In year 12, students work in small groups with a mentor from either Imperial, our partner university and globally top-10 ranked institution, a mentor from another prominent university, or a mentor from a relevant industry, to complete an academic research project on a topic within the mentor’s area of expertise. Students produce an academic report that will be published in the Imperial Maths School journal, a summary poster and present their research at Imperial at the end of the project. Some of our mentors and their projects from 2023/24 are featured below.

**Dr Marina Evangelou and Ella Orme**

Dr Marina Evangelou is a Senior Lecturer in Statistics at the Department of Mathematics at Imperial, and Ella Orme is one of the PhD students she is currently supervising. They develop statistical methods to analyse complex biomedical datasets and are both advocates for celebrating and promoting the representation of women in mathematics at Imperial.

__Our research project__

“Our research project asks Year 12 students to study real population data, applying statistical techniques to analyse genetic and biological data. Complex diseases like cancer and asthma can manifest and develop very differently in different individuals. By identifying groups of individuals based on their genetic and biological architecture, we will be able to understand better the way they experience disease and respond to treatments. Such information will be invaluable for better diagnosing and treating complex diseases.

Year 12 students will get to familiarise themselves with the fundamental concepts in linear algebra, statistics, and will work on a machine learning clustering algorithm! We hope that the students will take away a sense of curiosity when uncovering the mechanisms behind healthcare.

It’s also a great chance for them to see concepts they learn in school, like matrices, get applied to real research work. As part of the project the students will enjoy coding and enhance their presentation skills."

__Marina’s and Ella’s journeys to Maths__

Marina: “I was interested in mathematics ever since the age of five. I liked mathematics as soon as I started school and just said, ‘I will study mathematics,’ from then. I come from a family of science teachers, so it was normal within the family to talk about mathematics and science. I grew up in Cyprus and I was able to go to a special kind of a private institute specializing in Maths and Science like Imperial’s Maths School. Of course, while I was a student, even an undergraduate one in the UK, I did not imagine that I would stay in academia and pursue research in Mathematics!"

Ella: “I did A-levels in the UK, but there was very little support for me, and I struggled with learning the skills required for MAT/STEP, which I think can be quite demoralising for students in my position.

I was actually planning to study Chemistry for a while, but I realised I would miss Mathematics more. In university, when I began to hone my skills in research, I began to enjoy Mathematics a lot more. I took every opportunity to do Mathematics in a more biological setting, and the research project is based on my current PhD project!”

**Calvin Chen**
Calvin Chen is a PhD student in Theoretical Physics at the Department of Physics at Imperial. His work looks at the nature of causality in gravitational theories. He completed his undergraduate studies at Imperial and his Master’s degree at the University of Cambridge, before returning to Imperial.

__Calvin’s research project__

“I had a cool idea of introducing the Year 12 students to some modern mathematics in an accessible way. Usually what you see in high school mathematics can be 300 years old, and my project will use relatively modern concepts that were established in the past century.

We’ll be using things called ‘indices’ to compute topological properties of different spaces. In mathematics, we sometimes group surfaces by how many holes they have.

The classic example is a doughnut and a coffee mug. They may look different, but it’s possible to transform one into the other by twisting and stretching the shapes because they have the same number of holes. (In a coffee mug, it’s the hole in the handle; and in the doughnut, it’s the doughnut hole in the middle.)

Mathematicians have found ways to calculate certain topological properties in two-dimensional surfaces using indices. There’ll be a bit of coding and a lot of thinking. I hope the students see the fun in part of mathematics that connect to science.”

__Calvin’s journey to Maths__

“I wasn’t particularly interested in mathematics for a long time because I just was not very good at school. It was only when I began to improve that I got into a positive feedback loop where the better I was, the more I wanted to learn.

I was always a bit interested in theoretical physics in high school, just from reading popular science books. My favourite as a high schooler was probably ‘The Elegant Universe’ by Brian Greene.

I found thinking about deep concepts about the Universe really cool, but now as a PhD student, I find that just doing calculations and problem solving, then seeing it all click together at the end is what’s the most fun.”

**Dr Phil Ramsden**
Dr Phil Ramsden has been working at Imperial for 30 years as a Teaching Fellow and e-learning developer. He made his start teaching A-level Maths and Further Maths, and is now the Director of Cross-Curricular Mathematics Education at the Department of Mathematics.

__Phil’s research project__

“My research project looks at chaos theory in population biology. The population of a species fluctuates every year. A small population one year means a small population the next; but a large population one year can also mean a small population the next, because of competition for scarce resources.

In some circumstances, this can lead to seemingly random (and, in a certain sense, deeply unpredictable) patterns in population year-on-year, but those fluctuations actually come from a model that isn’t random at all. Indeed, that model is in some ways very simple, because all it depends on is an understanding of quadratic functions; but amazingly, there are conjectures about it that have still not been proved, and questions whose answers we simply don’t know.

My project will get students coding in Python, creating their own models and scripts. Because the project looks at a very established problem, there are loads of papers that students can look at and try to learn from. I want the Year 12 students to feel free to take their project in open-ended directions.”

__Phil’s journey to Maths__

“For me, it all started with an inspiring teacher whose fascination with, and love of, the subject shone through his lessons. I particularly remember the thrill of learning how calculus worked (in those days, we did some calculus in Year 11). It had been a coin toss between Maths and Science on the one hand, and my other great love, languages, on the other. My Year 11 lessons did more than anything else to swing me towards Mathematics.

There’s actually a personal Maths School connection – my Maths teacher left halfway through my Year 12 to go and teach at… Woodhouse! (No, no, I’m not angry. I’m over it.)

Anyway, by then I’d been bitten by the ‘Maths bug’ and I was hooked. I did Maths at Cambridge, actually leaning more towards Pure than Applied. I taught in schools and colleges for about seven years, and did a Master’s degree (and ultimately a doctorate) part-time. I jumped sectors to Higher Education in the 1990s, but I never forgot my background as a state school student and teacher.”

**Professor Richard Craster**
Professor Richard Craster is the Dean of the Faculty of Natural Sciences at Imperial. He was formerly the Head of the Department of Mathematics from 2011 to 2017. Though he’s very busy in his role as Dean, he still has time for his research in applied mathematics, notably in the fields of metamaterials and fluid mechanics.

__Richard’s research project__

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“My research project is about a game known as Sim. You can play it on the train with a paper and a pen. With two players, start by placing six points on a piece of paper so they form the points of hexagon. Then, each player takes turns drawing lines connecting two points together, and the first player to draw a triangle loses.

There’s actually a theory that can shows that no game of Sim can end in a tie – someone has to win and someone has to lose. But if you tweak the number of players or points on the piece of paper, that may not be the case anymore.

Year 12 students will explore the mathematics behind a seemingly simple game like Sim. They can choose to understand what determines whether a tie is possible in different variations of Sim, as well as develop their own strategies about the best way to win.

I like the idea of introducing abstract mathematical concepts to students in the form of games. Not only is it fun and engaging, and gets students playing against each other and learning in the process, but some of the best mathematicians were also obsessed with games.

I also think the research project teaches students about mathematical problems that don’t necessarily have solutions. How do we study these problems and understand valuable things about them when there’s no set answer?”

__Richard’s journey to Maths __

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“I am not sure there was a big moment where I discovered mathematics or even a part about school which I didn’t enjoy much. Eventually I discovered science in general, had an inspirational teacher, and found what they taught very interesting. Mathematics seemed fundamental to all of science and I felt that by understanding it well, then I could have more options later, so I chose Mathematics as a degree – a pragmatic argument which I think is still true!

It was at university that I really started to become seriously interested in mathematics itself. Seeing deeper ideas and their interconnections was fascinating and then I became a bit more serious! “