Major

Pure Mathematics

#1 University in Australia #22 University in the world

Explore abstract maths and discover the beautiful logic underlying the mathematical universe.

You'll dive into abstract concepts, proof, and logical reasoning—exploring areas like algebra, geometry, and topology. Pure mathematics is for students who love the intellectual challenge of uncovering how maths works at its deepest level. You'll develop rigorous thinking skills valued in research, academia, and fields where creative problem-solving is everything.

Your learning outcomes

By majoring in Pure Mathematics, you'll develop the knowledge and skills to:

  • Work with abstract mathematical concepts
  • Explore areas like algebra, geometry, analysis, and topology in depth
  • Develop deep logical reasoning and creative problem-solving abilities
  • Understand the underlying structures and beauty of mathematics
  • Contribute new ideas to mathematical knowledge and theory
  • Prepare yourself for advanced study in maths and research.

What you’ll study

You'll start by building rigorous proof skills and exploring foundational areas in calculus and linear algebra. In second year, you'll delve deeper into real analysis, abstract algebra and vector calculus. By third year, you'll tackle deeper study in algebra and metric spaces, and choose from specialized topics like number theory, geometry, or complex analysis – diving as deep as you want into pure maths.

Career outcomes

Graduates with a Pure Mathematics major pursue careers in academia, research, and fields where rigorous problem-solving and creative thinking are essential. The advanced analytical and logical reasoning skills you develop prepare you for postgraduate study in mathematics and related disciplines, as well as careers in tech, finance, and government where deep mathematical thinking is valued.

This major is available in the Bachelor of Science.

In the Pure Mathematics major, you’ll explore abstract structures and deep ideas that underpin modern mathematics.

Major structure

The Pure Mathematics major is made up of seven subjects (87.5 credit points) taken in your second and third year. Each subject is worth 12.5 credit points. Level 2 subjects are usually taken in second year, and Level 3 subjects in third year.

To complete this major, you’ll need:

  • 12.5 credit points of Level 2 major core
  • 12.5 credit points of Level 2 major elective (Group A)
  • 12.5 credit points of Level 2 major elective (Group B)
  • 25 credit points of Level 3 major electives
  • 25 credit points of Level 3 capstone

The rest of your degree will consist of a science core subject, elective subjects in science, and breadth (non-science) subjects.

Further information

You can find detailed information about your major – including structure, subject availability, and participation requirements – in the Handbook.

You can also explore your study pathway and sample course plans through My Course Planner.

Overview

Pure Mathematics graduates are valued for their rigorous analytical thinking and creative problem-solving abilities. While many pursue research and academia, your skills are also in demand across finance, technology, and government sectors where deep mathematical insight is essential.

Our graduates work as researchers, academic mathematicians, quant analysts, and specialist consultants.

Employers in this field include:

  • Universities and research institutions including the University of Melbourne, CSIRO, and international research centres
  • Financial services companies such as ANZ, NAB, and investment firms
  • Technology and software companies including Google, Amazon, and local tech firms
  • Government agencies including Treasury and the Australian Bureau of Statistics
  • Consulting firms including McKinsey and Deloitte.

For more career examples and profiles, visit Careers in Science.

Further study

At the end of your degree, you'll be well-placed to pursue graduate study in maths – for example, in the Master of Science (Mathematics and Statistics) or the Master of Data Science. You could also explore further study in other disciplines – in science, law, teaching, health, business, humanities, and more.

If you’re interested in graduate research, you can progress to the Master of Science to set you up for a PhD and a rewarding research career.