# Mathematical Sciences

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

## About the program

The Mathematical Sciences encompasses a diverse set of disciplines that share common ideas and themes that develop and become clear to high achieving students as they progress in their studies. Generally speaking, a deep understanding of the common ideas and their application in both theoretical and practical spheres comes as a result of high-level syntheses rather than low-level foundational learning.

We want to give our very best students the opportunity to attain this level of learning through a program which enables them to engage across the breadth of the subject and to develop depth in one or more subdisciplines. This program will form an outstanding foundation for honours at 4000-level in Pure Mathematics, Applied Mathematics, Statistics, Data Science or Financial Mathematics and Statistics and further studies including the Master of Mathematical Sciences degree.

## Requirements for completion

The Mathematical Sciences program is available only to students eligible to enroll in the Dalyell stream.

A program in Mathematical Sciences requires 66 credit points including:

(i) A 48 credit point major in either, Data Science, Financial Mathematics and Statistics, Mathematics or Statistics, and:

(ii) 6 credit points of 1000-level program core units according to the following rules:

(a) For students with a major in Financial Mathematics and Statistics, Mathematics or Statistics, 6 credit points of 1000-level program core (non-Data Science major) units in addition to those counted towards the major.

(b) For students with a major in Data Science, 6 credit points of 1000-level program core (Data Science major) units in addition to those counted towards the major.

(iii) 12 credit points of 2000-level and 3000-level selective units according to the following rules:

(a) For students with a major in Mathematics, 6 credit points of 2000-level program selective (Mathematics major) units and 6 credit points of 3000- or 4000-level selective units, in addition to those counted towards the major.

(b) For students with a major in Statistics, 6 credit points of 2000- level program selective set one (Statistics major) units, and 6 credit points of 2000-level program selective set two (Statistics major) in addition to those counted towards the major.

(c) For students with a major in Financial Mathematics and Statistics, 12 credit points of 2000-level program selective (Financial Mathematics and Statistics major) units in addition to those counted towards the major.

(d) For students with a major in Data Science, 6 credit points of 2000-level program selective (Data Science major) units in addition to those counted towards the major, and 6 credit points of 3000- or 4000-level selective units, in addition to those counted towards the major.

## First year

MATH1021/1921/1931 Calculus Of One Variable, MATH1023/1923/1933 Multivariable Calculus and Modelling and MATH1002/1902 Linear Algebra, DATA1002/1902 Informatics: Data and Computation, 3 credit points from a selection of MATH1004/1904 Discrete Mathematics or MATH1005/1905 Statistical Thinking with Data.

If you have room in your degree, you may take the combination of the 6 credit point unit DATA1001/1901 Foundations of Data Science (instead of MATH1005/1905) and MATH1004/1904 Discrete Mathematics.

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 and will equip you for all of the majors, Mathematics, Financial Mathematics and Statistics, Data Science and Statistics, that are offered in this program. 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. MATH1905 Statistical Thinking with Data or alternatively DATA1001/1901 Foundations of Data Science 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. DATA1002/1902 Informatics: Data and Computation introduces you to computation and data handling, essential skills in almost all areas of mathematics and statistics.

All first year MATH units are 3 credit point units. DATA units are 6 credit point units.

## Second year

Based on major choice, students complete 6 or 12 credit points, in addition to those counted towards the major, from a selection of: MATH2021/2921 Vector Calculus and Differential Equations, MATH2022/2922 Linear and Abstract Algebra, MATH2023/2923 Analysis, MATH2088/2988 Number Theory and Cryptography, MATH2070/2970 Optimisation and Financial Mathematics, STAT2011/2911 Probability and Estimation Theory, DATA2002/2902 Data Analytics: Learning from Data. For further information about each major, please look at the handbook page for that major.

The program aims to give you a broad foundational knowledge at 2000 level that will equip you for study of one or more majors in third year. The aim is for all students in the program to take at least three of the four areas represented by MATH2X21 Vector Calculus and Differential Eqs, MATH2X22 Linear and Abstract Algebra, STAT2X11 Probability and Statistical Models, and DATA2X02 Data Analytics: Learning from Data which represent applied mathematics, pure mathematics, theoretical statistics, and applied statistics respectively.

## Third year

Students completing a Mathematics or Data Science major complete 6 credit points from a wide selection of mathematics or statistics units in addition to those counted towards the major. Students completing a Statistics major, or a Financial Mathematics and Statistics major will take all four 3000-level units listed in their major.

For further information about each major, please look at the Table A handbook page for that major.

In your third year you must take at least one designated project unit as well as a range of other specialist units for the major that you have chosen.

## 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.

## 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 Mathematical Sciences 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, statistics and data science.
- Interpret information communicated in mathematical and statistical form.
- Analyse data in descriptive, interpretive and exploratory ways using graphical methods and visualisation tools.
- Communicate mathematical and statistical 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 and statistical terms using a variety of methods.
- Solve practical and abstract problems in the mathematical sciences 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.