Simon Fraser University
Engaging the World

Course Outlines

Spring 2024 - MATH 443 D100

Combinatorial Theory (3)

Class Number: 3796

Delivery Method: In Person

Overview

  • Course Times + Location:

    Jan 8 – Apr 12, 2024: Mon, Wed, Fri, 10:30–11:20 a.m.
    Burnaby

  • Exam Times + Location:

    Apr 17, 2024
    Wed, 3:30–6:30 p.m.
    Burnaby

  • Prerequisites:

    MATH 340 with a minimum grade of C- and either MATH 343 with a minimum grade of C- or MACM 201 with a minimum grade of B+.

Description

CALENDAR DESCRIPTION:

Design theory: Steiner triple systems, balanced incomplete block designs, latin squares, finite geometries. Enumeration: generating functions. Burnside's Lemma, Polya counting. Quantitative.

COURSE DETAILS:

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
  • Combinatorial techniques to study integer partitions

Grading

  • Assignments (6 assignments, equally weighted) 30%
  • Midterm 20%
  • Project 20%
  • Final Exam 30%

Materials

RECOMMENDED READING:

Analytic Combinatorics: A Multidimensional Approach
Marni Mishna Chapman and Hall/CRC
ISBN: 9781138489769

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

REQUIRED READING NOTES:

Your personalized Course Material list, including digital and physical textbooks, are available through the SFU Bookstore website by simply entering your Computing ID at: shop.sfu.ca/course-materials/my-personalized-course-materials.

Registrar Notes:

ACADEMIC INTEGRITY: YOUR WORK, YOUR SUCCESS

SFU’s Academic Integrity website http://www.sfu.ca/students/academicintegrity.html is filled with information on what is meant by academic dishonesty, where you can find resources to help with your studies and the consequences of cheating. Check out the site for more information and videos that help explain the issues in plain English.

Each student is responsible for his or her conduct as it affects the university community. Academic dishonesty, in whatever form, is ultimately destructive of the values of the university. Furthermore, it is unfair and discouraging to the majority of students who pursue their studies honestly. Scholarly integrity is required of all members of the university. http://www.sfu.ca/policies/gazette/student/s10-01.html