University of Adelaide

What you'll study

The programme builds a broad mathematical background in the early years before concentrating on advanced pure mathematics topics in the honours year. Typical first‑ and second‑year subjects include calculus, linear algebra, discrete mathematics, mathematical proof techniques, differential equations and introductory real analysis. Statistics and computational mathematics are also available to provide practical tools.

In the honours year you specialise in pure mathematics through advanced modules and a substantial research project. Common honours subjects and topics include:

• Advanced Real and Complex Analysis — rigorous study of limits, series, measure theory and complex function theory.
• Abstract Algebra — groups, rings, modules and field theory with an emphasis on proof and structure.
• Topology and Geometry — point‑set topology, algebraic topology basics or differential geometry depending on supervisor strengths.
• Functional Analysis and Operator Theory — for connections between analysis and applied areas.
• Number Theory, Algebraic Geometry or Logic — elective advanced topics reflecting staff research.
• Honours Research Thesis — a supervised, substantial piece of original work that develops research skills, problem formulation and mathematical exposition.

Assessment is a mix of problem sets, examinations, oral presentations and the honours thesis. Students are encouraged to engage with departmental seminars and research groups, and to take computational or statistical electives where appropriate.

Entry requirements

Admission is based on an acceptable secondary school qualification or equivalent tertiary study. Applicants typically need a strong background in senior secondary mathematics — for example, Mathematics Methods or the equivalent, and often a specialist or advanced mathematics subject is recommended. International applicants should present an equivalent secondary qualification (such as the IB) with adequate mathematics at higher level.

Domestic and international applicants whose first language is not English must meet the University's English language proficiency requirements (for example, an accepted IELTS, TOEFL or equivalent score). Entry into the honours year normally requires completion of the bachelor component with a sufficient grade point average and program‑specific honours eligibility criteria; selection for honours may be competitive and can include consideration of research potential.

Career prospects

Graduates with an honours year in pure mathematics are well placed for further research and postgraduate study (Master by Research or PhD) in mathematics or related disciplines. Career paths include:

• Academic and research roles in universities and research institutes.
• Quantitative and analytical positions in finance, risk management and fintech.
• Data science, analytics and software development roles that value advanced problem‑solving and formal reasoning.
• Government and defence research agencies requiring mathematical modelling and cryptography expertise.
• Teaching at secondary or tertiary levels (additional professional qualifications may be required for some teaching roles).

The honours year is particularly valuable for roles that require independent research, advanced proof techniques and the ability to communicate complex mathematical ideas clearly.

Why study at University of Adelaide

The University of Adelaide has a long tradition in mathematical sciences and offers an honours pathway that emphasises research training and close supervision by active academics. The School of Mathematical Sciences hosts research groups in analysis, algebra, geometry and applied mathematics, providing seminars, reading groups and opportunities to collaborate across disciplines.

Students benefit from small honours cohorts that allow tailored supervision, access to computing facilities and databases, and links with industry and research institutions in South Australia. The University also provides career development services, scholarship opportunities for high‑performing students, and pathways into postgraduate research both locally and internationally.