### Syllabus

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 hand-in 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 R2. 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 Rn, quaternions. Oct 3 Notes Quaternions and rotations in R3. 1.10.1. Oct 6 1.10 Isometries in R2. Second Assignment Due Oct 10 Notes Isometries in R2, 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 Rn. 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 Pn.COURSE EVALUATIONS 2.9.1, 2.9.2, 2.9.3. Nov 24 4.3–4.4 Desargues' Theorem, cross-ratio. Nov 28 Notes Cross-ratio, circle inversion. Dec 1 Notes. The upper half-plane 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.