# Mathematics and Computer Science

We talked about *Navier Stokes
equations*
and how they are a mathematical abstraction of the world around us. We
talked about how such differential equations cannot necessarily be
solved in practice, and therefore we need to form numerical solutions.
We mentioned that the Met office solves these equations on 1km^2 sized
grids across UK for weather prediction. We discussed a little what
uncertainty meant in this context, and how modelling could have a
deterministic part and a stochastic part.

Triggered by talking about what had come up in the first week of
lectures, we discussed the relationship between Computer Science and
Maths. In absolute terms we talked about how many of the challenges of
Computer Science are how to *implement* maths on a Computer (e.g. the
Turing test, the way a processor works). But for Mathematics,
particularly pure mathematics, there is a lot of interest in
*separating* the maths from the implementation. Mathematics can stand
alone, outside implementation, emerging purely through abstract thought.
We looked at the wikipedia page for *Principia
Mathematica* and
talked a little about set theory with a focus on *Godel’s incompleteness theorem*
and the *barber paradox*.

In the end we talked about the Spell Correction challenge for internet
companies make spell corrections? We speculated it was on the basis of
past data and probability may be used to rank the suggestions. We
thought that it might be a good idea to look at
**n***-gram
models* to understand this better.
We are hoping for Daniel Bernhardt to visit us (from Facebook’s London
office) to give a talk on this material.