Autumn 2027 · Western Sydney University · Parramatta

Two subjects for students who want to go deeper

If you want your master's to stretch you, these two Autumn subjects are built for it: small classes, real mathematics and a first taste of research. They suit students in Data Science, Artificial Intelligence, Research and Neuromorphic Engineering, and anyone else with the appetite.

The subjects

MATH7019 · 10 credit points

Mathematics of Signal Processing

Audio, images, sensor readings and neural recordings are all signals, and signals are vectors in a space with geometry. Once you see that, Fourier analysis, sampling, approximation, wavelets and sensor arrays stop being a bag of tricks and become one subject.

Topics
Inner products, bases and frames; Fourier analysis in discrete and continuous time; sampling and interpolation, including non-uniform sampling; time–frequency and wavelet analysis; array signal processing.
How it is taught
Lectures and tutorials on campus, with hands-on work in Julia. Texts: Vetterli, Kovačević and Goyal's Foundations of Signal Processing and Mallat's A Wavelet Tour of Signal Processing.
You need
Undergraduate linear algebra and some programming. Julia is easy to pick up if you know Python.
Status
Core for the Master of Neuromorphic Engineering; an elective for many other postgraduates.
MATH7001 · 20 credit points

Advanced Mathematical Investigations

A research subject. You investigate two topics in depth, one in each half of the semester, under close supervision. For each you write a report, with code where it helps, and present it as a researcher would; the semester ends with an oral exam on the class's topics.

Recent topics
Spiking neural networks; quantum error-correcting codes; diffusion models in machine learning; unlimited sampling; frame theory; sampling on polyhedral grids.
How it is taught
A weekly discussion on campus, plus individual supervision. Topics are agreed with you, so they can follow your interests.
You need
Undergraduate mathematics or statistics, and the willingness to read beyond the lecture notes. Outside the Master of Research the subject is taken by waiver, which is granted to students ready for it; I will help with the paperwork.
Why it helps with a PhD
It is a substantial block of supervised research, with written work and talks to show for it. That is the evidence a prospective supervisor looks for, and it lets you find out whether research suits you before you commit.

Why take them

Questions students ask

Are they hard?

They are demanding, as a master's subject should be. Students who keep up week by week do well, and the small classes mean help is close at hand.

Do I need to be a mathematician?

No. You need undergraduate linear algebra, comfort with some programming and curiosity. Students from computing, engineering and data science are welcome.

Can I take them in my degree?

Mathematics of Signal Processing is core for Neuromorphic Engineering and can be an elective in many other postgraduate programs. Advanced Mathematical Investigations is taken by waiver outside the Master of Research. Rules differ between degrees, so email me and we will work it out.

Can I take only one?

Yes. Each stands alone. Taking both is the stronger combination if research appeals to you.

Will Advanced Mathematical Investigations help me get into a PhD?

It gives you real, supervised research experience, two pieces of written work and a supervisor who has seen what you can do. Those are what a PhD application rests on.

Interested?

Both subjects run in Autumn 2027, starting in March, on campus at Parramatta. Enrol through the usual system. For Advanced Mathematical Investigations, please email first so we can talk about topics and arrange the waiver.

Taught by Paul Hurley, who works on signal processing, computational neuroscience and the mathematics that connects them.

Email Paul