Requirements/prerequisites:

Duration: 24 weeks

Number of lectures per week: 3 including totorials

Assessment:

End-of-year Examination: 3-hour end of year exam

Description:

• Generalised eigenspaces; Unique factorisation of polynomials; Minimal polynomial of a linear operator; Direct sums of vector spaces; Primary decompostion theorem; Jordan form.

• Linear forms and duality; Diagonalisation of scalar products (including hermitian); Quadratic forms; Sylvester's theorem; Spectral theorem for normal operators on finite dimensional Hilbert space.

• Multilinear algebra; Wedge product; Hodge star operator.

• Derivative as a linear operator; Equality of mixed partials.

• Introduction to manifolds; Differential forms; Poincare lemma and Stokes theorem; Gaussian curvature.

• Inverse function theorem; Implicit function theorem.

Mar 27, 2007