M336 starts in feb 2010. 4TMA's and 1 examination, like MS221. The M336 course covers two related topics: groups and geometry and is delivered in 16 well known OU type of books including exercises, solutions, summaries and so on. The group theory-stream consists of the following:

Axioms and examples

Subgroups

Generating subgroups

Cyclic groups

Group actions

Group axioms

Subgroups and cosets

Normal subgroups and quotient groups

Isomorphisms and homomorphisms

Generators and relations

Equivalent colourings

Group actions

The counting lemma

The cycle index

Polya's enumeration formula.

Direct products

Abelian groups and groups of small orders

Cyclic groups

Subgroups and quotient groups of cyclic groups

Direct products of cyclic groups

Finitely presented abelian groups

The reduction algorithm

Existence and uniqueness of torsion coefficients and rank

Finitely generated abelian groups

Finite abelian groups

Subgroups of abelian groups

Permutation groups

Conjugacy - p-groups

Sylow p-subgroups

Sylow's first and second theorems

Sylow's third theorem

Applications of the Sylow theorems

Subgroups of prime power order

Review

Groups of order 2p

Groups of order 12

Where now?

2-2018 Teaching by misleading

2 months ago

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