The second year essay is an opportunity to study a topic of your choice, and to gain some experience in mathematical writing.
Most of the advice that can be given about the essay is self evident, but is worth repeating.
Choose a subject that you are deeply interested in. If you are invested in your topic, the reading and writing will come much more naturally. Choosing the level of the topic may also take a few tries: if you can understand everything on first reading, then perhaps try and push yourself a bit harder; but conversely, if you are struggling to make it through any given text, then it may be prudent to scale back your topic. In particular, if you are blindly copying from a book because you cannot understand a proof, then it may be best to simply omit the proof.
The essay should be presented clearly and professionally; omit contractions and abbreviations, and consistently adhere to a set style guide.
Below, we have compiled a collection of previous essays that you can use for reference. You can use it to see past topics covered; to gauge how difficult or accessible topics should be; how long the essay should be; or just to read at leisure to learn about some new maths from other students – after all, second year essays should be accessible to other second year students.
We also have a collection of 3rd year essays:
| Mark | Title |
|---|---|
| 74 | Algebraic Differential Forms |
| 82 | Structural Foundations in Topoi |
| 83 | Eulerian and Hamiltonian Cycles in Cayley Graphs |
| 92 | Riemann Surfaces |