University of Technology Sydney

What you'll study

The PhD in Mathematical Sciences is a research degree focused on developing and delivering an original thesis under the supervision of academic staff. Candidates undertake an independent research project in areas such as pure mathematics (algebra, analysis, geometry), applied mathematics (mathematical modelling, dynamical systems), computational mathematics and numerical analysis, probability and stochastic processes, statistical theory and methodology, machine learning and data science, or interdisciplinary work linking mathematics with physics, engineering, finance, or computational biology.

While there are no prescribed coursework requirements in all cases, candidates may complete structured research training units, elective coursework modules or short intensive courses to strengthen methodological background and transferable skills. Typical training covers advanced topics such as:

• Advanced real and complex analysis, algebra and topology
• Numerical methods for differential equations, scientific computing and high‑performance computing
• Probability theory, stochastic processes and statistical inference
• Optimization, control theory and inverse problems
• Machine learning, data mining and computational statistics
• Mathematical modelling and applied analysis for physical and biological systems
• Research methods, academic communication, and responsible research practice

Progress is monitored through a candidature review process, including a confirmation of candidature (research plan and literature review), annual progress reports, and final thesis examination by external reviewers and a viva/defence where required.

Entry requirements

Applicants typically hold a relevant honours degree with a strong research component or a master’s degree with substantial research training in mathematics, statistics, or a closely related discipline. Selection is based on the quality of academic record, evidence of research potential, a clear research proposal or project outline, and the availability of suitable supervisory expertise within the school.

Additional application materials commonly required include:

• A detailed research proposal or statement of research interests
• Academic transcripts and certified degree documentation
• Curriculum vitae highlighting research experience and publications, if any
• References or academic referee reports commenting on research potential
• Proof of English language proficiency for international applicants, in accordance with university policy

Candidates are encouraged to contact potential supervisors in the School of Mathematical and Physical Sciences to discuss project suitability before applying. Conditional offers may specify completion of prerequisite coursework or research training where appropriate.

Career prospects

Graduates of the PhD in Mathematical Sciences pursue a broad range of careers. Many move into academic and research positions such as postdoctoral research fellowships and university teaching and research roles. Others find senior research and development roles in industry, including finance and quantitative analysis, data science and machine learning, engineering modelling and simulation, software and algorithm development, and government research agencies.

PhD skills in rigorous problem solving, mathematical modelling, computational methods and statistical reasoning are also highly valued in consulting, telecommunications, energy, pharmaceuticals and biotechnology sectors, as well as in policy and advisory roles that require quantitative expertise.

Why study at University of Technology Sydney

UTS offers a research environment with access to interdisciplinary collaborations, specialised computational facilities and active research groups in applied and theoretical mathematical sciences. The university emphasises industry engagement and translation of research, enabling candidates to pursue projects with practical impact and strong industry links where appropriate.

Candidates benefit from structured higher degree research training, mentoring from internationally active supervisors, seminar programmes and regular research symposia. The School provides support for research dissemination, including training in academic writing, presentation skills, grant applications and pathways for commercialisation or engagement with partner organisations.

UTS’s central Sydney location also facilitates connections with industry, government laboratories and other research institutions, supporting networking, co‑supervision and employment opportunities during and after candidature.