Syllabus

Mathematical and Computational Models in Biology

Biol 452/Math452

Fall 2013

Introduction:

Welcome! This course will introduce methods for developing and analyzing mathematical models of biological systems. We will cover a range of mathematical techniques and explore examples from various biological fields. You will learn these techniques both through lectures and by developing models in a lab using Mathematica and MATLAB (which we will teach you!).

Instructors:

Ty Hedrick:Maria Servedio:

Biology Department Biology Department

Wilson G40A Wilson 236

e-mail: e-mail:

phone: 962-0757 phone: 843-2692

Office hours: Th, 2-3pm Office hours: Tues 11-12

If you are unable to come during office hours meetings can be scheduled by appointment.

Lecture:

T, Th 9:30-10:45, GSB 1378

Labs:

M, 3-5, GSB 1370

The labs will be used to reinforce ideas learned during the lectures and to give you experience writing programs to analyze biological problems. You will learn both Mathematica and MATLAB in the labs.

Obtaining Mathematica and MATLAB:

Students can obtain both Mathematica and MATLAB from Software Acquisitions using your Onyen. Both packages are free for students. Please make sure you have them loaded on your computer by the FIRST lab. For MATLAB, only the base package (no toolboxes) are required if you need to save space when installing the program.

Textbook:

The textbook (required), which is available in Student Stores, is:

A Biologist’s Guide to Mathematical Modeling in Ecology and Evolution

by S.P. Otto and T. Day, Princeton University Press, 2007.

Evaluation:

Grades will be determined in the following way:

Weekly quizzes: 20%

Lab: 25%

Group project: 20%

Midterm: 15%

Final exam: 20%

Quizzes: On 10 Thursdays we will start the class with one-question quizzes. We will let you know ahead of time when these quizzes will be. After the quizzes are returned you will have the option to correct any errors (explaining the logic of the correction) to earn back up to half of the missed points, at the discretion of the instructors. Graded quizzes will be handed back by the Tuesday after they are given, and corrections are due in class on Thursday, two days later. Late corrections will not be accepted.

Lab assignments: You will be assigned questions to address during the labs. Labs will be due on the following Monday at the lab meeting time (3pm); lab assignments turned in late without a prior-approved extensionwill incur a 50% penalty. The key for each lab assignment will be posted the Tuesday after it is due. You will grade your work using the key and turn the graded assignment in by the following Monday at 3pm. During grading you may explain your errors and provide corrections to earn back up to half of the missed points, at the discretion of the instructors. Graded labs returned late incur a 50% penalty and no corrections are allowed. If either the original or graded version of a lab is more than one week late you will receive no credit for that lab assignment.

Group projects: You will end the semester with a group project on a topic of your choice. This project will give you the opportunity to explore a biological question of interest in more depth. Groups will consist of 3-4 students, and will be formed towards the beginning of October (see Schedule). Brief abstracts describing the topics for your projects will be due three weeks later.

Your group project will be presented in two ways, in 1) in class presentations during the last week of class, and 2) write-up presentations of your project.

In this course, you will be working with a Graduate Research Consultant, Caitlin Stern, who will assist you in the research project. The GRC Program is sponsored by the Office for Undergraduate Research ( We encourage you to visit this website to see other ways that you might engage in research, scholarship and creative performance while you are at Carolina.

Course Schedule

Date / Topic / Reading / Lab
Aug 20, 22 / Introduction and how to construct a model / Ch. 1, 2 / No lab
Aug 27, 29 / Deriving models & graphical analysis I / Ch. 3 / Intro to MMA
Sept 3, 5 / Deriving models & graphical analysisII / Ch. 4 / No lab
Sept 10, 12 / Equilibria and stability – one variable I / Ch. 5 / MMA
Sept 17, 19 / Equilibria and stability – one variable II, transformations / Ch. 6 / Intro to MATLAB
Sept 24, 26 / Equilibria and stability analysis, linear models with multiple variables I
MIDTERM: Thurs, Sept. 26 / Ch. 7 / MMA
Oct 1, 3 / Equilibria and stability analysis, linear models with multiple variables II / MATLAB
Oct 8, 10 / Equilibria and stability analysis, linear models with multiple variables III, class structure
Projects – form groups / MATLAB
Oct 15 / Equilibria and stability analysis, nonlinear models with multiple variables I / Ch. 8 / MMA
Oct 22, 24 / Equilibria and stability analysis, nonlinear models with multiple variables II
Projects – meet with GRC / MATLAB
Oct 29, 31 / General solutions and transformations – models with multiple variables I
Projects – abstracts due / Ch. 9 / MMA
Nov 5, 7 / General solutions and transformations – models with multiple variables II / MATLAB
Nov 12, 14 / Probabilistic models
Projects – meet with GRC / Ch. 13 / MMA
Nov 19, 21 / Discrete stochastic models / Ch. 14 – 14.3 / Project workday
Nov 26 / Periodic behavior / Ch. 11-11.5 / Project workday
Dec 3 / Project presentations (projects due Dec. 4th, 5pm) / Project presentations
Dec 10 / FINAL (8am start time)