Part III: Complex Manifolds (Lent Term 2022)

course description

examples  sheet 1 (updated 2 February 2022) , sheet 2, sheet 3, sheet 4

Moodle page for the course


Part II(C): Topics in Analysis (Lent Term 2020)

examples sheet 1, sheet 2, sheet 3, sheet 4

supporting materials:
A review of some results from IB Complex Analysis.
Notes by Prof. Ben Green on Runge's theorem (external link).


Part III: Differential Geometry (Michaelmas Term 2019)

course description

examples sheet 1, sheet 2, sheet 3, sheet 4

the final course schedule

skeleton notes (last updated November 2019, small changes on p.17):
smooth manifolds,   vector bundles,   Riemannian geometry
reference card on multilinear algebra
Note. In any given year only one of the topics `geodesics' or `Riemannian submanifolds' (found in the Riemannian geometry chapter) was lectured. There were minor variations in the smooth manifolds chapter.

Past exam papers: 2014,   2015,   2019


Part IB: Complex Analysis (Lent Term 2019)

examples  sheet 1 (updated 25 January 2019),   sheet 2,   sheet 3

supporting materials:
Isolated zeros and the identity theorem,   A lemma on holomorphic functions on an annulus,   An example of integration via a `keyhole' contour (updated 24-Feb: a typo corrected and the picture improved).


Part IB: Geometry (Lent Term 2018)

examples  sheet 1,   sheet 2,   sheet 3


Part III: Riemannian geometry (Lent Term 2017)

examples  sheet 1,   sheet 2,   sheet 3

the final course schedule

Past exam papers: 2012


Part II(D): Differential geometry (Michaelmas Term 2010)

examples sheet 1, sheet 2, sheet 3, sheet 4

supporting materials:
Triangulations and the Euler characteristic (a picture is missing as it was drawn by hand)

A set of notes (here is a direct link to the pdf file) by Prof. Gabriel Paternain (updated 28/11/12).
a link (taken from Gabriel Paternain's notes) to a great site about minimal surfaces

An animated gif showing an isometric deformation between catenoid and helicoid (taken from Wikipedia).

Imaginary is yet another great site featuring visualizations (including curves and surfaces), with free software and the mathematics behind it.


Part IB: Analysis II (Michaelmas Term 2009)

examples sheet 1, sheet 2, sheet 3, sheet 4

supporting materials:
Term by term integration and differentiation


Part II(D): Riemann Surfaces (Michaelmas Term 2007)

examples sheet 1, sheet 2, sheet 3, sheet 4

course notes (24-lecture version, pictures are missing as these were drawn by hand), updated 25-Feb-2013