189-348A Topics in Geometry

Olga Kharlampovich
MWF 12:30

• Symmetry and groups, Plane ornaments
  1. Isometries,
  2. Rosette groups,
  3. Strip patterns,
  4. Wallpatterns,
  5. Finite groups,
  6. Cayley Diagrams,
  7. Symmetry in the real world
• Euclidean and non-Euclidean geometry
  1. History
  2. Plane Euclidean geometry,
  3. Affine transformations in the Euclidean plane,
  4. Finite groups of isometries of E²,
  5. Geometry on the sphere,
  6. The projective plane P²,
  7. The hyperbolic plane
  8. Minkowski Space-Time

Textbooks:
L. Fejes Toth, Regular figures, Pergamon Press, 1964.
D.W. Farmer, Groups and symmetry, A guide to discovering mathematics,
AMS, Mathematical world, Vol. 5, 1996
P.J. Ryan, Euclidean and non-Euclidean geometry, An analytic approach,
Cambridge university press, 1997.
Prerequisites A semester of linear algebra or (and) some familiarity with
vectors and matrices. All the necessary background material will be included
in the lectures.
Evaluation 20% Midterm or Project+ 15% Assignments +65% Final
Office hours MWF 1:30{2:30, Burn. 926 , tel. 398-3808,
e-mail: olga@math.mcgill.ca
homepage: www.math.mcgill.ca/~olga