Fast and Exact Spin-s Spherical Harmonic Transforms

We demonstrate a fast spin-s spherical harmonic transform algorithm, which is flexible and exact for band-limited functions. In contrast to previous work, where spin transforms are computed independently, our algorithm permits the computation of several distinct spin transforms simultaneously. Specifically, only one set of special functions is computed for transforms of quantities with any spin, namely the Wigner d-matrices evaluated at {\pi}/2, which may be computed with efficient recursions. For any spin the computation scales as O(L^3) where L is the band-limit of the function. Our publicly available numerical implementation permits very high accuracy at modest computational cost. We discuss applications to the Cosmic Microwave Background (CMB) and gravitational lensing.Comment: 22 pages, preprint format, 5 figure

Strength in diversity: enhancing learning in vocationally-orientated, master's level courses

Postgraduate education in geography, especially at the Master’s level, is undergoing significant changes in the developed world. There is an expansion of vocationally-oriented degree programmes, increasing recruitment of international students, integration of work place skills, and the engagement of non-traditional postgraduate students as departments respond to policies for a more ‘inclusive’ higher education. This paper sets the context by outlining some programmatic changes in selected countries (Australia, the UK, and the USA). We briefly reflect on how postgraduate ‘bars’ or ‘levels’ are defined and explore in detail what ‘diversity’ or ‘heterogeneity’ means in these new postgraduate settings. The paper then explores some examples of practice drawn from our own experiences, whilst recognising that relevance will vary in other contexts. Finally we consider how diversity can be harnessed as a strength that has potential to enhance taught elements of contemporary postgraduate education in and beyond the discipline