**Part III: Differential Geometry (Michaelmas Term 2023)**

skeleton notes
(updated November 2019):

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.

**Part III: Complex Manifolds (Lent Term 2023)**

**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

*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

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