Students

MATH3900 – Geometry and Topology

2023 – Session 1, In person-scheduled-weekday, North Ryde

General Information

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Unit convenor and teaching staff Unit convenor and teaching staff
Frank Valckenborgh
frank.valckenborgh@mq.edu.au
Contact via email
12WW 613
Lecturer
Xuan Duong
xuan.duong@mq.edu.au
Contact via email
12WW 729
Credit points Credit points
10
Prerequisites Prerequisites
130cp including MATH2010 or MATH235
Corequisites Corequisites
Co-badged status Co-badged status
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.

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

Requirements to Pass this Unit

To pass this unit you must achieve a total mark equal to or greater than 50%.

Late Assessment Submission Penalty

Late assessments are not accepted in this unit unless a Special Consideration has been submitted and approved.

Special Consideration

The Special Consideration Policy aims to support students who have been impacted by short- term circumstances or events that are serious, unavoidable and significantly disruptive, and which may affect their performance in assessment.

Written Assessments/Quizzes/Tests: If you experience circumstances or events that affect your ability to complete the written assessments in this unit on time, please inform the convenor and submit a Special Consideration request through ask.mq.edu.au.

Assessment Tasks

Name Weighting Hurdle Due
Assignment 1 15% No Week 6
Class Test 15% No Week 9
Assignment 2 15% No Week 11
Final Exam 55% No Exam 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

Assessment Type 1: Quiz/Test
Indicative Time on Task 2: 6 hours
Due: Week 9
Weighting: 15%

 

This will be an invigilated test held in class 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: Exam 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 

We have two hours of lectures and one hour of SGTA per week.

Lectures: (beginning in Week 1) There is one two-hour lecture each week. 

SGTA: you should attend one one-hour SGTA each week (starting in week 1).

Required and Recommended Texts and/or Materials 

Additional notes will be attached to the course's iLearn page. 

The following textbook is useful as a supplementary resource, for additional questions and explanations. It is available from the Macquarie University library:

The Four Pillars of Geometry by John Stillwell 

Additional lecture notes are here:

Chris Cooper's Note on Geometry at https://coopersnotes.net/third_geometry%20vol%202.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. A 1-hour grace period is provided to students who experience a technical concern.

Communication

We will communicate with you via your university email or through announcements on iLearn. Queries to convenors can either be placed on the iLearn discussion board or sent to your lecturers from your university email address.

COVID Information

For the latest information on the University’s response to COVID-19, please refer to the Coro- navirus infection page on the Macquarie website: https://www.mq.edu.au/about/coronavirus- faqs. Remember to check this page regularly in case the information and requirements change during semester. If there are any changes to this unit in relation to COVID, these will be communicated via iLearn.

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

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:

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

Academic Integrity

At Macquarie, we believe academic integrity – honesty, respect, trust, responsibility, fairness and courage – is at the core of learning, teaching and research. We recognise that meeting the expectations required to complete your assessments can be challenging. So, we offer you a range of resources and services to help you reach your potential, including free online writing and maths support, academic skills development and wellbeing consultations.

Student Support

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

The Writing Centre

The Writing Centre provides resources to develop your English language proficiency, academic writing, and communication skills.

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

Student Services and Support

Macquarie University offers a range of Student Support Services including:

Student Enquiries

Got a question? Ask us via AskMQ, or contact Service Connect.

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.

Unit information based on version 2023.01R of the Handbook