Students

MATH3909 – Real and Functional Analysis

2021 – Session 2, Special circumstances

Session 2 Learning and Teaching Update

The decision has been made to conduct study online for the remainder of Session 2 for all units WITHOUT mandatory on-campus learning activities. Exams for Session 2 will also be online where possible to do so.

This is due to the extension of the lockdown orders and to provide certainty around arrangements for the remainder of Session 2. We hope to return to campus beyond Session 2 as soon as it is safe and appropriate to do so.

Some classes/teaching activities cannot be moved online and must be taught on campus. You should already know if you are in one of these classes/teaching activities and your unit convenor will provide you with more information via iLearn. If you want to confirm, see the list of units with mandatory on-campus classes/teaching activities.

Visit the MQ COVID-19 information page for more detail.

General Information

Download as PDF
Unit convenor and teaching staff Unit convenor and teaching staff Unit Convenor/Lecturer
Ji Li
Contact via Email
Room 710 in 12 WW
Monday 12:00-1:00
Lecturer
Paul Bryan
Contact via Email
12WW 535
Please refer to iLearn
Paul Bryan
Credit points Credit points
10
Prerequisites Prerequisites
((MATH2010 or MATH235) and (MATH2020 or MATH236)) or MATH3901 or MATH3902 or MATH3905 or MATH3906 or MATH331 or MATH332 or MATH335 or MATH336
Corequisites Corequisites
Co-badged status Co-badged status
Unit description Unit description
This unit is concerned with a review of the limiting processes of real analysis and an introduction to functional analysis. Through the discussion of such abstract notions as metric spaces, normed vector spaces and inner product spaces, we can appreciate an elegant and powerful combination of ideas from analysis and linear algebra.

Important Academic Dates

Information about important academic dates including deadlines for withdrawing from units are available at https://students.mq.edu.au/important-dates

Learning Outcomes

On successful completion of this unit, you will be able to:

  • ULO1: demonstrate a well- developed knowledge of the principles, concepts and techniques of a broad range of areas in analysis and applied mathematics, with significant depth in analysis and functional analysis.
  • ULO2: demonstrate an understanding of the breadth of mathematics, the multi-disciplinary role of mathematics and the way it contributes the development in other related fields of study.
  • ULO3: construct sustained logical, clearly presented and justified mathematical arguments incorporating deductive reasoning.
  • ULO4: formulate and model practical and abstract problems in mathematical terms using a variety of methods drawn from analysis and functional analysis.
  • ULO5: apply mathematical principles, concepts, techniques and technology efficiently to solve practical and abstract problems across a range of areas in analysis and functional analysis.
  • ULO6: interpret mathematical information communicated in wide range of forms.

General Assessment Information

HURDLES:  This unit has no hurdle requirements.

ASSIGNMENT SUBMISSION:  Assignment submission will be online through the iLearn page. 

Submit assignments online via the appropriate assignment link on the iLearn page. A personalised cover sheet is not required with online submissions. Read the submission statement carefully before accepting it as there are substantial penalties for making a false declaration.

•   Assignment submission is via iLearn. You should upload this as a single scanned PDF file.

•   Please note the quick guide on how to upload your assignments provided on the iLearn page.

•   Please make sure that each page in your uploaded assignment corresponds to only one A4 page (do not upload an A3 page worth of content as an A4 page in landscape). If you are using an app like Clear Scanner, please make sure that the photos you are using are clear and shadow-free.

•   It is your responsibility to make sure your assignment submission is legible.

•   If there are technical obstructions to your submitting online, please email us to let us know.

You may submit as often as required prior to the due date/time. Please note that each submission will completely replace any previous submissions. It is in your interests to make frequent submissions of your partially completed work as insurance against technical or other problems near the submission deadline.

LATE SUBMISSION OF WORK:  All assignments or assessments must be submitted by the official due date and time. No marks will be given to late work unless an extension has been granted following a successful application for Special Consideration. Please contact the unit convenor for advice as soon as you become aware that you may have difficulty meeting any of the assignment deadlines. It is in your interests to make frequent submissions of your partially completed work. Note that later submissions completely replace any earlier submission, and so only the final submission made before the due date will be marked.

FINAL EXAM POLICY:  Examinations for individuals or groups of students. All students are expected to ensure that they are available until the end of the teaching semester, that is, the final day of the official examination period. The only excuse for not sitting an examination at the designated time is because of documented illness or unavoidable disruption. In these special circumstances, you may apply for special consideration via ask.mq.edu.au.

SUPPLEMENTARY EXAMINATIONS:  

IMPORTANT: If you receive special consideration for the final exam, a supplementary exam will be scheduled in the interval between the regular exam period and the start of the next session. If you apply for special consideration, you must give the supplementary examination priority over any other pre-existing commitments, as such commitments will not usually be considered an acceptable basis for a second application for special consideration. Please ensure you are familiar with the policy prior to submitting an application. You can check the supplementary exam information page on FSE101 in iLearn (https://bit.ly/FSESupp) for dates, and approved applicants will receive an individual notification sometime in the week prior to the exam with the exact date and time of their supplementary examination.

Assessment Tasks

Name Weighting Hurdle Due
Assignment 1 15% No Week 7
iLearn Test 20% No Week 10
Assignment 2 15% No Week 12
Final Exam 50% No Exam period

Assignment 1

Assessment Type 1: Problem set
Indicative Time on Task 2: 10 hours
Due: Week 7
Weighting: 15%

 

The assignment will include a set of questions with short answers involving proofs and calculations.

 


On successful completion you will be able to:
  • demonstrate a well- developed knowledge of the principles, concepts and techniques of a broad range of areas in analysis and applied mathematics, with significant depth in analysis and functional analysis.
  • demonstrate an understanding of the breadth of mathematics, the multi-disciplinary role of mathematics and the way it contributes the development in other related fields of study.
  • construct sustained logical, clearly presented and justified mathematical arguments incorporating deductive reasoning.
  • formulate and model practical and abstract problems in mathematical terms using a variety of methods drawn from analysis and functional analysis.
  • apply mathematical principles, concepts, techniques and technology efficiently to solve practical and abstract problems across a range of areas in analysis and functional analysis.
  • interpret mathematical information communicated in wide range of forms.

iLearn Test

Assessment Type 1: Quiz/Test
Indicative Time on Task 2: 10 hours
Due: Week 10
Weighting: 20%

 

The test will cover both the real and functional analysis components of the unit.

 


On successful completion you will be able to:
  • demonstrate a well- developed knowledge of the principles, concepts and techniques of a broad range of areas in analysis and applied mathematics, with significant depth in analysis and functional analysis.
  • demonstrate an understanding of the breadth of mathematics, the multi-disciplinary role of mathematics and the way it contributes the development in other related fields of study.
  • construct sustained logical, clearly presented and justified mathematical arguments incorporating deductive reasoning.
  • formulate and model practical and abstract problems in mathematical terms using a variety of methods drawn from analysis and functional analysis.
  • apply mathematical principles, concepts, techniques and technology efficiently to solve practical and abstract problems across a range of areas in analysis and functional analysis.
  • interpret mathematical information communicated in wide range of forms.

Assignment 2

Assessment Type 1: Problem set
Indicative Time on Task 2: 10 hours
Due: Week 12
Weighting: 15%

 

The assignment will include a set of questions with short answers involving proofs and calculations.

 


On successful completion you will be able to:
  • demonstrate a well- developed knowledge of the principles, concepts and techniques of a broad range of areas in analysis and applied mathematics, with significant depth in analysis and functional analysis.
  • demonstrate an understanding of the breadth of mathematics, the multi-disciplinary role of mathematics and the way it contributes the development in other related fields of study.
  • construct sustained logical, clearly presented and justified mathematical arguments incorporating deductive reasoning.
  • formulate and model practical and abstract problems in mathematical terms using a variety of methods drawn from analysis and functional analysis.
  • apply mathematical principles, concepts, techniques and technology efficiently to solve practical and abstract problems across a range of areas in analysis and functional analysis.
  • interpret mathematical information communicated in wide range of forms.

Final Exam

Assessment Type 1: Examination
Indicative Time on Task 2: 15 hours
Due: Exam period
Weighting: 50%

 

The final exam will cover all topics of the unit

 


On successful completion you will be able to:
  • demonstrate a well- developed knowledge of the principles, concepts and techniques of a broad range of areas in analysis and applied mathematics, with significant depth in analysis and functional analysis.
  • demonstrate an understanding of the breadth of mathematics, the multi-disciplinary role of mathematics and the way it contributes the development in other related fields of study.
  • construct sustained logical, clearly presented and justified mathematical arguments incorporating deductive reasoning.
  • formulate and model practical and abstract problems in mathematical terms using a variety of methods drawn from analysis and functional analysis.
  • apply mathematical principles, concepts, techniques and technology efficiently to solve practical and abstract problems across a range of areas in analysis and functional analysis.
  • interpret mathematical information communicated in wide range of forms.

1 If you need help with your assignment, please contact:

  • the academic teaching staff in your unit for guidance in understanding or completing this type of assessment
  • the Learning Skills Unit for academic skills support.

2 Indicative time-on-task is an estimate of the time required for completion of the assessment task and is subject to individual variation

Delivery and Resources

There are one 2-hour lecture each week and one 1-hour SGTA.  We refer to i-learn for the details of timetable. 

Lecture notes will be available on iLearn.

The following texts are suggested for reference only, and it is not essential to own copies:

    Lay:  Analysis with an introduction to proof

    Gordon:  Real Analysis, A First course

    Burkill: A First Course in Mathematical Analysis

    Burkill and Burkill: A Second Course in Mathematical Analysis

    Young: An Introduction to Hilbert Space

Unit Schedule

Week Topic Assessment Due
Real Analysis  
1 The real number system.  
2 Sequences.  
3 Series  
4 Continuity  
5 Differentiation  
6 Integration  
  Mid session Break
Functional Analysis  
7 Metric spaces, open and closed sets, limits and continuity Assignment 1
8 Open and closed sets, limits and continuity  
9 Connectedness, completeness, compactness, continuous functions with compact domains  
10 Normed vector spaces, Banach spaces iLearn Test
11 Inner product spaces, Hilbert spaces  
12 Linear functionals, dual space Assignment 2
13 Revision  

Policies and Procedures

Macquarie University policies and procedures are accessible from Policy Central (https://staff.mq.edu.au/work/strategy-planning-and-governance/university-policies-and-procedures/policy-central). Students should be aware of the following policies in particular with regard to Learning and Teaching:

Students seeking more policy resources can visit the Student Policy Gateway (https://students.mq.edu.au/support/study/student-policy-gateway). It is your one-stop-shop for the key policies you need to know about throughout your undergraduate student journey.

If you would like to see all the policies relevant to Learning and Teaching visit Policy Central (https://staff.mq.edu.au/work/strategy-planning-and-governance/university-policies-and-procedures/policy-central).

Student Code of Conduct

Macquarie University students have a responsibility to be familiar with the Student Code of Conduct: https://students.mq.edu.au/admin/other-resources/student-conduct

Results

Results published on platform other than eStudent, (eg. iLearn, Coursera etc.) or released directly by your Unit Convenor, are not confirmed as they are subject to final approval by the University. Once approved, final results will be sent to your student email address and will be made available in eStudent. For more information visit ask.mq.edu.au or if you are a Global MBA student contact globalmba.support@mq.edu.au

Student Support

Macquarie University provides a range of support services for students. For details, visit http://students.mq.edu.au/support/

Learning Skills

Learning Skills (mq.edu.au/learningskills) provides academic writing resources and study strategies to help you improve your marks and take control of your study.

The Library provides online and face to face support to help you find and use relevant information resources. 

Student Enquiry Service

For all student enquiries, visit Student Connect at ask.mq.edu.au

If you are a Global MBA student contact globalmba.support@mq.edu.au

Equity Support

Students with a disability are encouraged to contact the Disability Service who can provide appropriate help with any issues that arise during their studies.

IT Help

For help with University computer systems and technology, visit http://www.mq.edu.au/about_us/offices_and_units/information_technology/help/

When using the University's IT, you must adhere to the Acceptable Use of IT Resources Policy. The policy applies to all who connect to the MQ network including students.

Changes since First Published

Date Description
13/07/2021 updated unit schedule