Department of Mathematics Syllabus
This syllabus is advisory only. For details on a particular instructor's syllabus (including books), consult the instructor's course page. For a list of what courses are being taught each quarter, refer to the Courses page.
Suggested Schedule:
Lecture(s) 
Sections 
Comments/Topics 
3 
Fundamental definitions: Affine sets, convex set, convex hull. Examples. 

3 
Caratheodory’s theorem, Radon’s theorem. 

3 
Helly’s theorem and applications. 

3 
Separating and supporting hyperplanes. Faces, extreme points. 

3 
Sets of constant width, diameter Borsuk’s problem. 

3 
Polyhedra and Polytopes. Examples and main operations (e.g. Projections, Schlegel Diagrams). 

3 
Graphs of polytopes, Euler’s formula. Coloring problems. 

3 
Duality and Polarity. 

3 
Convex bodies and Lattices. Minkowski’s first theorem, Blichfeldt’s theorem. 
Additional Notes: