Mathematics

Mathematics

Submitted by Detlev Conrad … on Fri, 05/18/2012 - 13:47

From 2008 until 2011 I obtained a First Class BSc in Mathematics at Sheffield Hallam University.

In my final year, my Thesis focussed on large number factorization, specifically the Quadratic Sieve, a mathematical method by which large numbers can be factorized reasonably quickly, including writing a basic implementation of it in C++. Today the Quadratic Sieve has been replaced by the Number Field Sieve which is faster, however also more difficult to implement if you are not a seasoned programmer. The underlying principles and ideas are the same, but while the Quadratic Sieve makes use of only real numbers, the Number Field Sieve uses complex numbers.


Further modules in my Final year were Analytical Fluid Flow, Modelling with Partial Differential Equations and Tensors.

  • Fluid Flow mainly picked my interest as an interesting module - and turned out to be in my eyes the most enjoyable of all my final year modules. In a nutshell, the mathematics of fluid dynamics seek to describe the beaviour of a gas or liquid. In ideal simplified cases this can be done analytically, however in real life we must approximate with simplyfying assumptions and numerical methods.
    It was my enjoyment of the Fluid Flow Module that made chose a fluid dynamics based PhD.
  • Partial Differential Equations are the mathematics that describe the movement around us, or at least a lot of it. Flows of liquids, conduction of heat, all these processes are described using partial differential equations. They were an ideal complementary module to Fluid Dynamics. Even more, it introduced me to the mathematics of computing solutions to problems described by partial differential equations.
  • Tensors are primarily used in relativity. However, they draw on partial differentials where they are also sometimes used as alternate notation to vectors. Having chosen two modules that draw on partial differentials and differential equations, it was a natural choice to compliment my choice with tensors. As it turned out, this was a very good choice, because as different as these three modules may seem, they all share some underlying principles.

Lastly, a compulsory module looked at modelling with mathematics, from problems such as malaria infection rates (described by differential equations) to image processing.