This course continues on from MATH1115, providing an in-depth development of fundamental concepts of calculus and linear algebra, with a particular emphasis on the underlying foundations of mathematics. The use and understanding of proof and abstract ideas will allow students to develop analytical skills which will form a base for further study in fundamental mathematics, as well as providing a foundation for a wide range of quantitative areas such as actuarial studies, computer science, economics, engineering, physics and statistics.
Topics to be covered include:
Calculus/Analysis – sequences and series, convergence tests, power series, Taylor series, a short introduction to metric spaces in the context of the calculus of functions of several variables, generalisation of the real analysis theory studied in MATH1115 to multivariable functions including limits and continuity, double integrals, Fubini's theorem, integrability of continuous functions, partial derivatives, gradients and directional derivatives, differentiation of multivariable functions, extreme values, vector-valued functions.
Linear Algebra – subspaces, span, linear independence, bases and dimension, linear maps, duality, eigenvalues and eigenvectors, inner product spaces, Gram-Schmidt orthogonalisation, operators on inner product spaces, the spectral theorem in finite dimensions, singular value decomposition.
Note: This is an Honours Pathway Course. It involves extra material and emphasises the use and understanding of proof and abstract ideas to a deeper conceptual level than MATH1014.
Learning Outcomes
Upon successful completion, students will have the knowledge and skills to:
- Explain the fundamental concepts of analysis and linear algebra and their role in modern mathematics and applied contexts.
- Demonstrate accurate and efficient use of analysis and linear algebra techniques.
- Demonstrate capacity for mathematical reasoning through analysing, proving and explaining concepts and theorems from analysis and linear algebra.
- Apply problem-solving using analysis and linear algebra techniques applied to diverse situations in physics, engineering and other mathematical contexts.
Indicative Assessment
- In-workshop assessment (0-5%) (0) [LO 1,2,3,4]
- Assignments and online quizzes (25-30%) (30) [LO 1,2,3,4]
- Tests during the semester (25-35%) (30) [LO 1,2,3,4]
- Final examination (35-45%) (40) [LO 1,2,3,4]
The ANU uses Turnitin to enhance student citation and referencing techniques, and to assess assignment submissions as a component of the University's approach to managing Academic Integrity. While the use of Turnitin is not mandatory, the ANU highly recommends Turnitin is used by both teaching staff and students. For additional information regarding Turnitin please visit the ANU Online website.
Workload
The expected workload will consist of approximately 130 hours throughout the semester including:
- Lecture component which may consist of an average of approximately 4 x 1-hour lectures per week (a combination of in-person and pre-recorded online lectures for a total of 52 hours over the 12 weeks of teaching).
- 10 x 1.5 hour workshops held in 10 of the 12 teaching weeks (A total of 15 hours of workshop time).
- Approximately 63 hours of self-study per semester which will include preparation for lectures, tests, quizzes and other assessment tasks.
Inherent Requirements
No specific inherent requirements have been identified for this course.
Requisite and Incompatibility
Prescribed Texts
Linear Algebra Done Right (3rd edition) by Sheldon Axler.
Course notes and/or references for the analysis side of the course will be provided on the MATH1116 course site in the Learning Management System during the semester.
Preliminary Reading
For the analysis side of the course, a portion of the content will require students to become familiar with various multi-variable calculus techniques. Some of the chapters in Essential Calculus (2nd edition) by James Stewart are used in MATH1014 as a reference for multi-variable calculus, and they are a recommended (but not compulsory) additional resource for MATH1116.
Fees
Tuition fees are for the academic year indicated at the top of the page.
Commonwealth Support (CSP) Students
If you have been offered a Commonwealth supported place, your fees are set by the Australian Government for each course. At ANU 1 EFTSL is 48 units (normally 8 x 6-unit courses). More information about your student contribution amount for each course at Fees.
- Student Contribution Band:
- 1
- Unit value:
- 6 units
If you are a domestic graduate coursework student with a Domestic Tuition Fee (DTF) place or international student you will be required to pay course tuition fees (see below). Course tuition fees are indexed annually. Further information for domestic and international students about tuition and other fees can be found at Fees.
Where there is a unit range displayed for this course, not all unit options below may be available.
| Units | EFTSL |
|---|---|
| 6.00 | 0.12500 |
Course fees
- Domestic fee paying students
| Year | Fee |
|---|---|
| 2025 | $4680 |
- International fee paying students
| Year | Fee |
|---|---|
| 2025 | $6720 |
Offerings, Dates and Class Summary Links
ANU utilises MyTimetable to enable students to view the timetable for their enrolled courses, browse, then self-allocate to small teaching activities / tutorials so they can better plan their time. Find out more on the Timetable webpage.
Class summaries, if available, can be accessed by clicking on the View link for the relevant class number.
Second Semester
| Class number | Class start date | Last day to enrol | Census date | Class end date | Mode Of Delivery | Class Summary |
|---|---|---|---|---|---|---|
| 8556 | 21 Jul 2025 | 28 Jul 2025 | 31 Aug 2025 | 24 Oct 2025 | In Person | N/A |