Instructor: Prof. Jesús A. De Loera.

email: jadeloera@ucdavis.edu there write if you have math questions,
but for administrative questions please use CANVAS.

http://www.math.ucdavis.edu/~deloera/TEACHING/MATH114

Phone: (530)-754 0502

Class Meetings: MWF 2:10-3:00 PM, Olson Hall 141.

Office hours: Wednesday 3:10pm-4:00pm or by appointment (it can also be zoom in the evening).
My office is at 1013 Physical and Data Sciences Building (between physics and chemistry).

The TA for this class is Aidan Epperly, his office hours are TBD
his email is (acepperly@ucdavis.edu).
We both will be glad to help you with any questions or problems you may have.

Text and References: There is not a single published 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.)

• The first four weeks the class will be based on the book Theory of Convex Sets by G.D. Chakerian and J.R. Sangwine-Yager.
  
• The second half of the course will be based on my own notes ``Actually doing it: A hands on introduction to Convex Polyhedra''
• The lectures will be recorded and available in CANVAS.

• Later in the class will also use software for manipulating polyhedra in the computer.
  For now, let me just mention Polymake I wrote a short introduction for you.

  Additional published book references include:

• N.Lauritzen, Undergraduate Convexity: From Fourier and Motzkin to Kuhn and Tucker, World Scientific, 2013.
• S. Lay, Convex sets and their applications, Dover, New York, 2007.
• I.M. Yaglom and V.G.Boltyansky, Convex Figures, Holt, Rinehart and Winston, 1961
• D. Barnette, Map coloring, polyhedra, and the four-color problem. The Dolciani Mathematical Expositions, 8. Math. Assoc. of America, Washington, D.C., 1983
• G. M. Ziegler, Lectures on Polytopes, Springer Verlag, New York, 1995.

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):

(FIRST MIDTERM TOPICS)

(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 (the 3 famous theorems) (g) Approximating convex bodies with polytopes. (h) Polarity and duality

(SECOND MIDTERM TOPICS)

(a) Structure of Polyhedra and Polytopes (Farkas, Weyl-Minkowski's theorem) (b) 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), diameter. (e) Metric Issues: Volumes and lattice points, widths. (f) Convex hulls, Simplex method and Reverse-search.

GRADING

• There are 100 points possible in the course.
• There will be two midterms exams , each exam will count 30 points.
  The midterm exams will be Monday April 28th and Wednesday May 28th.

  Each midterm exam will be take-home. Writing quality is particularly expected in the take-home exam.

  The written take-home response must be crafted in LaTEX. Here I provide you with a sample document in LaTEX.

• There will be a comprehensive final exam worth 40 points will take place June 12, 2025 at 3:30 pm
• Homework problems will be assigned continously (even during class), but they will not be collected,
  but homework problems will be used in questions in the take-home portion of each midterm.

  All Homework is posted online here:

  HOMEWORK PROBLEMS (first midterm)

  HOMEWORK PROBLEMS (second midterm)

• After collecting all the scores, I will assign grades based on the statistical information of the points obtained by all students
  I compute the mean, standard deviation, etc. and set letter grades according with those numbers. I will handle all grades via CANVAS' grade system.

• My teaching philosophy is very simple: Whoever does the work does the learning. I lecture and discuss things with you as most professors, but it is only through your work that YOU learn. I think of the course as we are climbing a mountain. I cannot carry you there, you have to put great personal effort to reach the summit of knowledge and wisdom. I serve as your personal tour guide, trying to guide you through the safest route to the summit. I do not want anybody to fall, but ultimately it is your responsability and dedication that leads to your success.
• For the above reason:
  • You will be tested via exams
  • You are expected to work hard outside the classroom solving homework exercises, reading, video watching outside of class, thinking about the theorems, etc.

    I estimate a minimum of 3 hours work at home per lecture.

  • Math is not an spectator sport, you engage! Thus I expect you to participate in class discussion, ask questions freely.
  • It is very easy to fall behind. Regular academic is much better than bursts of activity followed by inactivity.

• Basic real analysis (MAT 127A) and linear algebra (22A) or equivalent preparation are pre-requisites. If in doubt, please ask me.
• I am here to help you, I love teaching this subject and I sincerely hope you enjoy the course!



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Last modified 03-31-2025