Over halfway

I have just passed the halfway point of these two courses now. Perhaps it will feel more like downhill from now on. I hope so!

Having finished GR3 from M336 I switched back to Number Theory and went through book NT5 on multiplicative functions. The main multiplicative functions discussed were τ, σ and Euler's φ function. τ(n) is the number of distinct divisors of n, σ(n) is the sum of these distinct divisors of n and φ(n) is the number of positive integers not exceeding n which are coprime to n. Whenever I foray into number theory I always feel more at home. I love the eclectic mixture of puzzles and theories.

I then went back to completing GE2 from M336 on periodic and transitive tilings. This finally gave me the chance to thrash through some of the cards and overlays in the geometry envelope! A periodic tiling is just a tiling that has a translation subgroup that is generated by two independent non-zero translations (a so called wallpaper group). A transitive tiling is one where the symmetry group of the tiling acting on the tiling itself generates a single orbit. In essence, any tile can be mapped to any other tile by an element of the symmetry group of the whole tiling.

I quite liked this book. We delved into translational tilings and orbits of tiles, edges and vertices. We drew orbit diagrams and eventually pondered over the Grunbaum-Shephard classification of transitive tilings.

Now I have returned to unit 5 of Mathematical logic - Formal Proof - and I am beginning to feel that things are getting heavy again! In the mean time as Christmas is rushing up towards us I have been trying to get the next two TMAs completed. This I have nearly done. I have had my results for the first two and I scored a double 100, which surprised me a bit. My nerdy record at the OU is beginning to be a bit worrying because in the 21 assignments I have completed since 2009, I have only dropped 1 mark!