I am currently studying for a PhD in mathematics at the University of Nottingham under Professor Jim Langley. This page lists useful links and stuff. So... yay links. And papers. And dissertations. And stuff.

 

Completed work - Work in progress - Useful links

 

 

My own work (complete)

Title Updated Description
Hilbert's Problems (TeX) May 2007

My third year undergraduate project on Hilbert's Problems - a set of twenty-three problems posed by David Hilbert in 1900 at the International Congress of Mathematicians in Paris which he believed would shape the next century of mathematics. In particular, the project focuses on the first and third problems - that of the Continuum Hypothesis, following Cohen's independence proof; and the equidecomposability of polyhedra, following Hadwiger's Proof.

Dissertation Interim Report (TeX)

December 2007

The interim (end of first semester) report for my dissertation.
Nevanlinna Theory (TeX) April 2008 My fourth year dissertation, studying Nevanlinna Theory, a powerful tool in the arsenal of the analyst studying the value distribution of meromorphic functions. We begin by showing how the theory is derived, state several theorems, and then look at how it has been used by other authors, including in the fields of Hayman's Alternative and the zeros of certain differential polynomials.

 

 

Work in progress

Title Updated Description
Pairs of Non-Homogeneous Linear Differential Polynomials 7th February 2010

An investigation in to whether Jim Langley's 2005 paper can be generalised by relaxing the assumption that N(r,1/F) + N(r,1/G) = S(r,f).

Pairs of Non-Homogeneous Linear Differential Polynomials of identical order

29th March 2010 A special case of the above, assuming that the differential polynomials have the same order.

 

 

Useful links

Title Description

Jim Langley's research page

Professor Jim Langley's personal homepage.

Papers published by Jim Langley Complete list of Jim Langley's publications, including PDFs of most of them.

Jim Langley's Postgraduate notes on Complex Analysis (1MB)

Jim Langley's postgraduate notes on complex analysis.
UoN School of Maths University of Nottingham School of Mathematical Sciences homepage.
MathSciNet Searchable database of papers.