# Table 1: Mathematics

Table 1 lists units of study available to students in the Bachelor of Science and combined degrees. The units are available to students enrolled in other degrees in accordance with their degree resolutions.

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

## Mathematics |
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For a major in Mathematics, the minimum requirement is 24 credit points from senior units of study listed in this subject area. | |||

## Junior units of study |
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## Introductory level |
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MATH1111Introduction to Calculus - Departmental permission is required for this unit This unit of study is not Data Audit Committee Approved |
6 | A HSC General Mathematics N MATH1011 or MATH1901 or MATH1906 or MATH1001 or HSC Mathematics Extension 1 or HSC Mathematics Extension 2 or ENVX1001 Note: Department permission required for enrolmentStudents who have previously successfully studied calculus at a level at least equivalent to HSC Mathematics are prohibited. |
Semester 1 |

## Fundamental level |
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MATH1011Applications of Calculus This unit of study is not Data Audit Committee Approved |
3 | A HSC Mathematics N MATH1001 or MATH1901 or MATH1906 or MATH1111 or BIOM1003 or ENVX1001 |
Semester 1 Summer Main |

MATH1013Mathematical Modelling |
3 | A HSC Mathematics, or a Credit or higher in MATH1111 N MATH1003 or MATH1903 or MATH1907, MATH1003 or MATH1903 or MATH1907, MATH1003 or MATH1903 or MATH1907 |
Semester 2 Semester 2 Summer Main Summer Main |

MATH1014Introduction to Linear Algebra |
3 | A HSC Mathematics or MATH1111 N MATH1012 or MATH1002 or MATH1902, MATH1012 or MATH1002 or MATH1902, MATH1012 or MATH1002 or MATH1902 |
Semester 2 Semester 2 |

MATH1015Biostatistics This unit of study is not Data Audit Committee Approved |
3 | A HSC Mathematics N MATH1005 or MATH1905 or STAT1021 or STAT1022 or ECMT1010 or BIOM1003 or ENVX1001 or BUSS1020 |
Semester 1 |

## Regular level |
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MATH1001Differential Calculus This unit of study is not Data Audit Committee Approved |
3 | A HSC Mathematics Extension 1 N MATH1011 or MATH1901 or MATH1906 or MATH1111 or ENVX1001. |
Semester 1 Summer Main |

MATH1002Linear Algebra This unit of study is not Data Audit Committee Approved |
3 | A HSC Mathematics or MATH1111 N MATH1012 or MATH1014 or MATH1902 |
Semester 1 Summer Main |

MATH1003Integral Calculus and Modelling |
3 | A HSC Mathematics Extension 1, or MATH1001, or MATH1011, or a Credit or higher in MATH1111 N MATH1013 or MATH1903 or MATH1907, MATH1013 or MATH1903 or MATH1907, MATH1013 or MATH1903 or MATH1907 |
Semester 2 Semester 2 Summer Main Summer Main |

MATH1004Discrete Mathematics |
3 | A HSC Mathematics or MATH1111 N MATH1904 or MATH2011, MATH1904 or MATH2011, MATH1904 or MATH2011 |
Semester 2 Semester 2 Summer Main Summer Main |

MATH1005Statistics |
3 | A HSC Mathematics N MATH1015 or MATH1905 or STAT1021 or STAT1022 or ECMT1010 or ENVX1001 or BUSS1020, MATH1015 or MATH1905 or STAT1021 or STAT1022 or ECMT1010 or ENVX1001 or BUSS1020, MATH1015 or MATH1905 or STAT1021 or STAT1022 or ECMT1010 or ENVX1001 or BUSS1020 |
Semester 2 Semester 2 Summer Main Summer Main Winter Main Winter Main |

## Advanced level |
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MATH1901Differential Calculus (Advanced) This unit of study is not Data Audit Committee Approved |
3 | P HSC Mathematics Extension 2 N MATH1001 or MATH1011 or MATH1906 or MATH1111 or ENVX1001 |
Semester 1 |

MATH1902Linear Algebra (Advanced) This unit of study is not Data Audit Committee Approved |
3 | P HSC Mathematics Extension 2 N MATH1002 or MATH1012 or MATH1014 |
Semester 1 |

MATH1903Integral Calculus and Modelling Advanced |
3 | A HSC Mathematics Extension 2, or Credit or better in (MATH1001 or MATH1901) P HSC Mathematics Extension 2 N MATH1003 or MATH1013 or MATH1907, MATH1003 or MATH1013 or MATH1907, MATH1003 or MATH1013 or MATH1907 |
Semester 2 Semester 2 |

MATH1905Statistics (Advanced) |
3 | P HSC Mathematics Extension 2 N MATH1005 or MATH1015 or STAT1021 or STAT1022 or ECMT1010 or ENVX1001 or BUSS1020, MATH1005 or MATH1015 or STAT1021 or STAT1022 or ECMT1010 or ENVX1001 or BUSS1020, MATH1005 or MATH1015 or STAT1021 or STAT1022 or ECMT1010 or ENVX1001 or BUSS1020 |
Semester 2 Semester 2 |

## Special Studies level |
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MATH1906Mathematics (Special Studies Program) A - Departmental permission is required for this unit This unit of study is not Data Audit Committee Approved |
3 | N MATH1001 or MATH1011 or MATH1901 or MATH1111 or ENVX1001 Note: Department permission required for enrolmentEnrolment is by invitation only. Prerequisites: UAI (or ATAR equivalent) of at least 98.5 and result in Band E4 HSC Mathematics Extension 2 |
Semester 1 |

MATH1907Mathematics (Special Studies Program) B |
3 | P Distinction or greater in MATH1906 N MATH1003 or MATH1903 or MATH1013, MATH1003 or MATH1903 or MATH1013, MATH1003 or MATH1903 or MATH1013 Note: Department permission required for enrolment in the following sessions:Semester 2Enrolment is by invitation only. |
Semester 2 Semester 2 |

## Intermediate units of study |
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MATH2061Linear Mathematics and Vector Calculus This unit of study is not Data Audit Committee Approved |
6 | P (MATH1011 or MATH1001 or MATH1901 or MATH1906) and (MATH1014 or MATH1002 or MATH1902) and (MATH1003 or MATH1903 or MATH1907) N MATH2001 or MATH2901 or MATH2002 or MATH2902 or MATH2961 or MATH2067 |
Semester 1 Summer Main |

MATH2961Linear Mathematics and Vector Calculus Adv This unit of study is not Data Audit Committee Approved |
6 | P (MATH1901 or MATH1906 or Credit in MATH1001) and (MATH1902 or Credit in MATH1002) and (MATH1903 or MATH1907 or Credit in MATH1003) N MATH2001 or MATH2901 or MATH2002 or MATH2902 or MATH2061 or MATH2067 |
Semester 1 |

MATH2065Partial Differential Equations (Intro) |
6 | P (MATH1011 or MATH1001 or MATH1901 or MATH1906) and (MATH1014 or MATH1002 or MATH1902) and (MATH1003 or MATH1903 or MATH1907) N MATH2005 or MATH2905 or MATH2965 or MATH2067, MATH2005 or MATH2905 or MATH2965 or MATH2067, MATH2005 or MATH2905 or MATH2965 or MATH2067 |
Semester 2 Semester 2 Summer Main |

MATH2965Partial Differential Equations Intro Adv |
6 | P MATH2961 or Credit in MATH2061 N MATH2005 or MATH2905 or MATH2065 or MATH2067, MATH2005 or MATH2905 or MATH2065 or MATH2067, MATH2005 or MATH2905 or MATH2065 or MATH2067 |
Semester 2 Semester 2 |

MATH2068Number Theory and Cryptography |
6 | A MATH1014 or MATH1002 or MATH1902 P 6 credit points of Junior Mathematics units N MATH2988 or MATH3009 or MATH3024, MATH2988 or MATH3009 or MATH3024, MATH2988 or MATH3009 or MATH3024 |
Semester 2 Semester 2 |

MATH2988Number Theory and Cryptography Advanced |
6 | P A minimum of 9 credit points from ((Junior Advanced Mathematics, MATH2961, MATH2962, MATH2969, or Credit or greater in normal level Junior Mathematics, MATH2061, MATH2069) N MATH2068, MATH2068, MATH2068 |
Semester 2 Semester 2 |

MATH2069Discrete Mathematics and Graph Theory This unit of study is not Data Audit Committee Approved |
6 | P 6 credit points of Junior Mathematics units N MATH2011 or MATH2009 or MATH2969 |
Semester 1 |

MATH2969Discrete Mathematics and Graph Theory Adv This unit of study is not Data Audit Committee Approved |
6 | P 9 credit points of Junior Mathematics (advanced level or Credit at the normal level) N MATH2011 or MATH2009 or MATH2069 |
Semester 1 |

MATH2070Optimisation and Financial Mathematics |
6 | A MATH1003 or MATH1903 or MATH1907 P (MATH1011 or MATH1001 or MATH1901 or MATH1906) and (MATH1014 or MATH1002 or MATH1902) N MATH2010 or MATH2033 or MATH2933 or MATH2970 or ECMT3510, MATH2010 or MATH2033 or MATH2933 or MATH2970 or ECMT3510, MATH2010 or MATH2033 or MATH2933 or MATH2970 or ECMT3510 Students may enrol in both MATH2070 and MATH3075 in the same semester |
Semester 2 Semester 2 |

MATH2970Optimisation and Financial Mathematics Adv |
6 | A MATH1903 or MATH1907 or Credit in MATH1003 P (MATH1901 or MATH1906 or Credit in MATH1001) and (MATH1902 or Credit in MATH1002) N MATH2010 or MATH2033 or MATH2933 or MATH2070 or ECMT3510, MATH2010 or MATH2033 or MATH2933 or MATH2070 or ECMT3510, MATH2010 or MATH2033 or MATH2933 or MATH2070 or ECMT3510 Students may enrol in both MATH2970 and MATH3975 in the same semester |
Semester 2 Semester 2 |

MATH2962Real and Complex Analysis (Advanced) This unit of study is not Data Audit Committee Approved |
6 | P (MATH1901 or MATH1906 or Credit in MATH1001) and (MATH1902 or Credit in MATH1002) and (MATH1903 or MATH1907 or Credit in MATH1003) N MATH2007 or MATH2907 |
Semester 1 |

MATH2968Algebra (Advanced) |
6 | P 9 credit points of Junior Mathematics (advanced level or Credit at normal level) including (MATH1902 or Credit in MATH1002) N MATH2908 or MATH2918 or MATH2008, MATH2908 or MATH2918 or MATH2008, MATH2908 or MATH2918 or MATH2008 |
Semester 2 Semester 2 |

MATH2916Working Seminar A (SSP) - Departmental permission is required for this unit This unit of study is not Data Audit Committee Approved |
3 | P High Distinction average over 12 credit points of Junior Advanced Mathematics Note: Department permission required for enrolment |
Semester 1 |

MATH2917Working Seminar B (SSP) - Departmental permission is required for this unit This unit of study is not Data Audit Committee Approved |
3 | P High Distinction average over 12 credit points of Junior Advanced Mathematics Note: Department permission required for enrolment |
Semester 2 |

## Senior units of study |
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MATH3061Geometry and Topology |
6 | P 12 credit points of Intermediate Mathematics N MATH3001 or MATH3006, MATH3001 or MATH3006, MATH3001 or MATH3006 |
Semester 2 Semester 2 |

MATH3063Differential Equations and Biomaths This unit of study is not Data Audit Committee Approved |
6 | A MATH2061 P 12 credit points of Intermediate Mathematics N MATH3020 or MATH3920 or MATH3003 or MATH3923 or MATH3963 |
Semester 1 |

MATH3963Differential Equations and Biomaths (Adv) This unit of study is not Data Audit Committee Approved |
6 | A MATH2961 and MATH2962 P Credit average or greater in 12 credit points of Intermediate Mathematics N MATH3020 or MATH3920 or MATH3003 or MATH3923 or MATH3063 |
Semester 1 |

MATH3066Algebra and Logic This unit of study is not Data Audit Committee Approved |
6 | P 6 credit points of Intermediate Mathematics N MATH3062 or MATH3065 |
Semester 1 |

MATH3068Analysis |
6 | P 12 credit points of Intermediate Mathematics N MATH3008 or MATH2007 or MATH2907 or MATH2962, MATH3008 or MATH2007 or MATH2907 or MATH2962, MATH3008 or MATH2007 or MATH2907 or MATH2962 |
Semester 2 Semester 2 |

MATH3075Financial Mathematics |
6 | P 12 credit points of Intermediate Mathematics, including (MATH2070 or MATH2970) N MATH3975 or MATH3015 or MATH3933, MATH3975 or MATH3015 or MATH3933, MATH3975 or MATH3015 or MATH3933 |
Semester 2 Semester 2 |

MATH3975Financial Mathematics (Advanced) |
6 | P Credit average or greater in 12 credit points of Intermediate Mathematics (including MATH2070 or MATH2970) N MATH3933 or MATH3015 or MATH3075, MATH3933 or MATH3015 or MATH3075, MATH3933 or MATH3015 or MATH3075 |
Semester 2 Semester 2 |

MATH3076Mathematical Computing This unit of study is not Data Audit Committee Approved |
6 | P 12 credit points of Intermediate Mathematics and one of (MATH1001 or MATH1003 or MATH1901 or MATH1903 or MATH1906 or MATH1907) N MATH3976 or MATH3016 or MATH3916 |
Semester 1 |

MATH3976Mathematical Computing (Advanced) This unit of study is not Data Audit Committee Approved |
6 | P 12 credit points of Intermediate Mathematics and one of (MATH1903 or MATH1907), or Credit in MATH1003 N MATH3076 or MATH3016 or MATH3916 |
Semester 1 |

MATH3078PDEs and Waves |
6 | A (MATH2061 or MATH2961) and (MATH2065 or MATH2965) P 12 credit points of Intermediate Mathematics N MATH3018 or MATH3921 or MATH3978, MATH3018 or MATH3921 or MATH3978, MATH3018 or MATH3921 or MATH3978 |
Semester 2 Semester 2 |

MATH3978PDEs and Waves (Advanced) |
6 | A (MATH2061 or MATH2961) and (MATH2065 or MATH2965) P Credit average or greater in 12 credit points of Intermediate Mathematics N MATH3078 or MATH3018 or MATH3921, MATH3078 or MATH3018 or MATH3921, MATH3078 or MATH3018 or MATH3921 |
Semester 2 Semester 2 |

MATH3961Metric Spaces (Advanced) This unit of study is not Data Audit Committee Approved |
6 | A MATH2961 or MATH2962 P Credit average or greater in 12 credit points of Intermediate Mathematics units N MATH3001 or MATH3901 |
Semester 1 |

MATH3962Rings, Fields and Galois Theory (Adv) This unit of study is not Data Audit Committee Approved |
6 | A MATH2961 P Credit average or greater in 12 credit points of Intermediate Mathematics N MATH3062 or MATH3902 or MATH3002 Students are advised to take MATH2968 before attempting this unit. |
Semester 1 |

MATH3968Differential Geometry (Advanced) |
6 | A At least 6 credit points of Intermediate Advanced Mathematics or Senior Advanced Mathematics units P Credit average or greater in 12 credit points of Intermediate Mathematics, including MATH2961 N MATH3903, MATH3903, MATH3903 |
Semester 2 Semester 2 |

MATH3969Measure Theory and Fourier Analysis (Adv) |
6 | A At least 6 credit points of (Intermediate Advanced Mathematics or Senior Advanced Mathematics units) P Credit average or greater in 12 credit points Intermediate Mathematics N MATH3909, MATH3909, MATH3909 |
Semester 2 Semester 2 |

MATH3974Fluid Dynamics (Advanced) This unit of study is not Data Audit Committee Approved |
6 | A MATH2961 and MATH2965 P Credit average or greater in 12 credit points of Intermediate Mathematics N MATH3914 |
Semester 1 |

MATH3977Lagrangian and Hamiltonian Dynamics (Adv) |
6 | P Credit average or greater in 12 credit points of Intermediate Mathematics N MATH2904 or MATH2004 or MATH3917, MATH2904 or MATH2004 or MATH3917, MATH2904 or MATH2004 or MATH3917 |
Semester 2 Semester 2 |

### Mathematics

##### Junior units of study

###### Introductory level

**MATH1111 Introduction to Calculus - Departmental permission is required for this unit**

*This unit of study does not have Data Audit Committee approval*

###### Fundamental level

**MATH1011 Applications of Calculus**

*This unit of study does not have Data Audit Committee approval*

**MATH1013 Mathematical Modelling**

In this unit of study students learn how to construct, interpret and solve simple differential equations and recurrence relations. Specific techniques include separation of variables, partial fractions and first and second order linear equations with constant coefficients. Students are also shown how to iteratively improve approximate numerical solutions to equations.

**MATH1014 Introduction to Linear Algebra**

**MATH1015 Biostatistics**

*This unit of study does not have Data Audit Committee approval*

###### Regular level

**MATH1001 Differential Calculus**

*This unit of study does not have Data Audit Committee approval*

**MATH1002 Linear Algebra**

*This unit of study does not have Data Audit Committee approval*

This unit of study introduces vectors and vector algebra, linear algebra including solutions of linear systems, matrices, determinants, eigenvalues and eigenvectors.

**MATH1003 Integral Calculus and Modelling**

**MATH1004 Discrete Mathematics**

This unit provides an introduction to fundamental aspects of discrete mathematics, which deals with 'things that come in chunks that can be counted'. It focuses on the enumeration of a set of numbers, viz. Catalan numbers. Topics include sets and functions, counting principles, Boolean expressions, mathematical induction, generating functions and linear recurrence relations, graphs and trees.

**MATH1005 Statistics**

This unit offers a comprehensive introduction to data analysis, probability, sampling, and inference including t-tests, confidence intervals and chi-squared goodness of fit tests.

###### Advanced level

**MATH1901 Differential Calculus (Advanced)**

*This unit of study does not have Data Audit Committee approval*

**MATH1902 Linear Algebra (Advanced)**

*This unit of study does not have Data Audit Committee approval*

**MATH1903 Integral Calculus and Modelling Advanced**

This unit of study parallels the normal unit MATH1003 but goes more deeply into the subject matter and requires more mathematical sophisticaton.

**MATH1905 Statistics (Advanced)**

###### Special Studies level

**MATH1906 Mathematics (Special Studies Program) A - Departmental permission is required for this unit**

*This unit of study does not have Data Audit Committee approval*

**MATH1907 Mathematics (Special Studies Program) B**

##### Intermediate units of study

**MATH2061 Linear Mathematics and Vector Calculus**

*This unit of study does not have Data Audit Committee approval*

**MATH2961 Linear Mathematics and Vector Calculus Adv**

*This unit of study does not have Data Audit Committee approval*

The connection between matrices and linear transformations is studied in detail. Determinants, introduced in first year, are revised and investigated further, as are eigenvalues and eigenvectors. The calculus component of the unit includes local maxima and minima, the inverse function theorem and Jacobians.

There is an informal treatment of multiple integrals: double integrals, change of variables, triple integrals, line and surface integrals, Green's theorem and Stokes' theorem.

**MATH2065 Partial Differential Equations (Intro)**

**MATH2965 Partial Differential Equations Intro Adv**

**MATH2068 Number Theory and Cryptography**

**MATH2988 Number Theory and Cryptography Advanced**

**MATH2069 Discrete Mathematics and Graph Theory**

*This unit of study does not have Data Audit Committee approval*

**MATH2969 Discrete Mathematics and Graph Theory Adv**

*This unit of study does not have Data Audit Committee approval*

**MATH2070 Optimisation and Financial Mathematics**

The second part of the unit deals with utility theory and modern portfolio theory. Topics covered include: pricing under the principles of expected return and expected utility; mean-variance Markowitz portfolio theory, the Capital Asset Pricing Model, log-optimal portfolios and the Kelly criterion; dynamical programming. Some understanding of probability theory including distributions and expectations is required in this part.

Theory developed in lectures will be complemented by computer laboratory sessions using MATLAB. Minimal computing experience will be required.

**MATH2970 Optimisation and Financial Mathematics Adv**

**MATH2962 Real and Complex Analysis (Advanced)**

*This unit of study does not have Data Audit Committee approval*

**MATH2968 Algebra (Advanced)**

**MATH2916 Working Seminar A (SSP) - Departmental permission is required for this unit**

*This unit of study does not have Data Audit Committee approval*

**MATH2917 Working Seminar B (SSP) - Departmental permission is required for this unit**

*This unit of study does not have Data Audit Committee approval*

##### Senior units of study

**MATH3061 Geometry and Topology**

**MATH3063 Differential Equations and Biomaths**

*This unit of study does not have Data Audit Committee approval*

**MATH3963 Differential Equations and Biomaths (Adv)**

*This unit of study does not have Data Audit Committee approval*

**MATH3066 Algebra and Logic**

*This unit of study does not have Data Audit Committee approval*

The Propositional and Predicate Calculi are studied as model axiomatic systems in their own right, including sketches of 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 and the undecidability of First Order Logic.

**MATH3068 Analysis**

Power series are not adequate to solve the problem of representing periodic phenomena such as wave motion. This requires Fourier theory, the expansion of functions as sums of sines and cosines. This unit deals with this theory, Parseval's identity, pointwise convergence theorems and applications.

The unit goes on to introduce Bernoulli numbers, Bernoulli polynomials, the Euler MacLaurin formula and applications, the gamma function and the Riemann zeta function. Lastly we return to the foundations of analysis, and study limits from the point of view of topology.

**MATH3075 Financial Mathematics**

**MATH3975 Financial Mathematics (Advanced)**

**MATH3076 Mathematical Computing**

*This unit of study does not have Data Audit Committee approval*

**MATH3976 Mathematical Computing (Advanced)**

*This unit of study does not have Data Audit Committee approval*

**MATH3078 PDEs and Waves**

To pass MATH3078, students must achieve satisfactory performance in the in-semester assessment component in order to pass the unit of study.

**MATH3978 PDEs and Waves (Advanced)**

**MATH3961 Metric Spaces (Advanced)**

*This unit of study does not have Data Audit Committee approval*

**MATH3962 Rings, Fields and Galois Theory (Adv)**

*This unit of study does not have Data Audit Committee approval*

The basic theoretical tool needed for this program is the concept of a ring, which generalizes the concept of a field. The course begins with examples of rings, and associated concepts such as subrings, ring homomorphisms, ideals and quotient rings. These tools are then applied to study quotient rings of polynomial rings. The final part of the course deals with the basics of Galois theory, which gives a way of understanding field extensions.

**MATH3968 Differential Geometry (Advanced)**

**MATH3969 Measure Theory and Fourier Analysis (Adv)**

**MATH3974 Fluid Dynamics (Advanced)**

*This unit of study does not have Data Audit Committee approval*

**MATH3977 Lagrangian and Hamiltonian Dynamics (Adv)**

Students will be expected to solve fully dynamical systems of some complexity including planetary motion and to investigate stability using perturbation analysis. Hamilton-Jacobi theory will be used to elegantly solve problems ranging from geodesics (shortest path between two points) on curved surfaces to relativistic motion in the vicinity of black holes.

This unit is a useful preparation for units in dynamical systems and chaos, and complements units in differential equations, quantum theory and general relativity.