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• MATH3303/7333: Abstract Algebra & Number Theory, 2021

Six-page reports:

The following is a list of topics suitable for the reports, due on 21 May 2021 at 5pm. If you would like to choose your own topic, please first ask for permission.

Burnside's problem, Burnside's theorem, Cayley graphs, character theory, class groups, Coxeter groups, conjugacy class equation, discrete valuation rings, elliptic curves, Fuchsian groups, Galois groups, group actions, Hilbert's basis theorem, Hilbert's Nullstellensatz, homogeneous spaces, homology groups, Lie groups, Nilpotent groups, Ore's conjecture, principal ideal domains (PIDs), 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

Reports should be prepared in LaTeX using the following template. To turn this into a pdf documents resembling something like this, you may also need to download the style file. Please do not change the margins or font size of the .tex document.

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.)

• MATH4301: Advanced Algebra

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