# Mathematical Modelling (MATH 4090)

** Time and Place **

Winter 2019

MWF: 11:30-12:30

CB 120

** Starting Jan 23, Weds lectures are in the Gauss Lab. **

** Description **

This course will introduce the student to discrete, continuous and probabilistic modeling of problems from industry, finance and the life and physical sciences. The emphasis will be on the process of generating an appropriate model for the problem in question, so that the student can gradually develop intuition about the strengths and limits of modeling approaches. The student will complete a research project, developing and analyzing a model of a system of their choice.

** Syllabus: ** found here pdf file

** Lecture January 11 ** Class on Friday January 11 will be in Ross N619, the Mathematics & Statistics Control Lab. We will be studying random walks using Lego Mindstorm Robots.

** Project Presentations: TBA**

** Project information: ** Sample proposal and outline pdf file

** Project Rubric: ** Marking scheme pdf file

** Project Peer Evaluation Form - Presentations: ** Marking scheme pdf file

Possible topics: pdf file

Matlab refresher - Lab questions

** Homework Questions: ** pdf file

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Lab 1 - A man walks along a four-block stretch of Yonge St. If he is at corner 1, 2, or 3, then he walks to the left or right with equal probability. He continues until he reaches corner 4, which is a bar, or corner 0, which is his home. If he reaches either home or the bar, he stays there.

Questions:

What is the probability that the process will eventually reach an absorbing state?

What is the probability that the process will end up in a given absorbing state?

On average, how long will it take for the process to be absorbed?

On average, how many times will the process be in each transient state?

Extra notes: pdf file

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Lab 2 - Snakes and Ladders - Download the matlab code here doc file (Open the code in matlab and save it as a .m file.

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Lab 3 - Elevator Code - copy and paste into a Matlab script. Run the simulation before the lab on Wednesday and try to understand what it is doing.

doc file (Open the code in matlab and save it as a .m file.

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Lab 4 - discrete time dynamical systems pdf file, and some maple code maple code