General Teaching
I have made a Gaussian Elimination Calculator (or see Gauss-Jordan Algorithmus Rechner auf Deutsch) and an Inverse Algorithm Calculator (using Numbas), where you can enter a linear system as an augmented matrix, resp. a square matrix, and then tell it which row operations you would like to do. The aim is to enable students to concentrate on which steps are required to get the matrix into reduced row echelon form, rather than the individual calculations per entry.
Current Teaching
In the winter semester 2024/25, I am holding exercise classes for the course Foundations of Mathematics, lectured by Dr. Norbert Koksch, and for Discrete Structures for computer scientists. I'm also teaching a maths outreach class on Thursdays for school years 10-11.
Previous teaching
Summer 2024: Lectures for Linear Algebra and Analytical Geometry (LAAG) (lecture notes in German) and maths outreach class
Winter 2023/24: Linear Algebra for Physicists, Foundations of Mathematics and maths outreach class
Summer 2022: Linear Algebra 2 for Bachelor, Linear Algebra and Analytical Geometry and maths outreach class
Winter 2022/23: Linear Algebra 1 and Linear Algebra for computer scientists
Summer 2022: Linear Algebra and Analytical Geometry and Mathematical Methods for computer scientists
Winter 2021/22: Linear Algebra for Physicists und Linear Algebra for computer scientists
In Leicester I taught Elements of Number Theory, Linear Algebra and Plane Geometry.
Lecture notes Linear Algebra
Workbook Linear Algebra
I also prepared some documents to help students transition to university mathematics. For example this Introduction to proofs.
Cambridge Maths Tripos Groups Ia lecture course
In Michaelmas 2016 I lectured the Cambridge first year course on Groups (for the third time). Here is the lecture-accompanying blog Think for yourself, on which I particularly wrote about how to think about and learn maths at university.
Lecture notes (last update 16 January 2017)
Practice sheets (for personal practice, not for supervisions):
Practice Sheet A
Practice Sheet B
Practice Sheet C
Example sheets:
Example Sheet 1
Example Sheet 2
Example Sheet 3
Example Sheet 4
Previous year's example sheets and lecture notes can be found on the archive page.
Cambridge Maths Part III Category Theory lecture course
In Michaelmas 2013 I lectured the Part III course on Category Theory, as I also did in Michaelmas 2011 and 2012. Material is still here for interested people.
2013 example sheets:
Example Sheet 1
Example Sheet 2
Example Sheet 3
Example Sheet 4
Further examples:
Examples of categories and functors
Examples of adjunctions
Examples of coseparating sets and separating families
Notes on Adjunctions, Monads and Lawvere Theories by Filip Bár
Example sheets from previous years: on archive page.
