# Table 1: Financial Mathematics and Statistics

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 |
---|---|---|---|

## Financial Mathematics and Statistics |
|||

For a major in Financial Mathematics and Statistics, students are required to complete: | |||

(i) MATH3075/3975; | |||

(ii) STAT3011/3911; | |||

(iii) STAT3012/3912; and | |||

(iv) One of the following units of study: STAT3013/3913, STAT3014/3914, MATH3076/3976, MATH3078/3978, MATH3969, MATH3974 or INFO3404/3504 | |||

## Junior units of study |
|||

MATH1001Differential Calculus |
3 | A HSC Mathematics Extension 1 N MATH1111, MATH1901, MATH1906, MATH1011, ENVX1001 |
Semester 1 Summer Main |

MATH1901Differential Calculus (Advanced) |
3 | P HSC Mathematics Extension 2. This requirement may be varied. Students with an interest in mathematics, but without HSC mathematics Extension 2, should consult the unit of study coordinator. N MATH1111, MATH1001, MATH1011, MATH1906, ENVX1001 |
Semester 1 |

MATH1906Mathematics (Special Studies Program) A |
3 | P UAI (or ATAR equivalent) of at least 98.5 and result in Band E4 HSC Mathematics Extension 2; by invitation N MATH1011, MATH1111, MATH1001, MATH1901, ENVX1001 Note: Department permission required for enrolmentEnrolment is by invitation only. |
Semester 1 |

MATH1002Linear Algebra |
3 | A HSC Mathematics or MATH1111 N MATH1902, MATH1012, MATH1014 |
Semester 1 Summer Main |

MATH1902Linear Algebra (Advanced) |
3 | P HSC Mathematics Extension 2. This requirement may be varied. Students with an interest in mathematics, but without HSC mathematics Extension 2, should consult the unit of study coordinator. N MATH1014, MATH1012, MATH1002 |
Semester 1 |

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

MATH1903Integral Calculus and Modelling Advanced |
3 | A HSC Mathematics Extension 2 or Credit or better in MATH1001 or MATH1901 P HSC Mathematics Extension 2. This requirement may be varied. Students with an interest in mathematics, but without HSC mathematics Extension 2, should consult the unit of study coordinator. N MATH1003, MATH1013, MATH1907 |
Semester 2 |

MATH1907Mathematics (Special Studies Program) B |
3 | P Distinction in MATH1906; by invitation N MATH1003, MATH1903, MATH1013 Note: Department permission required for enrolmentEnrolment is by invitation only. |
Semester 2 |

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

MATH1905Statistics (Advanced) |
3 | P HSC Mathematics Extension 2. This requirement may be varied. Students with an interest in mathematics, but without HSC mathematics Extension 2, should consult the unit of study coordinator. N STAT1022, ECMT1010, ENVX1001, MATH1005, BUSS1020, STAT1021, MATH1015 |
Semester 2 |

## Intermediate units of study |
|||

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 MATH2933, MATH2970, MATH2033, ECMT3510, MATH2010 Students may enrol in both MATH2070 and MATH3075 in the same semester |
Semester 2 |

MATH2970Optimisation & 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 MATH2033, MATH2933, MATH2070, ECMT3510, MATH2010 Students may enrol in both MATH2970 and MATH3975 in the same semester |
Semester 2 |

STAT2011Statistical Models |
6 | P (MATH1001 or MATH1901 or MATH1906 or MATH1011) and (MATH1005 or MATH1905 or MATH1015 or STAT1021 or ECMT1010 or BUSS1020) N STAT2001, STAT2901, STAT2911 |
Semester 1 |

STAT2911Probability and Statistical Models (Adv) |
6 | P (MATH1903 or MATH1907 or Credit in MATH1003) and (MATH1905 or MATH1904 or Credit in MATH1005 or Credit in ECMT1010 or Credit in BUSS1020) N STAT2001, STAT2901, STAT2011 |
Semester 1 |

STAT2012Statistical Tests |
6 | P MATH1005 or MATH1905 or MATH1015 or ECMT1010 or BUSS1020 N STAT2912, STAT2004 |
Semester 2 |

STAT2912Statistical Tests (Advanced) |
6 | A STAT2911 P MATH1905 or Credit in MATH1005 or Credit in ECMT1010 or Credit in BUSS1020 N STAT2004, STAT2012 |
Semester 2 |

## Senior core units of study |
|||

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

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

STAT3011Stochastic Processes and Time Series |
6 | P (STAT2011 or STAT2911) and (MATH1003 or MATH1903 or MATH1907). N STAT3911, STAT3003, STAT3005, STAT3903, STAT3905 |
Semester 1 |

STAT3911Stochastic Processes and Time Series Adv |
6 | P (STAT2911 or credit in STAT2011) and (MATH1003 or MATH1903 or MATH1907) N STAT3003, STAT3005, STAT3011, STAT3905, STAT3903 |
Semester 1 |

STAT3012Applied Linear Models |
6 | P (STAT2012 or STAT2912) and (MATH1002 or MATH1014 or MATH1902) N STAT3004, STAT3002, STAT3904, STAT3902, STAT3912 |
Semester 1 |

STAT3912Applied Linear Models (Advanced) |
6 | P (STAT2912 or Credit in STAT2012) and (MATH2061 or MATH2961 or MATH1902) N STAT3904, STAT3004, STAT3002, STAT3012, STAT3902 |
Semester 1 |

## Senior elective units of study |
|||

STAT3013Statistical Inference |
6 | P (STAT2011 or STAT2911) and (STAT2012 or STAT2912) N STAT3901, STAT3001, STAT3913 |
Semester 2 |

STAT3913Statistical Inference Advanced |
6 | P STAT2911 and (STAT2012 or STAT2912) N STAT3001, STAT3901, STAT3013 |
Semester 2 |

STAT3014Applied Statistics |
6 | A STAT3012 or STAT3912 P STAT2012 or STAT2912 N STAT3902, STAT3006, STAT3914, STAT3002 |
Semester 2 |

STAT3914Applied Statistics Advanced |
6 | A STAT3912 P STAT2912 or credit or better in STAT2012. N STAT3006, STAT3902, STAT3014, STAT3907, STAT3002 |
Semester 2 |

MATH3076Mathematical Computing |
6 | P 12 credit points of Intermediate Mathematics and one of (MATH1001 or MATH1003 or MATH1901 or MATH1903 or MATH1906 or MATH1907) N MATH3016, MATH3976, MATH3916 |
Semester 1 |

MATH3976Mathematical Computing (Advanced) |
6 | P 12 credit points of Intermediate Mathematics and one of (MATH1903 or MATH1907) or Credit in MATH1003 N MATH3016, MATH3916, MATH3076 |
Semester 1 |

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

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

MATH3969Measure Theory & Fourier Analysis (Adv) |
6 | A At least 6 credit points of Advanced Mathematics units of study at Intermediate or Senior level P 12 credit points Intermediate Mathematics with average grade of at least credit N MATH3909 |
Semester 2 |

MATH3974Fluid Dynamics (Advanced) |
6 | A MATH2961, MATH2965 P 12 credit points of Intermediate Mathematics with average grade of at least Credit N MATH3914 |
Semester 1 |

INFO3404Database Systems 2 |
6 | A This unit of study assumes that students have previous knowledge of database concepts including (1) ER modelling, (2) the relational data model and (3) SQL. The prerequisite material is covered in INFO 2120/2820. Familiarity with a programming language (e.g. Java or C) is also expected. N INFO3504 |
Semester 2 |

INFO3504Database Systems 2 (Adv) |
6 | A This unit of study assumes that students have previous knowledge of database concepts including (1) ER modelling, (2) the relational data model and (3) SQL. The prerequisite material is covered in INFO 2120/2820. Sound experience with the C programming language and the Unix software development environment is also expected. P Distinction-level result in INFO2120 or INFO2820 or COMP2007 or COMP2907 N INFO3404 |
Semester 2 |

### Financial Mathematics and Statistics

For a major in Financial Mathematics and Statistics, students are required to complete:

(i) MATH3075/3975;

(ii) STAT3011/3911;

(iii) STAT3012/3912; and

(iv) One of the following units of study: STAT3013/3913, STAT3014/3914, MATH3076/3976, MATH3078/3978, MATH3969, MATH3974 or INFO3404/3504

##### Junior units of study

**MATH1001 Differential Calculus**

Credit points: 3 Session: Semester 1,Summer Main Classes: Two 1 hour lectures and one 1 hour tutorial per week. Prohibitions: MATH1111, MATH1901, MATH1906, MATH1011, ENVX1001 Assumed knowledge: HSC Mathematics Extension 1 Assessment: One 1.5 hour examination, assignments and quizzes (100%) Campus: Camperdown/Darlington, Sydney Mode of delivery: Normal (lecture/lab/tutorial) day

MATH1001 is designed to provide a thorough preparation for further study in mathematics and statistics. It is a core unit of study providing three of the twelve credit points required by the Faculty of Science as well as a Junior level requirement in the Faculty of Engineering.

This unit of study looks at complex numbers, functions of a single variable, limits and continuity, vector functions and functions of two variables. Differential calculus is extended to functions of two variables. Taylor's theorem as a higher order mean value theorem.

This unit of study looks at complex numbers, functions of a single variable, limits and continuity, vector functions and functions of two variables. Differential calculus is extended to functions of two variables. Taylor's theorem as a higher order mean value theorem.

Textbooks

As set out in the Junior Mathematics Handbook.

**MATH1901 Differential Calculus (Advanced)**

Credit points: 3 Session: Semester 1 Classes: Two 1 hour lectures and one 1 hour tutorial per week. Prerequisites: HSC Mathematics Extension 2. This requirement may be varied. Students with an interest in mathematics, but without HSC mathematics Extension 2, should consult the unit of study coordinator. Prohibitions: MATH1111, MATH1001, MATH1011, MATH1906, ENVX1001 Assessment: One 1.5 hour examination, assignments and quizzes (100%) Campus: Camperdown/Darlington, Sydney Mode of delivery: Normal (lecture/lab/tutorial) day

This unit is designed to provide a thorough preparation for further study in mathematics and statistics. It is a core unit of study providing three of the twelve credit points required by the Faculty of Science as well as a Junior level requirement in the Faculty of Engineering. It parallels the normal unit MATH1001 but goes more deeply into the subject matter and requires more mathematical sophistication.

Textbooks

As set out in the Junior Mathematics Handbook

**MATH1906 Mathematics (Special Studies Program) A**

Credit points: 3 Session: Semester 1 Classes: Two 1 hour lectures, one 1 hour seminar and one 1 hour tutorial per week. Prerequisites: UAI (or ATAR equivalent) of at least 98.5 and result in Band E4 HSC Mathematics Extension 2; by invitation Prohibitions: MATH1011, MATH1111, MATH1001, MATH1901, ENVX1001 Assessment: One 1.5 hour exam, assignments, classwork (100%) Campus: Camperdown/Darlington, Sydney Mode of delivery: Normal (lecture/lab/tutorial) day

Note: Department permission required for enrolment

Note: Enrolment is by invitation only.

This is an Advanced unit of study. Entry to Mathematics (Special Studies Program) A is restricted to students with a UAI of 98.5 and an excellent school record in Mathematics. Students will cover the material in MATH1901 Differential Calculus (Advanced). In addition there will be a selection of special topics, which are not available elsewhere in the Mathematics and Statistics program.

**MATH1002 Linear Algebra**

Credit points: 3 Session: Semester 1,Summer Main Classes: Two 1 hour lectures and one 1 hour tutorial per week. Prohibitions: MATH1902, MATH1012, MATH1014 Assumed knowledge: HSC Mathematics or MATH1111 Assessment: One 1.5 hour examination, assignments and quizzes (100%) Campus: Camperdown/Darlington, Sydney Mode of delivery: Normal (lecture/lab/tutorial) day

MATH1002 is designed to provide a thorough preparation for further study in mathematics and statistics. It is a core unit of study providing three of the twelve credit points required by the Faculty of Science as well as a Junior level requirement in the Faculty of Engineering.

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

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

Textbooks

As set out in the Junior Mathematics Handbook

**MATH1902 Linear Algebra (Advanced)**

Credit points: 3 Session: Semester 1 Classes: Two 1 hour lectures and one 1 hour tutorial per week. Prerequisites: HSC Mathematics Extension 2. This requirement may be varied. Students with an interest in mathematics, but without HSC mathematics Extension 2, should consult the unit of study coordinator. Prohibitions: MATH1014, MATH1012, MATH1002 Assessment: One 1.5 hour examination, assignments and quizzes (100%) Campus: Camperdown/Darlington, Sydney Mode of delivery: Normal (lecture/lab/tutorial) day

This unit is designed to provide a thorough preparation for further study in mathematics and statistics. It is a core unit of study providing three of the twelve credit points required by the Faculty of Science as well as a Junior level requirement in the Faculty of Engineering. It parallels the normal unit MATH1002 but goes more deeply into the subject matter and requires more mathematical sophistication.

Textbooks

As set out in the Junior Mathematics Handbook

**MATH1003 Integral Calculus and Modelling**

Credit points: 3 Session: Semester 2,Summer Main Classes: Two 1 hour lectures and one 1 hour tutorial per week. Prohibitions: MATH1013, MATH1903, MATH1907 Assumed knowledge: HSC Mathematics Extension 1 or MATH1001 or MATH1011 or a credit or higher in MATH1111 Assessment: One 1.5 hour examination, assignments and quizzes (100%) Campus: Camperdown/Darlington, Sydney Mode of delivery: Normal (lecture/lab/tutorial) day

MATH1003 is designed to provide a thorough preparation for further study in mathematics and statistics. It is a core unit of study providing three of the twelve credit points required by the Faculty of Science as well as a Junior level requirement in the Faculty of Engineering.This unit of study first develops the idea of the definite integral from Riemann sums, leading to the Fundamental Theorem of Calculus. Various techniques of integration are considered, such as integration by parts.The second part is an introduction to the use of first and second order differential equations to model a variety of scientific phenomena.

Textbooks

As set out in the Junior Mathematics Handbook

**MATH1903 Integral Calculus and Modelling Advanced**

Credit points: 3 Session: Semester 2 Classes: Two 1 hour lectures and one 1 hour tutorial per week. Prerequisites: HSC Mathematics Extension 2. This requirement may be varied. Students with an interest in mathematics, but without HSC mathematics Extension 2, should consult the unit of study coordinator. Prohibitions: MATH1003, MATH1013, MATH1907 Assumed knowledge: HSC Mathematics Extension 2 or Credit or better in MATH1001 or MATH1901 Assessment: One 1.5 hour examination, assignments and quizzes (100%) Campus: Camperdown/Darlington, Sydney Mode of delivery: Normal (lecture/lab/tutorial) day

MATH1903 is designed to provide a thorough preparation for further study in mathematics and statistics. It is a core unit of study providing three of the twelve credit points required by the Faculty of Science as well as a Junior level requirement in the Faculty of Engineering.

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

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

Textbooks

As set out in the Junior Mathematics Handbook

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

Credit points: 3 Session: Semester 2 Classes: Two 1 hour lectures, one 1 hour seminar and one 1 hour tutorial per week. Prerequisites: Distinction in MATH1906; by invitation Prohibitions: MATH1003, MATH1903, MATH1013 Assessment: One 1.5 hour exam, assignments, classwork (100%) Campus: Camperdown/Darlington, Sydney Mode of delivery: Normal (lecture/lab/tutorial) day

Note: Department permission required for enrolment

Note: Enrolment is by invitation only.

This is an Advanced unit of study. Entry to Mathematics (Special Studies Program) B is normally restricted to students with a Distinction in MATH1906. Students will cover the material in MATH1903 Integral Calculus and Modelling (Advanced). In addition there will be a selection of special topics, which are not available elsewhere in the Mathematics and Statistics program.

**MATH1005 Statistics**

Credit points: 3 Session: Semester 2,Summer Main,Winter Main Classes: Two 1 hour lectures and one 1 hour tutorial per week. Prohibitions: STAT1022, ECMT1010, MATH1015, ENVX1001, MATH1905, BUSS1020, STAT1021 Assumed knowledge: HSC Mathematics Assessment: One 1.5 hour examination, assignments and quizzes (100%) Campus: Camperdown/Darlington, Sydney Mode of delivery: Normal (lecture/lab/tutorial) day

MATH1005 is designed to provide a thorough preparation for further study in mathematics and statistics. It is a core unit of study providing three of the twelve credit points required by the Faculty of Science as well as a Junior level requirement in the Faculty of Engineering.

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.

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.

Textbooks

As set out in the Junior Mathematics Handbook

**MATH1905 Statistics (Advanced)**

Credit points: 3 Session: Semester 2 Classes: Two 1 hour lectures and one 1 hour tutorial per week. Prerequisites: HSC Mathematics Extension 2. This requirement may be varied. Students with an interest in mathematics, but without HSC mathematics Extension 2, should consult the unit of study coordinator. Prohibitions: STAT1022, ECMT1010, ENVX1001, MATH1005, BUSS1020, STAT1021, MATH1015 Assessment: One 1.5 hour examination, assignments and quizzes (100%) Campus: Camperdown/Darlington, Sydney Mode of delivery: Normal (lecture/lab/tutorial) day

This unit is designed to provide a thorough preparation for further study in mathematics and statistics. It is a core unit of study providing three of the twelve credit points required by the Faculty of Science as well as a Junior level requirement in the Faculty of Engineering. This Advanced level unit of study parallels the normal unit MATH1005 but goes more deeply into the subject matter and requires more mathematical sophistication.

Textbooks

As set out in the Junior Mathematics Handbook

##### Intermediate units of study

**MATH2070 Optimisation and Financial Mathematics**

Credit points: 6 Session: Semester 2 Classes: Three 1 hour lectures, one 1 hour tutorial and one 1 hour computer laboratory per week. Prerequisites: (MATH1011 or MATH1001 or MATH1901 or MATH1906) and (MATH1014 or MATH1002 or MATH1902) Prohibitions: MATH2933, MATH2970, MATH2033, ECMT3510, MATH2010 Assumed knowledge: MATH1003 or MATH1903 or MATH1907 Assessment: One 2 hour exam, assignments, quiz, project (100%) Campus: Camperdown/Darlington, Sydney Mode of delivery: Normal (lecture/lab/tutorial) day

Note: Students may enrol in both MATH2070 and MATH3075 in the same semester

Problems in industry and commerce often involve maximising profits or minimising costs subject to constraints arising from resource limitations. The first part of this unit looks at programming problems and their solution using the simplex algorithm; nonlinear optimisation & the Kuhn Tucker conditions.

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.

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 & Financial Mathematics Adv**

Credit points: 6 Session: Semester 2 Classes: Three 1 hour lectures, one 1 hour tutorial and one 1 hour computer laboratory per week (lectures given in common with MATH2070). Prerequisites: (MATH1901 or MATH1906 or Credit in MATH1001) and (MATH1902 or Credit in MATH1002) Prohibitions: MATH2033, MATH2933, MATH2070, ECMT3510, MATH2010 Assumed knowledge: MATH1903 or MATH1907 or Credit in MATH1003 Assessment: One 2 hour exam, assignments, quizzes (100%) Campus: Camperdown/Darlington, Sydney Mode of delivery: Normal (lecture/lab/tutorial) day

Note: Students may enrol in both MATH2970 and MATH3975 in the same semester

The content of this unit of study parallels that of MATH2070, but students enrolled at Advanced level will undertake more advanced problem solving and assessment tasks, and some additional topics may be included.

**STAT2011 Statistical Models**

Credit points: 6 Session: Semester 1 Classes: Three 1 hour lectures, one 1 hour tutorial and one 1 hour computer laboratory week. Prerequisites: (MATH1001 or MATH1901 or MATH1906 or MATH1011) and (MATH1005 or MATH1905 or MATH1015 or STAT1021 or ECMT1010 or BUSS1020) Prohibitions: STAT2001, STAT2901, STAT2911 Assessment: One 2 hour exam, assignments and/or quizzes, and computer practical reports (100%) Campus: Camperdown/Darlington, Sydney Mode of delivery: Normal (lecture/lab/tutorial) day

This unit provides an introduction to univariate techniques in data analysis and the most common statistical distributions that are used to model patterns of variability. Common discrete random models like the binomial, Poisson and geometric and continuous models including the normal and exponential will be studied. The method of moments and maximum likelihood techniques for fitting statistical distributions to data will be explored. The unit will have weekly computer classes where candidates will learn to use a statistical computing package to perform simulations and carry out computer intensive estimation techniques like the bootstrap method.

**STAT2911 Probability and Statistical Models (Adv)**

Credit points: 6 Session: Semester 1 Classes: Three 1 hour lectures, one 1 hour tutorial and one 1 hour computer laboratory per week. Prerequisites: (MATH1903 or MATH1907 or Credit in MATH1003) and (MATH1905 or MATH1904 or Credit in MATH1005 or Credit in ECMT1010 or Credit in BUSS1020) Prohibitions: STAT2001, STAT2901, STAT2011 Assessment: One 2 hour exam, assignments and/or quizzes, and computer practical reports (100%) Campus: Camperdown/Darlington, Sydney Mode of delivery: Normal (lecture/lab/tutorial) day

This unit is essentially an advanced version of STAT2011, with an emphasis being on the mathematical techniques used to manipulate random variables and probability models. Common random variables including the Poisson, normal, beta and gamma families are introduced. Probability generating functions and convolution methods are used to understand the behaviour of sums of random variables. The method of moments and maximum likelihood techniques for fitting statistical distributions to data will be explored. The unit will have weekly computer classes where candidates will learn to use a statistical computing package to perform simulations and carry out computer intensive estimation techniques like the bootstrap method.

**STAT2012 Statistical Tests**

Credit points: 6 Session: Semester 2 Classes: Three 1 hour lectures, one 1 hour tutorial and one 1 hour computer laboratory per week. Prerequisites: MATH1005 or MATH1905 or MATH1015 or ECMT1010 or BUSS1020 Prohibitions: STAT2912, STAT2004 Assessment: One 2 hour exam, assignments and/or quizzes, and computer practical reports (100%) Campus: Camperdown/Darlington, Sydney Mode of delivery: Normal (lecture/lab/tutorial) day

This unit provides an introduction to the standard methods of statistical analysis of data: Tests of hypotheses and confidence intervals, including t-tests, analysis of variance, regression - least squares and robust methods, power of tests, non-parametric tests, non-parametric smoothing, tests for count data, goodness of fit, contingency tables. Graphical methods and diagnostic methods are used throughout with all analyses discussed in the context of computation with real data using an interactive statistical package.

**STAT2912 Statistical Tests (Advanced)**

Credit points: 6 Session: Semester 2 Classes: Three 1 hour lectures, one 1 hour tutorial and one 1 hour computer laboratory per week. Prerequisites: MATH1905 or Credit in MATH1005 or Credit in ECMT1010 or Credit in BUSS1020 Prohibitions: STAT2004, STAT2012 Assumed knowledge: STAT2911 Assessment: One 2-hour exam, assignments and/or quizzes, computer practical reports and one computer practical exam (100%) Campus: Camperdown/Darlington, Sydney Mode of delivery: Normal (lecture/lab/tutorial) day

This unit is essentially an advanced version of STAT2012 with an emphasis on both methods and the mathematical derivation of these methods: Tests of hypotheses and confidence intervals, including t-tests, analysis of variance, regression - least squares and robust methods, power of tests, non-parametric methods, non-parametric smoothing, tests for count data, goodness of fit, contingency tables. Graphical methods and diagnostic methods are used throughout with all analyses discussed in the context of computation with real data using an interactive statistical package.

##### Senior core units of study

**MATH3075 Financial Mathematics**

Credit points: 6 Session: Semester 2 Classes: Three 1 hour lectures and one 1 hour tutorial per week. Prerequisites: 12 credit points of Intermediate Mathematics, including MATH2070 or MATH2970 Prohibitions: MATH3975, MATH3933, MATH3015 Assessment: Two class quizzes and one 2 hour exam (100%) Campus: Camperdown/Darlington, Sydney Mode of delivery: Normal (lecture/lab/tutorial) day

This unit is an introduction to the mathematical theory of modern finance. Topics include: notion of arbitrage, pricing riskless securities, risky securities, utility theory, fundamental theorems of asset pricing, complete markets, introduction to options, binomial option pricing model, discrete random walks, Brownian motion, derivation of the Black-Scholes option pricing model, extensions and introduction to pricing exotic options, credit derivatives. A strong background in mathematical statistics and partial differential equations is an advantage, but is not essential. Students completing this unit have been highly sought by the finance industry, which continues to need graduates with quantitative skills. The lectures in the Normal unit are held concurrently with those of the corresponding Advanced unit.

**MATH3975 Financial Mathematics (Advanced)**

Credit points: 6 Session: Semester 2 Classes: Three 1 hour lectures and one 1 hour tutorial per week. Prerequisites: 12 credit points of Intermediate Mathematics (including MATH2070 or MATH2970) with at least Credit average. Prohibitions: MATH3933, MATH3075, MATH3015 Assessment: Two class quizzes and one 2 hour exam (100%) Campus: Camperdown/Darlington, Sydney Mode of delivery: Normal (lecture/lab/tutorial) day

This unit is an introduction to the mathematical theory of modern finance. Topics include: notion of arbitrage, pricing riskless securities, risky securities, utility theory, fundamental theorems of asset pricing, complete markets, introduction to options, binomial option pricing model, discrete random walks, Brownian motion, derivation of the Black-Scholes option pricing model, extensions and introduction to pricing exotic options, credit derivatives. A strong background in mathematical statistics and partial differential equations is an advantage, but is not essential. Students completing this unit have been highly sought by the finance industry, which continues to need graduates with quantitative skills. Students enrolled in this unit at the Advanced level will be expected to undertake more challenging assessment tasks. The lectures in the Advanced unit are held concurrently with those of the corresponding Normal unit.

**STAT3011 Stochastic Processes and Time Series**

Credit points: 6 Session: Semester 1 Classes: Three 1 hour lectures and one 1 hour tutorial per week; ten 1 hour computer laboratories per semester. Prerequisites: (STAT2011 or STAT2911) and (MATH1003 or MATH1903 or MATH1907). Prohibitions: STAT3911, STAT3003, STAT3005, STAT3903, STAT3905 Assessment: One 2 hour exam, assignments and/or quizzes, and computer practical reports (100%) Campus: Camperdown/Darlington, Sydney Mode of delivery: Normal (lecture/lab/tutorial) day

Section I of this course will introduce the fundamental concepts of applied stochastic processes and Markov chains used in financial mathematics, mathematical statistics, applied mathematics and physics. Section II of the course establishes some methods of modeling and analysing situations which depend on time. Fitting ARMA models for certain time series are considered from both theoretical and practical points of view. Throughout the course we will use the S-PLUS (or R) statistical packages to give analyses and graphical displays.

**STAT3911 Stochastic Processes and Time Series Adv**

Credit points: 6 Session: Semester 1 Classes: Three 1 hour lecture, one 1 hour tutorial per week, plus an extra 1 hour lecture per week on advanced material in the first half of the semester. Seven 1 hour computer laboratories (on time series) in the second half of the semester (one 1 hour class per week). Prerequisites: (STAT2911 or credit in STAT2011) and (MATH1003 or MATH1903 or MATH1907) Prohibitions: STAT3003, STAT3005, STAT3011, STAT3905, STAT3903 Assessment: One 2 hour exam, assignments and/or quizzes, and computer practical reports (100%) Campus: Camperdown/Darlington, Sydney Mode of delivery: Normal (lecture/lab/tutorial) day

This is an Advanced version of STAT3011. There will be 3 lectures in common with STAT3011. In addition to STAT3011 material, theory on branching processes and Brownian bridges will be covered.

**STAT3012 Applied Linear Models**

Credit points: 6 Session: Semester 1 Classes: Three 1 hour lectures, one 1 hour tutorial and one 1 hour computer laboratories per week. Prerequisites: (STAT2012 or STAT2912) and (MATH1002 or MATH1014 or MATH1902) Prohibitions: STAT3004, STAT3002, STAT3904, STAT3902, STAT3912 Assessment: One 2 hour exam, assignments and/or quizzes, and computer practical reports (100%) Campus: Camperdown/Darlington, Sydney Mode of delivery: Normal (lecture/lab/tutorial) day

This course will introduce the fundamental concepts of analysis of data from both observational studies and experimental designs using classical linear methods, together with concepts of collection of data and design of experiments. First we will consider linear models and regression methods with diagnostics for checking appropriateness of models. We will look briefly at robust regression methods here. Then we will consider the design and analysis of experiments considering notions of replication, randomization and ideas of factorial designs. Throughout the course we will use the R statistical package to give analyses and graphical displays.

**STAT3912 Applied Linear Models (Advanced)**

Credit points: 6 Session: Semester 1 Classes: Three 1 hour lectures, one 1 hour tutorial and one 1 hour computer laboratory per week. Prerequisites: (STAT2912 or Credit in STAT2012) and (MATH2061 or MATH2961 or MATH1902) Prohibitions: STAT3904, STAT3004, STAT3002, STAT3012, STAT3902 Assessment: One 2 hour exam, assignments and/or quizzes, and computer practical reports (100%) Campus: Camperdown/Darlington, Sydney Mode of delivery: Normal (lecture/lab/tutorial) day

This unit is essentially an Advanced version of STAT3012, with emphasis on the mathematical techniques underlying applied linear models together with proofs of distribution theory based on vector space methods. There will be 3 lectures per week in common with STAT3012 and some advanced material given in a separate advanced tutorial together with more advanced assessment work.

##### Senior elective units of study

**STAT3013 Statistical Inference**

Credit points: 6 Session: Semester 2 Classes: Three 1 hour lectures, one 1 hour tutorial and one 1 hour computer laboratory per week. Prerequisites: (STAT2011 or STAT2911) and (STAT2012 or STAT2912) Prohibitions: STAT3901, STAT3001, STAT3913 Assessment: One 2 hour exam, assignments and/or quizzes, and computer practical reports (100%) Campus: Camperdown/Darlington, Sydney Mode of delivery: Normal (lecture/lab/tutorial) day

In this course we will study basic topics in modern statistical inference. This will include traditional concepts of mathematical statistics: likelihood estimation, method of moments, properties of estimators, exponential families, decision-theory approach to hypothesis testing, likelihood ratio test as well as more recent approaches such as Bayes estimation, Empirical Bayes and nonparametric estimation. During the computer classes (using R software package) we will illustrate the various estimation techniques and give an introduction to computationally intensive methods like Monte Carlo, Gibbs sampling and EM-algorithm.

**STAT3913 Statistical Inference Advanced**

Credit points: 6 Session: Semester 2 Classes: Three 1 hour lectures, one 1 hour tutorial and one 1 hour computer laboratory per week. Prerequisites: STAT2911 and (STAT2012 or STAT2912) Prohibitions: STAT3001, STAT3901, STAT3013 Assessment: One 2 hour exam, assignments and/or quizzes, and computer practical reports (100%) Campus: Camperdown/Darlington, Sydney Mode of delivery: Normal (lecture/lab/tutorial) day

This unit is an Advanced version of STAT3013, with emphasis on the mathematical techniques underlying statistical inference together with proofs based on distribution theory. There will be 3 lectures per week in common with some material required only in this advanced course and some advanced material given in a separate advanced tutorial together with more advanced assessment work.

**STAT3014 Applied Statistics**

Credit points: 6 Session: Semester 2 Classes: Three 1 hour lectures, one 1 hour tutorial and one 1 hour computer laboratory per week. Prerequisites: STAT2012 or STAT2912 Prohibitions: STAT3902, STAT3006, STAT3914, STAT3002 Assumed knowledge: STAT3012 or STAT3912 Assessment: One 2 hour exam, assignments and/or quizzes, and computer practical reports (100%) Campus: Camperdown/Darlington, Sydney Mode of delivery: Normal (lecture/lab/tutorial) day

This unit has three distinct but related components: Multivariate analysis; sampling and surveys; and generalised linear models. The first component deals with multivariate data covering simple data reduction techniques like principal components analysis and core multivariate tests including Hotelling's T^2, Mahalanobis' distance and Multivariate Analysis of Variance (MANOVA). The sampling section includes sampling without replacement, stratified sampling, ratio estimation, and cluster sampling. The final section looks at the analysis of categorical data via generalized linear models. Logistic regression and log-linear models will be looked at in some detail along with special techniques for analyzing discrete data with special structure.

**STAT3914 Applied Statistics Advanced**

Credit points: 6 Session: Semester 2 Classes: Three 1 hour lectures and one 1 hour computer laboratory per week plus an extra hour each week which will alternate between lectures and tutorials. Prerequisites: STAT2912 or credit or better in STAT2012. Prohibitions: STAT3006, STAT3902, STAT3014, STAT3907, STAT3002 Assumed knowledge: STAT3912 Assessment: One 2 hour exam, assignments and/or quizzes, and computer practical reports (100%) Campus: Camperdown/Darlington, Sydney Mode of delivery: Normal (lecture/lab/tutorial) day

This unit is an Advanced version of STAT3014. There will be 3 lectures per week in common with STAT3014. The unit will have extra lectures focusing on multivariate distribution theory developing results for the multivariate normal, partial correlation, the Wishart distribution and Hotelling's T^2. There will also be more advanced tutorial and assessment work associated with this unit.

**MATH3076 Mathematical Computing**

Credit points: 6 Session: Semester 1 Classes: Three 1 hour lectures and one 1 hour laboratory per week. Prerequisites: 12 credit points of Intermediate Mathematics and one of (MATH1001 or MATH1003 or MATH1901 or MATH1903 or MATH1906 or MATH1907) Prohibitions: MATH3016, MATH3976, MATH3916 Assessment: One 2 hour exam, assignments, quizzes (100%) Campus: Camperdown/Darlington, Sydney Mode of delivery: Normal (lecture/lab/tutorial) day

This unit of study provides an introduction to Fortran 95/2003 programming and numerical methods. Topics covered include computer arithmetic and computational errors, systems of linear equations, interpolation and approximation, solution of nonlinear equations, quadrature, initial value problems for ordinary differential equations and boundary value problems.

**MATH3976 Mathematical Computing (Advanced)**

Credit points: 6 Session: Semester 1 Classes: Three 1 hour lectures and one 1 hour tutorial per week. Prerequisites: 12 credit points of Intermediate Mathematics and one of (MATH1903 or MATH1907) or Credit in MATH1003 Prohibitions: MATH3016, MATH3916, MATH3076 Assessment: One 2 hour exam, assignments, quizzes (100%) Campus: Camperdown/Darlington, Sydney Mode of delivery: Normal (lecture/lab/tutorial) day

See entry for MATH3076 Mathematical Computing.

**MATH3078 PDEs and Waves**

Credit points: 6 Session: Semester 2 Classes: Three 1 hour lectures and one 1 hour tutorial per week. Prerequisites: 12 credit points of Intermediate Mathematics Prohibitions: MATH3921, MATH3018, MATH3978 Assumed knowledge: (MATH2061 or MATH2961) and (MATH2065 or MATH2965) Assessment: One 2 hour exam, assignments, quizzes (100%). To pass MATH3078/3978, students must achieve satisfactory performance in the in-semester assessment component. Campus: Camperdown/Darlington, Sydney Mode of delivery: Normal (lecture/lab/tutorial) day

This unit of study introduces Sturm-Liouville eigenvalue problems and their role in finding solutions to boundary value problems. Analytical solutions of linear PDEs are found using separation of variables and integral transform methods. Three of the most important equations of mathematical physics - the wave equation, the diffusion (heat) equation and Laplace's equation - are treated, together with a range of applications. There is particular emphasis on wave phenomena, with an introduction to the theory of sound waves and water waves.

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

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)**

Credit points: 6 Session: Semester 2 Classes: Three 1 hour lectures and one 1 hour tutorial per week. Prerequisites: 12 credit points of Intermediate Mathematics with at least Credit average Prohibitions: MATH3078, MATH3921, MATH3018 Assumed knowledge: (MATH2061 or MATH2961) and (MATH2065 or MATH2965) Assessment: One 2 hour exam, assignments, quizzes (100%). To pass MATH3078 or MATH3978, students must achieve satisfactory performance in the in-semester assessment component. Campus: Camperdown/Darlington, Sydney Mode of delivery: Normal (lecture/lab/tutorial) day

As for MATH3078 PDEs & Waves but with more advanced problem solving and assessment tasks. Some additional topics may be included.

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

Credit points: 6 Session: Semester 2 Classes: Three 1 hour lectures and one 1 hour tutorials per week. Prerequisites: 12 credit points Intermediate Mathematics with average grade of at least credit Prohibitions: MATH3909 Assumed knowledge: At least 6 credit points of Advanced Mathematics units of study at Intermediate or Senior level Assessment: One 2 hour exam, assignments, quizzes (100%) Campus: Camperdown/Darlington, Sydney Mode of delivery: Normal (lecture/lab/tutorial) day

Measure theory is the study of such fundamental ideas as length, area, volume, arc length and surface area. It is the basis for the integration theory used in advanced mathematics since it was developed by Henri Lebesgue in about 1900. Moreover, it is the basis for modern probability theory. The course starts by setting up measure theory and integration, establishing important results such as Fubini's Theorem and the Dominated Convergence Theorem which allow us to manipulate integrals. This is then applied to Fourier Analysis, and results such as the Inversion Formula and Plancherel's Theorem are derived. The Radon-Nikodyn Theorem provides a representation of measures in terms of a density. Probability theory is then discussed with topics including distributions and conditional expectation.

**MATH3974 Fluid Dynamics (Advanced)**

Credit points: 6 Session: Semester 1 Classes: Three 1 hour lectures and one 1 hour tutorial per week. Prerequisites: 12 credit points of Intermediate Mathematics with average grade of at least Credit Prohibitions: MATH3914 Assumed knowledge: MATH2961, MATH2965 Assessment: One 2 hour exam (100%) Campus: Camperdown/Darlington, Sydney Mode of delivery: Normal (lecture/lab/tutorial) day

This unit of study provides an introduction to fluid dynamics, starting with a description of the governing equations and the simplifications gained by using stream functions or potentials. It develops elementary theorems and tools, including Bernoulli's equation, the role of vorticity, the vorticity equation, Kelvin's circulation theorem, Helmholtz's theorem, and an introduction to the use of tensors. Topics covered include viscous flows, lubrication theory, boundary layers, potential theory, and complex variable methods for 2-D airfoils. The unit concludes with an introduction to hydrodynamic stability theory and the transition to turbulent flow.

**INFO3404 Database Systems 2**

Credit points: 6 Session: Semester 2 Classes: Lecture 2 hrs/week; Tutorial 1 hr/week; Practical assignment on database tuning. 6 hrs. Prohibitions: INFO3504 Assumed knowledge: This unit of study assumes that students have previous knowledge of database concepts including (1) ER modelling, (2) the relational data model and (3) SQL. The prerequisite material is covered in INFO 2120/2820. Familiarity with a programming language (e.g. Java or C) is also expected. Assessment: Through semester assessment (40%) Final Exam (60%) Campus: Camperdown/Darlington, Sydney Mode of delivery: Normal (lecture/lab/tutorial) day

This unit of study provides a comprehensive overview of the internal mechanisms and algorithms of Database Management Systems (DBMS) and other systems that manage large data collections. These skills are needed for successful performance tuning and to understand the scalability challenges faced by the information age. This unit builds upon the second- year INFO2120 - 'Database Systems 1' and correspondingly assumes a sound understanding of SQL, schema design and transactional programs.

The first part of this subject focuses on mechanisms for large-scale data management. It provides a deep understanding of the internal components of a database engine. Topics include: physical data organization and disk-based index structures, query processing and optimisation, locking and logging, and database tuning.

The second part focuses on the large-scale management of textual data such as by an information retrieval system or with web search engines. Topics include: distributed and replicated databases, information retrieval, document management, text index structures, and web-scale data processing.

The unit will be of interest to students seeking an introduction to database tuning, disk-based data structures and algorithms, and information retrieval. It will be valuable to those pursuing such careers as Software Engineers, Database Experts, Database Administrators, and e-Business Consultants.

The first part of this subject focuses on mechanisms for large-scale data management. It provides a deep understanding of the internal components of a database engine. Topics include: physical data organization and disk-based index structures, query processing and optimisation, locking and logging, and database tuning.

The second part focuses on the large-scale management of textual data such as by an information retrieval system or with web search engines. Topics include: distributed and replicated databases, information retrieval, document management, text index structures, and web-scale data processing.

The unit will be of interest to students seeking an introduction to database tuning, disk-based data structures and algorithms, and information retrieval. It will be valuable to those pursuing such careers as Software Engineers, Database Experts, Database Administrators, and e-Business Consultants.

**INFO3504 Database Systems 2 (Adv)**

Credit points: 6 Session: Semester 2 Classes: Lecture 2 hrs/week; Advanced Seminar 1 hr/week; Tutorial/lab after advanced seminar 1 hr/week; Project Work - own time 6 hrs. Prerequisites: Distinction-level result in INFO2120 or INFO2820 or COMP2007 or COMP2907 Prohibitions: INFO3404 Assumed knowledge: This unit of study assumes that students have previous knowledge of database concepts including (1) ER modelling, (2) the relational data model and (3) SQL. The prerequisite material is covered in INFO 2120/2820. Sound experience with the C programming language and the Unix software development environment is also expected. Assessment: Through semester assessment (40%) Final Exam (60%) Campus: Camperdown/Darlington, Sydney Mode of delivery: Normal (lecture/lab/tutorial) day

This unit of study provides a comprehensive overview of the internal mechanisms and algorithms of Database Management Systems (DBMS) and other systems that manage large data collections. These skills are needed for successful performance tuning and to understand the scalability challenges faced by the information age. This unit builds upon the second- year INFO2820 - 'Database Systems 1 (Adv)' and correspondingly assumes a sound understanding of SQL, schema design and transactional programs.

The first part of this subject focuses on mechanisms for large-scale data management. It provides a deep understanding of the internal components of a database engine. Topics include: physical data organization and disk-based index structures, query processing and optimisation, locking and logging, and database tuning.

The second part focuses on the large-scale management of textual data such as by an information retrieval system or with web search engines. Topics include: distributed and replicated databases, information retrieval, document management, text index structures, and web-scale data management.

This is an advanced alternative to INFO3404; it covers material at an advanced and challenging level. In particular, students in this advanced stream will study an actual DBMS implementation on the source code level, and also gain practical experience in extending the DBMS code base.

The first part of this subject focuses on mechanisms for large-scale data management. It provides a deep understanding of the internal components of a database engine. Topics include: physical data organization and disk-based index structures, query processing and optimisation, locking and logging, and database tuning.

The second part focuses on the large-scale management of textual data such as by an information retrieval system or with web search engines. Topics include: distributed and replicated databases, information retrieval, document management, text index structures, and web-scale data management.

This is an advanced alternative to INFO3404; it covers material at an advanced and challenging level. In particular, students in this advanced stream will study an actual DBMS implementation on the source code level, and also gain practical experience in extending the DBMS code base.