# Spring 2020 - MATH 743 G100

## Overview

• #### Course Times + Location:

Mo, We, Fr 10:30 AM – 11:20 AM
WMC 2830, Burnaby

• #### Exam Times + Location:

Apr 24, 2020
8:30 AM – 11:30 AM
AQ 5037, Burnaby

## Description

#### CALENDAR DESCRIPTION:

Design theory: Steiner triple systems, balanced incomplete block designs, latin squares, finite geometries. Enumeration: generating functions. Burnside's Lemma, Polya counting. Students with credit for MATH 443 may not take this course for further credit.

#### LEARNING OBJECTIVES:

- Successful students will master a collection techniques for enumerating combinatorial classes of objects with either recursive structure, or internal symmetry.

- Successful students will be able to identify combinatorial structure in mathematical objects from linear algebra and geometry, and they will possess strategies to exploit any underlying balance or symmetry.

- Successful students will be able to identify, and generate combinatorial design structures.

Course Details:

The modern world of combinatorics features a complicated web of amazing structures, many of which have deep connections to other subjects such as group theory, geometry, and algebra.  The goal of this course is to introduce some of these special structures, understand some of their properties, and make connections between them and to other areas of math.  Here is a taste of what we will discover:

• Systematic strategies for enumerating combinatorial classes, including Polya counting and generating functions
• Lattices and posets
• Combinatorial aspects of polytopes
• The projective line, Finite geometries, projective and affine.
• Steiner systems, block designs.

• Assignments (6 assignments, equally weighted) 30%
• Midterm 20%
• Final Exam 50%
• MATH 743 students will be assigned additional questions in the homework assignments and on the final exam.

## Materials

A Course in Combinatorics
2nd Edition
JH van Lint and RM Wilson
Cambridge
ISBN: 9780521006019