• Offered by Mathematical Sciences Institute
• ANU College ANU Joint Colleges of Science
• Course subject Mathematics
• Areas of interest Mathematics
• Course convener
• Dr Joan Licata
• Mode of delivery In Person
• Offered in First Semester 2022
Second Semester 2022
Advanced Mathematics and Applications 2 (MATH1116)

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 - 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 functions, curves and parametrisations, infinite series, convergence tests, power series, Taylor series;

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:

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 analysing, proving and explaining concepts and theorems 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

1. In-workshop assessment (0-5%) (0) [LO 1,2,3,4]
2. Assignments and online quizzes (25-30%) (30) [LO 1,2,3,4]
3. Tests during the semester (25-35%) (30) [LO 1,2,3,4]
4. Final examination (35-45%) (40) [LO 1,2,3,4]
5. The final weighting of the assessment will be determined in the class summary when published. (null) [LO null]

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.

The expected workload will consist of approximately 130 hours throughout the semester including:

• Face-to face component which may consist of 4 x 1 hour lecturer per week (48 hours) as well as 20 hours of workshop time.
• Approximately 62 hours of self-study per semester which will include preparation for lectures, quizzes and other assessment tasks.

## Inherent Requirements

There are no course-specific inherent requirements.

## Requisite and Incompatibility

To enrol in this course you must have completed MATH1115 with a mark of 60 or above or MATH1113 with a mark of 80 or above. You may not enrol in MATH1116 if you have previously completed MATH1014.

## Prescribed Texts

Essential Calculus (2nd edition) by James Stewart.

Linear Algebra Done Right (3rd edition) by Sheldon Axler.

## 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
Note: Please note that fee information is for current year only.

## Offerings, Dates and Class Summary Links

The list of offerings for future years is indicative only.
Class summaries, if available, can be accessed by clicking on the View link for the relevant class number.

### First Semester

Class number Class start date Last day to enrol Census date Class end date Mode Of Delivery Class Summary
4031 21 Feb 2022 28 Feb 2022 31 Mar 2022 27 May 2022 In Person N/A

### Second Semester

Class number Class start date Last day to enrol Census date Class end date Mode Of Delivery Class Summary
7011 25 Jul 2022 01 Aug 2022 31 Aug 2022 28 Oct 2022 In Person N/A