MATH 3MB3 – Introduction to Modelling

MATH 3MB3 – Introduction to Modelling

2024 Winter Term

Overview

This course serves as an introduction to mathematical modelling, where students will learn to translate complex, real-world systems into the language of mathematics in order to perform careful analyses and draw useful conclusions. Students will be taught to construct mathematical models, critically assess their assumptions and results, recognize model limitations, and clearly communicate their implications for real-world applications. Students will also gain experience programming in R to simulate models using computational methods, create informative data visualizations, and conduct reproducible research.

Course Description

MATH 3MB3 - Introduction to Modelling 3 unit(s)

Introduction to computational modelling using software such as R or MATLAB. Analytical modelling using algebra and calculus. The development and analysis of models will be illustrated with examples selected from biology, medicine, chemistry, physics, economics, or other areas of natural or social sciences. This course includes a scientific communication component.
Three lectures, one lab (one hour); one term
Prerequisite(s): One of MATH 1AA3, 1LT3, 1XX3, ARTSSCI 1D06 A/B, ISCI 1A24 A/B; and one of MATH 1B03, 1ZC3, 1ZZ5
Antirequisite(s): MATH 2E03

Course and Learning Objectives

Upon completion of this course, the student will be able to:

1. Identify a problem in a real-world setting and formulate a related research question suited to investigation with a mathematical model.

2. Construct a useful mathematical model that addresses a research question motivated by a real-world problem.

3. Analyze and simulate a mathematical model using analytical and computational methods.

4. Interpret model results, relating them back to the real-world application.

5. Identify model assumptions and describe how they induce limitations on the model’s application to the real world.

6. Clearly communicate across all of the above steps, in writing, orally, and using data visualizations where applicable.

Materials & Fees

Textbooks - Recommended

A. Sayama, Hiroki. Introduction to the Modeling and Analysis of Complex Systems. Published by Open
SUNY Textbooks, Milne Library, State University of New York at Geneseo, 2015. (Freely available online: https://milneopentextbooks.org/introduction-to-the-modeling-and-analysis-of-complex-systems/)

B. Douglas, Alex, et al. An Introduction to R. (Freely available online: https://intro2r.com/)

Software

We will be using R and RStudio for the computational aspects of this course, both of which are freely available. You can access this software on all computers found in on-campus computer labs. You may also download R and RStudio directly onto your own computers. More details on installation will be given in class.

Course Delivery

At this time, all lectures and labs have been scheduled to take place in person. In the event that course activities are moved to a virtual setting, lectures, labs, and office hours will take place on Zoom. To follow and participate in virtual course delivery, it is expected that you have reliable access to the following:

• A computer that meets performance requirements found here.

• An internet connection that is fast enough to stream video.

• Computer accessories that enable class participation, such as a microphone and speakers.

If course activities are moved to a virtual setting and the above requirements will not be met in your case, please contact [email protected] as soon as possible.  If you use assistive technology or believe that any of our platforms may be a barrier to participating in the course, please contact Student Accessibility Services ([email protected]) for support.

Course Webpage

The course webpage will be hosted on Avenue to Learn, and will feature important announcements, course content, and discussion boards. Students are expected to check the webpage regularly (at least weekly) for important course updates.

Assessments

Participation

Students will get the most out of this course through active participation. However, I don’t believe in measuring participation by how much is said in class. Instead, the participation grade will be tied to the weekly lab sessions (starting the week of January 15, 2024). Lab sessions will involve completing a lab activity and submitting each week’s lab activity through Avenue will get you credit for participating in that week of the course. There will be a total of 11 lab activities throughout the term. Your final participation grade will be calculated as: (number of lab activities completed)/11. If you complete at least 10 of the lab activities you will get full credit for participation, meaning you can miss one week throughout the course without it affecting your participation grade. More details of how to submit your lab activity will be given during the first lab.

Assignments

There will be three (3) assignments throughout the term. You are encouraged to collaborate with other students in the course on solving assignment problems, though each student must write up their own solutions independently. Copying with minor changes from solutions prepared by another person, publication, or website, with minor changes (e.g., using different symbols or a slightly different wording) and without proper attribution is plagiarism. Assignments will be submitted through Crowdmark and are tentatively scheduled as follows:

Tests

There will be two (2) tests throughout the term. The tests will be closed book, but students will be allowed to bring a cheat sheet of their own creation. More details, including specifics of the cheat sheet, will be discussed in class and posted on the course website closer to the date of the tests. Tests are tentatively scheduled as follows:

Final Project

The core of this course will be the Final Project, which will be completed in groups. Students will take on a modelling project from start to finish within a topic (from a list provided by the instructor): devising a research question, setting up a model to address it, analysing and simulating the model, presenting and interpreting the results, and assessing model limitations. The main submission will be a final written report and an oral presentation based on their project work at the end of the term. An emphasis will be placed on clear scientific communication; students are encouraged to access writing support in preparing their project submissions, and can do so through the Student Success Centre.