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4 cool topics you can study in maths

What’s maths got to do with it? Everything.
From developing artificial intelligence to predicting a cancer prognosis, mathematics touches every aspect of our lives. We talked to four Sydney mathematicians about their research and why maths (and the study of it) is so important.

Mathematics and statistics are vital to understanding every part of our world. It is a language, a tool for analysis and prediction, and a way of thinking.

We caught up with Dr Lamiae Azizi, Kevin Wang, Dr Diana Warren and Oded Yacobi to find out about their area of research in mathematics and statistics, to give you an idea of some of the interesting topics you could explore if you study maths with us.

Teaching machines to teach themselves

Probabilistic machine learning plays a central role in the development of artificial intelligence, seeking to teach a machine how to learn from experience.

Dr Lamiae Azizi, a senior lecturer in the School of Mathematics and Statistics and the Deputy Director at the Centre for Translational Data Science, is focused on developing and applying probabilistic machine learning models to problems including personalisation and decision making in various sectors, but particularly within healthcare.

“Everyone knows the role of a doctor in our society but not everyone understands that at the core of most technologies is maths,” says Azizi.

“In my area of work we develop mathematical models and algorithms that a machine, fed only with some observed data, can use to make predictions about future data and make decisions that are rational given these predictions.”

Dr Lamiae Azizi talking about her area of research at Raising the Bar 2018.

Dr Lamiae Azizi talking about her area of research at Raising the Bar 2018

 

Azizi’s research covers a range of areas and has many applications, such as working with biologists in genomics to work towards a cure for cancer and designing methods that can process large hyperspectral satellite images.

“I believe that the coolest things that are happening in artificial intelligence, are happening in the area of machine learning in general and probabilistic machine learning in particular,” she says.

“Mathematics provides us with the framework that allows us to better understand the world we live in and thus transform it.”

If you’re interested in understanding and exploring the possibilities of statistical machine learning, there are a range of statistics and data science units of study that you can incorporate in your degree.

Biological problem solving

Modern medicine relies very heavily on the machinery of mathematics and statistics to make sense of itself. Mathematics can be used to predict and model the behaviour of cancer, and to help us better understand genetics and DNA.

Kevin Wang, a PhD Candidate with the School of Mathematics and Statistics, works in the area of bioinformatics which applies theoretical mathematical methods to practical biological problems.

“I am working on a project with oncologists at the Melanoma Institute Australia which aims to improve the accuracy of predictions of survival times or cancer prognosis for patients,” says Wang.

“The growth mechanism of a tumour can often be linked to gene expression, which can be thought of as the information stored in a person's gene. The goal we are working towards is to obtain tissue samples from cancer patients in a clinic, sending those samples to a lab to measure gene expression and then providing patients with a prediction of their survival time or cancer prognosis.”

Kevin Wang presenting his research at a conference

Kevin Wang presenting his research at a conference

Wang explains that there can be multiple sources of variation during the process of measuring gene expression, which ultimately affects each patient’s prediction. His research focuses on eliminating these sources of variations to make them more accurate.

“Every problem in bioinformatics is a puzzle with no standard solution. This is a creative process and I have the freedom to use whatever method I want to reach the solution,” says Wang.

“The ability to critically think about data, work with data and to effectively communicate it are invaluable skills in any data-related job. And bioinformatics takes all of these skills to the extreme!”

If you’re interested in learning about how to take practical biological problems and converting them into something that can be solved using data, mathematics, statistics and computer science, bioinformatics is taught in a range of our undergraduate mathematics units.

Putting data to use

It’s no secret that making decisions based on actual evidence is key across all areas of research, work… and life. So, the importance of having people with the knowledge on how to use the data at our finger tips is only increasing over time.

“The 21st century has seen a ‘data deluge’, so an extraordinary amount of extraordinary data is now waiting for analysis,” explains Dr Diana Warren from the School of Mathematics and Statistics. “Data science allows us to make evidence-based decisions in almost every field imaginable.”

Warren is focused on developing a data science program that is accessible for every student across the University – no matter what their mathematical background, major or career focus.

Dr Diana Warren

Dr Diana Warren

“Data Science enhances study in any other area and will help reveal new insights. It can teach you how to problem-solve with data from any domain,” says Warren.

“Surprising breakthroughs will be facilitated by data-driven research, from cancer to climate change to astronomy.”

The new Data Science major can be undertaken as part of a range of degrees, so you can develop the kind of inferential thinking and computing skills necessary for the modern world of big data. We also have some Open Learning Environment units in data science that you could sink your teeth into.

Discovering hidden symmetries

Oded Yacobi, a senior lecturer in the School of Mathematics and Statistics, works in pure mathematics focusing his research on representation theory – the study of symmetry.

“We’ve discovered hidden symmetries using abstract methods, which has allowed us to resolve many long open questions and to also ask new questions,” says Yacobi.

“Representation theory is powerful because it allows us to understand symmetries of objects that are not obviously geometric. What does it mean for an equation to have symmetry and what does this say about the underlying structure that the equation is trying to model?”

Yacobi explains that answering these questions has significant consequences and is important for things like studying crystallography in chemistry, building the underlying theory of quantum computing and making models which predict the way robots will move.

Image of a "resolution of singularities" which is an example of the types of spaces Oded Yacobi studies.

Image of a "resolution of singularities" which is an example of the types of spaces Oded Yacobi studies.

 

“This is an exciting field which is rapidly changing, providing the opportunity to get in on the ground floor and contribute to fundamental developments. It helps develop an understanding of the connections between many central areas in mathematics, which is very useful beyond the mathematical realm,” says Yacobi.

“After all, mathematics is everywhere and the study of it will arm you with the fundamental tools needed to succeed in industry, government and beyond.”

Despite its abstract nature, this topic underlies much of our modern mathematical toolset, with remarkable applications in computer science, physics and other areas. Abstract algebra is covered in a number of our undergraduate mathematics units.

13 December 2018