I started studying with the Open University in 2018 shortly after completing my PhD in applied mathematics. The reason for this choice is purely based on love for the subject and curiosity to learn more pure and applied mathematics. My first degree was not in mathematics which sort of made me realise how much I really did miss the subject. I started with MST125 which was quite straight forward. I then moved onto M208 which was my first introduction to degree pure maths. Topics covered include real analysis, group theory and linear algebra.

I’ve just completed my exams and whilst awaiting results, I thought I’d write a reflection on the course. M208 was certainly very challenging to start with but much more enjoyable towards the end when the concepts really started to fit together. Whilst taking the course, the focus was more on getting through the books and completing TMAs (tutor marked assignments) before deadlines. Real analysis was quite new to me and required a different way of thinking about mathematics-emphasis was more on proofs, theorems and first principles. We explored behaviour of sequences and series, set theory, continuity, differentiation, integration, Taylor series and convergence. Throughout M208, I had access to face-to-face tutorials which was a blessing. My tutor was very passionate about the subject and I made the most of this opportunity. Whilst online tutorials are great, they don’t really have the feel of in-person tutorials.

The main struggle of M208 was the sheer volume of the material. Being a 60 credit module, there was a lot more to plough through compared to other 30 credit modules. Although Group theory was new to me, I found it really fun-it didn’t feel like hard grind to me and the theorems were rather nice and cohesive. Topics covered include symmetry and subgroups, permutations, cosets, group actions, homomorphisms, quotient groups and conjugacy, counting theorem, etc. Group theory is a bit like marmite in that you either like it (or get it) or you don’t and a lot of students who didn’t fancy abstract mathematics couldn’t wait for it to finish. Abstraction isn’t that bad and sometimes you just want to focus on the ideas without the distraction of the context. At the same time, it turns out that Group Theory has some surprisingly useful applications in website encryption, counting (counting theorem) and particle physics. Linear algebra was quite fun too and it was nice to delve a bit more into the purest aspects of it.

I found that the module tutors were one of the strong features of the course-very supportive and always available to answer questions. This is really important for topics like analysis where you might not immediately grasp concepts at first reading. M208 is really my first formal introduction to pure mathematics and I’ve really enjoyed it even though it was tough at the beginning. I fell behind on the workload as the books were very chunky and the pace of the course was very swift. I had to juggle this alongside full time work, exams, family, etc.

Going forward, I’m considering taking more pure mathematics modules. In particular, I would like to explore number theory a bit further but it seems my best option for level 2 is MST210 which is another 60 credit module but very applied math. There’s some number theory coverage in M303 which is another level 3 module. Complex analysis (M337) looks really appealing and very appropriate especially having completed real analysis.

Irrespective of whatever I choose to do next, this OU journey just gets more and more exciting! I’m ever so grateful for the opportunity to learn through the OU!