• Class Number 3586
• Term Code 3030
• Class Info
• Unit Value 6 units
• Mode of Delivery In Person
• COURSE CONVENER
• Prof John Urbas
• LECTURER
• Prof John Urbas
• Class Dates
• Class Start Date 24/02/2020
• Class End Date 05/06/2020
• Census Date 08/05/2020
• Last Date to Enrol 02/03/2020
SELT Survey Results

Analysis 2: Lebesgue Integration and Hilbert Spaces (MATH6212)

This course is intended both for continuing mathematics students and for other students using mathematics at a high level in theoretical physics, engineering and information technology, and mathematical economics.

Topics to be covered will normally include topics from the following, with some additions and variations each year

Measure and Integration - Lebesgue outer measure, measurable sets and integration, Lebesgue integral and basic properties, convergence theorems, connection with Riemann integration, Fubini's theorem, approximation theorems for measurable sets, Lusin's theorem, Egorov's theorem, Lp spaces, general measure theory, Radon-Nikodym theorem

Hilbert Spaces - elementary properties such as Cauchy Schwartz inequality and polarization, nearest point, orthogonal complements, linear operators, Riesz duality, adjoint operator, basic properties or unitary, self adjoint and normal operators, review and discussion of these operators in the complex and real setting, applications to L2 spaces and integral operators, projection operators, orthonormal sets, Bessel's inequality, Fourier expansion, Parseval's equality, applications to Fourier series.

## Learning Outcomes

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

1. Explain the fundamental concepts of advanced analysis such as topology and Lebeque integration and their role in modern mathematics and applied contexts
2. Demonstrate accurate and efficient use of advanced analysis techniques
3. Demonstrate capacity for mathematical reasoning through analyzing, proving and explaining concepts from advanced analysis
4. Use deep knowledge and understanding of advanced analysis, such as topology and Lebesgue integration, to formulate responses to complex concrete and abstract problems.

## Staff Feedback

Students will be given feedback in the following forms in this course:

• feedback to whole class, groups, individuals, focus group etc

## Student Feedback

ANU is committed to the demonstration of educational excellence and regularly seeks feedback from students. Students are encouraged to offer feedback directly to their Course Convener or through their College and Course representatives (if applicable). The feedback given in these surveys is anonymous and provides the Colleges, University Education Committee and Academic Board with opportunities to recognise excellent teaching, and opportunities for improvement. The Surveys and Evaluation website provides more information on student surveys at ANU and reports on the feedback provided on ANU courses.

## Other Information

Course delivery and assessment in 2020 was adjusted due to the COVID-19 pandemic. Any information below that replaces what was published in the Class Summary for Semester 1, 2020 was approved by the Associate Dean Education (as is required after 10% commencement of a course). Where an activity or assessment is not referenced below, it remains unchanged.

Teaching Activities

• Lectures were done by Zoom at the scheduled times.
• Workshops were done on Zoom at the scheduled times.

Assessment

Adjustments were made to assignment due dates; for details see the course Wattle site.

• Mid-term exam was cancelled.
• Final Exam was take-home.

Students were assessed through whichever of the following options gave a higher score or a passing grade.

• Assessment Option 1: 50% assignments, 50% final exam with a hurdle that the student must score at least 50% in the final exam to pass the course.
• Assessment Option 2: 30% assignments, 70% final exam with no hurdle.

## Class Schedule

Week/Session Summary of Activities Assessment
1 3 lectures per week, one tutorial per week, five assignments, midsemester and final exams.

Via wattle

## Assessment Summary

Assessment task Value Due Date Return of assessment Learning Outcomes
Assignments 30 % * * 1,2,3,4
Midsemester exam 25 % 30/03/2020 24/04/2020 1,2,3,4
Final exam 35 % 04/06/2020 02/07/2020 1,2,3,4

* If the Due Date and Return of Assessment date are blank, see the Assessment Tab for specific Assessment Task details

## Policies

ANU has educational policies, procedures and guidelines, which are designed to ensure that staff and students are aware of the University’s academic standards, and implement them. Students are expected to have read the Academic Misconduct Rule before the commencement of their course. Other key policies and guidelines include:

## Assessment Requirements

The ANU is using 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. For additional information regarding Turnitin please visit the Academic Integrity . In rare cases where online submission using Turnitin software is not technically possible; or where not using Turnitin software has been justified by the Course Convener and approved by the Associate Dean (Education) on the basis of the teaching model being employed; students shall submit assessment online via ‘Wattle’ outside of Turnitin, or failing that in hard copy, or through a combination of submission methods as approved by the Associate Dean (Education). The submission method is detailed below.

## Moderation of Assessment

Marks that are allocated during Semester are to be considered provisional until formalised by the College examiners meeting at the end of each Semester. If appropriate, some moderation of marks might be applied prior to final results being released.

## Examination(s)

Please note, that where a date range is used in the Assessment Summary in relation to exams, the due date and return date for mid-semester exams indicate the approximate timeframe in which the exam will be held; the due and return date for end of semester exams indicate the approximate timeframe in which the exam will be held and the date official end of Semester results are released on ISIS. Students should consult the course wattle site and the ANU final examination timetable to confirm the date, time and venue of the exam.

Value: 30 %
Learning Outcomes: 1,2,3,4

Assignments

Five assignments approximately due every two weeks.

There are 5 assignments due over the semester. It is intended that the marked assignments will be returned within 2 weeks after submission. Further details can be found on the Course Wattle site.

Value: 30-40%

The final value of the assignments is partially determined by performace in the end of semester exam. Minimum value is 30%

Value: 25 %
Due Date: 30/03/2020
Return of Assessment: 24/04/2020
Learning Outcomes: 1,2,3,4

Midsemester exam

To be held in Week 6 or 7, permitted materials are one A4 sheet of handwritten notes.

Value: 25%

Check the Course Wattle site or the Central ANU examination timetable to confirm the date, time and location of the exam.

Value: 35 %
Due Date: 04/06/2020
Return of Assessment: 02/07/2020
Learning Outcomes: 1,2,3,4

Final exam

To be held during the exam period, permitted materials are one A4 sheet of handwritten notes.

Value: 35-45%

The final value of the end of semester exam is partially determined by performance in the assignments. Minimum value is 35%

Check the Course Wattle site or the Central ANU examination timetable to confirm the date, time and location of the exam.

Academic integrity is a core part of the ANU culture as a community of scholars. At its heart, academic integrity is about behaving ethically, committing to honest and responsible scholarly practice and upholding these values with respect and fairness.

The ANU commits to assisting all members of our community to understand how to engage in academic work in ways that are consistent with, and actively support academic integrity. The ANU expects staff and students to be familiar with the academic integrity principle and Academic Misconduct Rule, uphold high standards of academic integrity and act ethically and honestly, to ensure the quality and value of the qualification that you will graduate with.

## Online Submission

You will be required to electronically sign a declaration as part of the submission of your assignment. Please keep a copy of the assignment for your records. Unless an exemption has been approved by the Associate Dean (Education) submission must be through Turnitin.

## Hardcopy Submission

For some forms of assessment (hand written assignments, art works, laboratory notes, etc.) hard copy submission is appropriate when approved by the Associate Dean (Education). Hard copy submissions must utilise the Assignment Cover Sheet. Please keep a copy of tasks completed for your records.

## Late Submission

Individual assessment tasks may or may not allow for late submission. Policy regarding late submission is detailed below:

• Late submission not permitted. If submission of assessment tasks without an extension after the due date is not permitted, a mark of 0 will be awarded.

## Referencing Requirements

Accepted academic practice for referencing sources that you use in presentations can be found via the links on the Wattle site, under the file named “ANU and College Policies, Program Information, Student Support Services and Assessment”. Alternatively, you can seek help through the Students Learning Development website.

## Returning Assignments

Assignments will be returned at tutorials, normally within two weeks of the due date.

## Extensions and Penalties

Extensions and late submission of assessment pieces are covered by the Student Assessment (Coursework) Policy and Procedure. Extensions may be granted for assessment pieces that are not examinations or take-home examinations. If you need an extension, you must request an extension in writing on or before the due date. If you have documented and appropriate medical evidence that demonstrates you were not able to request an extension on or before the due date, you may be able to request it after the due date.

Not permitted.

## Privacy Notice

The ANU has made a number of third party, online, databases available for students to use. Use of each online database is conditional on student end users first agreeing to the database licensor’s terms of service and/or privacy policy. Students should read these carefully. In some cases student end users will be required to register an account with the database licensor and submit personal information, including their: first name; last name; ANU email address; and other information.
If any student chooses not to agree to the database licensor’s terms of service or privacy policy, the student will not be able to access and use the database. In these circumstances students should contact their lecturer to enquire about alternative arrangements that are available.

Academic Quality Assurance Committee monitors the performance of students, including attrition, further study and employment rates and grade distribution, and College reports on quality assurance processes for assessment activities, including alignment with national and international disciplinary and interdisciplinary standards, as well as qualification type learning outcomes.

Since first semester 1994, ANU uses a grading scale for all courses. This grading scale is used by all academic areas of the University.

## Support for students

The University offers students support through several different services. You may contact the services listed below directly or seek advice from your Course Convener, Student Administrators, or your College and Course representatives (if applicable).

## Convener

 Prof John Urbas 61253876 John.Urbas@anu.edu.au

### Research Interests

• Partial Differential Equations
• Differential Geometry

## Instructor

 Prof John Urbas 61253876 John.Urbas@anu.edu.au