Math 426 Mathematical Modeling in Biology
Fall 2009

Dr. Shandelle M. Henson
Professor of Mathematics

Course Information

• Bulletin Description: Theory and application of linear and nonlinear mathematical models of biological processes. Topics selected from discrete- and continuous-time deterministic and stochastic modeling, analytic solution techniques, linearization, bifurcations, chaos, computer simulation, model parameterization, and model validation.
• Credits: 3
• Prerequisites: Math 141 (Calculus I)
• Time and place: TR 2:00-3:15 HYH 133
• Office: HYH 126
• Phone: 471-3388
• Office Hours: TR 3:30-6:00 and by appointment
• E-mail address: henson@andrews.edu
• Course URL: http://www.andrews.edu/~henson; click on "current course information"
• Textbook: Mathematical Modeling in Biology, by Henson and Hayward. We will be using an updated draft of these notes. The chapters will be provided to you free as pdf files.
• Suggested Reference Books for those interested in further studies:
  • (More biological) Population Biology, by Alan Hastings
  • (More mathematical) Mathematical Models in Biology, by Leah Edelstein-Keshet
  • (Even more mathematical) Mathematical Models in Population Biology and Epidemiology, by Brauer and Castillo-Chavez
• Hardware:You need access to a computer than runs MS Windows. A laptop is ideal for this class, but not necessary.
• Software:You need MS Excel. You also need access to MatLab or one of its freeware clones. For example, you can buy the student version of MatLab, or you can use Octave (a freeware version of MatLab).
• Important Dates:
  
  • Wednesday, Sept 2: Last day to drop and add without fee or entry on record
  • Monday, Sept 7: Labor Day holiday
  • Monday-Tuesday, Oct 12-13: Fall Break
  • Tuesday, Nov 24: Last day to withdraw with W, or change credit to audit
  • Thursday, Dec 3: Last day of classes
  • Friday, Dec 4: Reading Day
  • Thursday, Dec 10: Final Exam 1:30 - 3:30 PM, HYH 111

Course Content

• Topics: This is a research methods class. The course will integrate biological data and mathematical theory. Topics covered will include (not necessarily in this order):
  • Modeling
    • The modeling cycle
    • Simplifying assumptions
    • Translation of assumptions into mathematics
    • Parameterization
    • Model selection
    • Model analysis
    • Validation / Test of predictions
    • Revision of assumptions
  • Deterministic Dynamic Models (discrete time and continuous time)
    • Linear
    • Nonlinear
    • Linearization (Fundamental Theorem of Stability, Hartman Grobman Theorem, etc)
    • Bifurcations
  • Stochastic Dynamic Models (NLAR)
  • Genetics models
  • Epistemology (philosophy of science)
• Satellite Goals
  • Learn to program in MatLab and Excel.
  • Learn to give research talks.
  • Learn to read research papers.
  • Understand the connections between data, mathematics, and statistics in scientific methodology.
  • Learn critical thinking.
  • Learn how to conduct interdisciplinary collaboration.
  • Understand and reflect on ethical considerations and honesty in science.

Class Policies

• Attendance: Required.
• Check your email: You are responsible for any information I send the class by email. Check your Andrews email account regularly.
• Respect for every member of the classroom community--for each student, each classmate, and for the professor--will be observed at all times. Respect for professor and peers includes things such as no cell phones, arriving on time, not talking at inappropriate times, not using a laptop during lecture unless instructed to do so, and not walking in and out of class during the lecture. Also, you should not use iPods, earbuds, bluetooth devices, etc. in class.
• Honor (academic honesty): This department fully upholds the University policy on academic honesty, and regards any dishonesty, including plagiarism, as a serious offense. Dishonesty will result in a score of "zero" on that assignment or exam, and may result in failure in the course and/or further disciplinary action by the University.
• Maturity and personal responsibility are essential in this class: I respect my students as adults, and I respect their choices. Each student must take responsibility for her/his success or lack thereof. For example, deadlines will not be extended.
• Make-ups: 1) No make-up homework for any reason. (Instead, you are allowed to drop two homework scores.) 2) Make-up midterms will be given only in documented circumstances of illness, death in the family, or other grave situations. You MUST contact me immediately. 3) The Final Exam must be taken at the time scheduled by the University. Check the "Important Dates" above, and mark it on your calendar. If you miss the Final Exam for a legitimate reason, you will have to take an Incomplete in the course. If you miss the Final Exam for an illegitimate reason (for example, because of airline arrangements to fly home for your brother's wedding), you will receive a "zero" on the Final Exam. Warn your relatives of this if they have a tendency to buy you airline tickets without consulting you on times, or if they are planning weddings, etc.
• Collaboration: In this class you should learn how to collaborate across disciplines. Thus, collaboration on homework/projects is encouraged as long as each student is intellectually involved and independently writes up his or her own solutions. There is no collaboration on exams.

Course Requirements and Grades

• Homework: Homework will be posted on the class web site. No late homework is accepted, but the lowest two homework scores are dropped.
• Exams: There will be two exams: a midterm and a final.
• Attendance and in-class participation is required, and is counted as part of your grade.
• Project and presentation: The research project and presentation are due Nov 13.
• Grades: A course percentage grade will be calculated from homework (20%), midterm exam (20%), final exam (20%), attendance and participation (20%), project and presentation (20%). I use the following "guaranteed minimum grade" scale: 93-100 A; 90-92 A-; 87-89 B+; 83-86 B; 80-82 B-; ... ; 60-69 D; 0-59 F. A grade of "I" is available only under the conditions stated in University policies.