Simon Fraser University
Engaging the World

Course Outlines

Spring 2022 - MATH 443 D100

Combinatorial Theory (3)

Class Number: 3305

Delivery Method: In Person

Overview

  • Course Times + Location:

    Jan 10 – Apr 11, 2022: Mon, Wed, Fri, 10:30–11:20 a.m.
    Burnaby

  • Exam Times + Location:

    Apr 21, 2022
    Thu, 8:30–11:30 a.m.
    Burnaby

  • Prerequisites:

    MATH 340 or 332, with a minimum grade of C- and MACM 201 with a grade of at least 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

Registrar Notes:

ACADEMIC INTEGRITY: YOUR WORK, YOUR SUCCESS

SFU’s Academic Integrity web site 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

TEACHING AT SFU IN SPRING 2022

Teaching at SFU in spring 2022 will involve primarily in-person instruction, with safety plans in place.  Some courses will still be offered through remote methods, and if so, this will be clearly identified in the schedule of classes.  You will also know at enrollment whether remote course components will be “live” (synchronous) or at your own pace (asynchronous).

Enrolling in a course acknowledges that you are able to attend in whatever format is required.  You should not enroll in a course that is in-person if you are not able to return to campus, and should be aware that remote study may entail different modes of learning, interaction with your instructor, and ways of getting feedback on your work than may be the case for in-person classes.

Students with hidden or visible disabilities who may need class or exam accommodations, including in the context of remote learning, are advised to register with the SFU Centre for Accessible Learning (caladmin@sfu.ca or 778-782-3112) as early as possible in order to prepare for the spring 2022 term.