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## What will I study?

### Overview

You’ll complete this major as part of a Bachelor of Science degree.

This major gives you deep knowledge in one of four specialisations: **Pure Mathematics**, **Applied Mathematics**, **Operations Research and Discrete Mathematics,** and **Statistics and Stochastic Processes**.

In your **first** and **second years** you will complete subjects that are prerequisites for your major, including foundational mathematics and statistics subjects.

In your **third year**, you will complete 50 points (four subjects) of study that is deep and specialised study in your chosen specialisation of mathematics.

Throughout your degree you will also take science **elective** subjects and **breadth** (non-science) subjects, in addition to your major subjects and prerequisites.

Read more about studying mathematics and statistics at the University of Melbourne.

### Sample course plan

View some sample course plans to help you select subjects that will meet the requirements for this major.

#### Sample course plan - Pure Mathematics

#### KEY

- Major core prerequisite
- Science elective
- Breadth
- Major elective prerequisite
- Breadth/Elective
- Major core
- Major elective

These sample study plans assume that you have achieved a study score of at least 29 in VCE Specialist Mathematics 3/4, or equivalent. If you have no completed this previously, you may first need to enrol in MAST10005 Calculus 1 in your first semester.

Year 1

Total

100 Points

Semester 1

50 Points

- Major core prer...
##### MAST10006 Calculus 2

12.5 Points

- Science electiv...
12.5 Points

- Science electiv...
12.5 Points

- Breadth
12.5 Points

- Major core prer...
Semester 2

50 Points

- Major core prer...
##### MAST10007 Linear Algebra

12.5 Points

- Science electiv...
12.5 Points

- Science electiv...
12.5 Points

- Breadth
12.5 Points

- Major core prer...

Year 2

Total

100 Points

Semester 1

50 Points

- Major core prer...
##### MAST20026 Real Analysis

12.5 Points

- Science electiv...
12.5 Points

- Science electiv...
12.5 Points

- Breadth
12.5 Points

- Major core prer...
Semester 2

50 Points

- Major core prer...
##### MAST20022 Group Theory and Linear Algebra

12.5 Points

- Major elective ...
##### MAST20009 Vector Calculus

12.5 Points

- Science electiv...
12.5 Points

- Breadth/Electiv...
12.5 Points

- Major core prer...

Year 3

Total

100 Points

Semester 1

50 Points

- Major core
##### MAST30021 Complex Analysis

12.5 Points

- Major core
##### MAST30005 Algebra

12.5 Points

- Science electiv...
12.5 Points

- Breadth
12.5 Points

- Major core
Semester 2

50 Points

- Major core
##### MAST30026 Metric and Hilbert Spaces

12.5 Points

- Major elective
##### MAST30024 Geometry

12.5 Points

- Science electiv...
12.5 Points

- Breadth/Electiv...
12.5 Points

- Major core

#### Sample course plan - Applied Mathematics

#### KEY

- Major core prerequisite
- Science elective
- Breadth
- Major elective prerequisite
- Breadth/Elective
- Major core
- Major elective

These sample study plans assume that you have achieved a study score of at least 29 in VCE Specialist Mathematics 3/4, or equivalent. If you have no completed this previously, you may first need to enrol in MAST10005 Calculus 1 in your first semester.

Year 1

Total

100 Points

Semester 1

50 Points

- Major core prer...
##### MAST10006 Calculus 2

12.5 Points

- Major core prer...
##### COMP10001 Foundations of Computing

12.5 Points

- Science electiv...
12.5 Points

- Breadth
12.5 Points

- Major core prer...
Semester 2

50 Points

- Major core prer...
##### MAST10007 Linear Algebra

12.5 Points

- Science electiv...
12.5 Points

- Science electiv...
12.5 Points

- Breadth
12.5 Points

- Major core prer...

Year 2

Total

100 Points

Semester 1

50 Points

- Major core prer...
##### MAST20026 Real Analysis

12.5 Points

- Major elective ...
##### MAST20009 Vector Calculus

12.5 Points

- Science electiv...
12.5 Points

- Breadth
12.5 Points

- Major core prer...
Semester 2

50 Points

- Major core prer...
##### MAST20030 Differential Equations

12.5 Points

- Major elective ...
##### MAST20004 Probability

12.5 Points

- Science electiv...
12.5 Points

- Breadth/Electiv...
12.5 Points

- Major core prer...

Year 3

Total

100 Points

Semester 1

50 Points

- Major core
##### MAST30021 Complex Analysis

12.5 Points

- Major elective
##### MAST30030 Applied Mathematical Modelling

12.5 Points

- Science electiv...
12.5 Points

- Breadth
12.5 Points

- Major core
Semester 2

50 Points

- Major core
##### MAST30028 Numerical Methods & Scientific Computing

12.5 Points

- Major elective
##### MAST30001 Stochastic Modelling

12.5 Points

- Science electiv...
12.5 Points

- Breadth/Electiv...
12.5 Points

- Major core

#### Sample course plan - Operations Research & Discrete Mathematics

#### KEY

- Major core prerequisite
- Science elective
- Breadth
- Breadth/Elective
- Major core
- Major elective

These sample study plans assume that you have achieved a study score of at least 29 in VCE Specialist Mathematics 3/4, or equivalent. If you have no completed this previously, you may first need to enrol in MAST10005 Calculus 1 in your first semester.

Year 1

Total

100 Points

Semester 1

50 Points

- Major core prer...
##### MAST10006 Calculus 2

12.5 Points

- Science electiv...
12.5 Points

- Science electiv...
12.5 Points

- Breadth
12.5 Points

- Major core prer...
Semester 2

50 Points

- Major core prer...
##### MAST10007 Linear Algebra

12.5 Points

- Science electiv...
12.5 Points

- Science electiv...
12.5 Points

- Breadth
12.5 Points

- Major core prer...

Year 2

Total

100 Points

Semester 1

50 Points

- Major core prer...
##### MAST20026 Real Analysis

12.5 Points

- Major core prer...
##### MAST20004 Probability

12.5 Points

- Science electiv...
12.5 Points

- Breadth
12.5 Points

- Major core prer...
Semester 2

50 Points

- Major core prer...
##### MAST20018 Discrete Maths and Operations Research

12.5 Points

- Science electiv...
12.5 Points

- Science electiv...
12.5 Points

- Breadth/Electiv...
12.5 Points

- Major core prer...

Year 3

Total

100 Points

Semester 1

50 Points

- Major core
##### MAST30013 Techniques in Operations Research

12.5 Points

- Major core
##### MAST30021 Complex Analysis

12.5 Points

- Science electiv...
12.5 Points

- Breadth
12.5 Points

- Major core
Semester 2

50 Points

- Major core
##### MAST30012 Discrete Mathematics

12.5 Points

- Major elective
##### MAST30022 Decision Making

12.5 Points

- Science electiv...
12.5 Points

- Breadth/Electiv...
12.5 Points

- Major core

#### Sample course plan - Statistics & Stochastic Processes

#### KEY

- Major core prerequisite
- Science elective
- Breadth
- Major core
- Major elective
- Breadth/Elective

Year 1

Total

100 Points

Semester 1

50 Points

- Major core prer...
##### MAST10006 Calculus 2

12.5 Points

- Science electiv...
12.5 Points

- Science electiv...
12.5 Points

- Breadth
12.5 Points

- Major core prer...
Semester 2

50 Points

- Major core prer...
##### MAST10007 Linear Algebra

12.5 Points

- Science electiv...
12.5 Points

- Science electiv...
12.5 Points

- Breadth
12.5 Points

- Major core prer...

Year 2

Total

100 Points

Semester 1

50 Points

- Major core prer...
##### MAST20026 Real Analysis

12.5 Points

- Major core prer...
##### MAST20004 Probability

12.5 Points

- Science electiv...
12.5 Points

- Breadth
12.5 Points

- Major core prer...
Semester 2

50 Points

- Major core prer...
##### MAST20005 Statistics

12.5 Points

- Science electiv...
12.5 Points

- Science electiv...
12.5 Points

- Breadth
12.5 Points

- Major core prer...

Year 3

Total

100 Points

Semester 1

50 Points

- Major core
##### MAST30025 Linear Statistical Models

12.5 Points

- Major elective
##### MAST30020 Probability for Inference

12.5 Points

- Science electiv...
12.5 Points

- Breadth/Electiv...
12.5 Points

- Major core
Semester 2

50 Points

- Major core
##### MAST30001 Stochastic Modelling

12.5 Points

- Major elective
##### MAST30027 Modern Applied Statistics

12.5 Points

- Science electiv...
12.5 Points

- Breadth/Electiv...
12.5 Points

- Major core

#### Sample course plan - Pure Mathematics mid-year entry

#### KEY

- Major core prerequisite
- Science elective
- Breadth
- Major elective prerequisite
- Breadth/Elective
- Major core
- Major elective

These sample study plans assume that students have achieved a study score of at least 29 in VCE Specialist Mathematics 3/4, or equivalent. If students have no completed this previously, they may first need to enrol in MAST10005 Calculus 1 in their first semester.

Year 1

Total

100 Points

Semester 2

50 Points

- Major core prer...
##### MAST10006 Calculus 2

12.5 Points

- Science electiv...
12.5 Points

- Science electiv...
12.5 Points

- Breadth
12.5 Points

- Major core prer...
Summer

12.5 Points

- Major core prer...
##### MAST10007 Linear Algebra

12.5 Points

- Major core prer...
Semester 1

37.5 Points

- Major core prer...
##### MAST20026 Real Analysis

12.5 Points

- Science electiv...
12.5 Points

- Breadth
12.5 Points

- Major core prer...

Year 2

Total

100 Points

Semester 2

50 Points

- Major core prer...
##### MAST20022 Group Theory and Linear Algebra

12.5 Points

- Major elective ...
##### MAST20009 Vector Calculus

12.5 Points

- Science electiv...
12.5 Points

- Breadth
12.5 Points

- Major core prer...
Semester 1

50 Points

- Science electiv...
12.5 Points

- Science electiv...
12.5 Points

- Science electiv...
12.5 Points

- Breadth/Electiv...
12.5 Points

- Science electiv...

Year 3

Total

100 Points

Semester 2

50 Points

- Major core
##### MAST30021 Complex Analysis

12.5 Points

- Major core
##### MAST30026 Metric and Hilbert Spaces

12.5 Points

- Science electiv...
12.5 Points

- Breadth
12.5 Points

- Major core
Semester 1

50 Points

- Major elective
##### MAST30011 Graph Theory

12.5 Points

- Major core
##### MAST30005 Algebra

12.5 Points

- Science electiv...
12.5 Points

- Breadth/Electiv...
12.5 Points

- Major elective

### Explore this major

Explore the subjects you could choose as part of this major.

- 12.5 pts
Complex analysis is a core subject in pure and applied mathematics, as well as the physical and engineering sciences. While it is true that physical phenomena are given in terms of real numbers and real variables, it is often too difficult and sometimes not possible, to solve the algebraic and differential equations used to model these phenomena without introducing complex numbers and complex variables and applying the powerful techniques of complex analysis.

Topics include:the topology of the complex plane; convergence of complex sequences and series; holomorphic functions, the Cauchy-Riemann equations, harmonic functions and applications; contour integrals and the Cauchy Integral Theorem; singularities, Laurent series, the Residue Theorem, evaluation of integrals using contour integration, conformal mapping; and aspects of the gamma function.

- 12.5 pts
This subject provides a basis for further studies in modern analysis, geometry, topology, differential equations and quantum mechanics.It introduces the idea of a metric space with a general distance function, and the resulting concepts of convergence, continuity, completeness, compactness and connectedness. The subject also introduces Hilbert spaces: infinite dimensional vector spaces (typically function spaces) equipped with an inner product that allows geometric ideas to be used to study these spaces and linear maps between them.

Topics include: metric and normed spaces, limits of sequences, open and closed sets, continuity, topological properties, compactness, connectedness; Cauchy sequences, completeness, contraction mapping theorem; Hilbert spaces, orthonormal systems, bounded linear operators and functionals, applications.

- 12.5 pts
Algebra has a long history of important applications throughout mathematics, science and engineering, and is also studied for its intrinsic beauty. In this subject we study the algebraic laws satisfied by familiar objects such as integers, polynomials and matrices. This abstraction simplifies and unifies our understanding of these structures and enables us to apply our results to interesting new cases. Students will gain further experience with abstract algebraic concepts and methods. General structural results are proved and algorithms developed to determine the invariants they describe.

- 12.5 pts
Graphs model networks of all types such as telecommunication, transport, computer and social networks. They also model physical structures such as crystals and abstract structures within computer algorithms.

This subject is an introduction to the modern field of graph theory. It emphasises the relationship between proving theorems in mathematics and the construction of algorithms to find the solutions of mathematical problems within the context of graph theory. The subject provides material that supplements other areas of study such as operations research, computer science and discrete mathematics

- 12.5 pts
This subject is concerned with the study of objects, which are finite in number and typically computable. At a computational level one seeks efficient algorithms and methods for construction and counting of the objects.

The main topics to be covered are: enumeration, permutations, designs, finite geometry, words, Ramsey theory and physical combinatorics. Designs are relevant to statistics, Ramsey theory to computer science, and physical combinatorics to mathematical physics. Words are useful for representing and constructing objects and relating combinatorial objects to algebraic structures.

- 12.5 pts
This subject introduces three areas of geometry that play a key role in many branches of mathematics and physics. In differential geometry, calculus and the concept of curvature will be used to study the shape of curves and surfaces. In topology, geometric properties that are unchanged by continuous deformations will be studied to find a topological classification of surfaces. In algebraic geometry, curves defined by polynomial equations will be explored. Remarkable connections between these areas will be discussed.

Topics include: Topological classification of surfaces, Euler characteristic, orientability.Introduction to the differential geometry of surfaces in Euclidean space:smooth surfaces, tangent planes, length of curves, Riemannian metrics, Gaussian curvature, minimal surfaces, Gauss-Bonnet theorem.Complex algebraic curves, including conics and cubics, genus.