of assumed objectivity

Sally Haslanger (2013) has described a particular norm of objectivity, the norm of Assumed Objectivity, that she considers as morally problematic. This norm, when correctly applied, permits one to form essentialising beliefs about women. According Haslanger, under the conditions of gender inequality, adopting hurts the interest of women while serving the interests of men. Rae Langton (1993), in contrast, has argued that a moral critique of the norm has its shortcomings: if a particular norm is bad for some and good for others, then the grounds for rejecting the norm are weak. Thus, Langton has provided a non-moral critique of the norm that pertains to the rationality of the norm. She argues that the norm should be rejected because it fails to yield knowledge. Evangelia Papadaki (2008) has pointed to an inconsistency in Langton’s argument thereby concluding that the norm evades Langton’s non-moral critique. In this thesis, I will set out to argue the norm is vulnerable to a non-moral critique. I will argue that the beliefs arrived at fail to constitute knowledge, which gives us a rational justification to reject the norm of Assumed Objectivityhttps://www.ester.ee/record=b538084