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.

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	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%

All dates are given in Sydney time.

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.

Geometry
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
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.

These notes are also available as one book from Kopystop, 36 Mountain Street, Broadway.

See the course Canvas webpage for additional textbook references.

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
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	Tutorial 11 questions Tutorial 11 solutions	Topology Assignment - solutions Topology Quiz (10%) 12:00 November 17

Timetable

Show timetable / Hide timetable.

About the School

Research

Undergraduate Study

For Prospective Students

Internal Pages