Financial Mathematics and Statistics Descriptions

Errata
Item Errata Date
1.

The prerequisites have been removed for the following units:

MATH1021 Calculus Of One Variable
MATH1023 Multivariable Calculus and Modelling

12/12/2018
2.

The prerequisites have been removed and the assumed kowledge has changed for the following units:

MATH1921 Calculus Of One Variable (Advanced): Prerequisites have been removed. Assumed knowledge now reads: (HSC Mathematics Extension 2) OR (Band E4 in HSC Mathematics Extension 1) or equivalent.

MATH1931 Calculus Of One Variable (SSP): Prerequisites have been removed. Assumed knowledge  now reads: (HSC Mathematics Extension 2) OR (Band E4 in HSC Mathematics Extension 1) or equivalent.

MATH1923 Multivariable Calculus and Modelling (Adv): Prerequisites have been removed. Assumed knowledge now reads: (HSC Mathematics Extension 2) OR (Band E4 in HSC Mathematics Extension 1) or equivalent

MATH1933 Multivariable Calculus and Modelling (SSP):Prerequisites have been removed. Assumed knowledge now reads: (HSC Mathematics Extension 2) OR (Band E4 in HSC Mathematics Extension 1) or equivalent.

12/12/2018

FINANCIAL MATHEMATICS AND STATISTICS

Advanced coursework and projects will be available in 2020 for students who complete this major.

Financial Mathematics and Statistics major

A major in Financial Mathematics and Statistics requires 48 credit points from this table including:
(i) 12 credit points of 1000 level units according to the following rules:
(a) 3 credit points of calculus units; 3 credit points of multivariable calculus; 3 credit points of linear algebra units and 3 credit points of statistics units*. (Students in the Mathematical Sciences program must choose this option^); or
(b) 3 credit points of calculus units; 3 credit points of linear algebra units and 6 credit points of data science units*
(ii) 12 credit points of 2000-level core units
(iii) 6 credit points of 3000-level core units
(iv) 6 credit points of 3000-level interdisciplinary project units
(v) 6 credit points of 3000-level or 4000-level mathematical modelling units
(vi) 6 credit points of 3000-level or 4000-level statistical modelling units
*Students not enrolled in the BSc may substitute ECMT1010 or BUSS1020
^If elective space allows, students may substitute DATA1001/1901 for the statistics unit

Financial Mathematics and Statistics minor

A minor in Financial Mathematics and Statistics requires 36 credit points from this table including:
(i) 12 credit points of 1000 level units according to the following rules:
(a) 3 credit points of 1000-level calculus units; 3 credit points of multivariable calculus units; 3 credit points of linear algebra units and 3 credit points of statistics units; or
(b) 6 credit points of data science units; 3 credit points of calculus units and 3 credit points of linear algebra units
(ii) 12 credit points of 2000-level core units
(iii) 6 credit points of 3000-level core units
(iv) 6 credit points of 3000-level statistical modelling units

Units of study

The units of study are listed below.

1000-level units of study

Calculus
MATH1021 Calculus Of One Variable

Credit points: 3 Teacher/Coordinator: A/Prof Sharon Stephen Session: Semester 1,Semester 2,Summer Main Classes: 2x1-hr lectures; 1x1-hr tutorial/wk Prerequisites: NSW HSC 2 unit Mathematics or equivalent or a credit or above in MATH1111 Prohibitions: MATH1011 or MATH1901 or MATH1906 or ENVX1001 or MATH1001 or MATH1921 or MATH1931 Assumed knowledge: HSC Mathematics Extension 1 or equivalent. Assessment: 2 x quizzes (30%); 2 x assignments (5%); final exam (65%) Mode of delivery: Normal (lecture/lab/tutorial) day
Calculus is a discipline of mathematics that finds profound applications in science, engineering, and economics. This unit investigates differential calculus and integral calculus of one variable and the diverse applications of this theory. Emphasis is given both to the theoretical and foundational aspects of the subject, as well as developing the valuable skill of applying the mathematical theory to solve practical problems. Topics covered in this unit of study include complex numbers, functions of a single variable, limits and continuity, differentiation, optimisation, Taylor polynomials, Taylor's Theorem, Taylor series, Riemann sums, and Riemann integrals.
Textbooks
Calculus of One Variable (Course Notes for MATH1021)
MATH1921 Calculus Of One Variable (Advanced)

Credit points: 3 Teacher/Coordinator: A/Prof Sharon Stephen Session: Semester 1 Classes: 2x1-hr lectures; 1x1-hr tutorial/wk Prerequisites: NSW HSC 2 unit Mathematics or equivalent or a credit or above in MATH1111 Prohibitions: MATH1001 or MATH1011 or MATH1906 or ENVX1001 or MATH1901 or MATH1021 or MATH1931 Assumed knowledge: HSC Mathematics Extension 2 or equivalent. Assessment: 2 x quizzes (20%); 2 x assignments (10%); final exam (70%) Mode of delivery: Normal (lecture/lab/tutorial) day
Note: Department permission required for enrolment
Calculus is a discipline of mathematics that finds profound applications in science, engineering, and economics. This unit investigates differential calculus and integral calculus of one variable and the diverse applications of this theory. Emphasis is given both to the theoretical and foundational aspects of the subject, as well as developing the valuable skill of applying the mathematical theory to solve practical problems. Topics covered in this unit of study include complex numbers, functions of a single variable, limits and continuity, differentiation, optimisation, Taylor polynomials, Taylor's Theorem, Taylor series, Riemann sums, and Riemann integrals. Additional theoretical topics included in this advanced unit include the Intermediate Value Theorem, Rolle's Theorem, and the Mean Value Theorem.
Textbooks
As set out in the Junior Mathematics Handbook
MATH1931 Calculus Of One Variable (SSP)

Credit points: 3 Teacher/Coordinator: A/Prof Sharon Stephen Session: Semester 1 Classes: 2x1-hr lectures; and 1x1-hr tutorial/wk Prerequisites: NSW HSC 2 unit Mathematics or equivalent or a credit or above in MATH1111 Prohibitions: MATH1001 or MATH1011 or MATH1901 or ENVX1001 or MATH1906 or MATH1021 or MATH1921 Assumed knowledge: Band 4 in HSC Mathematics Extension 2 or equivalent. Assessment: Seminar participation (10%); 3 x special assignments (10%); 2 x quizzes (16%); 2 x assignments (8%); final exam (56%) Mode of delivery: Normal (lecture/lab/tutorial) day
Note: Department permission required for enrolment
Note: Enrolment is by invitation only
The Mathematics Special Studies Program is for students with exceptional mathematical aptitude, and requires outstanding performance in past mathematical studies. Students will cover the material of MATH1921 Calculus of One Variable (Adv), and attend a weekly seminar covering special topics on available elsewhere in the Mathematics and Statistics program.
Multivariable calculus
MATH1023 Multivariable Calculus and Modelling

Credit points: 3 Teacher/Coordinator: A/Prof Sharon Stephen Session: Semester 1,Semester 2,Summer Main Classes: 2x1-hr lectures; 1x1-hr tutorial/wk Prerequisites: NSW HSC 2 unit Mathematics or equivalent or a credit or above in MATH1111 Prohibitions: MATH1013 or MATH1903 or MATH1907 or MATH1003 or MATH1923 or MATH1933 Assumed knowledge: MATH1X21, HSC Mathematics Extension 1 or equivalent. Assessment: 2 x quizzes (30%); 2 x assignments (5%); final exam (65%) Mode of delivery: Normal (lecture/lab/tutorial) day
Calculus is a discipline of mathematics that finds profound applications in science, engineering, and economics. This unit investigates multivariable differential calculus and modelling. Emphasis is given both to the theoretical and foundational aspects of the subject, as well as developing the valuable skill of applying the mathematical theory to solve practical problems. Topics covered in this unit of study include mathematical modelling, first order differential equations, second order differential equations, systems of linear equations, visualisation in 2 and 3 dimensions, partial derivatives, directional derivatives, the gradient vector, and optimisation for functions of more than one variable.
Textbooks
Multivariable Calculus and Modelling (Course Notes for MATH1023)
MATH1923 Multivariable Calculus and Modelling (Adv)

Credit points: 3 Teacher/Coordinator: A/Prof Sharon Stephen Session: Semester 2 Classes: 2x1-hr lectures; and 1x1-hr tutorial/wk Prerequisites: NSW HSC 2 unit Mathematics or equivalent or a credit or above in MATH1111 Prohibitions: MATH1003 or MATH1013 or MATH1907 or MATH1903 or MATH1023 or MATH1933 Assumed knowledge: MATH1X21, HSC Mathematics Extension 2 or equivalent. Assessment: 2 x quizzes (20%); 2 x assignments (10%); final exam (70%) Mode of delivery: Normal (lecture/lab/tutorial) day
Note: Department permission required for enrolment
Calculus is a discipline of mathematics that finds profound applications in science, engineering, and economics. This unit investigates multivariable differential calculus and modelling. Emphasis is given both to the theoretical and foundational aspects of the subject, as well as developing the valuable skill of applying the mathematical theory to solve practical problems. Topics covered in this unit of study include mathematical modelling, first order differential equations, second order differential equations, systems of linear equations, visualisation in 2 and 3 dimensions, partial derivatives, directional derivatives, the gradient vector, and optimisation for functions of more than one variable. Additional topics covered in this advanced unit of study include the use of diagonalisation of matrices to study systems of linear equation and optimisation problems, limits of functions of two or more variables, and the derivative of a function of two or more variables.
Textbooks
As set out in the Junior Mathematics Handbook
MATH1933 Multivariable Calculus and Modelling (SSP)

Credit points: 3 Teacher/Coordinator: A/Prof Sharon Stephen Session: Semester 2 Classes: 2x1-hr lectures; and 1x1-hr tutorial/wk Prerequisites: NSW HSC 2 unit Mathematics or equivalent or a credit or above in MATH1111 Prohibitions: MATH1003 or MATH1903 or MATH1013 or MATH1907 or MATH1023 or MATH1923 Assumed knowledge: MATH1X21, Band 4 in HSC Mathematics Extension 2 or equivalent. Assessment: Seminar participation (10%); 3 x special assignments (10%); 2 x quizzes (16%); 2 x assignments (8%); final exam (56%) Mode of delivery: Normal (lecture/lab/tutorial) day
Note: Department permission required for enrolment
Note: Enrolment is by invitation only.
The Mathematics Special Studies Program is for students with exceptional mathematical aptitude, and requires outstanding performance in past mathematical studies. Students will cover the material of MATH1923 Multivariable Calculus and Modelling (Adv), and attend a weekly seminar covering special topics on available elsewhere in the Mathematics and Statistics program.
Linear algebra
MATH1002 Linear Algebra

Credit points: 3 Teacher/Coordinator: A/Prof Sharon Stephen Session: Semester 1,Summer Main Classes: 2x1-hr lectures; 1x1-hr tutorial/wk Prohibitions: MATH1012 or MATH1014 or MATH1902 Assumed knowledge: HSC Mathematics or MATH1111. Students who have not completed HSC Mathematics (or equivalent) are strongly advised to take the Mathematics Bridging Course (offered in February). Assessment: Online quizzes (20%); 4 x assignments (15%); final exam (65%) 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.
Textbooks
Linear Algebra: A Modern Introduction, (4th edition), David Poole
MATH1902 Linear Algebra (Advanced)

Credit points: 3 Teacher/Coordinator: A/Prof Sharon Stephen Session: Semester 1 Classes: 2x1-hr lectures; 1x1-hr tutorial/wk Prohibitions: MATH1002 or MATH1012 or MATH1014 Assumed knowledge: (HSC Mathematics Extension 2) OR (90 or above in HSC Mathematics Extension 1) or equivalent Assessment: Online quizzes (10%); 4 x assignments (20%); final exam (70%) Mode of delivery: Normal (lecture/lab/tutorial) day
Note: Department permission required for enrolment
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
Statistics
MATH1005 Statistical Thinking with Data

Credit points: 3 Teacher/Coordinator: A/Prof Sharon Stephen Session: Semester 1,Semester 2,Summer Main Classes: 2x1-hr lectures; 1x1-hr lab/wk Prohibitions: MATH1015 or MATH1905 or STAT1021 or STAT1022 or ECMT1010 or ENVX1001 or ENVX1002 or BUSS1020 or DATA1001 or DATA1901 Assumed knowledge: HSC Mathematics. Students who have not completed HSC Mathematics (or equivalent) are strongly advised to take the Mathematics Bridging Course (offered in February). Assessment: RQuizzes(10%); projects (25%); final exam (65%) Mode of delivery: Normal (lecture/lab/tutorial) day
In a data-rich world, global citizens need to problem solve with data, and evidence based decision-making is essential is every field of research and work.
This unit equips you with the foundational statistical thinking to become a critical consumer of data. You will learn to think analytically about data and to evaluate the validity and accuracy of any conclusions drawn. Focusing on statistical literacy, the unit covers foundational statistical concepts, including the design of experiments, exploratory data analysis, sampling and tests of significance.
Textbooks
Statistics, (4th Edition), Freedman Pisani Purves (2007)
MATH1905 Statistical Thinking with Data (Advanced)

Credit points: 3 Teacher/Coordinator: A/Prof Sharon Stephen Session: Semester 2 Classes: 2x1-hr lectures; 1x1-hr tutorial/wk Prohibitions: MATH1005 or MATH1015 or STAT1021 or STAT1022 or ECMT1010 or ENVX1001 or ENVX1002 or BUSS1020 or DATA1001 or DATA1901 Assumed knowledge: (HSC Mathematics Extension 2) OR (90 or above in HSC Mathematics Extension 1) or equivalent Assessment: 2 x quizzes (20%); 2 x assignments (10%); final exam (70%) Mode of delivery: Normal (lecture/lab/tutorial) day
Note: Department permission required for enrolment
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
A Primer of Statistics (4th edition), M C Phipps and M P Quine, Prentice Hall, Australia (2001)
Data science
DATA1001 Foundations of Data Science

Credit points: 6 Teacher/Coordinator: A/Prof Qiying Wang Session: Semester 1,Semester 2 Classes: 3x1-hr lectures; 1x2-hr lab/wk Prohibitions: DATA1901 or MATH1005 or MATH1905 or MATH1015 or MATH1115 or ENVX1001 or ENVX1002 or ECMT1010 or BUSS1020 or STAT1021 or STAT1022 Assessment: RQuizzes (10%); 3 x projects (30%); final exam (60%) Mode of delivery: Normal (lecture/lab/tutorial) day
DATA1001 is a foundational unit in the Data Science major. The unit focuses on developing critical and statistical thinking skills for all students. Does mobile phone usage increase the incidence of brain tumours? What is the public's attitude to shark baiting following a fatal attack? Statistics is the science of decision making, essential in every industry and undergirds all research which relies on data. Students will use problems and data from the physical, health, life and social sciences to develop adaptive problem solving skills in a team setting. Taught interactively with embedded technology, DATA1001 develops critical thinking and skills to problem-solve with data. It is the prerequisite for DATA2002.
Textbooks
Statistics, (4th Edition), Freedman Pisani Purves (2007)
DATA1901 Foundations of Data Science (Adv)

Credit points: 6 Teacher/Coordinator: A/Prof Qiying Wang Session: Semester 1,Semester 2 Classes: Lecture 3 hrs/week + Computer lab 2 hr/week Prohibitions: MATH1905 or ECMT1010 or ENVX2001 or BUSS1020 or DATA1001 or MATH1115 Assumed knowledge: An ATAR of 95 or more Assessment: RQuizzes (10%), Projects (30%), Final Exam (60%). Mode of delivery: Normal (lecture/lab/tutorial) day
DATA1901 is an advanced level unit (matching DATA1001) that is foundational to the new major in Data Science. The unit focuses on developing critical and statistical thinking skills for all students. Does mobile phone usage increase the incidence of brain tumours? What is the public's attitude to shark baiting following a fatal attack? Statistics is the science of decision making, essential in every industry and undergirds all research which relies on data. Students will use problems and data from the physical, health, life and social sciences to develop adaptive problem solving skills in a team setting. Taught interactively with embedded technology and masterclasses, DATA1901 develops critical thinking and skills to problem-solve with data at an advanced level. By completing this unit you will have an excellent foundation for pursuing data science, whether directly through the data science major, or indirectly in whatever field you major in. The advanced unit has the same overall concepts as the regular unit but material is discussed in a manner that offers a greater level of challenge and academic rigour.
Textbooks
All learning materials will be on Canvas. In addition, the textbook is Statistics (4th Edition) { Freedman, Pisani, and Purves (2007), which is available in 3 forms: 1) E-text $65 (www.wileydirect.com.au/buy/statistics-4th-international-student-edition/), 2) hard copy (Co-op Bookshop), and 3) the Library.

2000-level units of study

Core
MATH2070 Optimisation and Financial Mathematics

Credit points: 6 Teacher/Coordinator: Prof Martin Wechslberger Session: Semester 2 Classes: 3x1-hr lectures; 1x1-hr tutorial; and 1x1-hr computer lab/wk Prerequisites: (MATH1X21 or MATH1011 or MATH1931 or MATH1X01 or MATH1906) and (MATH1014 or MATH1X02) Prohibitions: MATH2010 or MATH2033 or MATH2933 or MATH2970 or ECMT3510 Assumed knowledge: MATH1X23 or MATH1933 or MATH1X03 or MATH1907 Assessment: 1 x2 exam (70%) , 1 x assignments (10%), 1 x quizzes (10%); 1 x computational project (10%). To pass the course at least 50% in the final exam is necessary. 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 and 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.
MATH2970 Optimisation and Financial Mathematics Adv

Credit points: 6 Teacher/Coordinator: Prof Martin Wechslberger Session: Semester 2 Classes: 3x1-hr lectures; 1x1-hr tutorial; and 1x1-hr computer lab/wk (lectures given in common with MATH2070). Prerequisites: [MATH19X1 or MATH1906 or (a mark of 65 or above in MATH1021 or MATH1001)] and [MATH1902 or (a mark of 65 or above in MATH1002)] Prohibitions: MATH2010 or MATH2033 or MATH2933 or MATH2070 or ECMT3510 Assumed knowledge: MATH19X3 or MATH1907 or a mark of 65 or above in MATH1003 or MATH1023 Assessment: 1 x2-hr exam (70%), 1 x assignment (10%), 1 x quiz (10%); 1 x computational project (10%). To pass the course at least 50% in the final exam is necessary. 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 Probability and Estimation Theory

Credit points: 6 Teacher/Coordinator: A/Prof Jennifer Chan Session: Semester 1 Classes: 3x1-hr lectures; 1x1-hr tutorial; and 1x1-hr computer lab/wk Prerequisites: (MATH1X21 or MATH1931 or MATH1X01 or MATH1906 or MATH1011) and (DATA1X01 or MATH10X5 or MATH1905 or STAT1021 or ECMT1010 or BUSS1020) Prohibitions: STAT2911 Assessment: 2 x quizzes (25%); weekly computer practical reports (10%); a 1-hr computer exam in week 13 (15%); and a final 2-hr exam (50%) Mode of delivery: Normal (lecture/lab/tutorial) day
This unit provides an introduction to probability, the concept of random variables, special distributions including the Binomial, Hypergeometric, Poisson, Normal, Geometric and Gamma and to statistical estimation. This unit will investigate univariate techniques in data analysis and for the most common statistical distributions that are used to model patterns of variability. You will learn the method of moments and maximum likelihood techniques for fitting statistical distributions to data. The unit will have weekly computer classes where you will learn to use a statistical computing package to perform simulations and carry out computer intensive estimation techniques like the bootstrap method. By doing this unit you will develop your statistical modeling skills and it will prepare you to learn more complicated statistical models.
Textbooks
An Introduction to Mathematical Statistics and Its Applications (5th edition), Chapters 1-5, Larsen and Marx (2012)
STAT2911 Probability and Statistical Models (Adv)

Credit points: 6 Teacher/Coordinator: A/Prof Jennifer Chan Session: Semester 1 Classes: 3x1-hr lectures; 1x1-hr tutorial; and 1x1-hr computer lab/wk Prerequisites: (MATH1X21 or MATH1931 or MATH1X01 or MATH1906 or MATH1011) and a mark of 65 or greater in (DATA1X01 or MATH10X5 or MATH1905 or STAT1021 or ECMT1010 or BUSS1020) Prohibitions: STAT2011 Assessment: 2 x quizzes (10%); 2 x assignments (5%); computer work (5%); weekly computer lab reports (5%); a computer lab exam (10%) and a final 2-hr exam (70%) Mode of delivery: Normal (lecture/lab/tutorial) day
This unit is essentially an advanced version of STAT2011, with an emphasis on the mathematical techniques used to manipulate random variables and probability models. Common distributions including the Poisson, normal, beta and gamma families as well as the bivariate normal are introduced. Moment 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 notions of conditional expectation and prediction will be covered as will be distributions related to the normal: chi^2, t and F. 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.
Textbooks
Mathematical Statistics and Data Analysis (3rd edition), J A Rice

3000-level units of study

Core
MATH3075 Financial Derivatives

Credit points: 6 Teacher/Coordinator: Prof Georg Gottwald Session: Semester 2 Classes: 3x1-hr lectures; 1x1-hr tutorial/wk Prerequisites: 12 credit points of Intermediate Mathematics, including (MATH2070 or MATH2970) Prohibitions: MATH3975 or MATH3015 or MATH3933 Assessment: 2 x assignments (20%); 2-hr final exam (80%) Mode of delivery: Normal (lecture/lab/tutorial) day
This unit will introduce you to the mathematical theory of modern finance with the special emphasis on the valuation and hedging of financial derivatives, such as: forward contracts and options of European and American style. You will learn about the concept of arbitrage and how to model risk-free and risky securities. Topics covered by this unit include: notions of a martingale and a martingale measure, the fundamental theorems of asset pricing, complete and incomplete markets, the binomial options pricing model, discrete random walks and the Brownian motion, the Black-Scholes options pricing model and the valuation and heding of exotic options. Students completing this unit have been highly sought by the finance industry, which continues to need graduates with quantitative skills. Lectures in the mainstream unit are held concurrently with those of the corresponding advanced unit.
MATH3975 Financial Derivatives (Advanced)

Credit points: 6 Teacher/Coordinator: Prof Georg Gottwald Session: Semester 2 Classes: 3x1-hr lectures; 1x1-hr tutorial/wk Prerequisites: Credit average or greater in 12 credit points of Intermediate Mathematics (including MATH2070 or MATH2970) Prohibitions: MATH3933 or MATH3015 or MATH3075 Assessment: 2 x assignments; 2-hr final exam (80%) Mode of delivery: Normal (lecture/lab/tutorial) day
This unit will introduce you to the mathematical theory of modern finance with the special emphasis on the valuation and hedging of financial derivatives, such as: forward contracts and options of European and American style. You will learn about the concept of arbitrage and how to model risk-free and risky securities. Topics covered by this unit include: the notions of a martingale and a martingale measure, the fundamental theorems of asset pricing, complete and incomplete markets, the binomial options pricing model, discrete random walks and the Brownian motion, the Black-Scholes options pricing model and the valuation and heding of exotic options. 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 advanced level will have to undertake more challenging assessment tasks, but lectures in the advanced level are held concurrently with those of the corresponding mainstream unit.
Interdisciplinary project
FMAT3888 Projects in Financial Mathematics

Credit points: 6 Teacher/Coordinator: Prof Mary Myerscough Session: Semester 2 Classes: 2hr lectures and 3 hrs/workshops per week Prerequisites: (MATH2070 or MATH2970) and (STAT2011 or STAT2911) Assumed knowledge: STAT2X11, MATH2X70 Assessment: Discipline content assignment (10%), discipline content quiz (20%), Discipline project report (10%), discipline project presentation (10%), reflective task (10%), team work process (10%), interdisciplinary project report (20%), interdisciplinary oroject presentation (10%) Mode of delivery: Block mode
Mathematics and statistics are powerful tools in finance and more generally in the world at large. To really experience the power of mathematics and statistics at work, students need to identify and explore interdisciplinary links. Engagement with other disciplines also provides essential foundational skills for using mathematical and statistical ideas in financial contexts and in the world beyond. In this unit you will commence by working on a group project in an area of financial mathematics or statistics. From this project you will acquire skills of teamwork, research, wring and project management as well as disciplinary knowledge. You will then have the opportunity to apply your disciplinary knowledge in an interdisciplinary team to identify and solve problems and communicate your findings.
SCPU3001 Science Interdisciplinary Project

Credit points: 6 Teacher/Coordinator: Pauline Ross Session: Intensive December,Intensive February,Intensive January,Intensive July,Semester 1,Semester 2 Classes: The unit consists of one seminar/workshop per week with accompanying online materials and a project to be determined in consultation with the partner organisation and completed as part of team with academic supervision. Prerequisites: Completion of 2000-level units required for at least one Science major. Assessment: group plan, group presentation, reflective journal, group project Mode of delivery: Normal (lecture/lab/tutorial) day
This unit is designed for students who are concurrently enrolled in at least one 3000-level Science Table A unit of study to undertake a project that allows them to work with one of the University's industry and community partners. Students will work in teams on a real-world problem provided by the partner. This experience will allow students to apply their academic skills and disciplinary knowledge to a real-world issue in an authentic and meaningful way. Participation in this unit will require students to submit an application to the Faculty of Science.
Mathematical modelling
MATH3076 Mathematical Computing

Credit points: 6 Teacher/Coordinator: Prof Georg Gottwald Session: Semester 1 Classes: 3x1-hr lectures; 1x1-hr computer lab/wk Prerequisites: 12 credit points of MATH2XXX and 6 credit points from (MATH1021 or MATH1001 or MATH1023 or MATH1003 or MATH19X1 or MATH19X3 or MATH1906 or MATH1907) Prohibitions: MATH3976 or MATH4076 Assessment: One 3 hour exam (55%), 2 assignments (15%+15%), 1 quiz (15%). To pass the course, students much achieve more than 50% on the final exam. Mode of delivery: Normal (lecture/lab/tutorial) day
This unit of study provides an introduction to 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, and optimisation.
MATH3979 Complex Analysis (Advanced)

Credit points: 6 Teacher/Coordinator: Prof Georg Gottwald Session: Semester 1 Classes: Lecture 3 hrs/week; tutorial 1 hr/week Prerequisites: [A mark of 65 or greater in 12cp from (MATH2021 or MATH2921 or MATH2022 or MATH2922 or MATH2023 or MATH2923 or MATH2061 or MATH2961 or MATH2065 or MATH2965 or MATH2962)] Prohibitions: MATH4079 or MATH3964 Assumed knowledge: MATH2023 or MATH2923 or MATH2962 or MATH3068 Assessment: 2 x assessment (30%), final exam worth (70%) (requires pass mark of 50% or more) Mode of delivery: Normal (lecture/lab/tutorial) day
This unit continues the study of functions of a complex variable introduced in the second year unit Analysis (MATH2023/2923). It is aimed at highlighting certain topics from analytic function theory that have wide applications and intrinsic beauty. By learning about the analysis of functions of a complex variable, you will acquire a very important background for mathematical areas such as dynamics, algebraic and differential geometry, and number theory; and advanced theoretical physics such as quantum mechanics, string theory, and quantum field theory. The unit will begin with a revision of properties of complex numbers and complex functions. This will be followed by material on conformal mappings, Riemann surfaces, complex integration, entire and analytic functions, the Riemann mapping theorem, analytic continuation, and Gamma and Zeta functions. Finally, special topics chosen by the lecturer will be presented, which may include elliptic functions, normal families, Julia sets, functions of several complex variables, or complex manifolds. At the end of this unit you will have received a broad introduction and gained a variety of tools to apply them within your further mathematical studies and/or in other disciplines.
Statistical modelling
STAT3022 Applied Linear Models

Credit points: 6 Teacher/Coordinator: Dr John Ormerod Session: Semester 1 Classes: Three 1 hour lectures, one 1 hour tutorial and one 1 hour computer laboratories per week. Prerequisites: STAT2X11 and (DATA2X02 or STAT2X12) Prohibitions: STAT3912 or STAT3012 or STAT3922 Assessment: 2 x assignment (15%), 3 x quizzes (30%), final exam (55%) Mode of delivery: Normal (lecture/lab/tutorial) day
In today's data-rich world more and more people from diverse fields are needing to perform statistical analyses and indeed more and more tools for doing so are becoming available; it is relatively easy to point and click and obtain some statistical analysis of your data. But how do you know if any particular analysis is indeed appropriate? Is there another procedure or workflow which would be more suitable? Is there such thing as a best possible approach in a given situation? All of these questions (and more) are addressed in this unit. You will study the foundational core of modern statistical inference, including classical and cutting-edge theory and methods of mathematical statistics with a particular focus on various notions of optimality. The first part of the unit covers various aspects of distribution theory which are necessary for the second part which deals with optimal procedures in estimation and testing. The framework of statistical decision theory is used to unify many of the concepts. You will apply the theory to various real-world problems using statistical software in laboratory sessions. By completing this unit you will develop the necessary skills to confidently choose the best statistical analysis to use in many situations.
STAT3922 Applied Linear Models (Advanced)

Credit points: 6 Teacher/Coordinator: Dr John Ormerod Session: Semester 1 Classes: Three 1 hour lectures, one 1 hour tutorial and one 1 hour computer laboratory per week. Prerequisites: STAT2X11 and [a mark of 65 or greater in (STAT2X12 or DATA2X02)] Prohibitions: STAT3912 or STAT3012 or STAT3022 Assessment: 2 x assignment (10%), 3 x quizzes (35%), final exam (55%) Mode of delivery: Normal (lecture/lab/tutorial) day
This unit 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. You will first consider linear models and regression methods with diagnostics for checking appropriateness of models, looking briefly at robust regression methods. Then you will consider the design and analysis of experiments considering notions of replication, randomization and ideas of factorial designs. Throughout the course you will use the R statistical package to give analyses and graphical displays. This unit is essentially an Advanced version of STAT3012, with additional emphasis on the mathematical techniques underlying applied linear models together with proofs of distribution theory based on vector space methods.
STAT3023 Statistical Inference

Credit points: 6 Teacher/Coordinator: Dr John Ormerod Session: Semester 2 Classes: Three 1 hour lectures, one 1 hour tutorial and one 1 hour computer laboratory per week. Prerequisites: STAT2X11 Prohibitions: STAT3913 or STAT3013 or STAT3923 Assumed knowledge: DATA2X02 or STAT2X12 Assessment: 2 x Quizzes (25%), Computer Lab Report (10%), Computer Exam (10%), Final Exam (55%) Mode of delivery: Normal (lecture/lab/tutorial) day
In today's data-rich world more and more people from diverse fields are needing to perform statistical analyses and indeed more and more tools for doing so are becoming available; it is relatively easy to point and click and obtain some statistical analysis of your data. But how do you know if any particular analysis is indeed appropriate? Is there another procedure or workflow which would be more suitable? Is there such a thing as the best possible approach in a given situation? All of these questions (and more) are addressed in this unit. You will study the foundational core of modern statistical inference, including classical and cutting-edge theory and methods of mathematical statistics with a particular focus on various notions of optimality. The first part of the unit covers various aspects of distribution theory which are necessary for the second part which deals with optimal procedures in estimation and testing. The framework of statistical decision theory is used to unify many of the concepts. You will apply the methods learnt to real-world problems in laboratory sessions. By completing this unit you will develop the necessary skills to confidently choose the best statistical analysis to use in many situations.
STAT3923 Statistical Inference (Advanced)

Credit points: 6 Teacher/Coordinator: Dr John Ormerod Session: Semester 2 Classes: Three 1 hour lectures, one 1 hour tutorial and one 2 hour advanced workshop. Prerequisites: STAT2X11 and a mark of 65 or greater in (DATA2X02 or STAT2X12) Prohibitions: STAT3913 or STAT3013 or STAT3023 Assessment: 2 x Quizzes (20%), weekly homework (5%), Computer Lab Reports (10%), Computer Exam (10%), Final Exam (55%) Mode of delivery: Normal (lecture/lab/tutorial) day
In today's data-rich world more and more people from diverse fields are needing to perform statistical analyses and indeed more and more tools for doing so are becoming available; it is relatively easy to point and click and obtain some statistical analysis of your data. But how do you know if any particular analysis is indeed appropriate? Is there another procedure or workflow which would be more suitable? Is there such thing as a best possible approach in a given situation? All of these questions (and more) are addressed in this unit. You will study the foundational core of modern statistical inference, including classical and cutting-edge theory and methods of mathematical statistics with a particular focus on various notions of optimality. The first part of the unit covers various aspects of distribution theory which are necessary for the second part which deals with optimal procedures in estimation and testing. The framework of statistical decision theory is used to unify many of the concepts. You will rigorously prove key results and apply these to real-world problems in laboratory sessions. By completing this unit you will develop the necessary skills to confidently choose the best statistical analysis to use in many situations.
STAT3021 Stochastic Processes

Credit points: 6 Teacher/Coordinator: Dr John Ormerod Session: Semester 1 Classes: 3 lectures per week, tutorial 1hr per week. Prerequisites: STAT2X11 and (MATH1003 or MATH1903 or MATH1907 or MATH1023 or MATH1923 or MATH1933) Prohibitions: STAT3911 or STAT3011 Assessment: 2 x Quiz (2 x 15%), 2 x Assignment (2 x 5%), Final Exam (60%) Mode of delivery: Normal (lecture/lab/tutorial) day
A stochastic process is a mathematical model of time-dependent random phenomena and is employed in numerous fields of application, including economics, finance, insurance, physics, biology, chemistry and computer science. After setting up basic elements of stochastic processes, such as time, state, increments, stationarity and Markovian property, this unit develops important properties and limit theorems of discrete-time Markov chain and branching processes. You will then establish key results for the Poisson process and continuous-time Markov chains, such as the memoryless property, super positioning, thinning, Kolmogorov's equations and limiting probabilities. Various illustrative examples are provided throughout the unit to demonstrate how stochastic processes can be applied in modeling and analyzing problems of practical interest. By completing this unit, you will develop the essential basis for further studies, such as stochastic calculus, stochastic differential equations, stochastic control and financial mathematics.

4000-level units of study

Mathematical modelling units
MATH4071 Convex Analysis and Optimal Control

Credit points: 6 Teacher/Coordinator: Prof Georg Gottwald Session: Semester 1 Classes: Lecture 3hours/week, tutorial 1hr/week Prerequisites: [A mark of 65 or greater in 12cp from (MATH2070 or MATH2970 or STAT2011 or STAT2911 or MATH2021 or MATH2921 or MATH2022 or MATH2922 or MATH2023 or MATH2923 or MATH2061 or MATH2961 or MATH2065 or MATH2965 or MATH2962 or STAT2012 or STAT2912 or DATA2002 or DATA2902) or [12 cp from (MATH3075 or MATH3975 or STAT3021 or STAT3011 or STAT3911 or STAT3888 or STAT3014 or STAT3914 or MATH3063 or MATH3963 or MATH3061 or MATH3961 or MATH3962 or MATH3963 or MATH3968 or MATH3969 or MATH3971 or MATH3974 or MATH3976 or MATH3977 or MATH3978 or MATH3979)] Prohibitions: MATH3971 Assumed knowledge: MATH2X21 and MATH2X23 and STAT2X11 Assessment: Assignment (15%), assignment (15%), exam (70%) Mode of delivery: Normal (lecture/lab/tutorial) day
The questions how to maximise your gain (or to minimise the cost) and how to determine the optimal strategy/policy are fundamental for an engineer, an economist, a doctor designing a cancer therapy, or a government planning some social policies. Many problems in mechanics, physics, neuroscience and biology can be formulated as optimisation problems. Therefore, optimisation theory is an indispensable tool for an applied mathematician. Optimisation theory has many diverse applications and requires a wide range of tools but there are only a few ideas underpinning all this diversity of methods and applications. This course will focus on two of them. We will learn how the concept of convexity and the concept of dynamic programming provide a unified approach to a large number of seemingly unrelated problems. By completing this unit you will learn how to formulate optimisation problems that arise in science, economics and engineering and to use the concepts of convexity and the dynamic programming principle to solve straightforward examples of such problems. You will also learn about important classes of optimisation problems arising in finance, economics, engineering and insurance.
MATH4076 Computational Mathematics

Credit points: 6 Teacher/Coordinator: Prof Georg Gottwald Session: Semester 1 Classes: Three 1 hour lectures and one 1 hour laboratory per week. Prerequisites: (A mark of 65 or greater in 12cp of MATH2XXX units of study) or [12cp from (MATH3061 or MATH3066 or MATH3063 or MATH3078 or or MATH3961 or MATH3962 or MATH3963 or MATH3969 or MATH3971 or MATH3974 or MATH3977 or MATH3978 or MATH3979)] Assumed knowledge: (MATH2X21 and MATH2X22) or (MATH2X61 and MATH2X65) Assessment: Quiz (15%), Assignment (15%), Assignment (15%), Final Exam (55%) Mode of delivery: Normal (lecture/lab/tutorial) day
Sophisticated mathematics and numerical programming underlie many computer applications, including weather forecasting, computer security, video games, and computer aided design. This unit of study provides a strong foundational introduction to modern interactive programming, computational algorithms, and numerical analysis. Topics covered include: (I) basics ingredients of programming languages such as syntax, data structures, control structures, memory management and visualisation; (II) basic algorithmic concepts including binary and decimal representations, iteration, linear operations, sources of error, divide-and-concur, algorithmic complexity; and (III) basic numerical schemes for rootfinding, integration/differentiation, differential equations, fast Fourier transforms, Monte Carlo methods, data fitting, discrete and continuous optimisation. You will also learn about the philosophical underpinning of computational mathematics including the emergence of complex behaviour from simple rules, undecidability, modelling the physical world, and the joys of experimental mathematics. When you complete this unit you will have a clear and comprehensive understanding of the building blocks of modern computational methods and the ability to start combining them together in different ways. Mathematics and computing are like cooking. Fundamentally, all you have is sugar, fat, salt, heat, stirring, chopping. But becoming a good chef requires knowing just how to put things together in creative ways that work. In previous study, you should have learned to cook. Now you're going to learn how to make something someone else might want to pay for more than one time.
Further units to be developed for offering in 2020.
Statistical modelling units
To be developed for offering in 2020