Mathematical Models of Population Growth
Revised: November 2006
Course Description
This is a seminar course open only to first year students. During the semester we will investigate various approaches and methods for modeling different types of populations using no more than high school-level mathematics. We'll consider both the quantitative and qualitative aspects of population dynamics, starting with simple population models and building towards systems of interacting populations or stochastic processes. Much of the course will be focused on interpreting situations, models, and results, and honing our basic scientific process skills (making an observation, forming a hypothesis, designing an experiment, interpreting results, revising the hypothesis, etc.). We will also spend a lot of time in the computer classroom, learning how to use a variety of software packages (for example: Excel, Vensim, MATLAB, Fathom) to assist us with the modeling process.
Objectives
1. To familiarized students with the fundamental concepts of mathematical modeling;
2. To develop students. analytical and interpretive skills, i.e. their ability to analyze a system both quantitatively and qualitatively and in turn make inferences about the situation being modeled;
3. To expose students to a variety of mathematical software in the framework of mathematical modeling;
4. To develop students' computational skills and savvy;
5. To expose students to applications of mathematics beyond the typical classroom setting.
Text
Mooney, Douglas and Randall Swift. A Course in Mathematical Modeling, The Mathematical Association of America, 1999.
Grading Procedure
Grading procedures and factors influencing course grade are left to the discretion of individual instructors, subject to general university policy. Commonly, the final grade will be based upon homework/labwork, in-class tests, a class journal, and a final project.
Attendance Policy
Attendance policy is left to the discretion of individual instructors, subject to general university policy.
Course Outline
As the textbook chosen for this class is considered supplemental, course topics may vary each semester. A general outline for this course could be:
-
Introduction to Mathematical Modeling (4 days)
o Discrete versus Continuous Methods
o Types of Change -
Difference Equation Models
o Deterministic Models (12 days)
+ Exponential Growth and Decay
+ Logistic Models
+ Equilibrium Values -
Stochastic Models (9 days)
+ Overview of Basic Statistics
+ Demographic versus Environmental Stochasticity -
Matrix Models (12 Days)
o Overview of Basic Matrix Algebra
o Leslie Matrices and Age-Structured Populations
o Interpretation and use of Eigenvalues
o Markov Chains and Transition Matrices - Metapopulations and Agent-Based Models (4 days)
-
Possible Additional Topics (4 days)
o Life Tables
o Capture-Recapture and Population Estimation
o Regression Models