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/academicappeals.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.
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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. Glidereflections. 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: K_{5} 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, ncolourings, 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 FourColor 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 24/828/8 
Geometry 1A Geometry 1B Geometry 1C Geometry 1D 
No tutorial  
Week 2 31/84/9 
Geometry 2A Geometry 2B Geometry 2C Geometry 2D Geometry 2E 
Tutorial 1 questions Tutorial 1 solutions 

Week 3 7/911/9 
Geometry 3A Geometry 3B Geometry 3C Geometry 3D Geometry 3E 
Tutorial 2 questions Tutorial 2 solutions 

Week 4 14/918/9 
Geometry 4A Geometry 4B Geometry 4C Geometry 4D Geometry 4E 
Tutorial 3 questions Tutorial 3 solutions 
Geometry Assignment  questions 
Week 5 21/925/9 
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 28/92/10 
Geometry 6A Geometry 6B Geometry 6C 
Tutorial 5 questions Tutorial 5 solutions 
Geometry Quiz (10%) 9:00 October 1 
Midsemester break  
Week 7 12/1016/10 
Topology 7A Topology 7B Topology 7C Topology 7D Topology 7E 
Tutorial 6 questions Tutorial 6 solutions 
Geometry Assignment  solutions 
Week 8 19/1023/10 
Topology 8A Topology 8B Topology 8C Topology 8D Topology 8E 
Tutorial 7 questions Tutorial 7 solutions 
Geometry Quiz  solutions Topology Assignment  questions 
Week 9 26/1030/10 
Topology 9A Topology 9B Topology 9C Topology 9D Topology 9E 
Tutorial 8 questions Tutorial 8 solutions 

Week 10 2/116/11 
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 9/1113/11 
Topology 11A Topology 11B Topology 11C Topology 11D Topology 11E 
Tutorial 10 questions Tutorial 10 solutions 

Week 12 16/1120/11 
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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