SF & JS Two-Subject Moderatorship )

**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

File translated from T

On 27 Mar 2007, 14:21.