# My year at the African Institute for Mathematical Sciences (AIMS) in 2025
# Introduction
I'm spending my 2025 doing a master's in mathematical sciences at what is sometimes called (opens new window) Muizenberg's "monastery of mathematics", the African Institute for Mathematical Sciences (AIMS). (opens new window)
The founder of AIMS, Neil Turok, wrote an inspiring article on Nature (opens new window) in 2011 about why he started AIMS in a derelict art-deco hotel in one of Cape Town's seaside suburbs. The institute has since grown to multiple African countries and expanded to providing a master's in AI, in addition to the master's in mathematics.
I joined the mathematics programme in January to expand my mathematical knowledge and skills, and to evaluate whether I should pursue further opportunities in academica. I will be updating this page with summaries of the courses and experiences I've had at AIMS as the year progresses.
# Structure of the programme
The AIMS master's programme (opens new window) is divided into three phases:
- Skills courses,
- Review courses, and
- A research project.
Each course lasts three weeks and we do two courses during each three week block.
# Courses
# Block 1 (13 - 31 January): Two skills courses
# Python
An introduction to Python. Since I've done a lot of Python programming before, I used the time to review some of my undergraduate calculus and linear algebra.
# Mathematical problem-solving
This course focussed on a review of methods for proving mathematical theorems.
Our group's final project considered the "egg drop problem" where a farmer enters a (fictional) competition to test the durability of eggs.
I have to admit that I felt quite a lot of nerdy pleasure at solving some of these seemingly inane mathematical questions.
# Block 2 (3 - 21 February): Two skills courses
This block properly challenged me, because not only had I caught a cold, but I also contended with two subjects which I knew very little about.
# Physics problem-solving
This course discussed approaching broad physics questions, such as: "how long would it take a molecule in the center of a room to reach the edge of the room?" using a problem-solving approach.
This course properly challenged me since I haven't considered a single physics problem since my second-year at university in 2014 (more than ten years ago!).
# Statistical skills
This was my first "real" statistics course ever. I enjoyed the combination of rigorous mathematics, combined with exploration and creativity when it came to presenting and analysing data.
During the last week, we had to submit a group report on the data of one of the UN's Sustainable Goals.
Wackerly, Mendenhall, and Scheaffer's Mathematical Statistics with Applications book helped me immensely during this course.
# Block 3 (3 - 20 March): One skill course and one review course
# SageMath
For this course, we are learning how to use the SageMath (opens new window) programming language (which is based on Python) for mathematical problems. So far, it has not yet been very challenging, but it is good to know what the capabilities of SageMath are. I have found it to be more user-friendly than languages such as R or MATLAB.
# Formal methods for software development
For our very first review course this year, we could decide between:
- Classical mechanics,
- Invariant rings and quotient varieties, or
- Formal methods for software development.
I decided on formal methods for software development, because I didn't do any courses on formal verification during my undergraduate degrees.
In week one, we did a review of the different types of formal methods that exist for software development, including model checking and formal verification. In week two and three, we learned to develop and verify Dafny (opens new window) programs.
# Generative modeling (audit/DNF)
I considered doing one of the AI stream's courses in generative modeling during this block. I audited the course for the first few days, but realised that it was too ambitious.
Instead, I am learning more about deep learning by myself with 3Blue1Brown's Neural Network playlist (opens new window) and the Understanding Deep Learning book (opens new window).
# Block 4 (24 March - 11 April): Two review courses
Our first block with only review courses. Things are about to start getting more interesting...
# Quantum information
We are covering classical information during week one, i.e. Shannon entropy. During week two and three, we will cover some axioms of quantum mechanics and quantum information.
So far, it's been interesting to see probability theory come up again.
Update on 18 April:
This turned out to be one of the most difficult courses I've ever done. This is what some of my notes ended up looking like:
# Analytical techniques in mathematical biology
I have never done any biology-related course at university before, but I selected this course because I didn't have the prerequisite knowledge required for the third course, Geophysical Fluid Dynamics.
This course will focus on applying models of differential equations to biological systems such as cell growth and the spread of pandemics.
Update on 18 April:
This turned out to be a fun one. The lecturer made it accessible even for those of us who don't have much experience in differential equations. Here's a snippet of my notes of drawing equalibrium points and systems of solutions:
# Block 5 (22 April - 9 May): Two review courses
# Networks
Graph theory and linear algebra for network analysis with practical applications.
# Algebraic systems biology
From The case for algebraic biology: from research to education (opens new window):
If calculus can be an effective tool for tackling biological problems, why not algebra?
Course page freely available here (opens new window).
# Ad-hoc events/lectures
- 15 January 2025: (Future) quantum computing research at AIMS SA by Dr Ryan Sweke.
- 19 February 2025: AIMS Seminar series, 'The fundamental constants at the heart of measurement and physics' by Prof Jean Philiip Uzan.
- 18 March 2025: AIMS Seminar series, 'Computational & systems medicine' by Prof Dr Sara Vieira-Silva
- 17 April 2025: NITheCS & CoRE AI Masterclass, 'A Practical Introduction to Reinforcement Learning' by Prof James Brusey (Coventry University, UK).
# To be continued...
- 3 (three) course blocks to go.
- 1 (one) research project to go.