• Offered by Mathematical Sciences Institute
• ANU College ANU Joint Colleges of Science
• Course subject Mathematics
• Areas of interest Mathematics
• Course convener
• EmPr John Urbas
• Mode of delivery In Person
• Co-taught Course
• Offered in First Semester 2025
Analysis 1: Metric spaces and Applications (MATH6110)

This course introduces the key concepts of modern real analysis. The philosophy of this course is that modern analysis plays a fundamental role in mathematics itself and in applications to areas such as physics, computer science, economics and engineering.

Topics to be covered include:

• Elementary set theory
• Metric spaces
• Uniform convergence
• Continuity
• The contraction mapping principle
• Integral equations
• Differential equations
• Topological spaces

Note: This course will have shared lectures with MATH2320 and MATH3116. Graduate students obtain a deeper understanding through an extension course which consists of 1 additional lecture each week.

## Learning Outcomes

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

1. Explain the fundamental concepts of real analysis and their role in modern mathematics and applied contexts.
2. Demonstrate accurate and efficient use of real analysis techniques.
3. Demonstrate capacity for mathematical reasoning through analyzing, proving and explaining concepts from real analysis.
4. Apply problem-solving using real analysis techniques applied to diverse situations in physics, engineering and other mathematical contexts.
5. Ability to use deep knowledge and understanding of advanced real analysis to formulate responses to complex concrete and abstract problems.

## Indicative Assessment

1. Assignments (15) [LO 1,2,3,4]
2. Mid semester exam (20-30%) (25) [LO 1,2,3,4]
3. Final exam (30-40%) (35) [LO 1,2,3,4]
4. Assignments on special topic (25) [LO 1,2,3,4,5]
5. Precise weights of % ranges to be determined in consultation with the class at first lecture. (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 will consist of 12 x 3 hours lectures per semester (36 hours) and 10 hours of workshops throughout the semester.
• 12 x 1 hour extension lectures per semester (12 hours).
• Approximately 72 hours of self-study which will include preparation for lectures, workshops, assignments and exams.

## Inherent Requirements

There are no course-specific inherent requirements.

## Requisite and Incompatibility

You will need to contact the Mathematical Sciences Institute to request a permission code to enrol in this course.

## Prescribed Texts

No prescribed texts.

## 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

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.

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
2612 17 Feb 2025 24 Feb 2025 31 Mar 2025 23 May 2025 In Person N/A