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Department of Mathematics

Study Guide

MATH 300, 2006 -- Geometry & Topology


RossMoore-med.jpg ElenaVinogradova-med.jpg
* Elena Vinogradova
 email.gif, Office: E7A-418,
phone.gif 9850 8920
* Dr Ross Moore
  email.gif, Office: E7A-419,
phone.gif 9850 8955

Lecture Times

* Monday
9:00am in X5B-143, with Elena Vinogradova;
* Tuesday
9:00am in X5B-143, with Elena Vinogradova;
* Thursday
10:00am in E5A-116, with Ross Moore;
* Friday
10:00am in W5C-211, with Ross Moore.

Topics, Notes & Textbooks

* ``Geometry''
Lecture Notes for MATH300:
Projective Geometry, Perspectivities and Projectivities Symmetry.

* ``Topology''
Lecture Notes for MATH300:
Introduction, Topological Spaces, Surfaces, Surfaces and Surgery, Characterising Surfaces, Graphs on Surfaces, Graph and Map Colouring, Knots and Links, The Alexander Number, Finitely Generated Abelian Groups, The Face Group of a Knot, The Alexander Module, Enumerating Knots.


* Geometry
by DA Brannan, MF Esplen, J Gray.
published by Cambridge University Press.

Interesting Online Material

* Geometric Topology
Reference List
* Geometry
The Geometry Junkyard
* Geometry
The Geometry Center
* Knots
The KnotPlot Site

Week Monday Assessment Geometry Topology
1 27 Feb   Projective Geometry General Topological Concepts
2 6 Mar   The Collinearity Lemma and Desargues' Theorem
3 13 Mar   Duality, Pappus' Theorem Classification of Surfaces
4 20 Mar Finite Projective Planes
5 27 Mar Assign't G1 Perspectivities and projectivities
6 3 Apr Assign't T1 Cross-ratio and the fundamental theorem of projective geometry
7 10 April   Symmetry
Isometries, translations, etc.
Graphs & Maps on Surfaces
2-week break, incl. Easter: Apr 14 - Apr 30
8 1 May Assign't G2 Groups of symmetries, central symmetries Graph & Map Colouring
9 8 May Assign't T2 Frieze patterns, wall-paper patterns Knots & Links
10 15 May   Ruler & Compass Constructions The Alexander number, group and polynomial of knots & links
11 22 May   Basic constructions
12 29 May Assign't G3 The field of constructible numbers
13 5 June Assign't T3 Topics (if any) not completed in previous weeks; else Revision


There will be six (6) assignments, three (3) in Geometry (G1-G3) and three (3) in Topology (T1-T3), contributing 20% to your final mark. Assignments are due at 10pm on the Thursday of the relevant week. The final examination is of 3 hours duration and contribute 80% to your final mark.

* Assignment G1
Questions, Solutions.
* Assignment T1
Questions, Solutions.
* Assignment G2
Questions, Solutions.
* Assignment T2
Questions, Solutions.
* Assignment G3
Questions, Solutions.
* Assignment T3
Questions, Solutions.

Expected Participation

Students are expected to demonstrate their participation in this unit by submitting reasonable attempts to at least four (4) of the six (6) assignments.

Please contact one of the lecturers in case of difficulty over this. A note submitted through the Student Centre or a medical certificate will not exempt you from missing assignments. You may be asked instead to submit a late assignment.


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Copyright & Site information

Ross Moore 2006-12-18