**Jozsef Solymosi**

*Office: MATH 220*

**MATH 309 Section 201**

Term II, 2016-17

** **

**Topics in
Geometry**

** **

**Prerequisite:** One of MATH 152, MATH 221, MATH 223 and
one of MATH 220, MATH 226, CPSC 121. ** Specifically, it will be assumed
that students are familiar with basic techniques of mathematical proof and
reasoning such as induction and proof by contradiction.** Students
will be expected to write logically correct and mathematically coherent proofs
as part of homework and examinations.

** **

**The course syllabus will be as follows:**

** **

_ **EulerÕs formula****. **Convexity,** **Graphs,
Trees, Convex
Polyhedron, Planar
Graphs.** **

_ **Planar Graphs****. **Drawings, Colouring, Structure, KuratowskiÕs
Theorem.

_ **Geometric Graphs. **Drawings, Intersections,
Crossings.

_ **Crossing Number****. **Basic Probability,
Upper and
Lower** **Bounds.

_ **Point-Line incidences.** Szemeredi-Trotter
Theorem (bounds on incidences)

_ **Metric problems in Discrete Geometry. **The
unit distances problem, distinct
distances.

** **

_ **Combinatorics of point-sets. **Erdos-Szekeres Theorem, Halving lines.

_ **Circle Packing. **Planar circle packing,
Lattice Packing, Sphere Packing. (Chapter 1. In **Combinatorial geometry **)

** **

_ **Geometry of Numbers.** PickÕs Theorem,** **MinkowskiÕs Theorem, applications. (Chapter 1. In **Combinatorial geometry **)

Course notes (relevant notes from the web) will be provided after
lectures. There are two advanced books which cover most of the topics of the
course.

_ **Lectures on discrete
geometry**** / Jiri Matousek.**

_ **Combinatorial geometry ****[electronic
resource via UBC Library] / J‡nos Pach, Pankaj K. Agarwal.**

**Evaluation: **There will be two midterm exams and
one final exam, as well as weekly homework assignments. Homework will be
assigned on Thursdays, and due the following Thursday in class. Late homework
will not be accepted.

** **

** **

The **course mark **will be computed as follows:

Final Exam: 50 percent

Midterm Exams: 20 percent x 2 = 40 percent

Homework: 10 percent

You are required to be present at all examinations. No makeup
tests will be given. Non-attendance at an exam will result in a mark of zero
being recorded.

**Midterm exam
dates: Feb 16 and Mar 16.**

Office hours: Tuesdays 11:00-12:00 or by appointments (MATH 220)

HW #4
Due date: February 14.

HW #5
Due date: March 14.

HW #6
Due date: April 6.

Practice
questions (with hints) We are going to discuss the problems in class in
February 14.

HW
#4 solutions (for selected problems)

First
midterm (with solutions)

Second
midterm (with solutions)