Teaching
Infrastructure for mathematics
Infrastructure for mathematics is an interactive research-data management course specifically aimed at mathematicians. It welcoms maths undergraduates, graduate students, and early postdocs (as well as anyone interested from neighbouring disciplines). In summer 2023, the course took place once a week on Friday mornings at Leipzig Uni as a combined 90min 'Vorlesung und Übung', for six weeks. If you attended that class and want it examined or would like to obtain a certificate of participation, drop me an email. Four of the lectures combined also formed a one-day course in the Magdeburg graduate school MathCore in autumn 2023.
Topics of the course are as listed below, each number corresponding to one chapter of lecture notes. These notes will be made available for download here once they are ready.
1 Motivation: what pitfalls are there in producing and reusing maths research and what concepts do you need to be aware of to avoid those? What is research data, why would you need to 'manage' it, and what is mathematical research about? Download: mathsrdm_chapter1v01.pdf
2 The FAIR principles: how do you make sure you take into account all the knowledge out there and how do you ensure future generations can use your results? Download: mathsrdm_chapter2v01.pdf
2 Good scientific practice: what is good practice, how do you properly do science and write mathematics, and what do the DFG guidelines imply for mathematics research? Download: mathsrdm_chapter3v01.pdf
4 MaRDI: what is the Mathematical Research Data Initiative and what can it do for you?
5 Knowledge graphs: how can you find, identify, and link information online?
6 Benchmarks and interoperability: how can you be sure you compare your results in a sensible way against the best ones out there and how can you seamlessly hand a piece of mathematics from one researcher to the next?
7 Reproducibility, versioning, and serialisation: how do you present and preserve your mathematics such that your peers can arrive at the same results with the same material? Download: mathsrdm_chapter6v01.pdf
8 Technical peer-review processes: what is peer review, how does publishing work, and how are different pieces of mathematics treated in such a process?
9 Repositories: what are sensible locations to store your results and what does sensible mean?
10 Copyright, licences, ethical considerations, data protection: are these topics relevant for mathematics and what services are out there to help you in case?
11 Research-data management plans: what to write in a funding proposal.
12 Research-data scary tales, escape rooms, and a computer-algebra game.
You are welcome to use the slide presentations of individual sessions for your own purposes as long as you cite me as an author (I'll put them on Zenodo once the lecture notes are complete, making citation and reuse easier). Download: 1whatis_v2, 2FAIR, 3gsp
Additional course material, e.g. pictures of blackboard discussions, is available on the MaRDI cloud. Drop me an email for the link.
Past
I have been teaching and marking classes for undergraduate and graduate Mathematics, Statistics, and Computer Science students and postdocs on and off from 2009 until 2019, at Karlsruhe and Warwick universities and at MiS MPG. In 2016 I won the Warwick Awards for Teaching Excellence for postgraduate students who teach (WATE PGR).
Winter 2017/18
Sara Kališnik Verovšek and me co-taught a course called Mathematics of Data for interested PhD students and postdoctoral researchers at the Max-Planck-Institute for Mathematics in the Sciences. The aim of this course was to show applications of topology and algebraic geometry to statistical data analysis. The lecture announcement can be found here and the content of the lectures I covered is listed below.
Lecture 1, October 11: The first introductory lecture is all about linear models. The theory and practice is based on Chapters 1 to 5 from Julian Faraway's book Linear Models with R. The R code for the little example we look at can be found here. During the lecture I run this code using RStudio.
Lecture 2, October 18: The second introductory lecture illustrates Bayesian and frequentists methods for parameter estimation using simple coin tossing experiments. The slides with the short motivation were taken from Ken Rice's homepage. The theory is based on Devinder Sivia's book Data Analysis: a Baysian tutorial. We use Craig Zirbel's tool for generating confidence intervals.
Lecture 3, November 1: The third lecture introduces likelihood ratio tests as a technique in frequentist model selection. We define algebraic statistical models using the article by Drton and Sullivant (2007), and we discuss how the language of algebraic geometry can help to investigate the asymptotic behaviour of likelihood ratio tests when the parameter space is a semi-algebraic set. This is based on the work by Drton (2009). Illustrations are taken from Drton (2006).
Lecture 4, November 8: The fourth lecture introduces Bayesian networks. Geiger, Meek, and Sturmfels (2006) have shown that so-called decomposable BNs are toric varieties. We follow Geiger, Heckerman, King, and Meek (2001), and Geiger and Meek, in showing that BNs are curved exponential families and how an implicit characterisation of these models which uses the language of algebraic geometry can be used for model selection.
Summer 2015
I spent my annual leave volunteering with Warwick in Africa (WiA) for six weeks. WiA is an initiative at the University of Warwick that has been running for more than a decade now and continues to send enthusiastic undergraduate and graduate students to Tanzania, Ghana, and South Africa where they teach either Maths or English (and sometimes both). I was based at Fons Luminis Secondary School in Soweto where I met the amazing people pictured below.
