This page contains the supporting material for my BKO portfolio.

BKO document

My portfolio can be found here, as a pdf document.

Material for Topologie en Meetkunde

I have taught the 3rd year bachelor course Topologie en Meetkunde in the academic years 2019-20, 2020-21, and 2021-22. During this period I have developed various teaching materials.

The exercise sheets for the course are meant to be structured in a scaffolded manner, with exercises arranged by topics and ordered by difficulty. The first werkcollege took place before the first lecture; so the first sheet of exercises was a recap of Inleiding Topologie. After that, a new sheet was provided each week: Week 1, Week 2, Week 3, Week 4, Week 5, Week 6, Week 7, Week 8, Week 9. An additional sheet dealing with category theory was provided.

I have also prepared animated kennisclips covering some of the main results from the course: Introduction, Fundamental group of the circle, the topology in the fundamental groupoid, the theorem of van Kampen, introduction to surfaces, the classification of surfaces. These are meant to be watched by the students before the corresponding lectures, in order to build intuition before they see the concepts fully formally.

In order to motivate discussion among students, I prepared some Wooclap quizzes. These were used by the TAs to begin the Tuesday sessions of the werkcollege and took around 30 minutes. They also helped to identify common misunderstandings.

In order to make more transparent to the students what they are meant to be working on each week, this year I prepared a timeline of the course. It includes deadlines, recommended exercises, and the material that will be discussed in the lectures. It can be found here.

In the 2020/21 iteration, the midterm was replaced by a project to be carried out in pairs. The instructions I prepared can be found here.

Material for Symplectic Geometry

I taught the Mastermath Symplectic Geometry course in the academic year 2018-19, jointly with F. Ziltener. The course was divided into various topics. The ones I taught were Symplectic Linear Algebra, the theory of normal forms, and an introduction to Symplectic Topology.

As part of my teaching, I decided to lengthen the existing set of notes. You can find the result here. The original notes, due to F. Pasquotto, can be found here (I include these, with the permission of F. Pasquotto, for comparison).

Lecture notes on 3-dimensional Contact Topology

In order to complete the course “Teaching in Higher Education” I had to submit some original teaching materials. I decided to rework (part of) the last chapter of my Symplectic Geometry notes into a “lecture format”. This meant restructuring the material so that it would fit into a 3-hour lecture in which lecture parts alternate with exercises of various kinds. The document can be found here.

Lecture notes on Morse theory

In August 2018 I gave one of the lectures during the Utrecht Geometry Summer School. The goal was to introduce students to Morse theory, assuming “analysis in multiple variables” as the only prerrequisite (in particular, no prior background on manifolds). The notes can be found here and the exercises here.

Student evaluations

Caracal evaluation for Bewijzen in de Wiskunde 2021-22. Rated 4.6/5.

Caracal evaluation for Topologie en Meetkunde 2021-22. Rated 4.7/5.

Caracal evaluation for Topologie en Meetkunde 2020-21. Rated 4/5.

Caracal evaluation for Topologie en Meetkunde 2019-20. Rated 4.7/5.

Student evaluation for the Mastermath Symplectic Geometry 2018-19. Rated 6.4/10 and 4/5 (not sure why there are two marks and why they differ so much).

Statements from students

Statement from a former master student whose thesis I supervised.

Statement from a former bachelor student whose thesis I supervised.

Reports on my teaching

Evaluation of a Topologie en Meetkunde lecture (2022), by Prof. E. van den Ban.

Evaluation of a Symplectic Geometry lecture (2019), by F. Staals (Department of Computer Science)

Completion of the course “Teaching in Higher Education”

In 2018/19 I attended the course “Teaching in Higher Education”, which was meant as a preparatory course to obtain the BKO. It was taught by Dr. Elma Zijderveld. Rather embarrasingly, I cannot find the original certificate of completion, but an email stating so can be found here.