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M336 Groups & Geometry Stuff

M336 - when the end is near

Here are the old exam papers, 1994 - 2001, which you can't get from OUSA.

Health warning:  This is not official Open University material.  All  errors, misconceptions and misleading statements are my very own

M336 Course notes

Block 2 Basics

Very short intro notes / tips for each unit in this block.

 

GE1 Counting with groups

Summary of all the methods of counting with groups.

 

GR1

A slightly different take on prime factorisation, lcm and hcf

 

GR2

Comparison of the properties of groups of order 8

 

Block 2 dayschool

Handouts from Silvia Barbina's gig on 11 Jan 2014 in Coulsdon.

Block 4

3-d lattices

GE5

Some indirect symmetries of the cube. Fun pickies from a question I used at last year's dayschool

 

GE6: Exercise 1.6

Explanation of what you're actually doing when you describe an offset.

 

GE6

Some pickies of 3-d lattices that might help you visualise how the different types emerge.

 

GE6

Bravais Lattices - all you need to know in one song.  And here's a truly atrocious rendering of it.

 

Block 4 dayschool

Handouts from Silvia Barbina's kneesup at Coulsdon on 26 Apr 2014

 

exam tips bravais lattice song

These are miscellaneous notes on topics/exercises that some students have found difficult.  I'll drop in my dayschool handouts after each event, and add in other interesting things when I come across any.

reduced basis for a lattice Glide reflections colourings wallpapers - standard form

Click on graphic to view / download

Dihedral group D6 M336 exam solutions

BUT: you're honour-bound to try the questions before you look at my answers!

Click to enlarge Exam Tips.

Groups stuff

How to count the number of elements of a certain order in Abelian groups.

 

D6: The Full Monty

Revision: A summary of all the groups stuff applied to D6 (my fave group).

 

Subgroups & orders

Revision: All the theorems about orders of subgroups and a few other useful theorems about orders.

 

Proofs & Strategies

This is the official M336 P&S Booklet containing useful summaries and stuff

 

Exam solutions

These are  the latest versions  for 1994 - 2012.

Click on graphic to view / download

Block 1

Block 2

IB1 Degrees

Some alternative ways of thinking about the degree of a tile or vertex.

 

IB2 Order! Order!

Order of a group vs order of an element

 

IB2 Elements of D6

 

IB4 Dihedral group

Cayley table for D10, using colours for group elements.  How cool is that!

 

Block 1 dayschool

Handouts from the session in Coulsdon on 16 November 2013.

Tilings definitions dihedral group in colour

 

GE3 Glide stuff

A general note on glides, to sort out what the different forms of notation mean

 

GE3: Exercise 1.8

How to find a reduced basis for a lattice - easy if you draw the picture!

 

GE3: Minimality region

They liked this picky at the dayschool, so here it is.

 

GE4: Exercise 2.7

Wallpaper stuff - starting off with standard form and going backwards.

 

Block 3 dayschool

Handouts from the gig at Coulsdon on 8 March.

Block 3

order of a group vs order of an element Block 2 Symmetries of a hexagon dayschool prime factorisation groups of order 8 ds4 pickie

Shirleen Stibbe's OU stuff

dayschool3 minimality region subgroups ds3 pickie

Update 10/6/2014: Corrected minor typo in Q16 (a) of 2012 solutions.

menger lattice fractal 2 lagrange_1 rip m336 crying girl Apples for sale at an orchard in Upstate New York