#mmathphys

I’m currently (Nov 2019) a third year Masters of Maths&Physics student at the University of Warwick, UK. 

Being MathPhys means I get to enjoy a diverse set of optional modules, but also that I had to be quite decisive in the first two years about which streams of maths and physics id have to avoid, because I simply don’t have the credits (and the Time) to do all of them. 

I chose to essentially ignore Algebra, Topology & Astro, just because analysis and particles was somewhat more appealing to me. I did independent study into Groups and Rings, but it was decidedly not formal, just enough to help get a beginner understanding of Ideals and the quotient groups. 

(idk how to format this properly and it’s late, I cbb to look it up, soz)

MATHS:

In my first year I did Analysis I (limits), Anal II (differentiability), LinAlg (vectors&matrices), DiffEqns (ODEs), SetTheory, Methods of MathPhys (line integrals)

In my second year I did Anal3 (integrability), Variational Principles, PDEs (BVPs), Theory of ODEs (IVPs and Phases), MVC (vector calculus) Mehods 2 (fourier anal, intro to Tensors)

In my 3rd year I am (planning) on doing Functional Anal1 (inf-dim vector spaces), FA2 (banach and their duals?), Fluid Dynamics (idk why it’s a maths module?), Complex Anal (complex integrals?)

PHYSICS:

first year I did Quantum (square well), E&M (4 laws), Foundations (waves&thermal), Mech. and S.rel., programming (python), intro to particles

second year I did Quantum (H-atom and QHO), EM&optics (Maxwell and matter), Fluids (intro to N-S), Thermal 2 (idk why it’s two we didn't do thermal 1?, statmech), Hamiltonian Mech, Computational (python)

CMP1 is a 10 week module, spanning from halfway through Term 1 to halfway through term 2 in yr 3, and is focused on using quantum mechancis to discuss solid matter, with a focus on crystals.

We will apparently be discussing free electron models, band theories, semiconductors, magnetism, and superconductors with a neat aside on why frogs levitate in strong magnetic fields (very excited to learn this)

So far the actual Quantum Nature of the course hasn’t been very forthright, but I’m assured that it will make an appearance, we have just discussed Brillouin Zones and the reciprocal Lattice vector, after some 1d diatomic chains and their dispersion relations.

Plasma Electrodynamics is a 5 week module, from wk6 to 10 of winter term of yr 3, that builds upon the electrodynamics module from the first five weeks in a highly applicative way. 

Scientific Computing is Hard! :(

I started programming at university, but the only experience were found in the two previous term-length modules on python, where the hardest things we had to do were error approximations via MonteCarlo Sims and solving ODEs with premade packages. 

SciComp is a module about C,  and thus it's the first module where we actually need to care about memory and have to spend a lot of care with the code.

First two assignments weren't terrible, about functions and pointers, or pointers to arrays which act as pointers and pointers to pointers to arrays etc, and although it was initially easy to get confused about * and & operators for dereferencing and initializing pointers / memory locations, they were okay.

But 3rd and 4th assignments are horrible, the 3rd assignment gave us a piece of botched code and a specification to solve an inhomo complex pde (or two inhomo coupled pdes) and just let us at it, almost all of what I typed I had to try and learn from online, there was so much I didn't feel I knew or even knew I had to know. And the 4th isn’t much better, this time we have a 2d state vector nonlin inhomo pde and have to solve it completely from scratch. We haven’t discussed stability or discretization for nonlinear situations at all and it’s definitely taking up most of my time (I should definintely be working on it rn but haha?)

I’m continuing with the module, but I hope I take enough modules by the end of the year such that my Year’s Grade doesn’t get overly screwed by my inevitable bad mark.

Functional Analysis 1 is a 10 week module in my first term of yr 3, and is described as a module about inf-dim Hilbert spaces, we are as I’m typing this, on our 7th chapter, and ch.7 was Hilbert Spaces.

Obviously there was a lot of BuildUp, we started with reminding ourselves what a vector space was (studied rigorously last in 1st year) and then normed spaces, completion of spaces, the lebesgue spaces, inner product spaces and then Hilbert Spaces (a complete inner product space equipped with the natural norm)

Most of that has been fun for me, as in previous years I haven't delved into norms, or topologies, and decided at the last minute to not study measure theory, but I am excited to see where we are going with them, apparently we are dipping into Spectral Theory and Sturm-Liouville problems (which I understand are related to Fourier Analysis and Quantum Mechanics? not sure)

Electrodynamcis was a 5 week module in my third year first term, and we started somewhere a bit Rogue compared to where we ended my 2nd year Elecotrmagnetic Theory and Optics module, because we moved from Boundary Conditions on E,D,B,H and fields in nonvacuous space, to optics, and then this module started and it started with revising the Lorentz Transform of my first year mechanics and relativity class.

But it quickly became obvious why, we discussed the notion of a 4-vector and then 4-tensors and why they transform under a Lorentz Boost among their other concepts such as the covariant vs contravariance etc. etc. and then we started EM theory in relativistic framework. Great Fun. 

Derived the Faraday Stress Tensor and showed how the 4 potential forms it, derived the Maxwell's equations’ equivalent form and had a discussion about Gauge.

Went on to prove that in the Lorenz Gauge, the form 4-pot as a retarded time volume integral of 4-current density and then used that (kinda cheatingly) in Antennae Theory before returning to Relativistic framework to discuss Synchrotron Radiation before tantalizing us with notions of Lagrangian ED and the Stress-Energy Tensor.

Quantum Physics of Atoms was a 5 week module at the start of my third year, and was my first proper foray into actual quantum physics, in previous years we had been introduced to phenomena (spin and superpositions and wavefunctions etc.) and certain easy systems (hydrogenic system, quantum harmonic oscillator, infinite square well etc.), but this module actually felt... proper, if a bit short.

We discussed approximate methods of QP, Perturbation Theory and the Variational Method, and applied it to several things, such as Spin-Orbit Coupling and the Zeeman Effects, and also to some many particle atoms to discuss spin multiplets and Hund’s Rules, finishing with some TimeDependent PT with Quantum Jumps

Nondegenerate PT  was fun but I was concerned it wouldn’t be useful, but then when covering Degenerate PT I was glad to learn that it’s about creating a set of eigenstates that can be used in NdPT, thus making the practice with that feel worthwhile. 

The Variational Method was interesting, but we didn’t go very far with it, but it had flashes of my 2nd year modules on Hamiltonian Mechanics and Variational Principles which was lit, but I hope we use it more in our optional modules this or next year.