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Major: Pure Mathematics

Pure Mathematics


Department of Mathematics and Statistics
Faculty of Science and Engineering

This major must be completed as part of an award. The general requirements for the award must be satisfied in order to graduate.

Requirements for the Major:

Completion of a minimum of 36 credit points including the following prescribed units:

Credit points

100 level

Mathematics IA (3)
Mathematics IA (Advanced) (3)
Mathematics IB (3)
Mathematics IB (Advanced) (3)
Introductory Statistics (3)
Statistical Data Analysis (3)

200 level

Mathematics IIA (3)
Mathematical Methods II (3)
Mathematics IIB (3)
Pure Mathematics II (3)
Mathematical Techniques (3)
Applied Mathematics II (3)
3cp from
Applied Statistics (3)
Probability (3)
Introduction to Probability (3)
Computer Simulation (3)
Operations Research I (3)

300 level

Algebra IIIA (3)
Pure Mathematics Capstone (3)
3cp from
Mathematical Theory of Risk (3)
Waves (3)
Nonlinear Dynamics and Chaos (3)
Mathematical Methods (3)
Partial Differential Equations (3)
Algebraic Structures (3)
Concepts in Geometry and Topology (3)
Analysis (3)
Topics in Pure Mathematics (3)
Techniques in Partial Differential Equations (3)
Computational Techniques (3)
Advanced Mathematical Modelling and Optimisation (3)
Topics in Applied Mathematics (3)
9cp from
Algebraic Structures (3)
Geometry and Topology (3)
Concepts in Geometry and Topology (3)
Real and Functional Analysis (3)
Analysis (3)
Algebra IIIB (3)
Topics in Pure Mathematics (3)


Overview and Aims of the Program Pure Mathematics focuses on a deep understanding of the properties and interrelationships that arise in study algebraic and topological structures, and in the application of the ideas of calculus in a wide range of settings such as harmonic and functional analysis; which are of profound importance in answering questions of interest in diverse areas ranging from computer science and engineering to physics, statistics and chemistry. Graduates with a major in Pure Mathematics will have developed a broad understanding of modern mathematical ideas and techniques and the capacity to develop appropriate mathematical structures to facilitate the analysis of problems occurring across a wide domain of applications. These attributes, together with training in critical and analytical thinking and well developed skills in effectively communicating complex ideas make Macquarie's Pure Mathematics graduates highly sought after employees, as well as providing a strong, well-balanced foundation for those who wish to progress to further study.
Graduate Capabilities

The Graduate Capabilities Framework articulates the fundamentals that underpin all of Macquarie’s academic programs. It expresses these as follows:

Cognitive capabilities
(K) discipline specific knowledge and skills
(T) critical, analytical and integrative thinking
(P) problem solving and research capability
(I) creative and innovative

Interpersonal or social capabilities
(C) effective communication
(E) engaged and ethical local and global citizens
(A) socially and environmentally active and responsible

Personal capabilities
(J) capable of professional and personal judgement and initiative
(L) commitment to continuous learning

Program Learning Outcomes By the end of this program it is anticipated you should be able to:
• demonstrate a mastery of the principles, ideas and application of mathematical techniques from Pure Mathematics, Applied Mathematics and Statistics appropriate for a mathematics professional.
• demostrate a sophisticated understanding of the key concepts relating to algebraic structures, topology and analysis.
• exhibit a well developed facility with, and an in-depth knowledge of a range of specialised areas in Pure Mathematics.
• formulate abstract mathematical ideas and arguments and communicate them in a effective and concise manner appropriate to the intended audience.
• characterise mathematically interesting properties using precise definitions and apply mathematical reasoning to deduce the implications that follow from possessing such properties.
• analyse the validity of mathematical arguments, correct deficiencies and remove unnecessary constraints.
• integrate a wide range of sophisticated mathematical ideas to analyse and solve substantial problems.
• make efficient use of appropriate technology to address a wide range of mathematical problems requiring extensive computation and manipulation of data.
• recognise ethical issues associated with professional mathematical practice and be equipped to respond appropriately to such issues within a principled and ethical framework.
Learning and Teaching Methods The Major in Pure Mathematics is designed to prepare graduates as ethical professionals for work in industry, research organisations and academia, and the learning and teaching methods are designed to provide students with the opportunity to gain and demonstrate the knowledge, skills and capabilities required for this purpose.

The academics involved with this program are active researchers, which enables them to integrate cutting-edge research into the units that they teach. The majority of the units in this program involve students working through a carefully selected range of problems, projects and activities that provide opportunities to sharpen understanding, develop skills, and explore the application of a variety of techniques relevant to the content of the unit. Communication skills are developed through oral and written presentations designed for a range of audiences.

The theoretical components of units are presented in lectures and develop the underlying theory, in addition to developing analytical and problem solving skills. All units have weekly face-to-face activities. Assignments are used for formative and summative purposes.

The major culminates with a Capstone unit that involves students working on a substantial project of an appropriate degree of complexity for a pure mathematical professional at the commencement of their career. Students work autonomously under the guidance of academic staff. The project allows students to apply the knowledge and skills they have developed in their studies to a substantial problem in an integrated manner.
Assessment Units in the Major in Pure Mathematics use a variety of types of assessment. These assessments are designed not just to test discipline-specific knowledge, but all aspects of professional competency include professional practice, project work, design and communication skills. In addition to formal assessments, students are provided with informal feedback from staff and their peers throughout the program.

Assessment types are very diverse and include:
Assignments – these test the understanding of a learning outcome by means of small size problems
Programming Assignments - allow students to demonstrate their competency in developing programs of varying complexity.
Reports and documents – These can range from small scale professionally presented project reports to the preparation of substantial documents presenting a body of mathematical work.
Oral presentations - these test students ability to communicate the results of their work
Group reports – are used when group projects are conducted.
Final exams - The majority of the units will have a final examination where the ability to synthesize and apply knowledge is assessed.
Quizzes and in-class tests assess student learning part-way through the unit and provide feedback to students on learning progress.
Tutorial assessment – assess students work in formal tutorial sessions where students receive the support of tutors and other staff
Recognition of Prior Learning

Macquarie University may recognise prior formal, informal and non-formal learning for the purpose of granting credit towards, or admission into, a program. The recognition of these forms of learning is enabled by the University’s Recognition of Prior Learning (RPL) Policy (see and its associated Procedures and Guidelines. The RPL pages contain information on how to apply, links to registers, and the approval processes for recognising prior learning for entry or credit.

Information can be found at:

Support for Learning

Macquarie University aspires to be an inclusive and supportive community of learners where all students are given the opportunity to meet their academic and personal goals. The University offers a comprehensive range of free and accessible student support services which include academic advice, counselling and psychological services, advocacy services and welfare advice, careers and employment, disability services and academic skills workshops amongst others. There is also a bulk billing medical service located on campus.

Further information can be found at

Campus Wellbeing contact details:
Phone: +61 2 9850 7497

Program Standards and Quality

The program is subject to an ongoing comprehensive process of quality review in accordance with a pre-determined schedule that complies with the Higher Education Standards Framework. The review is overseen by Macquarie University's peak academic governance body, the Academic Senate and takes into account feedback received from students, staff and external stakeholders.

Graduate Destinations and Employability The major employment sectors for graduates with an undergraduate degree with a major in Pure Mathematics are:
Education and Training
Professional, scientific and technical services
Financial and insurance services
Public administration and safety
Retail trade
Health care and social assistance
Transport, postal and warehousing
Wholesale trade
Information, media and telecommunications
Assessment Regulations

This program is subject to Macquarie University regulations, including but not limited to those specified in the Assessment Policy, Academic Honesty Policy, the Final Examination Policy and relevant University Rules. For all approved University policies, procedures, guidelines and schedules visit

Inherent requirements are the essential components of a course or program necessary for a student to successfully achieve the core learning outcomes of a course or program. Students must meet the inherent requirements to complete their Macquarie University course or program.

Inherent requirements for Macquarie University programs fall under the following categories:

Physical: The physical inherent requirement is to have the physical capabilities to safely and effectively perform the activities necessary to undertake the learning activities and achieve the learning outcomes of an award.

Cognition: The inherent requirement for cognition is possessing the intellectual, conceptual, integrative and quantitative capabilities to undertake the learning activities and achieve the learning outcomes of an award.

Communication: The inherent requirement for communication is the capacity to communicate information, thoughts and ideas through a variety of mediums and with a range of audiences.

Behavioural: The behavioural inherent requirement is the capacity to sustain appropriate behaviour over the duration of units of study to engage in activities necessary to undertake the learning activities and achieve the learning outcomes of an award.

For more information see

2019 Unit Information

When offered:
S1 Day
Permission of Executive Dean of Faculty
HSC Chinese, CHN113, CHN148