M208 - TMA02 - Kick off

Completed 3 out of 5 questions of M208 - TMA02 today. TMA02 is entirely on Group Theory.
The first question lists three algebraic structures which are possibly groups. Using the group axioms you have to determine if the structures are a group.
The second question is about a 2D object for which all geometric symmetries must be determined. The symmetries have to be written down in 2 line permutation notation. From these a Cayley Table for the group must be set up. Finally you have to determine with which well known group our group is isomorphic.
The third question is about cyclic groups, isomorphisms between them and subgroups of them.
Q4 and Q5 TBD at a later date / time. ( M208 is thus still on schedule. )

I often 'read ahead' in various mathematics books., those who are subscribed to my blog know that combinatorics, algebra and number theory are my favourite subjects ( not necessarily in that particular order ). Anyway, the subject that is 'holding me back' most and which I merely see as a 'supporting' subject is complex analysis. Sofar it occurred in Lie Theory and Analytic Number Theory. Subjects that ( I hope ) temporarily closed their doors on me. It's time to handle this issue. I found a series of 24 Mathematica Notebooks on 'Complex Analysis with Mathematica. Learning more practical applicationa of Mathematica -and- Complex Anallysis sounds great. - Because they are so obvious I forgot to mention fractals where complex functions play a major role.