MATH3061 Geometry and Topology
General Information
This page contains information on the senior mainstream unit of study MATH3061.
- Taught in Semester 2.
- Credit point value: 6.
- Classes per week: Three lectures and one tutorial.
- Lecturer(s): Yusra Naqvi and Bregje Pauwels .
Please refer to the Senior Mathematics and Statistics Handbook for all questions relating to Senior Mathematics and Statistics. In particular, see the handbook entry for MATH3061 for further information relating to MATH3061.
You may also view the description of MATH3061 and the description of in the University's course search database.
For enrolled students or other authorized people only, here is a link to the Canvas page for MATH3061.
Students have the right to appeal any academic decision made by the School or Faculty: see sydney.edu.au/students/academic-appeals.html.
Consultation
| Lecturer | Availability | Time | Office |
|---|---|---|---|
| Yusra Naqvi | Weeks 1 – 6 | Wednesday 9:00 – 10:00 | online |
| Bregje Pauwels | Weeks 7 – 12 | Wednesday 9:00 – 10:00 | online |
Assessment
| Date* | Description | Better mark | Weighting |
|---|---|---|---|
| 23:59 September 25 | Geometry Assignment | 10% | |
| 9:00 October 1 | Geometry Quiz | 10% | |
| 23:59 November 6 | Topology Assignment | 10% | |
| 12:00 November 17 | Topology Quiz | 10% | |
| Exam | 60% |
Check your marks EdStem Lecture recordings Online resources References
Enquiries
All enquiries about this unit of study should be directed to MATH3061@sydney.edu.au. Any mathematical questions sent to this email address will be redirected to the EdStem forum (NOTE: to register for this course on EdStem you first need to do it through Canvas). Please give your name and SID when emailing us. We reserve the right not to reply to anonymous emails. We will use Canvas for assignment submission.
If you experience problems reading pdf files online, here are some useful tips.
Unit outline
Canvas webpage
The MATH3061 Canvas webpage contains details about consultations, assessment, textbooks, objectives, and learning outcomes for MATH3061.
This part of the course will explore geometric transformations and properties that are invariant under these transformations.
- Week 1
- Linear algebra review. The Euclidean plane. Transformations. Isometries.
- Week 2
- Transformation groups. Reflections. Fixed points. Rotations.
- Week 3
- Involutions. Glide-reflections. Classification of isometries. Parity.
- Week 4
- Symmetry groups. Affine transformations. Derivative of an isometry.
- Week 5
- The projective plane. Projective lines. Collineations.
- Week 6
- Conics. Classification of Conics.
Topology is the study of surfaces under continuous deformation. That is, we allow ourselves to stretch surfaces but not to tear them.
- Week 7
- Graphs, subdivision, sums of degrees = twice the number of edges, connectedness, circuits, trees.
- Week 8
- Disc, annulus, torus, Möbius band, Klein bottle, sphere, projective planes, homeomorphism, stereographic projection.
- Week 9
- Triangulated surfaces, Euler characteristic, invariance under subdivision, cutting, pasting, boundaries, orientation, edge equation.
- Week 10
- Classification of surfaces, genus, oriented closed surfaces in three dimensions, handles, crosscaps.
- Week 11
- Platonic surfaces. Graphs on surfaces: K5 is not planar. Map colouring: the five colour theorem, the Heawood estimate for maps on surfaces.
- Week 12
- Knots: Polygonals knots, knots diagrams, the unknot, trefoil knots, figure eight knots, knot colouring. Knot determinants, n-colourings, Seifert surfaces, and knot genus.
Textbook and references
Lecture notes will be published in the resource table below.
Supplementary notes for both parts of math3061 are available online:- Nigel O’Brian's Geometry lecture notes.
- Jonathan Hillman's Topology lecture notes.
See the course Canvas webpage for additional textbook references.
Further reading and resources (topology)
- Topological equivalence of a torus and a coffee cup
- The Klein bottle (YouTube video)
- Gluing a torus bottle (YouTube video)
- An Introduction to Topology, E. C. Zeeman
- Platonic solids (Wikipedia)
- The Four-Color Problem: Concept and Solution, Steven G. Krantz.
- The Rolfsen Knot Table
- Torus knots
- Seifert surface
Online resources
| Resources | Canvas | Lecture recordings | Ed discussion |
|---|
| Lectures | Tutorials | Assessment | |
|---|---|---|---|
| Week 1 24/8-28/8 |
Geometry 1A Geometry 1B Geometry 1C Geometry 1D |
No tutorial | |
| Week 2 31/8-4/9 |
Geometry 2A Geometry 2B Geometry 2C Geometry 2D Geometry 2E |
Tutorial 1 questions Tutorial 1 solutions |
|
| Week 3 7/9-11/9 |
Geometry 3A Geometry 3B Geometry 3C Geometry 3D Geometry 3E |
Tutorial 2 questions Tutorial 2 solutions |
|
| Week 4 14/9-18/9 |
Geometry 4A Geometry 4B Geometry 4C Geometry 4D Geometry 4E |
Tutorial 3 questions Tutorial 3 solutions |
Geometry Assignment - questions |
| Week 5 21/9-25/9 |
Geometry 5A Geometry 5B Geometry 5C Geometry 5D Geometry 5E |
Tutorial 4 questions Tutorial 4 solutions |
Geometry Assignment (10%) Due 23:59 September 25 |
| Week 6 28/9-2/10 |
Geometry 6A Geometry 6B Geometry 6C |
Tutorial 5 questions Tutorial 5 solutions |
Geometry Quiz (10%) 9:00 October 1 |
| Mid-semester break | |||
| Week 7 12/10-16/10 |
Topology 7A Topology 7B Topology 7C Topology 7D Topology 7E |
Tutorial 6 questions Tutorial 6 solutions |
Geometry Assignment - solutions |
| Week 8 19/10-23/10 |
Topology 8A Topology 8B Topology 8C Topology 8D Topology 8E |
Tutorial 7 questions Tutorial 7 solutions |
Geometry Quiz - solutions Topology Assignment - questions |
| Week 9 26/10-30/10 |
Topology 9A Topology 9B Topology 9C Topology 9D Topology 9E |
Tutorial 8 questions Tutorial 8 solutions |
|
| Week 10 2/11-6/11 |
Topology 10A Topology 10B Topology 10C Topology 10D Topology 10E |
Tutorial 9 questions Tutorial 9 solutions |
Topology Assignment (10%) Due 23:59 November 6 Topology Quiz - sample quiz |
| Week 11 9/11-13/11 |
Topology 11A Topology 11B Topology 11C Topology 11D Topology 11E |
Tutorial 10 questions Tutorial 10 solutions |
|
| Week 12 16/11-20/11 |
Topology 12A Topology 12B Topology 12C Topology 12D Topology 12E |
Tutorial 11 questions Tutorial 11 solutions |
Topology Assignment - solutions Topology Quiz (10%) 12:00 November 17 |
Timetable
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