## Teaching

#### • MATH3303: Abstract Algebra & Number Theory, 2019

Assignments:

Assignment 1 is due on 21 March, 4pm (worked out Solutions to assignment 1).

Assignment 2 is due on 2 May, 4pm (worked out Solutions to assignment 2).

Quizzes:

First quiz (Ole's solutions, probably all wrong).

Second quiz (Ole's solutions, definitely all wrong).

Presentations:

The following is a list of topics suitable for the 5-minute presentations
to be held in week 10:
Burnside's problem,
Burnside's theorem,
Cayley graphs,
character theory,
class groups,
Coxeter groups,
conjugacy class equation,
elliptic curves,
Fuchsian groups,
Galois groups,
group actions,
homogeneous space,
homology groups,
Lie groups,
nilpotent groups,
Ore's conjecture,
projective linear group,
root systems,
representations of groups,
the Grigorchuk group,
the modular group,
the Monster,
the socle of a group,
the word problem,
Thompson's group F,
Weyl groups,
wreath products

Sample beamer files for the presentations.

The essential files are the beamer file Hodge-polynomials.tex and the beamer style file beamerthemeSOW.sty.

Old exams:

The 2013 Exam (Ole's worked out Solutions, probably all wrong.)

The 2014 Exam (Sam's worked out Solutions, 100% correct.)

The 2015 Exam (Ole's worked out Solutions, probably all wrong.)

The 2016 Exam (Ole's worked out Solutions, probably all wrong.)

The 2017 Exam (Ole's worked out Solutions, probably all wrong.)

The 2018 Exam (Ole's worked out Solutions, probably all wrong.)

#### • MATH4301: Advanced Algebra

You can download the assignment on Coxeter groups, with worked out solutions
here.

#### • MATH3500: Problems & Applications in Modern Mathematics

The notes of the module on the Riemann Hypothesis are
here.