## Mathematical Modeling in Biology, M375, Fall 2002

• Class meetings: Tuesday and Thursday, Tu-Th 11-12:30 , RLM 6.118
• Office: RLM 9.114
• Office Hours: TBA
• Phone: 471-7121
• TA: Helena Ristov
• Office:  TBA
• Office Hours: Tu-Th 2-3

• email: hristov@math.utexas.edu
Purpose: There are several purposes to this class.  The main one is to learn how to relate mathematical structures to real-world (especially biological) systems.  This is a 2-step process.  Most real-world systems are horribly complicated, and we must make simplifying assumptions to reduce everything to the study of a few essential variables, described by a few essential equations, with parameters that can be determined experimentally.  That's the first step, and requires a fair level of scientific sophistication.  However, it does not require a lot of mathematical sophistication.  The second step is to solve these equations, either by hand or by computer, and interpret the results to obtain useful information about the underlying system.

The equations we will be concentrating on are differential equations, and a secondary goal of this course is to learn how to analyze differential equations.  Compared to a course like M427K, we will be spending little time on how to solve differential equations, and lots of time on why, and on how to interpret the results.

The prerequisites are calculus (M408D or equivalent) and a willingness to think mathematically about the real world. Taking M427K, either beforehand or concurrently, is useful but not essential.

• Textbook: Modeling Differential Equations in Biology, by Clifford Taubes.  We will cover roughly chapters 1-17.
• Computers:  Computers make "step 2" remarkably easy in many cases, and it would be criminal not to learn how to take advantage of that.   Accounts on the math department computer system will be given out, and roughly half the homework will be computer based.
• Attendance: Attendance and participation is mandatory.  This is a small seminar-style class, and reading the book alone is no substitute for learning from, and contributing to, class discussions.  If you must miss a class, please tell the professor or the TA in advance.
• Homework: There will be weekly homework.  Every other week, the homework will consist of computer exercises.
• Collaboration:  Science is not a solitary endeavor!  We encourage collaboration for everything but the midterm and final exams.  In fact, collaboration is required for the computer segments.  As Dr. Uhlenbeck remarked when teaching this class: "One person versus a computer is unfair competition (the computer wins)".
• Exams: There will be one midterm during the week of October 14-18.
• Term projects: Each student (or rather, team of students) is expected to do a minor project and a major project.  The minor project is presented to the class in late October, the major project at the end of the term.  The major project is typically, but not necessarily, an extension of the minor project.
• Grading:  All students who do the work can expect at least a B.  Assuming all work is done reasonably, your grade will be based on the top five of the following eight items:
• 1) Class participation and regular homework
• 2) Computer exercises
• 3) Minor project
• 4) Midterm
• 5,6) Major project (counts twice)
• 7,8) Final exam (counts twice).  If your scores from the first six items are good enough for you, you are welcome to skip the final.
• Disabilities: The University of Texas at Austin provides upon request appropriate academic accommodations for qualified students with disabilities. For more information, contact the Office of the Dean of Students at 471-6259, 471-4641 TTY

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