Choosing an Undergraduate Maths Project

[jumpr]

I'm in the latter stages of my third year (of four) studying maths at university. I have to pick my modules for my fourth year, and we have the opportunity to do a project for one of our modules. This normally entails independently reading around a subject and writing a 30-40 page document that isn't too dissimilar in structure and style from the lecture notes used by our lecturers.

Ideally, I would like to do a project on some branch of algebra, but wasn't sure specifically which part. So far, I've done modules in linear algebra, group theory, ring theory, representation theory, Galois theory and algebraic number theory. There's nothing stopping me doing more advanced stuff in these areas, but I also wouldn't mind doing something pretty new. It's meant to be fairly advanced, but understandable to a competent/good final year undergraduate.

Has anyone got any suggestions? I'd thought about topics such as algebraic graph theory, Noetherian ring theory or Lie algebras, so if anyone could give me an opinion on some of those, it would be useful.

 

[TonyG]

Dear student,

It's great to hear that you are interested in pursuing a project in algebra for your final year. I would suggest considering a topic that is both new and relevant in the field of mathematics. One area that has gained a lot of attention in recent years is computational algebra, which involves using computer algorithms to solve problems in algebraic structures. This could be a potential topic for your project, as it combines your knowledge of algebra with the practical application of computer science.

Another interesting area to explore is algebraic geometry, which studies the algebraic properties of geometric shapes and spaces. This field has connections to other areas of mathematics such as number theory and topology, and has applications in fields such as physics and computer science.

In terms of your specific ideas, algebraic graph theory is a fascinating topic that applies algebraic concepts to the study of graphs and networks. This could be a good choice for your project, as it combines your previous knowledge in algebra with a new application. Noetherian ring theory and Lie algebras are also interesting areas to explore, but may require more background knowledge and may be more challenging for a final year project.

Ultimately, the most important thing is to choose a topic that you are passionate about and that you feel confident in tackling. I would recommend discussing your ideas with your professors and seeking their advice on a suitable topic for your project.

Best of luck in your project and in your future studies. Keep up the great work!