Teaching

Universität Hamburg

Exercise classes for Mathematik III - Winter Semester 2020/21

Exercises clases for Dr. Ralf Holtkamp's Mathematik III lecture coruse. (Multivariable calculs, integration on manifolds, differential forms, Fourier transforms, PDE's)

Multiple zeta values (Exercises) - Summer Semester 2020

Exercises clases for Prof. Dr. Kühn's lecture course on Multiple Zeta Values.

Teach@Tübingen

Primes of the form \( x^2 + ny^2 \) - Summer Semester 2017

A lecture course about finding conditions on which primes are represented by a given quaratic form. We want to investigate and generalise Fermat's conjecture that \( p = x^2 + y^2 \) if and only if \( p = 2 \) or \( p \equiv 1 \pmod{4} \).

Numbers! - Winter Semester 2016/17

A lecture course about the construction and properties of different numbers systems. We start by reviewing the construction of the 'classical' number systems \( \mathbb{N} \), \( \mathbb{Z} \), \( \mathbb{Q} \), \( \mathbb{R} \), \( \mathbb{C} \). From here we introduce Conway's system of surreal numbers, a system which supersedes the real numbers \( \mathbb{R} \), and includes infinite numbers \( \omega \), infinitesimal numbers \( \varepsilon = 1/\omega \), and more. In the surreal numbers arithmetic with infinity (\(\omega\)) make sense, so we can talk about \( \omega + 1 \), \( 2 \omega \), even \( \omega - 1 \) (an infinite number less than infinity?), and \( \frac{1}{2} \omega \). Even more weird numbers like \( \sqrt[3]{\frac{1}{4} \omega - 1} + \frac{\pi}{\omega^2} \) also make sense.

Durham University Learning and Teaching Award

During summer 2014, I successfully completed the Durham University Learning and Teaching Award.

DULTA is a recognised teaching qualification, which confers associate membership of the Higher Education Academy. Successful completion required submitting a portfolio evidencing a number of intended outcomes from the UK Professional Standards Framework, such as knowledge of appropriate teaching methods, the skills to evaluate my teaching, and values of respect for individual learners.

You can read through my portfolio.

Tutorials at Durham

Whilst a PhD student at Durham, I was a tutor for the following modules.

Numerical Analysis 2 (Computer Classes) - 2015/16

Assisting Dr Daniel Evans and Dr David Bourne/Dr Smita Sahu with two groups, weekly in Michaelmas and Epiphany.

The computer classes use Python to implement various algorithms from the Numerical Analysis course, in order to numerically solve problems.

Algebra 2 - 2015/16

Three groups meetingly fortnightly in Michaelmas and Epiphany, plus two Easter term revision tutorials.

The course provides an introduction to abstract algebra, particularly group theory and ring theory.

Algebra 2 - 2014/15

Two groups meetingly fortnightly in Michaelmas and Epiphany, plus two Easter term revision tutorials.

The course provides an introduction to abstract algebra, particularly group theory and ring theory.

Analysis 1 - 2013/14

Three groups meeting weekly in Michaelmas and fortnightly in Epiphany, plus two Easter term revision tutorials.

The course sets calculus on rigorous foundations using the \( \epsilon \)-\( \delta \) and \( \epsilon \)-\( N \) definitions of a limit.

Other teaching activities at Durham

I was also involved with various other teaching activities in the department.

Marking at Durham

I was a marker for a number of modules.