Simon Fraser University
Engaging the World

Course Outlines

Summer 2025 - MATH 894 G200

Reading (2)

Entropy & Diversity: The Axiomatic Approach

Class Number: 5001

Delivery Method: In Person

Overview

  • Course Times + Location:

    Location: TBA

  • Instructor:

    Caroline Colijn

  • Instructor:

    Paul Tupper

  • Instructor:

    Caroline Colijn
    ccolijn@sfu.ca

  • Instructor:

    Paul Tupper
    pft3@sfu.ca
    1 778 782-8636

Description

COURSE DETAILS:

Topic: Entropy and Diversity: The Axiomatic Approach

Topic list: 

  • information theory and its relationship to diversity measures and functions: Shannon entropy, relative entropy; deformations of Shannon entropy
  • the use of functional equations to describe classes of diversity definitions and characterize their properties.
  • the use of the axiomatic method to address the challenge of defining biological diversity measures
  • applications to conservation and infectious disease

Enrollment: Instructor’s permission required.

COURSE-LEVEL EDUCATIONAL GOALS:

Goals

  1. We will read Chapters 1-9 (or selections, if this is infeasible) of Tom Leinster’s book, Entropy and Diversity: The Axiomatic Approach. This book brings a mathematical rigour to the debate about how to formally define concepts of diversity that reflect both phylogenetic relatedness and relative abundance. The question 'what is diversity?' has surprising mathematical depth. This book spans a wide breadth of mathematics, from functional equations to geometric measure theory, from probability theory to number theory.
  2. We will apply distinct definitions of diversity to salmon populations, with conservation applications, and to genomic data for the bacteria Streptococcus pneumoniae.

Assessment overview:
The student will present the content of the chapter to the professors (Paul Tupper, Caroline Colijn), weekly.
Assessment will be based on (1) mathematical understanding (40%) (2) successful solution of exercises from Leinster’s book (40%) (3) presentation clarity (20%).

Grading

  • Mathematical Understanding 40%
  • Successful solution of exercises from Leinster'sbook 40%
  • Presentation Clarity 20%

NOTES:

Students will prepare and present each lecture, and distribute notes beforehand. Students will be evaluated on preparation, clarity and understanding of the material.

REQUIREMENTS:

Prerequisites:
A graduate-level or upper-undergraduate-level background in information theory, biological diversity measures, data science, and mathematical biology.
Possible audience: Graduate only.

Materials

REQUIRED READING:

Entropy and Diversity: The Axiomatic Approach

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.

Graduate Studies Notes:

Important dates and deadlines for graduate students are found here: http://www.sfu.ca/dean-gradstudies/current/important_dates/guidelines.html. The deadline to drop a course with a 100% refund is the end of week 2. The deadline to drop with no notation on your transcript is the end of week 3.

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.