# Mathematics and Physics - 3rd Year

The second year introduced some of the most fundamental ideas of physics as well as some important theorems and techniques from mathematics. When we try to apply these to explain the phenomena we observe, we nearly always require one more ingredient namely approximation. This should be familiar from the second year fluid mechanics module, which looked at some approximate solutions to the (Navier-Stokes) equations of fluid flow. In the third year, we will see that it is the case in nearly all branches of physics and applied mathematics.

The type of approximations used to find satisfactory explanations of what we observe turn out to be similar whether the underlying laws are those of classical mechanics, statistical mechanics or quantum mechanics. Typically, one sets up an idealised model of some phenomenon, solves the equations of the model (often with further approximations) and relates the results back to what is observed experimentally. Sometimes the same model and approximations are appropriate in different circumstances. For example, the behaviour of electrons in metals and in white dwarf stars is described by the same model.

The third year combines modules, which deal with the theoretical description of phenomena we observe, with modules designed to extend your understanding of pure mathematics and the fundamental principles of physics. As in the second year, it should be possible to cover most areas of physics, while in mathematics you will need to be more selective. In mathematics you can opt to continue a broad training by taking the second year modules you didn't take last year and/or develop your interest in your preferred areas by choosing the appropriate third year modules.