The Recommended Exercises are for further practice only. They will help you better understand the key concepts of the course. You should work on the problems associated to each lecture before the following lecture. The handin assignments will be posted on Virtual Campus.
Date  Section  Topics  Recommended Exercises for Further Practice 
Sep 8  Problems and paradoxes.  
Sep 12  Notes, 1.1  Euclidean space, Euclid's postulates, analytic geometry.  1.3.2 
Sep 15  Notes, 1.2–1.6  Definition of an isometry, congruence, reflections, translations, rotations.  1.2.1, 1.2.2, 1.4.1, 1.5.1, 1.6.1 
Sep 19  Notes  Basic properties of isometries, orientation.  1.6.2 
Sep 22  Notes  Complex numbers and isometries of R^{2}.
isoperimetric inequality.
First Assignment Due 

Sep 26  Notes, 1.7  Applications of isometries, isoperimetric inequality.  1.7.1, 1.7.2, 1.7.3, 1.7.4, 1.7.5, 1.7.6 
Sep 29  Notes  Formula for a reflection in R^{n}, quaternions.  
Oct 3  Notes  Quaternions and rotations in R^{3}.  1.10.1. 
Oct 6  1.10 
Isometries in R^{2}.
Second Assignment Due 

Oct 10  Notes  Isometries in R^{2}, Cartan–Dieudonné Theorem.  
Oct 13  1.8  The parallel postulate and its consequences, similar triangles.  1.8.5, 1.8.6, 1.8.7, 1.8.8, 1.8.9. 
Oct 17  1.8, 1.9  Congruence of triangles, angles on an arc. Third Assignment Due 
1.9.1, 1.9.3, 1.9.6, 1.9.7, 1.9.9, 1.9.11, 1.9.12. 
Oct 20  Notes  Further examples of Euclidean geometry, isometries of R^{n}.  
Oct 24  Study Week  
Oct 27  Study Week  
Oct 31  Notes  Platonic solids, Euler's Theorem, classification of Platonic solids.  
Nov 3  Midterm Exam  
Nov 7  2.1–2.2  Geodesics on a surface, geodesics on a sphere.  
Nov 10  Notes.  Isometries of a sphere.  
Nov 14  2.3–2.4  Spherical triangles, area of a spherical triangle.  2.4.1. 
Nov 17  2.9  Mapmaking and projections. Fourth Assignment Due 

Nov 21  2.9, 4.1–4.2  Stereographic projection, projective geometry, perspective, the projective space P^{n}. COURSE EVALUATIONS 
2.9.1, 2.9.2, 2.9.3. 
Nov 24  4.3–4.4  Desargues' Theorem, crossratio.  
Nov 28  Notes  Crossratio, circle inversion.  
Dec 1  Notes.  The upper halfplane model of hyperbolic geometry. Fifth Assignment Due 

Dec 5  Notes.  Stereographic projection and inversion, the Poicaré disk model of hyperbolic geometry, false perspectives and optical illusion. 