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Richard Pinch answered on 30 Jun 2020: last edited 30 Jun 2020 8:30 am
I work on a range of problems but they are all about data — finding patterns in very large amounts of information and making sense of what those patterns mean. Mathematics is a vital part of that. Right now I’m starting a project about looking for computer viruses in emails. So I need probability to answer the question “what’s the chance of a certain pattern occurring at random?” and its close relative, statistics, to answer the question “is this pattern so unlikely to occur at random that I should assume it is deliberate?” To say what I mean by “pattern” would take too long here, but it is a sort of algebra. So for example 112233 is a simple pattern. More complicated is the pattern 11XX33 where X denotes a number but we don’t know which. So 112233 is an example of 11XX33, and so is 114433 and 115533, 116633, and so on, but not 117833, because X denotes the same thing wherever it occurs. Virus writers try to disguise their code by making it different every time, so our project is to spot patterns in common between the various malicious emails, which are rare enough that they don’t occur by chance in genuine emails.

Daniel Bearup answered on 30 Jun 2020:
I work on problems relating to how our environment is changing. Specifically, I am interested in how we are affecting populations of animals (plants, fish, insects etc).
For example, I use maths to describe how a population changes over time. To do this, I think about different things that might affect a population’s size, like food availability or the effect of other species within a habitat, and come up with a mathematical description of them (usually a differential equation). I can then use these mathematical models to predict what might happen in the future or how a specific change to conditions might affect a population.

Omduth Coceal answered on 1 Jul 2020:
Hmmm…. all sorts of problems, using all sorts of maths. For example, to solve problems in air pollution you need to understand how particles move in turbulent flows. This gets you thinking about the equations that govern fluid flow. They are partial differential equations, which need calculus and numerical analysis to solve. You can also approach the problem by thinking about random walks. This requires a different way of thinking using probability concepts. If you consider chemical reactions then you need yet more maths concepts to solve the nonlinear systems of equations that you get. It goes on and on. The opportunity and need to apply maths to real problems is endless.

Alan Champneys answered on 2 Jul 2020:
I solve all kinds of problems for example recently I have been working on a model for how workplaces can safely come out of lockdown. The importance is that everyone should behave responsibly and submit to regular testing. We have shown that if as few as 20% don’t then you cannot really be safe from an infection spreading in the office. This uses
– probability and chance
– algebra
– computer algorithms
– plotting graphs
and many other things you learn later in school like matrices, vectors and calculus 
Chris Budd answered on 2 Jul 2020:
I apply maths to solve problems in the real world. For example I am mostly working on problems associated with COVID19. I also work on problems in weather forecasting. The key mathematical tool to do this is called a partial differential equation. It is probably fair to say that most things in the universe can be expressed in terms of partial differential equations. Solve these and then you can find out how the universe works. So the equations for understanding COVID19 are exactly these, and solving them helps me to predict how safe supermarkets are, for example.

Katy Tant answered on 3 Jul 2020:
My work is focussed on trying to look inside solid objects without cutting them up! I do this by sending ultrasonic waves into solid objects. By analysing the way these waves reflect and scatter I can build up a picture of what the object looks like inside. This is often how we look inside the human body – for example when we want to image a foetus or the brain. But we can also use the same ideas to image the Earth’s crust or test aircraft components for flaws. In all of these cases, we want to understand how the waves interact with the object. And these waves can be represented by mathematical models which require aspects of calculus, trigonometry, probability, statistics, computer algorithms and much more!

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