An Introduction to Mathematical Modelling: Discrete Time and Probability

MATH 5350 3.00

AN INTRODUCTION TO MATHEMATICAL MODELLING: DISCRETE TIME AND PROBABILITY

M.A. for Teachers Program

Lecturer:Professor Neal Madras

Office: S616 Ross

e-mail:

Telephone: (416) 736-5250 ext. 33971

Web page:

Office hours:Following class, or by prior arrangement before class,or

1:15-2:15 Mondays, or 9:30-10:30 Thursdays.

I am also available (in person or by phone) by appointment on most days.

Lectures:Monday 6:00-9:00 in S130 Ross Building

Prerequisites:The essential prerequisites for the present course are undergraduate calculus and linear algebra. A basic knowledge of probability will be helpful but not required.

Text:There is a course kit on sale in the bookstore with excerpts from three texts and one monograph:

E.A. Bender, “An Introduction to Mathematical Modeling” (Dover, 1978)

F.R. Giordano, M.D. Weir, and W.P. Fox, “A First Course in Mathematical Modeling” (Third Edition) (Brooks/Cole, 2003)

D. Mooney and R. Swift, “A Course in Mathematical Modeling” (MAA, 1999)

T.C. Schelling, “Micromotives and Macrobehavior” (W.W. Norton, 1978).

Additional material will be distributed in class.

Grading:Homework :60%

Project/presentation:25%

Participation/labs:15%

Description:Mathematical models are used to describe real-world situations so that they can be studied mathematically (graphically, numerically, symbolically, etc.) Often there are several ways to model a given problem, and different models may or may not give different answers. This course examines issues regarding formulation, analysis, and interpretation of mathematical models, using examples from science, business, and other areas of application. Among the topics introduced will be scaling, probability, discrete dynamical systems, and simulation. Models will be investigated with and without technology.

Continued….

SUMMARY OF TOPICS:

Units, scaling, and dimensional analysis

Graphical models

Dynamical models in discrete time

Models with one variable or with several variables

Equilibrium and stability

Optimization

Discrete probability and Markov chains

Simulation

ADDITIONAL INFORMATION:

1. Some class time will spent on computer work in the Gauss Lab, S110 Ross. You will need a door access card if you wish to use the lab outside of class time; during class time, you will be able to enter the lab. More information will be forthcoming.
2. Important dates: see

gradstudies.yorku.ca/current-students/student-status/important-dates

1. More information about the projects will come soon.
2. Important information for students in all York courses is at

secretariat.info.yorku.ca/files/CourseInformationForStudentsAugust20121.pdf