Math 108: Modeling Biological Growth and Form ( Fall, 2003)


What is this course all about? Modeling Biological Growth and Form is a course devoted to the mathematics of life. In particular, we will consider such questions as: How do you model the growth of a population of animals? and How do mathematicians quantify symmetry? Why do spiraling patterns exist in plants and animals and how do we model them? We will model the spiral growth of seashells and the branching patterns found in trees. We will also consider fractal growth in general. The course will be project-driven, and it will make extensive use of the computer program Maple. There will be supplemental readings assigned outside of class. The course will rely on ideas from a wide range of mathematical fields including: geometry, linear algebra, mathematical modeling, and computer graphics.

Instructor: Judy Holdener

Office Hours:

Mon. 2:00 - 3:00
Tues. 2:00 - 3:00
Wed. 2:00 - 3:00
Thurs. 1:00 - 3:00 (and by appointment)

Software: There will be a considerable amount of work done with the aid of the computer algebra system, MAPLE. The MAPLE program is available for your use in Peirce 001 (evenings only), and in other public network sites. I will assume no prior knowledge of MAPLE, so you will learn what you need to know as we go.

Course Objectives:
1. To see mathematics applied to nature.
2. To learn how to construct basic mathematical models.
3. To gain experience with computer programming.
4. To learn how to communicate mathematical ideas in writing and in speaking.
5. To be exposed to a wide variety of mathematics.
6. To learn how to work with open-ended problems.

Weekly Homework and Projects: Computer projects and/or reading or writing assignments or problem-sets will be assigned on a weekly basis. Much of the work will consist of projects started in class and finished outside of class. When submitting work electronically save your file into your personal folder at P:\class\math\holdener\math108\yourusername

HOMEWORK POLICY

  1. Homework is due at the START of class on the assigned due date, unless I specify otherwise. Late homework will not be accepted. If you know you will be missing class for some reason (e.g., an athletic event), turn in your assignment BEFORE you leave. Under extenuating circumstances extensions may be granted, but this should be discussed with me well in advance.
  2. Your homework will be evaluated on neatness, completeness, and correctness.
  3. Group work is encouraged, but assignments must be written up individually unless you are told otherwise. Copied work will receive no credit.
  4. You are encouraged to get help from me on anything!

The Final Project.

The final project will involve independent study of a topic related to the course material. You are encouraged to choose a topic of interest to you, and you will be given a great deal of freedom to tap your own personal strengths. For example, if you like to program then you may choose to explore a computer model; perhaps you will elaborate on a model that we covered in class and then write about it. Or you might choose to write a mathematical paper or construct a webpage about a topic related to the course. I will mention possible ideas for the final project throughout the semester, and you should be keeping the project in mind as we go.

The final project will be worth a total of 25% of your final grade. The grade on your final project will be based on the paper and/or program you write as well as your work and performance in a class poster session which will be held in lieu of the final exam (see below).

Deadlines for the final project. Your grade on the final project will be based, in part, on whether you meet the following deadlines.
Choice of Topic...............................................................Thursday, Nov. 6
Final paper (or webpage) due.........................................Thursday, Dec. 11
Poster Session.................................................................Thursday, Dec. 16, 6:30-9:30PM

Exams. There will be just one midterm in the course; the final project will replace the final exam, and the rest of your grade will be determined by class projects, papers, and homework sets.

Exam 1............................................................Thursday, Oct. 2
Exam 2............................................................Thursday, Nov. 20

Grades. Your grade will be based on weekly homework/projects, the final project, and two exams. Each is weighted as follows.
  % of Total
Homework/Projects/Papers  

35

The Final Project  

25

2 Exams  
30
Class Participation  

10

Class Attendance. Note above that Class Partipication accounts for 10% of your final grade. Obviously, if you are not in class, then you can not participate in class. If you have more than 2 unexcused absences, then your (total) grade will drop by half a letter grade. If you have more than 4 unexcused absences, then your total grade will drop by a full letter grade. Tardiness can also effect your grade. Come to class and be on time!

Learning Disabilities. If you have a disability and therefore a need for some type of accommodation(s) in order to participate fully in this class, please feel free to discuss your concerns in private with me, but you should also consult Ms. Erin Salva (Coordinator of Disability Services; Office of the Dean for Academic Advising, PBX 5453) as soon as possible. It is Ms. Salva (in consultation with the L.E.A.R.N. committee) who has the authority and the expertise to decide on the accommodations that are appropriate for your disability. Though I am happy to help you in any way I can, I cannot make any accommodations for learning (or other) disabilities without proper authorization from Ms. Salva.

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