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 computer science, engineering, economics, statistics and physics.
Topics to be covered include:
Analysis - introduction to metric spaces in the context of the calculus of functions of several variables; double integrals, partial derivatives, gradients and directional derivatives, extreme values; vector functions, curves and parametrizations; infinite series, convergence tests, power series, Taylor series;
Algebra – theory and application of Euclidean vector spaces, vector spaces, linear independence, bases and dimension, eigenvalues and eigenvectors, orthogonality and least squares.
Note: This is an Honours Pathway Course. It involves extra material and emphasizes 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:
On satisfying the requirements of this course, students will have the knowledge and skills to:
1. Explain the fundamental concepts of analysis and linear algebra and their role in modern mathematics and applied contexts.
2. Demonstrate accurate and efficient use of analysis and linear algebra techniques.
3. Demonstrate capacity for mathematical reasoning through analyzing, proving and explaining concepts from analysis and linear algebra.
4. Apply problem-solving using analysis and linear algebra techniques applied to diverse situations in physics, engineering and other mathematical contexts.
Indicative Assessment
Assessment will be based on:
- Workshop participation (0-5%; LO 1-4)
- Assignments and online quizzes (25-30%; LO 1-4)
- Exams (65-75%; LO 1-4)
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
Four lectures per week and regular workshops.Requisite and Incompatibility
Prescribed Texts
Essential Calculus (2nd edition) by James Stewart.
Linear Algebra textbook to be advised.
Majors
Minors
Fees
Tuition fees are for the academic year indicated at the top of the page.
If you are a domestic graduate coursework or international student you will be required to pay tuition fees. Tuition fees are indexed annually. Further information for domestic and international students about tuition and other fees can be found at Fees.
- Student Contribution Band:
- 2
- Unit value:
- 6 units
If you are an undergraduate student and 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). You can find your student contribution amount for each course 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 |
|---|---|
| 2019 | $3840 |
- International fee paying students
| Year | Fee |
|---|---|
| 2019 | $5460 |
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 |
|---|---|---|---|---|---|---|
| 7504 | 22 Jul 2019 | 29 Jul 2019 | 31 Aug 2019 | 25 Oct 2019 | In Person | View |