# Mathematics

The School of Mathematics and Statistics is situated in the Faculty of Science. Units of study in this major are available at standard and advanced level.

## About the major

Mathematics is powerful, beautiful and diverse. It is a language, a tool for analysis and prediction, and a way of thinking about the world. At 1000- and 2000-level, this major equips students with the foundational ideas of mathematics: abstract algebra, vector calculus and calculus of several variables, as well as formal proof and analysis.

At 3000-level and beyond, you will have a choice from a wide range of electives in both pure and applied areas of mathematics, including number theory, dynamical systems, geometry, topology and mathematical computing. The range of units available has been designed to cater for you - whether you intend to become a professional mathematician or to follow other interests with a highly sought-after set of mathematical skills.

All units in the mathematics major at 1000- and 2000-level are offered at Advanced level (with a 9 in the second place in the number in the unit code) as well as at standard level.

## Requirements for completion

A major in Mathematics requires 48 credit points, consisting of:

(i) 12 credit points of 1000-level units as follows: 6 credit points of calculus units; 3 credit points of linear algebra units; and 3 credit points of statistics or discrete mathematics units

(ii) 12 credit points of 2000-level core units

(iii) 6 credit points of 2000-level selective units

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

(v) 12 credit points of 3000-level selective units

A minor in Mathematics is available and articulates to this major.

## First year

MATH1021/1921/1931, MATH1023/1923/1933 and MATH1002/1902, and 3 credit points from a selection of: MATH1004/1904 or MATH1005/1905. If you are taking a Science degree you must take either MATH1005/1905 or the combination DATA1001 and MATH1004/1904.

The first year units provide a strong foundation for further learning and a broad introduction to the Mathematical Sciences. MATH1021/1921/1931 and MATH1023/1923/1933 extend your knowledge of calculus and introduce you to calculus of several variables and mathematical modelling with differential equations. MATH1002/1902 introduces you to linear algebra, including matrices and their applications. MATH1005/1905 introduces you to working with data and MATH1004/1904 is a unit on discrete mathematics, which is the mathematics of counting and arrangement.

All first year MATH units are 3 credit point units.

## Second year

MATH2021/2921 and MATH2022/2922 and 6 credit points from a selection of: MATH2023/2923 and MATH2068/2988.

Second year units in the Mathematics major give you core knowledge and skills which will be a solid and flexible foundation for a wide range of options in third year and beyond. MATH2021/2921 introduces you to vector calculus, a key theory in many areas of application and extends your knowledge of differential equations. MATH2022/2922 extends your understanding of linear algebra and introduces you to topics in abstract algebra such as group theory. MATH2023/2923 opens the world of Analysis to you. Analysis is the deep theoretical foundation of calculus, and sequences and series, for example. MATH2068/2988 introduces you to number theory and cryptography which underlies digital security systems. If you are unsure which selective to choose, MATH2023/2923 gives you the most options in third year. Alternatively, if you have space for an elective, you can choose to do both MATH2023/2923 and MATH2068/2088.

## Third year

A 3000-level project unit and 12 credit points from a selection of MATH3XXX units.

In your third year you must take the designated project unit. This is only offered at standard level. For your other units you have a very wide choice which allows you to specialise in an area that interests you or to explore Mathematics more widely.

## Fourth year

The fourth year is only offered within the combined Bachelor of Science/Bachelor of Advanced Studies course.**Advanced coursework**

The Bachelor of Advanced Studies advanced coursework option consists of 48 credit points, which must include a minimum of 24 credit points in a single subject area at 4000-level, including a project unit of study worth at least 12 credit points. Space is provided for 12 credit points towards the second major (if not already completed). 24 credit points of advanced study will be included in the table for 2020.**Honours**

Students who complete a major in Mathematics may go on to honours in either Applied Mathematics or Pure Mathematics, depending on their interests and the units that they have chosen in their third year. Students must satisfy honours admission requirements. Both Applied Mathematics and Pure Mathematics honours require 24 credit points of coursework and 24 credit points of project work.

Honours units of study will be available in 2020.

## Contact and further information

W www.maths.usyd.edu.au/

First year enquiries email:

Other undergraduate enquiries email:

All enquiries phone: +61 2 9351 5804 or +61 2 9351 5787

**School of Mathematics and Statistics**

Level 5, Carslaw Building F07

University of Sydney NSW 2006

Professor Mary Myerscough

T +61 2 9351 3724

E

## Learning Outcomes

Students who graduate from Mathematics will be able to show:

- Ability to construct logical, clearly presented and justified arguments incorporating deductive reasoning
- Knowledge of the principles and concepts of a broad range of fundamental areas in mathematics
- Ability to formulate and model practical and abstract problems in mathematical terms using a variety of methods
- Ability to apply mathematical principles, concepts, techniques and technology to solve practical and abstract problems and interpret results critically
- Understanding of the breadth of the discipline, its role in other fields and the way that other fields contribute to development in Mathematics
- Appropriate interpretation of information communicated in mathematical form
- Appropriate presentation of information, reason and conclusions in a variety of modes to diverse audiences (expert and non-expert).