# 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 measure 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:

(a) 6 credit points of calculus units; 3 credit points of linear algebra units; and 3 credit points of statistics* or discrete mathematics units or

(b) 6 credit points of calculus units; 3 credit points of linear algebra units; and 3 credit points of statistics^ for students in the Mathematical Sciences program

(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 or 4000-level selective units

*Bachelor of Science students may substitute DATA1001 Foundations of Data Science or ENVX1002 Introduction to Statistical Methods and students not enrolled in the Bachelor of Science may substitute DATA1001 Foundations of Data Science, ECMT1010 Introduction to Economic Statistics or BUSS1020 Quantitative Business Analysis

^If elective space allows, students may substitute DATA1001/1901 Foundations of Data Science for the statistics unit

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

## First year

MATH1021/1921/1931 Calculus Of One Variable, MATH1023/1923/1933 Multivariable Calculus and Modelling and MATH1002/1902 Linear Algebra, and 3 credit points from a selection of: MATH1004/1904 Discrete Mathematics or MATH1005/1905 Statistical Thinking with Data. If you are taking a Science degree you must take either MATH1005/1905 Statistical Thinking with Data or the combination DATA1001/1901 Foundations of Data Science and MATH1004/1904 Discrete Mathematics.

The first year units provide a strong foundation for further learning and a broad introduction to the Mathematical Sciences. MATH1021/1921/1931 Calculus of One Variable and MATH1023/1923/1933 Multivariable Calculus and Modelling extend your knowledge of calculus and introduce you to calculus of several variables and mathematical modelling with differential equations. MATH1002/1902 Linear Algebra introduces you to linear algebra, including matrices and their applications. MATH1005/1905 Statistical Thinking with Data introduces you to working with data and MATH1004/1904 Discrete Mathematics 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 Vector Calculus and Differential Equations and MATH2022/2922 Linear and Abstract Algebra and 6 credit points from a selection of: MATH2023/2923 Analysis and MATH2088/2988 Number Theory and Cryptography.

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 Vector Calculus and Differential Equations introduces you to vector calculus, a key theory in many areas of application and extends your knowledge of differential equations. MATH2022/2922 Linear and Abstract Algebra extends your understanding of linear algebra and introduces you to topics in abstract algebra such as group theory. MATH2023/2923 Analysis opens the world of Analysis to you. Analysis is the deep theoretical foundation of calculus, and sequences and series, for example. MATH2088/2988 Number Theory and Cryptography introduces you to number theory and cryptography which underlies digital security systems. If you are unsure which selective to choose, MATH2023/2923 Analysis gives you the most options in third year. Alternatively, if you have space for an elective, you can choose to do both MATH2023/2923 Analysis and MATH2088/2988 Number Theory and Cryptography.

## Third year

A 3000-level project unit and 12 credit points from a selection of MATH3XXX units and selected MATH40XX units that are available as advanced units to students completing a Mathematics major.

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, with a minimum of 24 credit points at 4000-level or above. Of these 24 credit points, you must complete a project unit of study worth at least 12 credit points.**Honours**

Meritorious students in the Bachelor of Science/Bachelor of Advanced Studies may apply for admission to Honours within a subject area of the Bachelor of Advanced Studies. Admission to Honours requires the prior completion of all requirements of the Bachelor of Science, including Open Learning Environment (OLE) units. If you are considering applying for admission to Honours, ensure your degree planning takes into account the completion of a second major and all OLE requirements prior to Honours commencement.

Unit of study requirements for Honours in the area of Mathematics: completion of 24 credit points of project work and 24 credit points of coursework.

## Contact and further information

W sydney.edu.au/science/schools/school-of-mathematics-and-statistics

First year enquiries email:

Other undergraduate enquiries email:

All enquiries phone: +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:

- Exhibit a broad and coherent body of knowledge in the principles and concepts of a range of foundation areas in mathematics.
- Describe the breadth of the discipline, its role in other fields and the way that other fields contribute to development in mathematics.
- Interpret information communicated in mathematical form.
- Communicate mathematical concepts and findings through a range of modes for a variety of purposes and audiences, and effectively respond to questions and challenges.
- Construct logical, clearly presented and justified arguments incorporating inductive reasoning.
- Formulate and model practical and abstract problems in mathematical terms using a variety of methods.
- Solve practical and abstract problems in mathematics using a range of concepts, techniques and technologies, working professionally, ethically and responsibly and with consideration of social and cultural perspectives, as individuals or as part of collaborative, interdisciplinary teams.