Maths and Computational Biology

Lectures

This subject offers a profound look into the mathematical and computational aspects of biological processes. It integrates principles of mathematics, computer science, and biology to delve into intricate biological systems such as sequence alignment and SIR models. The lectures present a thorough exploration of the mathematical models and the computational knowledge required to implement the models in python…

Lectures commence at 9am on Mondays, Wednesdays, and Fridays. The Monday and Friday lectures focus on the mathematical principles behind the content while the Wednesday lecture focuses on the code. The curriculum is structured to sequentially introduce the mathematical and computational aspects which become more complex as the year progresses.

Michaelmas:

• Block A: Introduction: You are taught from scratch Python in both Pycharm and Jupyter Notebook. If you enjoyed the coding section in Part IA Mathematics or Math Bio then you will find this a good refresher or introduction to Python. However, it is very fast paced therefore if you struggled previously you may find it hard to keep up. Following the introduction the course teaches data visualisation through imported libraries such as matplotlib and seaborn and then goes into stochastic models. Stochastic models section is quite mathematical covering random variables, sampling, Monte Carlo simulation and numerical optimisation. You will also learn how to code the stochastic models.
• Block B: Bioinformatics: This section purely focuses on coding. You will be taught how to code models that can perform different types of sequence alignments. I can’t talk about the Phylogeny section as it was not covered in previous years.

Lent:

• Block C: Foundations: This is a very mathematically heavy block that expands on statistical knowledge taught at A level and Part IA Mathematical Biology. Starting with Binomial distribution and rapidly progressing into more advanced distributions. This is followed by Bayesian methodologies and linear algebra which includes vectors within biological systems.
• Block D: Systems: A deep dive into the intricacies of biological systems examined in both discrete and continuous time frames. This mathematically rigorous module delves into stochasticity, models fitting to data, and a detailed examination of time-resolved data. Students will be able to bridge mathematical principles with biological processes, offering an integrative understanding of systems dynamics.

Easter:

• Block E: Data Science: An advanced exploration of data analysis in the realm of biology. This block introduces the foundational concepts of clustering and classification, combining mathematical approaches with biological data sets. Here, students will learn how to efficiently categorise and interpret vast biological data, reinforcing the symbiotic relationship between maths and biology.

Supervisions

Supervision work is always maths practice questions. Much like IA, supervisions are an ideal time to discuss the questions and clarify concepts. This is critical as the content layers over the year and therefore without understanding of the basic knowledge you will struggle to implement the more complicated concepts.

Practicals

Practicals are every week and are directly related to the current lecture content following on from Wednesdays coding lecture. The practicals all follow the same format of questions progressing in difficulty. This helps you understand how to create the coding models required and there are PhD and Postdoc students as in IA practicals to help you. This year the completion of practical work will provide 10% of your grade.

Coursework and Exams

The coursework is divided into 2 parts. Each is a project and directly relates to the coding work you have done. Both projects are worth 15% and are given out in Lent term. 10% of the final mark is from a 3 hour computer examination sat in June which focuses on the implementation of computational methods learnt in practicals. If you understood the coursework and practicals this is a very straightforward exam. The final 50% of the final mark is from a 3 hour mathematical theory paper sat in June covering all the mathematical concepts learnt. Both are closed book exams so memorisation of key concepts is essential.

Useful resources