Applications of Calculus in Medicine and Biology (Math 4)

Mathematical Biology (Math 27)
Spring 2012
Instructor: Professor Dorothy Wallace

Have you ever wondered why medical schools require calculus? Or why biology has recently been described as "the most mathematical science"?  Math 4/27 will show how real researchers in medicine and biology use mathematical models to predict change and design strategies for controlling epidemics, administering drugs, managing ecosystems, and other applications.  Using basic calculus and a free application, The Big Green Ordinary Differential Equation Machine, you can study a multitude of real situations.  We use a text book developed especially for this course, Situated Complexity, by yours truly, available at Wheelock Books.  At the Society for Mathematical Biology conference in July 2010 students from Math 4 and 27 presented three papers that began as projects in this course.  At SMB 2011 two students presented papers, one of which began as research in Math 4.  One student from Math 27 last year is currently continuing research begun in that class as a Presidential Scholar.

Math 4 is for students with one semester of calculus at least.   See the Biology Department web site for how this course fits into prerequisites for the Biology major.  The goal of Math 4 is to enable students to read critically and think about the research literature in medical and biological modeling with differential equations.  

Math 27 is for students with more mathematical background.  Math 22 or the equivalent is a required prerequisite for Math 27.  The goal of Math 27 is to enable students to conduct their own independent research projects in mathematical biology after completing the course, if they so desire.   This course prepares you to do more research in a senior thesis, Presidential Scholar, Neukom intern or for course credit via Math 87.  Math 27 students are encouraged to become familiar with Matlab if they so desire.

Both courses meet in the same room at the same time.  The difference is that in Math 4 we will prepare to read the research literature, finally doing so around week 5 or 6.  In Math 27 we will be reading the research literature from the start of the course.  

Grading: In both courses the grades will be based on 3 papers, however the topics will be different.  All three papers are weighted equally.  Sometimes you will invent your own research topic and sometimes you will build on work done by others (such as prior research done in this course or found in the literature).  

Attendance: This quarter we meet T-Th 10-11:50 and Wed 3-4.  We spend class time on many examples and case studies not included in the text. We will frequently use the Wednesday time slot to participate in a research seminar in mathematical biology (timed this way just for you).  Students from Math 23 (Differential equations) may also attend and participate in the seminar, as well as students engaged in independent study in mathematical biology.  Attendance at the x-hour is required of Math 27 students when we use it, and of Math 4 students on certain days (to be announced).  Do not schedule other activities during this time.

Text: Math 4 is using the latest version of Situated Complexity available at Wheelock Books.  Math 27 is using Mathematical Biology by Murray.   It is mostly used as a reference text, but you should own it because it is a classic.  Math 27 students are also invited to get a copy of the Math 4 text, extras will be available.

Office hours: Wallace's office: Kemeny 204.  Office hours: M 1-2, W 2-3, Th 12-2 and by appointment.

Honor principle: All authors must contribute substantially to any paper with their names on it.  All sources must be appropriately cited.  Any suspicion of plagiarism will be forwarded to the COS.

Religious observance: Some students may wish to take part in religious observances that occur during this academic term. If you have a religious observance that conflicts with your participation in the course, please meet with me before the end of the second week of the term to discuss appropriate accommodations.