Here are the course notes:

**Andrew's Lectures**:

- Classical Mechanics Primer – Manifolds; Vector fields; Symplectic manifolds and what they're good for.
- More Mechanics – Hamiltonian flows and hamiltonian vector fields; Tautological 1-form on the cotangent bundle; The symplectic form; Geodesic equations and Christoffel symbols.
- Hamiltonian Flows and Actions – Proof that Hamiltonian flow for the energy function gives geodesic motion; Poisson brackets; The action principle.
- The Quantum Particle – Parameterized particle and its quantization; Operator ordering ambiguities, and diffeomorphism invariance a principle for resolving them; removing the parameterization dependence.
- The Supersymmetric Quantum Particle – Adding supersymmetry to the particle action; Symmetries of the action and their conserved charges.
- N=2 Supersymmetric Quantum Mechanics and Differential Forms
- Gauge Theories
- BRST & Lie Algebra Cohomology

**Derek's Lectures:**

- The Real Scalar Field – Basic example of a gauge theory: the "N-component real scalar field"; Promoting global symmetries to local 'gauge' symmetries; Bundles; Scalar field as a section of a trivial vector bundle.
- Scalar Field in Bundle Language – Generalizing the N-component real scalar field to the case of a nontrivial bundle.
- Principal Bundles –
*G*-bundles and principal*G*-bundles; The frame bundle; Getting a principal bundle from any "bundle of gadgets" using "generalized frames".- (Actually, this lecture was delivered by Eric Babson, in my absence; these are the notes I gave Eric for the lecture, not notes from his actual lecture. Eric gave some examples, including the principal bundles corresponding to the two nontrivial vector bundle examples in Lecture 2.)

- Associated Bundles – Reconstructing a "bundle of gadgets" from its principal bundle of generalized frames; Examples of associated bundles; Vector bundles from representations; Gauge transformations as sections of an associated bundle of groups.
- Connections and Holonomy – Ehresmann connections on a principal G-bundle; Horizontal lifts and parallel translation; Holonomy; Wilson loops.
- Covariant Derivatives – Using a principal bundle connection for parallel transport in any associated bundle; Covariant derivatives in associated vector bundles; Connection and covariant derivatives in local coordinates.
- BF Theory and 3d Gravity – Introduction to BF theory, with 3d gravity as a special case.

(If you have a UCD Math account, you can also get these notes via the svn by navigating to wally/quantum_geometry)