A Taylor-like Expansion of a Commutator with a Function of Self-Adjoint, Pairwise Commuting Operators

Let $A$ be a $\nu$-vector of self-adjoint, pairwise commuting operators and $B$ a bounded operator of class $C^{n_0}(A)$. We prove a Taylor-like expansion of the commutator $[B,f(A)]$ for a large class of functions f\colon\mathbm{R}^\nu \to \mathbm{R}, generalising the one-dimensional result where $A$ is just a self-adjoint operator. This is done using almost analytic extensions and the higher-dimensional Helffer-Sj\"ostrand formula.Comment: To appear in Math.Scan

Involving teaching assistants in the design of large courses

The use of teaching assistants in the execution of large courses is common practice across universities worldwide. However, this task is mostly conducted disjoint, where the course responsible sketch out the teaching assistants specific tasks, such as to assist during practical or theoretical exercises and correction of homework, reports etc. which then is being conducted in a no questions asked fashion by the teaching assistants often in an environment where the course responsible is not present. It boils down to that one person (the course responsible) constructs the material, which then is thrown over the wall to the other person (the teaching assistant) who is going to try to turn this material into learning. The result of this is often, that the good learning intentions behind the material is lost in this line of communication, where the teaching assistant lack the exact idea of the exercise, or sufficient background knowledge for framing the context, and further, that the course responsible is out of sync with the students hurdles in achieving learning. On the other hand the teaching assistants belong to per see the brightest part of the student spectrum and as such posses a capacity beyond what is utilized in such a traditional setup. This project explores how to utilize teaching assistants in the process of designing a new course, and discusses the consequences of this involvement

What is CSR? - a review of different theoretical perspectives and case studies of Cheminova and Systematic

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