# Mathematical Sciences

Unit outlines will be available through Find a unit outline two weeks before the first day of teaching for 1000-level and 5000-level units, or one week before the first day of teaching for all other units.

## Mathematical Sciences

### Master of Mathematical Sciences

### Graduate Diploma in Mathematical Sciences

### Graduate Certificate in Mathematical Sciences

#### 3000-level electives

**DATA3888 Data Science Capstone**

**FMAT3888 Projects in Financial Mathematics**

**MATH3061 Geometry and Topology**

**MATH3066 Algebra and Logic**

The Propositional and Predicate Calculi are studied as model axiomatic systems in their own right, including proofs of consistency and completeness. The final part of the course introduces precise notions of computability and decidability, through abstract Turing machines, culminating in the unsolvability of the Halting Problem the undecidability of First Order Logic, and a discussion of Godel's Incompleteness Theorem.

Classical and novel arithmetics are introduced, unified and described abstractly using field and ring axioms and the language of field extensions. Quotient rings are introduced, which are used to construct different finite and infinite fields. A construction of the real numbers, by factoring out rings of Cauchy sequences of rationals by the ideal of sequences, is presented. Axiomatics are placed in the context of reasoning within first order logic and set theory.

**MATH3888 Projects in Mathematics**

**MATH3975 Financial Derivatives (Advanced)**

**STAT3021 Stochastic Processes**

**STAT3921 Stochastic Processes (Advanced)**

**STAT3888 Statistical Machine Learning**

**STAT3922 Applied Linear Models (Advanced)**

**STAT3923 Statistical Inference (Advanced)**

#### 4000-level electives

**AMSI4001 AMSI Summer School**

**MATH4061 Metric Spaces**

**MATH4062 Rings, Fields and Galois Theory**

**MATH4063 Dynamical Systems and Applications**

**MATH4068 Differential Geometry**

**MATH4069 Measure Theory and Fourier Analysis**

**MATH4071 Convex Analysis and Optimal Control**

*This unit of study is not available in 2021*

**MATH4074 Fluid Dynamics**

**MATH4076 Computational Mathematics**

**MATH4077 Lagrangian and Hamiltonian Dynamics**

**MATH4078 PDEs and Applications**

**MATH4079 Complex Analysis**

**MATH4511 Arbitrage Pricing in Continuous Time**

**MATH4512 Stochastic Analysis**

**MATH4513 Topics in Financial Mathematics**

**MATH4311 Algebraic Topology**

**MATH4312 Commutative Algebra**

**MATH4313 Functional Analysis**

**MATH4314 Representation Theory**

**MATH4315 Variational Methods**

*This unit of study is not available in 2021*

**MATH4411 Applied Computational Mathematics**

**MATH4412 Advanced Methods in Applied Mathematics**

**MATH4413 Applied Mathematical Modelling**

*This unit of study is not available in 2021*

**MATH4414 Advanced Dynamical Systems**

*This unit of study is not available in 2021*

**STAT4021 Stochastic Processes and Applications**

**STAT4022 Linear and Mixed Models**

**STAT4023 Theory and Methods of Statistical Inference**

**STAT4025 Time Series**

**STAT4026 Statistical Consulting**

**STAT4027 Advanced Statistical Modelling**

**STAT4028 Probability and Mathematical Statistics**

**STAT4528 Probability and Martingale Theory**

#### 5000-level electives

**DATA5441 Networks and High-dimensional Inference**

**DATA5710 Applied Statistics for Complex Data**

**DATA5711 Bayesian Computational Statistics**

**MATH5310 Topics in Algebra**

*This unit of study is not available in 2021*

**MATH5311 Topics in Algebra (Alt)**

**MATH5320 Topics in Analysis**

**MATH5321 Topics in Analysis (Alt)**

**MATH5331 Topics in Geometry (Alt)**

**MATH5340 Topics in Topology**

**MATH5341 Topics in Topology (Alt)**

**MATH5411 Special Topics in Applied Mathematics (Alt)**

**MATH5420 Deterministic and Stochastic Systems**

**MATH5421 Deterministic and Stochastic Systems (Alt)**

**MATH5431 Mathematical Models for Natural Phenomena Alt**

**MATH5550 Optimal Control and Game Theory**

*This unit of study is not available in 2021*

**MATH5551 Stochastics and Finance**

*This unit of study is not available in 2021*

**STAT5610 Advanced Inference**

*This unit of study is not available in 2021*

**STAT5611 Statistical Methodology**

#### Research core project units

**MSCI5101 Mathematical Sciences Project A**

**MSCI5102 Mathematical Sciences Project B**

**MSCI5103 Mathematical Sciences Project C**

**MSCI5104 Mathematical Sciences Project D**