- The topics to be covered include the following: Groups and subgroups: revision of de nitions with the standard examples (GLn, Z, Z mod n, dihedral
groups, Sn and An, introduction of basic properties such as uniqueness of identities and inverses, subgroup tests, Cayley tables, etc. Cosets and Lagrange's Theorem, direct products, statement without proof of the classification of fi nitely generated abelian groups. Homomorphisms. Quotient groups and normal subgroups. Group actions (orbits, stabilizers).
First Isomorphism Theorem (2nd and 3rd stated without proof). Cayley graphs.
Rings, Fields, Integral Domains. Field of fractions of an integral domain. Polynomial rings, including factorization of polynomials over a fi eld. Ring homomorphisms and quotient rings. Prime and maximal ideals.
Introduction to extension fields: Algebraic extensions (defi nition of a vector space will be briefly recalled and hopefully de finition of a module will be at least mentioned in passing).UFDs and Euclidean domains.
Mechanics of Rigid and Deformable Bodies
General information about the level 3 honours programme.