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.


Part III: Differential Geometry (Michaelmas Term 2018)

course description

examples sheet 1, sheet 2 (updated 30 October 2018), sheet 3, sheet 4

Last example class:   Monday 21 January at 2pm in MR11

the final course schedule

skeleton notes (updated December 2018)
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


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(C): Topics in Analysis (Lent Term 2014)

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


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 III: Complex Manifolds (Lent Term 2009)

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


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