When I was in high school, I was fortunate to have participated in a few years of Olympiad Maths trainings in Hong Kong. Having learnt a range of mathematical concepts during these trainings, I found studying abstract systems and mathematical methods and finding ways to integrate them when solving problems truly enjoyable.
I was also fascinated by how ideas in different branches of Maths were closely interconnected, e.g. sometimes we can find a geometric interpretation of a result in algebra. Therefore, I decided to pursue a Maths degree in order to have a deeper understanding of the beauty of Mathematics.
Among all courses I have taken so far, I enjoyed the courses on group theory the most. I knew nothing about groups before I went to Cambridge, and so it seemed to be very hard to understand when it was first introduced to me during the IA Groups (a course in first year Cambridge Maths) lectures. However, once I got used to the basics, I started to appreciate the beautiful structures of groups. For instance, we may have two groups sharing very similar properties. Then by using certain criteria we may actually prove that they are “homomorphic” to each other. Sometimes we can divide a group into smaller classes with nice properties, producing a new funny group, i.e. the “quotient” group. Apart from these examples, mathematicians still have numerous ideas on how we can play with groups, and some other abstract objects like rings, fields and modules. Having completed IA Groups and IB Groups, Rings and Modules, I still wish to know more about the structures of these objects, and so I plan to study group theory at a more advanced level by taking several Part II courses on abstract algebra next year.
Besides lectures and supervisions, recently I enjoy going to the Murray Edwards Maths gathering every Sunday.
This is a new activity which has just started this year. It provides all girls doing Maths at Murray Edwards with an invaluable opportunity to sit down together, have some snacks and drinks, and most importantly, talk about Maths that they have been involved in. A few weeks ago, I shared about how we can make use of Set Theory to solve and visualize a Number Theory problem. I felt very grateful to have received some very thoughtful responses from my peers. Giving this talk did not only boost my confidence in creating and talking about my own ideas in Maths, but also allow me to gain insights from others’ responses.
The beauty of Mathematics, in which different theories are blended together to make new discoveries, never fails to amaze me. If it does amaze you as well, you should definitely consider studying Maths, as there are no better ways to satisfy your love for Maths. A Maths degree will also equip students with the ability to understand and analyze the complexities of the world better and therefore benefit them in everyday life.
I would encourage those who are interested in doing a Maths degree to participate in Olympiad Maths events, or read Maths beyond the A-level syllabus. This should give you a good taste of the subject. And always remember that the key in Maths is to SOLVE problems. So happy solving!