# Financial Mathematics and Statistics

Unit outlines will be available through Find a unit outline two weeks before the first day of teaching for 1000-level and 5000-level units, or one week before the first day of teaching for all other units.

## FINANCIAL MATHEMATICS AND STATISTICS

## 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) 18 credit points of 2000-level core units

(iii) 12 credit points of 3000-level core units

(iv) 6 credit points of 3000-level interdisciplinary project 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) 18 credit points of 2000-level core units

(iii) 6 credit points of 3000-level core 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: Refer to the unit of study outline https://www.sydney.edu.au/units Session: Intensive February,Semester 1,Semester 2 Classes: Refer to the unit of study outline https://www.sydney.edu.au/units Prohibitions: MATH1011 or MATH1901 or MATH1906 or ENVX1001 or MATH1001 or MATH1921 or MATH1931 Assumed knowledge: HSC Mathematics Extension 1 or equivalent. Assessment: Refer to the unit of study outline https://www.sydney.edu.au/units 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.

Students are strongly recommended to complete MATH1021 of MATH1921 before commencing MATH1023 or MATH1923.

Students are strongly recommended to complete MATH1021 of MATH1921 before commencing MATH1023 or MATH1923.

Textbooks

Calculus of One Variable (Course Notes for MATH1021)

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

Credit points: 3 Teacher/Coordinator: Refer to the unit of study outline https://www.sydney.edu.au/units Session: Semester 1 Classes: Refer to the unit of study outline https://www.sydney.edu.au/units Prohibitions: MATH1001 or MATH1011 or MATH1906 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: Refer to the unit of study outline https://www.sydney.edu.au/units 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. Students are strongly recommended to complete MATH1021 of MATH1921 before commencing MATH1023 or MATH1923.

Textbooks

As set out in the Junior Mathematics Handbook

**MATH1931 Calculus Of One Variable (SSP)**

Credit points: 3 Teacher/Coordinator: Refer to the unit of study outline https://www.sydney.edu.au/units Session: Semester 1 Classes: Refer to the unit of study outline https://www.sydney.edu.au/units Prohibitions: MATH1001 or MATH1011 or MATH1901 or ENVX1001 or MATH1906 or MATH1021 or MATH1921 Assumed knowledge: (HSC Mathematics Extension 2) OR (Band E4 in HSC Mathematics Extension 1) or equivalent. Assessment: Refer to the unit of study outline https://www.sydney.edu.au/units 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: Refer to the unit of study outline https://www.sydney.edu.au/units Session: Intensive February,Semester 1,Semester 2 Classes: Refer to the unit of study outline https://www.sydney.edu.au/units Prohibitions: MATH1013 or MATH1903 or MATH1907 or MATH1003 or MATH1923 or MATH1933 Assumed knowledge: Knowledge of complex numbers and methods of differential and integral calculus including integration by partial fractions and integration by parts as for example in MATH1021 or MATH1921 or MATH1931 or HSC Mathematics Extension 2 Assessment: Refer to the unit of study outline https://www.sydney.edu.au/units 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.

Students are strongly recommended to complete MATH1021 of MATH1921 before commencing MATH1023 or MATH1923.

Students are strongly recommended to complete MATH1021 of MATH1921 before commencing MATH1023 or MATH1923.

Textbooks

Multivariable Calculus and Modelling (Course Notes for MATH1023)

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

Credit points: 3 Teacher/Coordinator: Refer to the unit of study outline https://www.sydney.edu.au/units Session: Semester 2 Classes: Refer to the unit of study outline https://www.sydney.edu.au/units 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: Refer to the unit of study outline https://www.sydney.edu.au/units 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. Students are strongly recommended to complete MATH1021 of MATH1921 before commencing MATH1023 or MATH1923.

Textbooks

As set out in the Junior Mathematics Handbook

**MATH1933 Multivariable Calculus and Modelling (SSP)**

Credit points: 3 Teacher/Coordinator: Refer to the unit of study outline https://www.sydney.edu.au/units Session: Semester 2 Classes: Refer to the unit of study outline https://www.sydney.edu.au/units Prohibitions: MATH1003 or MATH1903 or MATH1013 or MATH1907 or MATH1023 or MATH1923 Assumed knowledge: (HSC Mathematics Extension 2) OR (Band E4 in HSC Mathematics Extension 1) or equivalent. Assessment: Refer to the unit of study outline https://www.sydney.edu.au/units 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: Refer to the unit of study outline https://www.sydney.edu.au/units Session: Semester 1 Classes: Refer to the unit of study outline https://www.sydney.edu.au/units 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: Refer to the unit of study outline https://www.sydney.edu.au/units 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

Linear Algebra: A Modern Introduction, (4th edition), David Poole

**MATH1902 Linear Algebra (Advanced)**

Credit points: 3 Teacher/Coordinator: Refer to the unit of study outline https://www.sydney.edu.au/units Session: Semester 1 Classes: Refer to the unit of study outline https://www.sydney.edu.au/units Prohibitions: MATH1002 or MATH1014 Assumed knowledge: (HSC Mathematics Extension 2) OR (90 or above in HSC Mathematics Extension 1) or equivalent Assessment: Refer to the unit of study outline https://www.sydney.edu.au/units 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

**MATH1014 Introduction to Linear Algebra**

Credit points: 3 Teacher/Coordinator: Refer to the unit of study outline https://www.sydney.edu.au/units Session: Intensive February,Semester 2 Classes: Refer to the unit of study outline https://www.sydney.edu.au/units Prohibitions: MATH1002 or MATH1902 Assumed knowledge: Coordinate geometry, basic integral and differential calculus, polynomial equations and algebraic manipulations, equivalent to HSC Mathematics Assessment: Refer to the unit of study outline https://www.sydney.edu.au/units Mode of delivery: Block mode

This unit is an introduction to Linear Algebra. Topics covered include vectors, systems of linear equations, matrices, eigenvalues and eigenvectors. Applications in life and technological sciences are emphasised.

Textbooks

A First Course in Linear Algebra (3rd edition), David Easdown, Pearson Education (2010)

###### Statistics

**MATH1005 Statistical Thinking with Data**

Credit points: 3 Teacher/Coordinator: Refer to the unit of study outline https://www.sydney.edu.au/units Session: Intensive February,Semester 1,Semester 2 Classes: Refer to the unit of study outline https://www.sydney.edu.au/units Prohibitions: MATH1015 or MATH1905 or STAT1021 or ECMT1010 or ENVX1001 or ENVX1002 or BUSS1020 or DATA1001 or DATA1901 Assumed knowledge: HSC Mathematics Advanced or equivalent. Assessment: Refer to the unit of study outline https://www.sydney.edu.au/units 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 in 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: Refer to the unit of study outline https://www.sydney.edu.au/units Session: Semester 2 Classes: Refer to the unit of study outline https://www.sydney.edu.au/units Prohibitions: MATH1005 or MATH1015 or STAT1021 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: Refer to the unit of study outline https://www.sydney.edu.au/units 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

Statistics (4th Edition) Â¿ Freedman, Pisani, and Purves (2007)

###### Data science

**DATA1001 Foundations of Data Science**

Credit points: 6 Teacher/Coordinator: Refer to the unit of study outline https://www.sydney.edu.au/units Session: Semester 1,Semester 2 Classes: Refer to the unit of study outline https://www.sydney.edu.au/units Prohibitions: DATA1901 or MATH1005 or MATH1905 or MATH1015 or MATH1115 or ENVX1001 or ENVX1002 or ECMT1010 or BUSS1020 or STAT1021 Assessment: Refer to the unit of study outline https://www.sydney.edu.au/units 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

All learning material will be on Canvas. In addition, the optional textbook is Statistics by Freedman, Pisani and Purves (2007)

**DATA1901 Foundations of Data Science (Adv)**

Credit points: 6 Teacher/Coordinator: Refer to the unit of study outline https://www.sydney.edu.au/units Session: Semester 1,Semester 2 Classes: Refer to the unit of study outline https://www.sydney.edu.au/units Prohibitions: MATH1005 or MATH1905 or ECMT1010 or ENVX1001 or ENVX1002 or BUSS1020 or DATA1001 or MATH1115 or MATH1015 or STAT1021 Assumed knowledge: An ATAR of 95 or more Assessment: Refer to the unit of study outline https://www.sydney.edu.au/units 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 optional textbook is Statistics by Freedman, Pisani, and Purves (2007).

#### 2000-level units of study

###### Core

**DATA2002 Data Analytics: Learning from Data**

Credit points: 6 Teacher/Coordinator: Refer to the unit of study outline https://www.sydney.edu.au/units Session: Semester 2 Classes: Refer to the unit of study outline https://www.sydney.edu.au/units Prerequisites: 6 cp of DATA1X01 or ENVX1001 or ENVX1002 or STAT2X11 or BUSS1020 or ECMT1010 or STAT1021 or [MATH1115 and MATH10X5] or [MATH1905 and MATH1XXX] Prohibitions: STAT2012 or STAT2912 or DATA2902 Assumed knowledge: Basic linear algebra and some coding for example MATH1014 or MATH1002 or MATH1902 and DATA1001 or DATA1901 Assessment: Refer to the unit of study outline https://www.sydney.edu.au/units Mode of delivery: Normal (lecture/lab/tutorial) day

Technological advances in science, business and engineering have given rise to a proliferation of data from all aspects of our life. Understanding the information presented in these data is critical as it enables informed decision making into many areas including market intelligence and science. DATA2002 is an intermediate unit in statistics and data sciences, focusing on learning data analytic skills for a wide range of problems and data In this unit, you will learn how to ingest, combine and summarise data from a variety of data models which are typically encountered in data science projects as well as reinforcing your programming skills through experience with a statistical programming language. You will also be exposed to the concept of statistical machine learning and develop the skills to analyse various types of data in order to answer a scientific question. From this unit, you will develop knowledge and skills that will enable you to embrace data analytic challenges stemming from everyday problems.

**DATA2902 Data Analytics: Learning from Data (Adv)**

Credit points: 6 Teacher/Coordinator: Refer to the unit of study outline https://www.sydney.edu.au/units Session: Semester 2 Classes: Refer to the unit of study outline https://www.sydney.edu.au/units Prerequisites: 6 cp of DATA1901 or STAT2911 or (MATH1905 and MATH1XXX) or a mark of 65 or above in (DATA1001 or ENVX1001 or ENVX1002 or BUSS1020 or ECMT1010 or STAT1021 or STAT2011) or an average mark of 65 or above in (MATH10X5 and MATH1115) Prohibitions: STAT2012 or STAT2912 or DATA2002 Assumed knowledge: Basic linear algebra and some coding for example MATH1014 or MATH1002 or MATH1902 and DATA1001 or DATA1901 Assessment: Refer to the unit of study outline https://www.sydney.edu.au/units Mode of delivery: Normal (lecture/lab/tutorial) day

Technological advances in science, business, and engineering have given rise to a proliferation of data from all aspects of our life. Understanding the information presented in these data is critical as it enables informed decision making into many areas including market intelligence and science. DATA2902 is an intermediate unit in statistics and data sciences, focusing on learning advanced data analytic skills for a wide range of problems and data In this unit, you will learn how to ingest, combine and summarise data from a variety of data models which are typically encountered in data science projects as well as reinforcing your programming skills through experience with statistical programming language. You will also be exposed to the concept of statistical machine learning and develop the skills to analyse various types of data in order to answer a scientific question. From this unit, you will develop knowledge and skills that will enable you to embrace data analytic challenges stemming from everyday problems.

**MATH2070 Optimisation and Financial Mathematics**

Credit points: 6 Teacher/Coordinator: Refer to the unit of study outline https://www.sydney.edu.au/units Session: Semester 2 Classes: Refer to the unit of study outline https://www.sydney.edu.au/units 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: Refer to the unit of study outline https://www.sydney.edu.au/units 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 and the Capital Asset Pricing Model. 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 and the Capital Asset Pricing Model. 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: Refer to the unit of study outline https://www.sydney.edu.au/units Session: Semester 2 Classes: Refer to the unit of study outline https://www.sydney.edu.au/units 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: Refer to the unit of study outline https://www.sydney.edu.au/units 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: Refer to the unit of study outline https://www.sydney.edu.au/units Session: Semester 1 Classes: Refer to the unit of study outline https://www.sydney.edu.au/units 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: Refer to the unit of study outline https://www.sydney.edu.au/units 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: Refer to the unit of study outline https://www.sydney.edu.au/units Session: Semester 1 Classes: Refer to the unit of study outline https://www.sydney.edu.au/units 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: Refer to the unit of study outline https://www.sydney.edu.au/units 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 has 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.

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: Refer to the unit of study outline https://www.sydney.edu.au/units Session: Semester 2 Classes: Refer to the unit of study outline https://www.sydney.edu.au/units Prerequisites: 12 credit points chosen from MATH2XXX or STAT2XXX or DATA2X02 Prohibitions: MATH3975 or MATH3015 or MATH3933 Assessment: Refer to the unit of study outline https://www.sydney.edu.au/units Mode of delivery: Normal (lecture/lab/tutorial) day

Note: It is possible to enrol in MATH2070 and MATH3075 in the same semester

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: Refer to the unit of study outline https://www.sydney.edu.au/units Session: Semester 2 Classes: Refer to the unit of study outline https://www.sydney.edu.au/units Prerequisites: A mark of 65 or above in 12cp from (MATH2XXX or STAT2XXX or DATA2X02) Prohibitions: MATH3933 or MATH3015 or MATH3075 Assessment: Refer to the unit of study outline https://www.sydney.edu.au/units Mode of delivery: Normal (lecture/lab/tutorial) day

Note: MATH2X70 and MATH3975 may be taken in the same semester

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.

**STAT3021 Stochastic Processes**

Credit points: 6 Teacher/Coordinator: Refer to the unit of study outline https://www.sydney.edu.au/units Session: Semester 1 Classes: Refer to the unit of study outline https://www.sydney.edu.au/units Prerequisites: STAT2X11 and (MATH1003 or MATH1903 or MATH1907 or MATH1023 or MATH1923 or MATH1933) Prohibitions: STAT3911 or STAT3011 or STAT3921 or STAT4021 Assessment: Refer to the unit of study outline https://www.sydney.edu.au/units 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.

**STAT3921 Stochastic Processes (Advanced)**

Credit points: 6 Teacher/Coordinator: Refer to the unit of study outline https://www.sydney.edu.au/units Session: Semester 1 Classes: Refer to the unit of study outline https://www.sydney.edu.au/units Prerequisites: (STAT2011 or STAT2911) and MATH1003 or MATH1903 or MATH1907 or MATH1023 or MATH1923 or MATH1933 Prohibitions: STAT3011 or STAT3911 or STAT3021 or STAT3003 or STAT3903 or STAT3005 or STAT3905 or STAT4021 Assessment: Refer to the unit of study outline https://www.sydney.edu.au/units 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 basic properties and limit theory of discrete-time Markov chains and branching processes. You will then establish key results for the Poisson process and continuous-time Markov chains, stopping times and martingales. Various illustrative examples are provided throughout the unit to demonstrate how stochastic processes can be applied in modelling and analysing 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. Students who undertake the advanced unit MATH3921 will be expected to have a deeper, more sophisticated understanding of the theory in the unit and to be able to work with more complicated applications than students who complete the regular MATH3021 unit.

###### Interdisciplinary project

**FMAT3888 Projects in Financial Mathematics**

Credit points: 6 Teacher/Coordinator: Refer to the unit of study outline https://www.sydney.edu.au/units Session: Semester 2 Classes: Refer to the unit of study outline https://www.sydney.edu.au/units Prerequisites: (MATH2070 or MATH2970) and (STAT2011 or STAT2911) Assumed knowledge: STAT2X11, MATH2X70 Assessment: Refer to the unit of study outline https://www.sydney.edu.au/units 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: Refer to the unit of study outline https://www.sydney.edu.au/units Session: Intensive February,Intensive July,Semester 1,Semester 2 Classes: Refer to the unit of study outline https://www.sydney.edu.au/units Prerequisites: 96 credit points Assessment: Refer to the unit of study outline https://www.sydney.edu.au/units Mode of delivery: Normal (lecture/lab/tutorial) day

This interdisciplinary unit provides students with the opportunity to address complex problems identified by industry, community, and government organisations, and gain valuable experience in working across disciplinary boundaries. In collaboration with a major industry partner and an academic lead, students integrate their academic skills and knowledge by working in teams with students from a range of disciplinary backgrounds. This experience allows students to research, analyse and present solutions to a realÂ¿world problem, and to build on their interpersonal and transferable skills by engaging with and learning from industry experts and presenting their ideas and solutions to the industry partner.