Students
MATH3900 – Geometry and Topology
2021 – Session 1, Special circumstances
Notice
As part of Phase 3 of our return to campus plan, most units will now run tutorials, seminars and other small group activities on campus, and most will keep an online version available to those students unable to return or those who choose to continue their studies online.
To check the availability of face-to-face and online activities for your unit, please go to timetable viewer. To check detailed information on unit assessments visit your unit's iLearn space or consult your unit convenor.
General Information
Download as PDF
| Unit convenor and teaching staff |
Unit convenor and teaching staff
Lecturer
Xuan Duong
Contact via E-mail
12 Wally's Walk, Room 729
Please refer to iLearn
Lecturer
Ross Moore
Contact via E-mail
12 Wally's Walk, Room 734
Please refer to iLearn
Christine Hale
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|---|---|
| Credit points |
Credit points
10
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| Prerequisites |
Prerequisites
130cp including MATH2010 or MATH235
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| Corequisites |
Corequisites
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| Co-badged status |
Co-badged status
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| Unit description |
Unit description
This unit is designed to widen geometric intuition and horizons by studying topics such as projective geometry, topology of surfaces, graph theory, map colouring, ruler-and-compass constructions, knot theory and isoperimetric problems.
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Important Academic Dates
Information about important academic dates including deadlines for withdrawing from units are available at https://www.mq.edu.au/study/calendar-of-dates
Learning Outcomes
On successful completion of this unit, you will be able to:
- ULO1: Formulate and model practical and abstract problems in mathematical terms using methods from geometry and topology
- ULO2: Apply concepts and techniques of geometry and topology to practical and abstract problems
- ULO3: Use axioms and definitions correctly within a mathematical argument
- ULO4: Apply the mathematical notions of invariant and isomorphism in order to discriminate and classify geometric objects
General Assessment Information
Assessment consists of Assignment 1 with weight 15% due on Wed 31 Mar (week 6), Assignment 2 with weight 15% due on Wed 19 May (week 11), Class test (online) with weight 15% on Mon 3 May (week 9), and Final Exam with weight 55%.
LATE SUBMISSION OF WORK: All assessment tasks must be submitted by the official due date and time. In the case of a late submission for a non-timed assessment (e.g. an assignment), if special consideration has NOT been granted, 20% of the earned mark will be deducted for each 24-hour period (or part thereof) that the submission is late for the first 2 days (including weekends and/or public holidays). For example, if an assignment is submitted 25 hours late, its mark will attract a penalty equal to 40% of the earned mark. After 2 days (including weekends and public holidays) a mark of 0% will be awarded. Timed assessment tasks (e.g. tests, examinations) do not fall under these rules.
Assessment Tasks
| Name | Weighting | Hurdle | Due |
|---|---|---|---|
| Assignment 1 | 15% | No | Week 6 |
| Class Test (Online) | 15% | No | Week 9 |
| Assignment 2 | 15% | No | Week 11 |
| Final Exam | 55% | No | Formal University Examination Period |
Assignment 1
Assessment Type 1: Problem set
Indicative Time on Task 2: 5 hours
Due: Week 6
Weighting: 15%
The assignments will include questions from both the topology and the geometry component of the unit.
On successful completion you will be able to:
- Formulate and model practical and abstract problems in mathematical terms using methods from geometry and topology
- Apply concepts and techniques of geometry and topology to practical and abstract problems
- Use axioms and definitions correctly within a mathematical argument
- Apply the mathematical notions of invariant and isomorphism in order to discriminate and classify geometric objects
Class Test (Online)
Assessment Type 1: Quiz/Test
Indicative Time on Task 2: 6 hours
Due: Week 9
Weighting: 15%
This will be an online test and cover both the geometry and the topology components of the unit.
On successful completion you will be able to:
- Formulate and model practical and abstract problems in mathematical terms using methods from geometry and topology
- Apply concepts and techniques of geometry and topology to practical and abstract problems
- Use axioms and definitions correctly within a mathematical argument
- Apply the mathematical notions of invariant and isomorphism in order to discriminate and classify geometric objects
Assignment 2
Assessment Type 1: Problem set
Indicative Time on Task 2: 5 hours
Due: Week 11
Weighting: 15%
The assignments will include questions from both the topology and the geometry component of the unit.
On successful completion you will be able to:
- Formulate and model practical and abstract problems in mathematical terms using methods from geometry and topology
- Apply concepts and techniques of geometry and topology to practical and abstract problems
- Use axioms and definitions correctly within a mathematical argument
- Apply the mathematical notions of invariant and isomorphism in order to discriminate and classify geometric objects
Final Exam
Assessment Type 1: Examination
Indicative Time on Task 2: 12 hours
Due: Formal University Examination Period
Weighting: 55%
This will be an invigilated exam that covers all aspects of the unit
On successful completion you will be able to:
- Formulate and model practical and abstract problems in mathematical terms using methods from geometry and topology
- Apply concepts and techniques of geometry and topology to practical and abstract problems
- Use axioms and definitions correctly within a mathematical argument
- Apply the mathematical notions of invariant and isomorphism in order to discriminate and classify geometric objects
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 Writing Centre 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
Classes
Lectures: you should attend two one-hour lectures each week.
SGTA: you should attend one one-hour SGTA each week (starting in week 2).
Required and Recommended Texts and/or Materials
Additional notes will be attached to the course's iLearn page. Also recommended for the course is the following online texts:
The Four Pillars of Geometry by John Stillwell
Chris Cooper's Note on Geometry at https://coopersnotes.net/third_geometry.html
Chris Cooper's Note on Topology at https://coopersnotes.net/third_topology.html
Technology Used and Required
Students are expected to have access to an internet enabled computer with a web browser and Adobe Reader software. There are computers for student use in the Library and MUSE.
Difficulties with your home computer or internet connection do not constitute a reasonable excuse for lateness of, or failure to submit, assessment tasks.
Unit Schedule
Week 1: Geometry: Euclidean geometry in the complex plane
Week 2: Topology: Topological spaces
Week 3: Geometry: Affine functions
Week 4: Topology: Surfaces and Surgery
Week 5: Geometry: Affine geometry
Week 6: Topology: Graphs on Surfaces, Graphs and Map Colouring
Week 7: Geometry: Projective geometry
Week 8: Topology: Knots and Links
Week 9: Geometry: Projective geometry; Test online
Week 10: Topology: The Alexander number of a Knot, The Alexander Group of a Knot
Week 11: Geometry: Constructions in geometry and number fields
Week 12: Topology: The Alexander Module, The Alexander Polynomial
Week 13: Revisions
Policies and Procedures
Macquarie University policies and procedures are accessible from Policy Central (https://policies.mq.edu.au). Students should be aware of the following policies in particular with regard to Learning and Teaching:
- Academic Appeals Policy
- Academic Integrity Policy
- Academic Progression Policy
- Assessment Policy
- Fitness to Practice Procedure
- Grade Appeal Policy
- Complaint Management Procedure for Students and Members of the Public
- Special Consideration Policy
Students seeking more policy resources can visit Student Policies (https://students.mq.edu.au/support/study/policies). It is your one-stop-shop for the key policies you need to know about throughout your undergraduate student journey.
To find other policies relating to Teaching and Learning, visit Policy Central (https://policies.mq.edu.au) and use the search tool.
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 Services and 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.
Student Enquiries
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
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 from Previous Offering
Last year, the topology part was delivered in the first 6 weeks, and geometry part in the second 6 weeks.
This year, topology and geometry parts will be delivered in alternate weeks, geometry in weeks 1,3,5,7, 9, 11
and topology in weeks 2,4,6,8,10 and 12.
In the last delivery, there was 4 hours of lecture each week. In this delivery, there are 2 hours of lecture and 1 hour of SGTA.
Changes since First Published
| Date | Description |
|---|---|
| 11/02/2021 | Updated Assessment and Delivery and Resources sections. |
Unit information based on version 2021.02 of the Handbook