MATH3061 Geometry and Topology
General Information
This page contains information on the Senior mainstream Unit of Study MATH3061 Geometry and Topology.
 Taught in Semester 2.
 Credit point value: 6.
 Classes per week: Three lectures and one tutorial.
 Lecturer(s): Nathan Brownlowe and Laurentiu Paunescu .
Please refer to the Senior Mathematics and Statistics Handbook for all questions relating to Senior Mathematics and Statistics. In particular, see the MATH3061 handbook entry for further information relating to MATH3061.
You may also view the description of MATH3061 in the central units of study database.
Students have the right to appeal any academic decision made by the School or Faculty. For further information, see the Science Faculty web site.
Enquries
All inquiries about this unit of study should be directed to
MATH3061@sydney.edu.au.
Information Sheet
The MATH3061 Information Sheet contains details of the lecturers and lecture times, consultation times, tutorials, assessment, textbooks, objectives, and learning outcomes for MATH3061.
If you experience problems reading pdf files online, here are some useful tips.
Check your marks Course outline Online resources References Timetable
Information about the exam
For general information about exams, and the exam timetable, please see the University's examinations web page.Please note that the questions for the geometry and topology sections of the course must be answered in separate booklets.
The exam is based on all the material covered in lectures, tutorials, assignments, and the quizzes. The best way to prepare for the exam is to read through and think about your lecture notes and then to try to solve as many questions as possible (without looking at the solutions) from the lectures, tutorials, and assignments. You might like to look at the 2013 MATH3061 exam. Here are the solutions to this exam:
Geometry Solutions Topology Solutions.
We recommend that you do not look at these solutions until you have first attempted to do all of the questions in the exam.In addition, here are the questions for the 2014 exam.
Course outline
The course will closely follow the "Geometry" lecture notes by O'Brian.
 Week 1
 Reading for Week 1: pages 1–29, but not the section on Symmetries. [The coordinate formula for a halfturn does not appear in this part of the O'Brian notes. FYI, the image of a point (x,y) under a halfturn about point P(p,q) is (2p−x,2q−y).]
 Week 2
 Reading for Week 2: pages 30–36. Handout on properties of rotations from lecture 6.
 Week 3
 Reading for Week 3: pages 37–40, omit Chapter 3, then pages 51–56.
 Week 4
 Reading for Week 4: pages 57–58 and pages 67–70 of Chapter 4, omit the remainder of Chapter 4 and all of Chapter 5, then pages 97–99.
 Week 5
 Reading for Week 5: pages 100–107.
 Week 6
 Reading for Week 6: page 113 to first half of page 121. Handout end of proof from the last Geometry lecture.
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.
 Week 13
 Knot determinants, ncolourings, Seifert surfaces, and knot genus.
Textbook and references
Lecture notes for both parts of MATH3061 are available for purchase as a book from Kopystop at 36 Mountain Street, Broadyway. See the course information sheet 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  Information sheet  Blackboard  Lecture recordings  Ed discussion  

Monday lecture  Wednesday lecture  Thursday lecture  Tutorials  Assessment  
Week 1 31/74/8 
Geometry 11  Geometry 12  Geometry 13  No tutorial  
Week 2 7/811/8 
Geometry 21  Geometry 22  Geometry 23  Tutorial 2 Solutions 2 

Week 3 14/818/8 
Geometry 31  Geometry 32  Geometry 33  Tutorial 3 Solutions 3 
Assignment 1  questions 
Week 4 21/825/8 
Geometry 41  Geometry 42  Geometry 43  Tutorial 4 Solutions 4 
Assignment 1 Due 24 August Quiz 1  sample A Quiz 1  sample B 
Week 5 28/81/9 
Geometry 51  Geometry 52  Geometry 53  Tutorial 5 Solutions 5 
Assignment 1  solutions 
Week 6 4/98/9 
Geometry 61  Geometry 62  Quiz 1  Tutorial 6 Solutions 6 
Quiz 1 9:00 AM, 7 September 
Week 7 11/915/9 
Geometry 71  USyd staff strike  Topology 73  Tutorial 7 Solutions 7 

Week 8 18/922/9 
Topology 81  Topology 82  Topology 83  Tutorial 8 Solutions 8 

Midsemester break  
Week 9 2/106/10 
Labour day public holiday  Topology 92  Topology 93  Tutorial 9 Solutions 9 
Assignment 2  questions 
Week 10 9/1013/10 
Topology 101  Topology 102  Topology 103  Tutorial 10 Solutions 10 

Week 11 16/1020/10 
Topology 111  Topology 112  Topology 113  Tutorial 11 Solutions 11 
Assignment 2 Due 19 October Quiz 2  sample Quiz 2  sample (solutions) 
Week 12 23/1027/10 
Topology 121  Topology 122  Topology 123  Tutorial 12 Solutions 12 
Assignment 2  solutions 
Week 13 30/103/11 
Topology 131  Topology 132  Quiz 2  Tutorial 13 Solutions 13 
Quiz 2 9:00 AM, 2 November Quiz 2 solutions 
MATH3061 students: please check that your marks for Geometry Assignment and Geometry Quiz have been recorded correctly by pressing the "Check marks" button.
Please note that any corrections to Geometry Assignment marks must be made by Friday, Sep 22.
Please note that any corrections to Geometry Quiz marks must be made by Friday, Sep 22.
Timetable
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