# Financial Mathematics and Statistics

##### Errata

item | Errata | Date |
---|---|---|

1. | MATH1021 Calculus Of One Variable: Semester 2 session has been added. |
1/2/2018 |

2. | MATH3976 Mathematical Computing (Advanced) Prerequisites should read: 12 credit points of MATH2XXX and [3 credit points from (MATH1923 or MATH1903 or MATH1933 or MATH1907), or a mark of 65 or above in (MATH1023 or MATH1003)] |
6/2/2018 |

## 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) 6 credit points of calculus units; 3 credit points of linear algebra units and 3 credit points of statistics units; 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) 12 credit points of 3000-level interdisciplinary project and core units

(iv) 6 credit points of 3000-level statistical modelling units

(v) 6 credit points of 3000-level mathematical modelling units

## 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 units

**MATH1021 Calculus Of One Variable**

Credit points: 3 Session: Semester 1 Classes: 2x1-hr lectures; 1x1-hr tutorial per week Prohibitions: MATH1011 or MATH1901 or MATH1906 or MATH1111 or ENVX1001 or MATH1001 or MATH1921 or MATH1931 Assumed knowledge: HSC Mathematics Extension 1. Students who have not completed HSC Extension 1 Mathematics (or equivalent) are strongly advised to take the Extension 1 Mathematics Bridging Course (offered in February). Assessment: exam, quizzes, assignments 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

As set out in the Junior Mathematics Handbook.

**MATH1921 Calculus Of One Variable (Advanced)**

Credit points: 3 Session: Semester 1 Classes: 2x1-hr lectures; and 1x1-hr tutorial per week Prohibitions: MATH1001 or MATH1011 or MATH1906 or MATH1111 or ENVX1001 or MATH1901 or MATH1021 or MATH1931 Assumed knowledge: (HSC Mathematics Extension 2) OR (Band E4 in HSC Mathematics Extension 1) or equivalent. Assessment: exam, quizzes, assignments 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 Session: Semester 1 Classes: 2x1-hr lectures; 1x1-hr seminar; and 1x1-hr tutorial per week Prohibitions: MATH1001 or MATH1011 or MATH1901 or MATH1111 or ENVX1001 or MATH1906 or MATH1021 or MATH1921 Assumed knowledge: Band E4 in HSC Mathematics Extension 2 or equivalent. Assessment: exam, quizzes, assignments, seminar participation 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 units

**MATH1023 Multivariable Calculus and Modelling**

Credit points: 3 Session: Semester 2 Classes: 2x1-hr lectures; 1x1-hr tutorial per week Prohibitions: MATH1013 or MATH1903 or MATH1907 or MATH1003 or MATH1923 or MATH1933 Assumed knowledge: HSC Mathematics Extension 1. Students who have not completed HSC Extension 1 Mathematics (or equivalent) are strongly advised to take the Extension 1 Mathematics Bridging Course (offered in February). Assessment: exam, quizzes, assignments 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

As set out in the Junior Mathematics Handbook

**MATH1923 Multivariable Calculus and Modelling (Adv)**

Credit points: 3 Session: Semester 2 Classes: 2x1-hr lectures; and 1x1-hr tutorial per week Prohibitions: MATH1003 or MATH1013 or MATH1907 or MATH1903 or MATH1023 or MATH1933 Assumed knowledge: (HSC Mathematics Extension 2) OR (Band E4 in HSC Mathematics Extension 1) or equivalent. Assessment: exam, quizzes, assignments 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 Session: Semester 2 Classes: 2x1-hr lectures; 1x1-hr seminar; and 1x1-hr tutorial per week Prohibitions: MATH1003 or MATH1903 or MATH1013 or MATH1907 or MATH1023 or MATH1923 Assumed knowledge: Band E4 in HSC Mathematics Extension 2 or equivalent. Assessment: exam, quizzes, assignments, seminar participation 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.

###### Statistics units

**MATH1005 Statistical Thinking with Data**

Credit points: 3 Session: Semester 2,Summer Main,Winter Main Classes: Lectures 2 hrs/week; Practical 1 hr/week Prohibitions: MATH1015 or MATH1905 or STAT1021 or STAT1022 or ECMT1010 or ENVX1001 or ENVX1002 or BUSS1020 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: One 1.5 hour examination, assignments and quizzes (100%) 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.

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

Freedman, Pisani and Purves, Statistics, Norton, 2007

**MATH1905 Statistical Thinking with Data (Advanced)**

Credit points: 3 Session: Semester 2 Classes: Two 1 hour lectures and one 1 hour tutorial per week. Prohibitions: MATH1005 or MATH1015 or STAT1021 or STAT1022 or ECMT1010 or ENVX1001 or ENVX1002 or BUSS1020 Assumed knowledge: (HSC Mathematics Extension 2) OR (90 or above in HSC Mathematics Extension 1) or equivalent Assessment: One 1.5 hour examination, assignments and quizzes (100%) 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

As set out in the Junior Mathematics Handbook

**MATH1015 Biostatistics**

Credit points: 3 Session: Semester 1 Classes: Two 1 hour lectures and one 1 hour tutorial per week. Prohibitions: MATH1005 or MATH1905 or STAT1021 or STAT1022 or ECMT1010 or BIOM1003 or ENVX1001 or ENVX1002 or BUSS1020 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: One 1.5 hour examination, assignments and quizzes (100%) Mode of delivery: Normal (lecture/lab/tutorial) day

MATH1015 is designed to provide a thorough preparation in statistics for students in the Biological and Medical Sciences. It offers a comprehensive introduction to data analysis, probability and sampling, inference including t-tests, confidence intervals and chi-squared goodness of fit tests.

Textbooks

As set out in the Junior Mathematics Handbook

###### Linear algebra units

**MATH1002 Linear Algebra**

Credit points: 3 Session: Semester 1,Summer Main Classes: Two 1 hour lectures and one 1 hour tutorial per week. 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: One 1.5 hour examination, assignments and quizzes (100%) 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. Prohibitions: MATH1002 or MATH1012 or MATH1014 Assumed knowledge: (HSC Mathematics Extension 2) OR (90 or above in HSC Mathematics Extension 1) or equivalent Assessment: One 1.5 hour examination, assignments and quizzes (100%) 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

###### Data science units

**DATA1001 Foundations of Data Science**

Credit points: 6 Teacher/Coordinator: Dr Di Warren Session: Semester 1,Semester 2 Classes: lecture 3 hrs/week; computer tutorial 2 hr/week Prohibitions: MATH1005 or MATH1905 or MATH1015 or MATH1115 or ENVX1001 or ENVX1002 or ECMT1010 or BUSS1020 or STAT1021 Assessment: assignments, quizzes, presentation, exam 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, Fourth Edition, Freedman Pisani Purves

#### 2000-level units of study

###### Core

**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: (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: One 2 hour exam, assignments, quiz, project (100%) 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.

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 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: [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: One 2 hour exam, assignments, quizzes (100%) 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 Session: Semester 1 Classes: Three 1 hour lectures, one 1 hour tutorial and one 1 hour computer laboratory week. Prerequisites: (MATH1X21 or MATH1931 or MATH1X01 or MATH1906 or MATH1011) and (MATH1XX5 or STAT1021 or ECMT1010 or BUSS1020) Prohibitions: STAT2901 or STAT2001 or STAT2911 Assessment: One 2 hour exam, assignments and/or quizzes, and computer practical reports (100%) 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, continuous models including the normal and exponential will be studied along with elementary regression models. 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: [MATH19X3 or MATH1907 or (a mark of 65 in MATH1023 or MATH1003)] and [MATH1905 or MATH1904 or (a mark of 65 in MATH1005 or ECMT1010 or BUSS1020)] Prohibitions: STAT2001 or STAT2901 or STAT2011 Assessment: One 2 hour exam, assignments and/or quizzes, and computer practical reports (100%) 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.

#### 3000-level units of study

###### Interdisciplinary project and major core units

MATH3070, MATH3970, STAT3021 to be developed for offering in 2019.

###### Mathematical modelling units

**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 MATH2XXX and 6 credit points from (MATH1021 or MATH1001 or MATH1023 or MATH1003 or MATH19X1 or MATH19X3 or MATH1906 or MATH1907) Prohibitions: MATH3976 or MATH3016 or MATH3916 Assessment: One 2 hour exam, assignments, quizzes (100%) 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 MATH2XXX and [6 credit points from (MATH1923 or MATH1903 or MATH1933 or MATH1907), or a mark of 65 or above in (MATH1023 or MATH1003)] Prohibitions: MATH3076 or MATH3016 or MATH3916 Assessment: One 2 hour exam, assignments, quizzes (100%) Mode of delivery: Normal (lecture/lab/tutorial) day

See entry for MATH3076 Mathematical Computing.

MATH3979 to be developed for offering in 2019.

###### Statistical modelling units

STAT3023, STAT3022 and STAT3922 to be developed for offering in 2019.

###### Minor core

MATH3X70 to be developed for offering in 2019.