Standing up for teaching: the 'crime' of striving for excellence

In recent years a proliferation of local and national teaching awards has occurred in many countries. The new language of excellence has led institutions and policy-makers to embrace teaching awards. Although these award schemes harbour competing and coexisting drivers and appeal to different stakeholders for different reasons, they have helped to raise the profile and importance of teaching in higher education. At the same time, the idea of recognising individuals as excellent teachers remains distasteful to many educators. Awards remain controversial as they compete with traditional ideals of egalitarianism which dominate the education profession. In the backdrop of lingering controversy, this short opinion paper reflects on the costs of standing up for teaching after applying for and successfully winning a National Award for Sustained Excellence in Teaching. Using an acronym it describes the CRIME of excellence and makes the case for teaching awards criteria to recognise critical forms of scholarship. While definitions of excellence will always be contestable it argues that teaching awards are not mutually exclusive from an individual ethos of striving for continuous improvement. The paper concludes that the education profession does a great disservice to the status of teaching if we shame and snipe away at those judged by peers as our best

On the Construction of Simply Connected Solvable Lie Groups

Let $\omega_\mathfrak{g}$ be a Lie algebra valued differential $1$-form on a manifold $M$ satisfying the structure equations $d \omega_\mathfrak{g} + \frac{1}{2} \omega_\mathfrak{g}\wedge \omega_\mathfrak{g}=0$ where $\mathfrak{g}$ is solvable. We show that the problem of finding a smooth map $\rho:M\to G$, where $G$ is an $n$-dimensional solvable Lie group with Lie algebra $\mathfrak{g}$ and left invariant Maurer-Cartan form $\tau$, such that $\rho^* \tau= \omega_\mathfrak{g}$ can be solved by quadratures and the matrix exponential. In the process we give a closed form formula for the vector fields in Lie's third theorem for solvable Lie algebras. A further application produces the multiplication map for a simply connected $n$-dimensional solvable Lie group using only the matrix exponential and $n$ quadratures. Applications to finding first integrals for completely integrable Pfaffian systems with solvable symmetry algebras are also given.Comment: 22 pages. Fixed typos from version 1, and added more details in the example