Majors in mathematical and statistical sciences
Mathematics and Statistics are at the leading edge of knowledge, providing important new insights into nature, technology and business, while drawing on a rich history of ideas as old as civilisation itself. This major will enable you to gain depth of knowledge in a specialised area, as well as equip you with transferable skills related to conceptual understanding, problem solving, and teamwork.
There are four specialisations within the Mathematics and Statistics major. Students must complete the requirements for at least one of these specialisations.

Applied Mathematics specialisation
In the Applied Mathematics specialisation, students develop the principles and techniques that allow mathematicians to develop models of the world around us. Such models enable mathematicians to predict the changes in environmental, chemical and financial systems that will occur as inputs change.
Hear from a past student about Applied Mathematics:
Subject choices
Note: The information below is for students studying fulltime and commencing in the startofyear intake. Subject sequences may differ for students studying parttime or commencing midyear. Students are encouraged to seek individual course advice if needed.
Level1 subjects (first year)
Students take one of the standard firstyear mathematics pathways.
Bachelor of Science students also take level1 subjects from at least one other science area of study as well as breadth subject(s).
Level2 subjects (second year)
Students take the following level2 Mathematics and Statistics subjects in their second year:
Semester 1 MAST20009 Vector Calculus MAST20004 Probability (optional)
or
MAST20006 Probability for Statistics (optional)Semester 2 MAST20030 Differential Equations Semester 1 or 2 MAST20026 Real Analysis Note: Students who completed MAST10009 Accelerated Mathematics 2 do not take MAST20026 Real Analysis.
Computing requirement
In addition, students who do not already have evidence of competence in computer programming must complete one of the following computing subjects:
 COMP10001 Foundations of Computing
This subject is offered in semester 1 and 2 and may be taken in first or second year.  COMP20005 Engineering Computation
ENGR10003 Engineering Systems Design 2 is recommended as background knowledge for COMP20005 but is not required. This subject can be taken in semester 1 or 2.  PHYC20013 Laboratory and Computational Physics 2
Firstyear physics is required as a prerequisite for PHYC20013. This subject can be taken in semester 1 or 2.
Evidence of competence in computer programming could include passing a relevant Year 12 subject, or a statement of achievement from a relevant MOOC, or passing a programming competency test administed by another University of Melbourne School. For full details see the handbook entry for MAST30028 Numerical Methods and Scientific Computing.
Level3 subjects (third year)
Students must complete the following subjects to satisfy the requirements for the Applied Mathematics specialisation.
Both of: MAST30021 Complex Analysis (semester 1 or 2)
 MAST30028 Numerical Methods and Scientific Computing (semester 2)
plus two of:
 MAST30030 Applied Mathematical Modelling (semester 1)
 MAST30031 Methods of Mathematical Physics (semester 2)
 MAST30001 Stochastic Modelling (semester 2)
Note: Students wishing to take MAST30001 must first complete MAST20004 Probability or MAST20006 Probability for Statistics.
 COMP10001 Foundations of Computing

Discrete Mathematics and Operations Research specialisation
The specialisation in Discrete Mathematics and Operations Research gives students a firm foundation in two areas of mathematics and statistics:
 Discrete Mathematics, the study of algorithmic development including the programming of the most efficient mathematical solutions, has arisen from the huge revolution in computing in recent decades.
 Operations Research provides a scientific approach to decision making. It involves formulating mathematical models of these problems, and developing mathematical tools to obtain solutions.
Hear from a past student about Discrete Mathematics and Operations Research:
Subject choices
Note: The information below is for students studying fulltime and commencing in the startofyear intake. Subject sequences may differ for students studying parttime or commencing midyear. Students are encouraged to seek individual course advice if needed.
Level1 subjects (first year)
Students take one of the standard firstyear mathematics pathways.
Bachelor of Science students also take level1 subjects from at least one other science area of study as well as breadth subject(s). Students are also recommended to take a computing subject such as COMP10001 Foundations of Computing.
Level2 subjects (second year)
Students take the following level2 Mathematics and Statistics subjects in their second year:
Semester 1 MAST20004 Probability
or
MAST20006 Probability for StatisticsSemester 2 MAST20018 Discrete Mathematics and Operations Research MAST20005 Statistics (optional) Semester 1 or 2 MAST20026 Real Analysis Note: Students who completed MAST10009 Accelerated Mathematics 2 do not take MAST20026 Real Analysis.
Level3 subjects (third year)
Students must complete the following subjects to satisfy the requirements for the Discrete Mathematics and Operations Research specialisation.
All of: MAST30021 Complex Analysis (semester 1 or 2)
 MAST30013 Techniques in Operations Research (semester 1)
 MAST30012 Discrete Mathematics (semester 2)
plus one of:
 MAST30001 Stochastic Modelling (semester 2)
 MAST30011 Graph Theory (semester 1)
 MAST30025 Linear Statistical Models (semester 1)
Note: Students wishing to take MAST30025 must first complete MAST20005 Statistics.  MAST30022 Decision Making (semester 2)

Pure Mathematics specialisation
Mathematics is both an art and a science, and pure mathematics is its foundation. A specialisation in pure mathematics gives students the opportunity to study the basic concepts that underly all mathematical applications.
Subject choices
Note: The information below is for students studying fulltime and commencing in the startofyear intake. Subject sequences may differ for students studying parttime or commencing midyear. Students are encouraged to seek individual course advice if needed.
Level1 subjects (first year)
Students take one of the standard firstyear mathematics pathways.
Bachelor of Science students also take level1 subjects from at least one other science area of study as well as breadth subject(s). Students are also recommended to take a computing subject such as COMP10001 Foundations of Computing.
Level2 subjects (second year)
Students take the following level2 Mathematics and Statistics subjects in their second year:
Semester 1 MAST20026 Real Analysis Note: Students who completed MAST10009 Accelerated Mathematics 2 do not take MAST20026 Real Analysis.
Semester 2 MAST20022 Group Theory and Linear Algebra Semester 1 or 2 MAST20009 Vector Calculus Level3 subjects (third year)
Students must complete the following subjects to satisfy the requirements for the Pure Mathematics specialisation.
All of: MAST30021 Complex Analysis (semester 1 or 2)
 MAST30005 Algebra (semester 1)
 MAST30026 Metric and Hilbert Spaces (semester 2)
plus one of:
 MAST30011 Graph Theory (semester 1)
 MAST30012 Discrete Mathematics (semester 2)
 MAST30024 Geometry (semester 2)

Statistics and Stochastic Processes specialisation
The Statistics and Stochastic Processes specialisation gives students a firm foundation in two areas:
 Applied statistics develops, tests and deploys tools that measure, control and reduce the uncertainty in the environment, marketplace or in biological entities.
 Stochastic processes provides models for random processes in the environment such as financial markets, living organisms, populations, genetics, epidemics, queues and earthquakes.
Subject choices
Note: The information below is for students studying fulltime and commencing in the startofyear intake. Subject sequences may differ for students studying parttime or commencing midyear. Students are encouraged to seek individual course advice if needed.
Level1 subjects (first year)
Students take one of the standard firstyear mathematics pathways.
Bachelor of Science students also take level1 subjects from at least one other science area of study as well as breadth subject(s). Students are also recommended to take a computing subject such as COMP10001 Foundations of Computing.
Level2 subjects (second year)
Students take the following level2 Mathematics and Statistics subjects in their second year:
Semester 1 MAST20004 Probability
or
MAST20006 Probability for StatisticsSemester 2 MAST20005 Statistics Semester 1 or 2 MAST20026 Real Analysis Note: Students who completed MAST10009 Accelerated Mathematics 2 do not take MAST20026 Real Analysis.
Level3 subjects (third year)
Students must complete the following subjects to satisfy the requirements for the Statistics and Stochastic Processes specialisation.
Both of: MAST30025 Linear Statistical Models (semester 1)
 MAST30001 Stochastic Modelling (semester 2)
plus at least one of:
 MAST30020 Probability for Inference (semester 1)
Note: If MAST20006 Probability for Statistics was chosen in second year, a grade of at least H2B is required in MAST20006 for entry to MAST30020.  MAST30027 Modern Applied Statistics (semester 2)
plus (if only one of the subjecs MAST30020 Probability for Inference and MAST30027 Modern Applied Statistics was chosen)
 Any other level3 MAST subject offered by the School of Mathematics and Statistics*
* Note: MAST30034 Applied Data Science is taught by the School of Computing and Information Systems so can not be used as a fourth subject for the Statistics and Stochastic Processes specialisation.
With continued advances in the technologies for collecting biological information and data, there is an everincreasing demand for professional scientists with skills in computational biology.
This major relies on contributions from biology, mathematics and statistics, and computer science. Students will gain an understanding of the analysis and interpretation of biological phenomena using mathematical and statistical models and stateoftheart computational tools. You will learn how to develop new algorithms for studying biological data.
From advanced genomics to quantitative ecology, the major will expose you to a diverse array of life sciences specialisations in which mathematics and computation are an essential tool.
This major is offered jointly by the School of Mathematics and Statistics and the School of Biosciences.
Subject choices
Note: The information below is for students studying fulltime and commencing in the startofyear intake. Subject sequences may differ for students studying parttime or commencing midyear. Students are encouraged to seek individual course advice if needed.
First year (level 1)
Students complete one of the standard firstyear mathematics pathways.
Students also complete the following subjects from computing and biology:
 COMP10001 Foundations of Computing (semester 1)
 COMP10002 Foundations of Algorithms (semester 2)
 BIOL10005 Genetics & the Evolution of Life (semester 2)
Students are encouraged to choose chemistry subjects for their remaining level1 science electives, if possible.
Second and third year (level 2 and 3)
Semester 3  MAST20031 Analysis of Biological Data††  GENE20001 Principles of Genetics  Elective  Breadth 
Semester 4  COMP20008 Elements of Data Processing  BCMB20002 Biochemistry & Molecular Biology* or one other level2 biosciences subject**  Elective  Breadth 
Semester 5  MAST30032 Biological Modelling and Simulation  Elective†  Elective†  Breadth/Elective 
Semester 6  MAST30033 Statistical Genomics  BIOL30003 Case Studies in Computational Biology  Elective†  Breadth/Elective 
Notes:
* BCMB20002 requires one of the firstyear Chemistry subjects CHEM10004 or CHEM10009 as a prerequisite.
** See the handbook for a full list of permitted level2 biosciences subjects.
† At least one of these electives must be a Level 3 subject from an approved Science discipline to complete the major. See the handbook for a complete list of approved disciplines.
†† Students who prefer a more mathematically detailed treatment of statistics can complete MAST20005 Statistics (semester 4) and one of MAST20004 Probability or MAST20006 Probability for Statistics (semester 3) instead of MAST20031.
Combining the major with the Diploma in Mathematical Sciences
Students intending to pursue the Master of Computational Biology with a mathematical focus or the Master of Science (Mathematics and Statistics) are encouraged to complete the Diploma in Mathematical Sciences concurrently with their Computational Biology major.
The major in Data Science has an emphasis on statistics and computer science. It provides a strong foundation in the statistical aspects of data analysis (data collection, data mining, modelling and inference), as well as the principles of computer science (algorithms, data structures, data management and machine learning). The major is designed to give students an intellectual understanding of how to integrate and apply statistical and computing principles to solve large scale, realworld data science problems. It is suitable for students interested in a career in government or industry or who wish to pursue specialised graduate study.
This major is offered jointly by the School of Mathematics and Statistics and the School of Computing and Information Systems.
Subject choices
Note: The information below is for students studying fulltime and commencing in the startofyear intake. Subject sequences may differ for students studying parttime or commencing midyear. Students are encouraged to seek individual course advice if needed.
First year (level 1)
Students complete one of the standard firstyear mathematics pathways.
Students also complete firstyear computing subjects:
 COMP10001 Foundations of Computing (semester 1)
 COMP10002 Foundations of Algorithms (semester 2)
Second and third year (level 2 and 3)
Semester 3 
MAST20004 Probability or MAST20006 Probability for Statistics  COMP20008 Elements of Data Processing  Elective  Breadth 
Semester 4  MAST20005 Statistics  Elective  Elective  Breadth 
Semester 5  MAST30025 Linear Statistical Models  COMP30027 Machine Learning  Elective  Breadth/Elective 
Semester 6  MAST30027 Modern Applied Statistics  MAST30034 Applied Data Science  Elective  Breadth/Elective 
Inspired by physics with mathematical methods and rigour, this major will integrate knowledge principally from physics and mathematics to equip you with the necessary tools to think critically about the world and how it works.
You will gain a deep understanding of the physical world and develop skills in analysis, problem solving and critical thinking that will enable you to adapt to a wide range of tasks in research, teaching and management.
This major is offered jointly by the School of Mathematics & Statistics and the School of Physics.
Hear from a past student about Mathematical Physics:
Subject choices
Note: The information below is for students studying fulltime and commencing in the startofyear intake. Subject sequences may differ for students studying parttime or commencing midyear. Students are encouraged to seek individual course advice if needed.
Level1 subjects (first year)
Students are expected to take one of the standard firstyear mathematics pathways.
Students are also expected to complete firstyear physics:
One of
 PHYC10001 Physics 1: Advanced (semester 1)
 PHYC10003 Physics 1 (semester 1)
 PHYC10005 Physics 1: Fundamentals (semester 1)
and one of
 PHYC10002 Physics 2: Advanced (semester 2)
 PHYC10004 Physics 2: Physical Science & Technology (semester 2)
 PHYC10006 Physics 2: Life Sciences & Environment (semester 2)
See here for advice about which physics subjects to choose. Students also take other level1 science and breadth subjects in their first year.
Level2 subjects (second year)
Students are recommended to take the following level2 subjects in their second year:
Semester 1  MAST20009 Vector Calculus  MAST20026 Real Analysis Note: Students who completed MAST10009 Accelerated Mathematics 2 do not take MAST20026 Real Analysis.  PHYC20012 Quantum and Thermal Physics 
Semester 2  MAST20022 Group Theory and Linear Algebra or MAST20030 Differential Equations  PHYC20015 Special Relativity and Electromagnetism  PHYC20013 Laboratory and Computational Physics 2 
Level3 subjects (third year)
Students must complete the following subjects to satisfy the requirements for the Mathematical Physics major.
Both of
 MAST30021 Complex Analysis (semester 1 or 2)
 PHYC30018 Quantum Physics (semester 1)
plus one of
 MAST30026 Metric and Hilbert Spaces (semester 2)
Note: Students wishing to take MAST30026 Metric and Hilbert Spaces must choose MAST20022 Group Theory and Linear Algebra in their secondyear.
 MAST30031 Methods of Mathematical Physics (semester 2)
Note: Students wishing to take MAST30031 Methods of Mathematical Physics must choose MAST20030 Differential Equations in their secondyear.
plus one of
 PHYC30016 Electrodynamics (semester 1)
 PHYC30017 Statistical Physics (semester 2)