# 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.

Unit of study |
Credit points |
A: Assumed knowledge P: Prerequisites C: Corequisites N: Prohibition |
Session |
---|---|---|---|

## Mathematical Sciences |
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## Master of Mathematical Sciences |
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Students complete 96 credit points including: | |||

(a) No more than 24 credit points of 3000-level electives; and | |||

(b) No more than 48 credit points of 4000-level electives; and | |||

(c) At least 12 credit points of 5000-level electives; and | |||

(d) 24 credit points of research core project units. | |||

## Graduate Diploma in Mathematical Sciences |
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Students must complete 72 credit points including: | |||

(a) No more than 24 credit points of 3000-level electives; and | |||

(b) At least 24 credit points of electives at 4000-level or above, and | |||

(c) 24 credit points of research core project units | |||

## Graduate Certificate in Mathematical Sciences |
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Students must complete 48 credit points including: | |||

(a) No more than 24 credit points of 3000-level electives; and | |||

(b) At least 24 credit points of electives at 4000-level or above. | |||

## 3000-level electives |
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DATA3888Data Science Capstone |
6 | P DATA2001 or DATA2901 or DATA2002 or DATA2902 or STAT2912 or STAT2012 |
Semester 1 |

FMAT3888Projects in Financial Mathematics |
6 | A STAT2X11, MATH2X70 P (MATH2070 or MATH2970) and (STAT2011 or STAT2911) |
Semester 2 |

MATH3061Geometry and Topology |
6 | A Theory and methods of linear transformations and vector spaces, for example MATH2061, MATH2961 or MATH2022 P 12 credit points of MATH2XXX N MATH3001 or MATH3006 |
Semester 2 |

MATH3066Algebra and Logic |
6 | A Introductory knowledge of group theory. For example as in MATH2X22 P 6 credit points of MATH2XXX N MATH3062 or MATH3065 |
Semester 1 |

MATH3888Projects in Mathematics |
6 | P (MATH2921 or MATH2021 or MATH2065 or MATH2965 or MATH2061 or MATH2961 or MATH2923 or MATH2023) and (MATH2922 or MATH2022 or MATH2061 or MATH2961 or MATH2088 or MATH2988) |
Semester 2 |

MATH3975Financial Derivatives (Advanced) |
6 | P A mark of 65 or above in 12cp from (MATH2XXX or STAT2XXX or DATA2X02) N MATH3933 or MATH3015 or MATH3075 MATH2X70 and MATH3975 may be taken in the same semester |
Semester 2 |

STAT3021Stochastic Processes |
6 | P STAT2X11 and (MATH1003 or MATH1903 or MATH1907 or MATH1023 or MATH1923 or MATH1933) N STAT3911 or STAT3011 or STAT3921 or STAT4021 |
Semester 1 |

STAT3921Stochastic Processes (Advanced) |
6 | P (STAT2011 or STAT2911) and MATH1003 or MATH1903 or MATH1907 or MATH1023 or MATH1923 or MATH1933 N STAT3011 or STAT3911 or STAT3021 or STAT3003 or STAT3903 or STAT3005 or STAT3905 or STAT4021 |
Semester 1 |

STAT3888Statistical Machine Learning |
6 | A STAT3012 or STAT3912 or STAT3022 or STAT3922 P STAT2X11 and (DATA2X02 or STAT2X12) N STAT3914 or STAT3014 |
Semester 2 |

STAT3922Applied Linear Models (Advanced) |
6 | P STAT2X11 and [a mark of 65 or greater in (STAT2X12 or DATA2X02)] N STAT3912 or STAT3012 or STAT3022 |
Semester 1 |

STAT3923Statistical Inference (Advanced) |
6 | P STAT2X11 and a mark of 65 or greater in (DATA2X02 or STAT2X12) N STAT3913 or STAT3013 or STAT3023 |
Semester 2 |

## 4000-level electives |
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AMSI4001AMSI Summer School |
6 | A Completed a first degree with a major in Mathematics, Statistics, Financial Mathematics and Statistics, Data Science or equivalent Note: Department permission required for enrolmentThis unit has been designed to enable University of Sydney students to continue to take advantage of the premier Mathematics and Statistics summer school held in Australia. The University of Queensland and Melbourne already offer similar shell units to their honours and masters students respectively. |
Intensive February |

MATH4061Metric Spaces |
6 | A Real analysis and vector spaces. For example (MATH2922 or MATH2961) and (MATH2923 or MATH2962) P An average mark of 65 or above in 12cp from the following units (MATH2X21 or MATH2X22 or MATH2X23 or MATH3061 or MATH3066 or MATH3063 or MATH3076 or MATH3078 or MATH3962 or MATH3963 or MATH3968 or MATH3969 or MATH3971 or MATH3974 or MATH3976 or MATH3977 or MATH3978 or MATH3979) N MATH3961 |
Semester 1 |

MATH4062Rings, Fields and Galois Theory |
6 | P (MATH2922 or MATH2961) or a mark of 65 or greater in (MATH2022 or MATH2061) or 12cp from (MATH3061 or MATH3066 or MATH3063 or MATH3076 or MATH3078 or MATH3962 or MATH3963 or MATH3968 or MATH3969 or MATH3971 or MATH3974 or MATH3976 or MATH3977 or MATH3978 or MATH3979) N MATH3062 or MATH3962 |
Semester 1 |

MATH4063Dynamical Systems and Applications |
6 | A Linear ODEs (for example, MATH2921), eigenvalues and eigenvectors of a matrix, determinant and inverse of a matrix and linear coordinate transformations (for example, MATH2922), Cauchy sequence, completeness and uniform convergence (for example, MATH2923) P (A mark of 65 or greater in 12cp of MATH2XXX units of study) or [12cp from (MATH3061 or MATH3066 or MATH3076 or MATH3078 or MATH3961 or MATH3962 or MATH3968 or MATH3969 or MATH3971 or MATH3974 or MATH3976 or MATH3977 or MATH3978 or MATH3979)] |
Semester 1 |

MATH4068Differential Geometry |
6 | A Vector calculus, differential equations and real analysis, for example MATH2X21 and MATH2X23 P (A mark of 65 or greater in 12cp of MATH2XXX units of study) or [12cp from (MATH3061 or MATH3066 or MATH3063 or MATH3076 or MATH3078 or MATH3961 or MATH3962 or MATH3963 or MATH3969 or MATH3971 or MATH3974 or MATH3976 or MATH3977 or MATH3978 or MATH3979)] N MATH3968 |
Semester 2 |

MATH4069Measure Theory and Fourier Analysis |
6 | A (MATH2921 and MATH2922) or MATH2961 P (A mark of 65 or greater in 12cp of MATH2XXX units of study) or [12cp from the following units (MATH3061 or MATH3066 or MATH3063 or MATH3076 or MATH3078 or MATH3961 or MATH3962 or MATH3963 or MATH3969 or MATH3971 or MATH3974 or MATH3976 or MATH3977 or MATH3978 or MATH3979)] N MATH3969 |
Semester 2 |

MATH4071Convex Analysis and Optimal Control This unit of study is not available in 2021 |
6 | A MATH2X21 and MATH2X23 and STAT2X11 P [A mark of 65 or above in 12cp of (MATH2XXX or STAT2XXX or DATA2X02)] or [12cp of (MATH3XXX or STAT3XXX)] N MATH3971 |
Semester 1 |

MATH4074Fluid Dynamics |
6 | A (MATH2961 and MATH2965) or (MATH2921 and MATH2922) P (A mark of 65 or above in 12cp of MATH2XXX ) or (12cp of MATH3XXX ) N MATH3974 |
Semester 1 |

MATH4076Computational Mathematics |
6 | A (MATH2X21 and MATH2X22) or (MATH2X61 and MATH2X65) P [A mark of 65 or above in (12cp of MATH2XXX) or (6cp of MATH2XXX and 6cp of STAT2XXX or DATA2X02)] or (12cp of MATH3XXX) |
Semester 1 |

MATH4077Lagrangian and Hamiltonian Dynamics |
6 | A 6cp of 1000 level calculus units and 3cp of 1000 level linear algebra and (MATH2X21 or MATH2X61) P (A mark of 65 or greater in 12cp of MATH2XXX units of study) or [12cp from (MATH3061 orMATH3066 or MATH3063 or MATH3076 or MATH3078 or MATH3961 or MATH3962 or MATH3963 or MATH3968 or MATH3969 or MATH3971 or MATH3974 or MATH3976 or MATH3978 or MATH3979)] N MATH3977 |
Semester 2 |

MATH4078PDEs and Applications |
6 | A (MATH2X61 and MATH2X65) or (MATH2X21 and MATH2X22) P [A mark of 65 or greater in 6cp from (MATH2X21 or MATH2X65 or MATH2067) and a mark of 65 or greater 6cp from (MATH2X22 or MATH2X61)] or [12cp from (MATH3061 or MATH3066 or MATH3063 or MATH3076 or MATH3961 or MATH3962 or MATH3963 or MATH3968 or MATH3969 or MATH3971 or MATH3974 or MATH3976 or MATH3977 or MATH3979)] N MATH3078 or MATH3978 |
Semester 2 |

MATH4079Complex Analysis |
6 | A Good knowledge of analysis of functions of one real variable, working knowledge of complex numbers, including their topology, for example MATH2X23 or MATH2962 or MATH3068 P (A mark of 65 or above in 12cp of MATH2XXX) or (12cp of MATH3XXX) N MATH3979 or MATH3964 |
Semester 1 |

MATH4511Arbitrage Pricing in Continuous Time |
6 | A Familiarity with basic probability (eg STAT2X11), with differential equations (eg MATH3X63, MATH3X78) and with basic numerical analysis and coding (eg MATH3X76), achievement at credit level or above in MATH3XXX or STAT3XXX units or equivalent. |
Semester 1 |

MATH4512Stochastic Analysis |
6 | A Students should have a sound knowledge of probability theory and stochastic processes from, for example, STAT2X11 and STAT3021 or equivalent. |
Semester 2 |

MATH4513Topics in Financial Mathematics |
6 | A Students are expected to have working knowledge of Stochastic Processes, Stochastic Calculus and mathematical methods used to price options and other financial derivatives, for example as in MATH4511 or equivalent |
Semester 2 |

MATH4311Algebraic Topology |
6 | A Familiarity with abstract algebra and basic topology, e.g., (MATH2922 or MATH2961 or equivalent), (MATH3961 or equivalent) and (MATH2923 or equivalent). |
Semester 2 |

MATH4312Commutative Algebra |
6 | A Familiarity with abstract algebra, e.g., MATH2922 or equivalent. |
Semester 2 |

MATH4313Functional Analysis |
6 | A Real Analysis (e.g., MATH2X23 or equivalent), and, preferably, knowledge of Metric Spaces. |
Semester 1 |

MATH4314Representation Theory |
6 | A Familiarity with abstract algebra, specifically vector space theory and basic group theory, e.g., MATH2922 or MATH2961 or equivalent. N MATH3966 |
Semester 1 |

MATH4315Variational Methods This unit of study is not available in 2021 |
6 | A Assumed knowledge of MATH2X23 or equivalent; MATH4061 or MATH3961 or equivalent; MATH3969 or MATH4069 or MATH4313 or equivalent. That is, real analysis, basic functional analysis and some acquaintance with metric spaces or measure theory. |
Semester 2 |

MATH4411Applied Computational Mathematics |
6 | A A thorough knowledge of vector calculus (e.g., MATH2X21) and of linear algebra (e.g., MATH2X22). Some familiarity with partial differential equations (e.g., MATH3X78) and mathematical computing (e.g., MATH3X76) would be useful. |
Semester 1 |

MATH4412Advanced Methods in Applied Mathematics |
6 | A A thorough knowledge of vector calculus (e.g., MATH2X21) and of linear algebra (e.g., MATH2X22). Some familiarity with partial differential equations (e.g., MATH3X78) and mathematical computing (e.g., MATH3X76) would be useful. |
Semester 2 |

MATH4413Applied Mathematical Modelling This unit of study is not available in 2021 |
6 | A MATH2X21 and MATH3X63 or equivalent. That is, a knowledge of linear and simple nonlinear ordinary differential equations and of linear, second order partial differential equations. |
Semester 1 |

MATH4414Advanced Dynamical Systems This unit of study is not available in 2021 |
6 | A Assumed knowledge is vector calculus (e.g., MATH2X21), linear algebra (e.g., MATH2X22), dynamical systems and applications (e.g., MATH4063 or MATH3X63) or equivalent. Some familiarity with partial differential equations (e.g., MATH3978) and mathematical computing (e.g., MATH3976) is also assumed. |
Semester 2 |

STAT4021Stochastic Processes and Applications |
6 | A STAT2011 or STAT2911, and MATH1003 or MATH1903 or MATH1907 or MATH1023 or MATH1923 or MATH1933 or equivalent. That is, students are expected to have a thorough knowledge of basic probability and integral calculus and to have achieved at credit level or above in their studies in these topics. N STAT3011 or STAT3911 or STAT3021 or STAT3003 or STAT3903 or STAT3005 or STAT3905 or STAT3921. |
Semester 1 |

STAT4022Linear and Mixed Models |
6 | A Material in DATA2X02 or equivalent and MATH1X02 or equivalent; that is, a knowledge of applied statistics and an introductory knowledge to linear algebra, including eigenvalues and eigenvectors. N STAT3012 or STAT3912 or STAT3022 or STAT3922 or STAT3004 or STAT3904. |
Semester 1 |

STAT4023Theory and Methods of Statistical Inference |
6 | A STAT2X11 and (DATA2X02 or STAT2X12) or equivalent. That is, a grounding in probability theory and a good knowledge of the foundations of applied statistics. N STAT3013 or STAT3913 or STAT3023 or STAT3923 |
Semester 2 |

STAT4025Time Series |
6 | P STAT2X11 and (MATH1X03 or MATH1907 or MATH1X23 or MATH1933) N STAT3925 |
Semester 1 |

STAT4026Statistical Consulting |
6 | P At least 12cp from STAT2X11 or STAT2X12 or DATA2X02 or STAT3XXX N STAT3926 |
Semester 1 |

STAT4027Advanced Statistical Modelling |
6 | A A three year major in statistics or equivalent including familiarity with material in DATA2X02 and STAT3X22 (applied statistics and linear models) or equivalent P (STAT3X12 or STAT3X22 or STAT4022) and (STAT3X13 or STAT3X23 or STAT4023) |
Semester 2 |

STAT4028Probability and Mathematical Statistics |
6 | A STAT3X23 or equivalent: that is, a sound working and theoretical knowledge of statistical inference. N STAT4528 |
Semester 1 |

STAT4528Probability and Martingale Theory |
6 | A STAT2X11 or equivalent and STAT3X21 or equivalent; that is, a good foundational knowledge of probability and some acquaintance with stochastic processes. N STAT4028 |
Semester 1 |

## 5000-level electives |
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DATA5441Networks and High-dimensional Inference |
6 | A Linear algebra (matrices, eigenvalues, etc.); introductory concepts in statistics (statistical models, inference); a programming language. |
Semester 1 |

DATA5710Applied Statistics for Complex Data |
6 | A Familiarity with probability theory at 4000 level (e.g., STAT4211 or STAT4214 or equivalent) and with statistical modelling (e.g., STAT4027 or equivalent). Please consult with the coordinator for further information.Note: Department permission required for enrolmentThis unit is only available in even years. |
Intensive August Intensive March |

DATA5711Bayesian Computational Statistics |
6 | A Familiarity with probability theory at 4000 level (e.g., STAT4211 or STAT4214 or equivalent) and with statistical modelling (e.g., STAT4027 or equivalent). Please consult with the coordinator for further information.Note: Department permission required for enrolmentThis unit is only available in odd years. |
Intensive August Intensive March |

MATH5310Topics in Algebra This unit of study is not available in 2021 |
6 | A Familiarity with abstract algebra (e.g., MATH4062 or equivalent) and commutative algebra (e.g., MATH4312 or equivalent). Please consult with the coordinator for further information. |
Semester 1 |

MATH5311Topics in Algebra (Alt) |
6 | A Familiarity with abstract algebra (e.g., MATH4062 or equivalent) and commutative algebra (e.g., MATH4312 or equivalent). Please consult with the coordinator for further information. |
Semester 1 |

MATH5320Topics in Analysis |
6 | A Familiarity with metric spaces (e.g., MATH4061 or equivalent) and higher analysis (e.g., MATH4313 or MATH4315 or equivalent). Please consult with the coordinator for further information. |
Semester 1 |

MATH5321Topics in Analysis (Alt) |
6 | A Familiarity with metric spaces (e.g., MATH4061 or equivalent) and higher analysis (e.g., MATH4313 or MATH4315 or equivalent). Please consult with the coordinator for further information. |
Semester 1 |

MATH5331Topics in Geometry (Alt) |
6 | A Familiarity with metric spaces (e.g., MATH4061 or equivalent) and differential geometry (e.g., MATH4068 or equivalent). Please consult with the coordinator for further information. |
Semester 2 |

MATH5340Topics in Topology |
6 | A Familiarity with metric spaces (e.g., MATH4061 or equivalent) and algebraic topology (e.g., MATH4311 or equivalent). Please consult with the coordinator for further information. |
Semester 2 |

MATH5341Topics in Topology (Alt) |
6 | A Familiarity with metric spaces (e.g., MATH4061 or equivalent) and algebraic topology (e.g., MATH4311 or equivalent). Please consult with the coordinator for further information. |
Semester 2 |

MATH5411Special Topics in Applied Mathematics (Alt) |
6 | A Familiarity with the methods of classical applied mathematics (e.g., MATH4412) and the ability to write code and numerical schemes to solve standard applied mathematical problems (e.g., MATH4411 or equivalent). Please consult with the coordinator for further information. |
Semester 1 |

MATH5420Deterministic and Stochastic Systems |
6 | A Familiarity with the methods of classical applied mathematics (e.g., MATH4412) and some experience of probabilistic systems (e.g., STAT3021, MATH4311 or equivalent). Please consult with the coordinator for further information. |
Semester 2 |

MATH5421Deterministic and Stochastic Systems (Alt) |
6 | A Familiarity with the methods of classical applied mathematics (e.g., MATH4412) and some experience of probabilistic systems (e.g., STAT3021, MATH4311 or equivalent). Please consult with the coordinator for further information. |
Semester 2 |

MATH5431Mathematical Models for Natural Phenomena Alt |
6 | A Familiarity with the modelling and analysis using differential equations (e.g., MATH3063, MATH4063, MATH3078, MATH4078 or MATH4074) and the ability to write code and numerical schemes to solve standard applied mathematical problems (e.g., MATH4076 or MATH3076 or MATH4411 or equivalent). Please consult with the coordinator for further information. |
Semester 2 |

MATH5550Optimal Control and Game Theory This unit of study is not available in 2021 |
6 | A At least 6 credit points of (2000-level Advanced Mathematics or 3000-level Advanced Mathematics or 4000-level Mathematics units) or equivalent.This unit is only available in even years. |
Semester 2 |

MATH5551Stochastics and Finance This unit of study is not available in 2021 |
6 | A Students should have a sound knowledge of probability theory and stochastic processes from, for example, STAT2X11 and STAT3021 or equivalent.This unit is only available in odd years. |
Semester 1 |

STAT5610Advanced Inference This unit of study is not available in 2021 |
6 | A Familiarity with probability theory at 4000 level (e.g., STAT4211 or STAT4214 or equivalent) and with statistical modelling (e.g., STAT4027 or equivalent). Please consult with the coordinator for further information.This unit is only available in even years. |
Semester 2 |

STAT5611Statistical Methodology |
6 | A Familiarity with probability theory at 4000 level (e.g., STAT4211 or STAT4214 or equivalent) and with statistical modelling (e.g., STAT4027 or equivalent). Please consult with the coordinator for further information.This unit is only available in odd years. |
Semester 2 |

## Research core project units |
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MSCI5101Mathematical Sciences Project A |
6 | A A major in mathematics, statistics, data science, or financial mathematics and statistics, with a WAM of 65 or equivalent. |
Semester 1 Semester 2 |

MSCI5102Mathematical Sciences Project B |
6 | A A major in mathematics, statistics, data science, or financial mathematics and statistics, with a WAM of 65 or equivalent. C MSCI5101 |
Semester 1 Semester 2 |

MSCI5103Mathematical Sciences Project C |
6 | A A major in mathematics, statistics, data science, or financial mathematics and statistics, with a WAM of 65 or equivalent. C MSCI5102 |
Semester 1 Semester 2 |

MSCI5104Mathematical Sciences Project D |
6 | A A major in mathematics, statistics, data science, or financial mathematics and statistics, with a WAM of 65 or equivalent. C MSCI5103 |
Semester 1 Semester 2 |