Writing into design: An embedded writing course for architectural studies

Architects must be able to express their ideas clearly to communicate their designs; at the same time graduate professional degree programs demand advanced critical literacy and academic writing skills. Competence in this domain for high school graduates in South Africa often falls short of the expected proficiencies of first-year students at tertiary level. To address this gap, an embedded writing course was integrated into the first-year Design Studio and History of Architecture course. This intervention adopted the approaches provided by writing-intensive pedagogy, successfully improving students’ written expression, and their ability to engage with their architectural studies in deeper and more critical ways

The Pure State Space of Quantum Mechanics as Hermitian Symmetric Space

The pure state space of Quantum Mechanics is investigated as Hermitian Symmetric Kaehler manifold. The classical principles of Quantum Mechanics (Quantum Superposition Principle, Heisenberg Uncertainty Principle, Quantum Probability Principle) and Spectral Theory of observables are discussed in this non linear geometrical context.Comment: 18 pages, no figure

Variations, approximation, and low regularity in one dimension

We investigate the properties of minimizers of one-dimensional variational problems when the Lagrangian has no higher smoothness than continuity. An elementary approximation result is proved, but it is shown that this cannot be in general of the form of a standard Lipschitz "variation". Part of this investigation, but of interest in its own right, is an example of a nowhere locally Lipschitz minimizer which serves as a counter-example to any putative Tonelli partial regularity statement. Under these low assumptions we find it nonetheless remains possible to derive necessary conditions for minimizers, in terms of approximate continuity and equality of the one-sided derivatives.Comment: v3, 60 pages. To appear in CoVPDE. Minor cosmetic correction

On Differential Structure for Projective Limits of Manifolds

We investigate the differential calculus defined by Ashtekar and Lewandowski on projective limits of manifolds by means of cylindrical smooth functions and compare it with the C^infty calculus proposed by Froehlicher and Kriegl in more general context. For products of connected manifolds, a Boman theorem is proved, showing the equivalence of the two calculi in this particular case. Several examples of projective limits of manifolds are discussed, arising in String Theory and in loop quantization of Gauge Theories.Comment: 38 pages, Latex 2e, to be published on J. Geom. Phys minor misprints corrected, reference adde

A one-dimensional variational problem with continuous Lagrangian and singular minimizer

We construct a continuous Lagrangian, strictly convex and superlinear in the third variable, such that the associated variational problem has a Lipschitz minimizer which is non-differentiable on a dense set. More precisely, the upper and lower Dini derivatives of the minimizer differ by a constant on a dense (hence second category) set. In particular, we show that mere continuity is an insufficient smoothness assumption for Tonelli’s partial regularity theorem