Simon Fraser University
Engaging the World

Course Outlines

Spring 2025 - MATH 469 D100

Topics in Graphs and Trees in Biomathematics (3)

Class Number: 2789

Delivery Method: In Person

Overview

  • Course Times + Location:

    Jan 6 – Apr 9, 2025: Mon, Wed, Fri, 11:30 a.m.–12:20 p.m.
    Burnaby

  • Exam Times + Location:

    Apr 11, 2025
    Fri, 12:00–3:00 p.m.
    Burnaby

  • Prerequisites:

    One of MATH 343, MATH 345, MATH 360, with a minimum grade of C-. Strongly Recommended: Experience with a computing platform such as R, MATLAB, or Python.

Description

CALENDAR DESCRIPTION:

A survey of contemporary methods and applications of discrete mathematical models focusing on graphs, networks, and trees in evolutionary biology, ecology, and epidemiology. Using discrete models and integrating real data, students will focus on understanding, analyzing, and applying recent scientific literature. Course may be repeated for credit under a different topic.

COURSE DETAILS:

This course will give students an expanded repertoire for how mathematics can represent phenomena and data in a quantitative way: food webs, metabolic networks, social networks, evolutionary patterns (gene trees, species trees), and more. The course has a modular structure. This year, we will describe random graphs as models for social networks, and answer questions like: do you expect your friends to have more friends than you do? Why? How can we understand communities in social networks? How can we describe evolution using trees? We will cover counting trees and reasoning with trees and graphs. The course will introduce you to a useful toolkit in discrete mathematics and biomathematics. 


This course also connects to key skills needed in data science and computer science (for example working with tree and graph data structures). 

COURSE-LEVEL EDUCATIONAL GOALS:

Mastery of discrete mathematics tools and applications in biology: 

  • Learn to use graphs and trees to represent data, with biological applications

  • Develop reasoning skills about trees and graphs

  • Use computational methods to construct discrete representations of systems

  • Explore features of trees and graphs, interpret these and build reasoning about the system or data in question

Grading

  • Participation/attendance 2%
  • 4 homework assignments (7% each) 28%
  • Midterm exam 30%
  • Final exam 40%

NOTES:

Graduate students will do a project.

Materials

MATERIALS + SUPPLIES:

This course draws on several reading materials. These are not required but will be useful. 


Networks: An Introduction by Mark Newman
Phylogeny: Discrete and Random Processes in Evolution 

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

RELIGIOUS ACCOMMODATION

Students with a faith background who may need accommodations during the term are encouraged to assess their needs as soon as possible and review the Multifaith religious accommodations website. The page outlines ways they begin working toward an accommodation and ensure solutions can be reached in a timely fashion.