• Offered by Mathematical Sciences Institute
• ANU College ANU Joint Colleges of Science
• Course subject Mathematics
• Areas of interest Mathematics
• Course convener
• Dr Griff Ware
• Mode of delivery In Person
• Offered in First Semester 2021
Advanced Mathematics and Applications 1 (MATH1115)

This course has been adjusted for remote participation in Sem 1 2021 due to COVID-19 restrictions. On-campus activities will also be available.

This course begins an in-depth study of the 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 - suprema and infima of sets of real numbers, completeness, Riemann-Darboux definition of integration, introductory formal logic, axioms for the real numbers, sequences, convergence, limits, continuity, related real analysis theorems including the monotone convergence theorem for sequences of real numbers and the Bolzano-Weierstrass theorem, existence of extrema, differentiation, applications of derivatives, proof of the fundamental theorem of calculus, Taylor polynomials, l'Hospital's rules, inverse functions;

Linear Algebra - solving linear equations, matrix equations, linear independence, matrix transformations, matrix operations, matrix inverses, abstract vector spaces, subspaces, dimension and rank, determinants, Cramer's rule, complex numbers.

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 MATH1013.

## Learning Outcomes

Upon successful completion, students will have the knowledge and skills to:

1. Explain the fundamental concepts of calculus and linear algebra and their role in modern mathematics and applied contexts.
2. Demonstrate accurate and efficient use of calculus and linear algebra techniques.
3. Demonstrate capacity for mathematical reasoning through analysing, proving and explaining concepts and theorems from calculus and linear algebra.
4. Apply problem-solving using calculus and linear algebra techniques applied to diverse situations in physics, engineering and other mathematical contexts.

## Other Information

Secondary School Prerequisite: A satisfactory pass in the ACT Specialist Mathematics double major, NSW HSC Mathematics Extension 2 or equivalent. Students with excellent results in either the ACT Specialist Mathematics major-minor, NSW HSC Mathematics Extension 1, or equivalent, may be permitted to enrol.

Students enrolled in MATH1115 may be eligible to take MATH2222 and should contact the course convenor of MATH2222 for a permission code.

## Indicative Assessment

1. In-workshop assessment (0-5%) (0) [LO 1,2,3,4]
2. Assignments and online quizzes (20-25%) (20) [LO 1,2,3,4]
3. Tests during the semester (25-30%) (30) [LO 1,2,3,4]
4. Final examination (40-50%) (50) [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

If you have previously completed MATH1013 or MATH1113 then you can only enrol in MATH1115 with the permission of the course convener.

## Prescribed Texts

• Essential Calculus (2nd edition) by James Stewart.

• Elementary Linear Algebra: Applications Version (10th or 11th edition) by Howard Anton and Chris Rorres.

## Assumed Knowledge

Students are assumed to have taken the highest level of high school mathematics available. For ACT students this means a double major in specialist mathematics. For NSW students this means HSC Maths Extension 2. Other students should have equivalent background knowledge.

## 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
2021 \$4110
International fee paying students
Year Fee
2021 \$5880
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
3228 22 Feb 2021 01 Mar 2021 31 Mar 2021 28 May 2021 In Person View