University of Adelaide

What you'll study

The Pure Mathematics major emphasises rigorous foundations and abstract theory. Core topics include real and complex analysis, abstract algebra (groups, rings and fields), linear algebra and advanced calculus. As you progress you encounter higher-level subjects such as topology, differential equations from a theoretical perspective, measure theory, functional analysis, number theory and algebraic structures.

• First year: foundational calculus, linear algebra, introductory proof techniques and discrete mathematics to build the language of modern mathematics.
• Second year: intermediate real analysis, abstract algebra and beginning topics in topology and complex analysis, together with elective choices that broaden mathematical maturity.
• Third year: advanced analysis, algebraic topics (for example Galois theory or ring theory), specialised subjects such as functional analysis, differential topology or advanced number theory, plus a capstone project or research‑style module.
• Honours pathway: students who wish to pursue research or further study may undertake a separate honours year involving a substantial research project and advanced coursework.

Entry requirements

Applicants are expected to demonstrate strong mathematical preparation from secondary study. Typical prerequisites include senior secondary mathematics (for example Mathematical Methods and, where available, Specialist Mathematics) with high achievement. Selection considers overall academic performance and relevant mathematics results.

International applicants must meet the University of Adelaide's English language requirements and provide equivalent secondary qualifications; mature‑age applicants and those with tertiary study in a quantitative discipline are considered on the basis of prior academic performance. Specific entry pathways, credit for prior learning and bridging options are available and assessed individually by the university.

Career prospects

Graduates with a major in Pure Mathematics are well placed for a range of careers that value rigorous analytical thinking and problem solving. Common destinations include:

• Further research and academia via honours and postgraduate study (Master’s, PhD).
• Data science, analytics and machine learning roles where mathematical modelling and abstraction are key.
• Finance, quantitative analysis and risk management, including roles in banking and investment where theoretical modelling supports practical decision making.
• Software development, cryptography and cybersecurity, where algorithmic thinking and discrete mathematics are applied.
• Government and policy roles involving quantitative policy analysis, modelling and advisory work.
• Secondary and tertiary teaching after completion of required professional or postgraduate qualifications.

Why study at University of Adelaide

The University of Adelaide’s School of Mathematical Sciences offers research‑led teaching and a collaborative environment with a strong tradition in both pure and applied mathematics. Students benefit from access to active research seminars, close mentoring by academic staff, and opportunities to participate in research projects and honours study.

The university’s connections with industry and other research institutions in South Australia provide pathways to internships, multidisciplinary projects and professional networks. Small cohort sizes in advanced subjects support personalised feedback and preparation for postgraduate study or careers that require high levels of mathematical sophistication.