Course Information

Instructor: Prof. Jesús A. De Loera.


Phone: (530)-554 9702

Meetings: MWF 10:00-10:50 AM, Physics 140.

Office hours: Wednesday 4:10pm-5:00pm and Friday 11:10pm-12:00pm or by appointment. My office is 3228 Math. Sciences Building.
NOTE: Jan 22nd, 29th, March 5th, Office hours will be changed to other times.

The TA for this class is Mr. Steven Lu, his office hours are 11:00-11:50am on Wednesdays at 3125 MSB (
We will be glad to help you with any questions or problems you may have.

Text and References: There is not a single text for this class, but there are several notes and reference material for the class.
The key material can be downloaded here for free! ( You are kindly asked not to waste paper if you intend to print them.)

Description: This course is an undergraduate-level introduction to the geometry of convex sets and their applications. Convex sets are perhaps the simplest geometric objects, examples include balls, cubes, ellipses, polyhedra, and linear spaces. Their simplicity makes them very important and we will look at the structure of convex sets and how to answer fundamental questions about them, such as: What is their volume? What is the smallest convex set that contains another set? How wide is the convex set? etc. We will also care about computing with convex sets and functions. The nice feature of this topic is that, with very little, one can construct beautiful deep mathematics. We will have a lot of fun!

Topics to be covered in 114 (breakup of topics is approximate):


(a) Convex sets, Basic linear geometry in Euclidean space, (b) Linear, Affine, and Convex Combinations & Hulls. (c) Families of Convex bodies: Balls and Ellipsoids, Polytopes and Polyhedra (d) Supporting hyperplanes and Separation, Width and diameter. (e) Faces and Extreme points, Krein-Milman theorem. (f) Caratheodory, Helly and Radon (their famous theorems)


(a) Polarity and Duality. (b) Structure of Polyhedra and Polytopes (Farkas, Weyl-Minkowski's theorem) (c) Main constructions and Visualization (e.g. Prisms, Pyramids, Projections, Schlegel Diagrams, Nets). (d) Combinatorial & Computational Issues: Faces, Euler's formula, Graphs of polytopes (Steinitz, Balinski's theorem).