Studying Mathematics at Oxford
I am about to go into my third and final year of studying Mathematics at Trinity College Oxford and so far all in all, it has been an extremely rewarding, challenging and enjoyable experience. Hopefully this blog post will give you some deeper insight into what studying Mathematics at Oxford (especially in your first year) is actually like!
I’ll start by outlining the structure of the course. So the BA (bachelor’s degree) is three years long but if you get a 2:1 (60%) in that then you automatically have the option to continue studying for one more year to obtain an MA (master’s degree). From my understanding, most people do choose to take this master’s degree but I personally am not going to – simply because I have a graduate job lined up that I am extremely keen to start as soon as possible. I’ll therefore be focussing on the BA part of the degree and in particular the first couple of years.
The first year of your degree is called “Prelims” and all of the modules here are mandatory – meaning that you start your degree with a solid foundation of understanding of all the most important branches of mathematics. These can be widely thought of as either pure or applied modules.
The pure modules comprise “Analysis”, “Linear Algebra” and “Group Theory”. Analysis is the biggest jump from school to university as it involves proving everything from definitions and axioms, requiring lots of rigour and precision, and is therefore split into three modules (Analysis 1,2 and 3). The course starts with sequences and series and checking for convergence, then moving onto checking whether functions are continuous and differentiable and then finally looking at defining an integral. Analysis can seem rather tedious but it is a very important foundation for various areas of mathematics and it provides insight into why things that we take as true are actually true. Linear algebra is more of a continuation from school mathematics and is made up of Linear Algebra 1 and 2 – looking at matrices, eigenvalues, eigenvectors and orthogonality. And then group theory is a very interesting continuation from linear algebra looking abstractly at symmetries.
The applied modules are much wider-reaching. Calculus from school (differentiation and differential equations) is built on with modules in “Introduction to Calculus” and then “Multivariable Calculus”. You are then introduced to a method of solving differential equations called “Fourier Analysis”. There are also relatively self-explanatory modules in “Probability” and “Statistics” and “Computational Mathematics”. And then somewhat between the pure and applied sides of mathematics lies a module in “Geometry”.
So in total there are 14 modules in the first year. Each year is made up of three terms: Michalemas, Hilary and Trinity; and each term is made up of 8 weeks. In any one term in first year, there are five modules, each with two (one hour) lectures a week, one problem sheet a week (which takes a few hours) and one (usually one hour) tutorial going over the lecture content and problem sheet. So it does end up being a pretty much 40 hour work week, but unlike a typical 9-5, you choose when you do the majority of the work. Lectures in first year tend to be 9-11 every weekday morning which means an earlier start then many other subjects but it sets the productive tone of the day well and leaves the rest of the day free for personal study or other activities which is definitely a good thing in some ways!
Alongside these modules there is also computational mathematics coursework using MatLab software. There are a few lessons and problem sheets and then you are given a few weeks to complete two mini projects on MatLab and submit them. This is a fantastic introduction to coding and you can use MatLab as much or as little as you wish to with your core modules described above. The coursework counts towards your final grade in Prelims and you therefore need 40% to pass. The rest of the first year modules are assessed in written exams at the end of first year. You need 40% to pass all of these and there is the opportunity for resits in September before you start second year if this is not that case. However, it’s important to know that first year exams do not count at all towards your final degree grade, so that takes a lot of the pressure off!
The first year is called “Part A” and then the second and third years are called “Part B” and “Part C” respectively. In the second year, the first term’s worth of pure modules are all compulsory: “Metric Spaces & Complex Analysis”, “Linear Algebra” and “Differential Equations 1”, but from there onwards, you get to choose all your modules! There is actually therefore an extremely large amount of choice in an Oxford Mathematics degree compared to other courses, which is rather unexpected. For example in second year I chose to study the modules: “Probability”, “Statistics”, “Quantum Theory”, “Differential Equations 2”, “Integration”, “Integral Transforms”, “Mathematical Biology”, “Calculus of Variations” and “Special Relativity” – so very varied!
There is a similar structure of work in the second year except the problem sheets are longer and you therefore have one per module per fortnight rather than every week. This allows for greater flexibility but means you have to be better at organisation and time-management, which are of course very helpful skills to develop. The second year exams count for 40% of your degree and third year exams count for 60%.
Overall I would thoroughly recommend Mathematics as a degree if you’ve enjoyed the problem solving aspects of mathematics at school. It is an extremely interesting degree which sets you up with a wide range of transferable skills and gives you the option to go down whichever mathematical path sparks your interest!