Fall 2005

MATH 478.01 (3 credits), Tu_Th, 1:00PM-2:15PM, Wickersham 226

**Textbook:***Essential Mathematical Biology*, Nicholas F. Britton, Springer-Verlag, 2003, ISBN 1-85233-536-X.**Instructor:**Dr. Buchanan

Office: Wickersham 218, Phone: 872-3659, FAX: 871-2320

Office Hours: 9:00AM-9:50AM (MTuWThF), or by appointment

Email:`Robert.Buchanan@millersville.edu`

Course URL:`http://banach.millersville.edu/~bob/math478B`**Prerequisites:**A grade of C- or better in MATH 365 (

*Ordinary Differential Equations*) is the prerequisite for this course.**Coverage:**- The list of topics to be covered in this course includes:
- Dynamic modeling using difference equations
- Linear models
- Nonlinear models
- Variations on the logistic model
- Stability analysis of discrete models

- Structured population models
- Matrix algebra background
- Linear models
- Projection matrices
- Analysis of models using eigenvectors and eigenvalues

- Nonlinear continuous models of species interactions
- Predator-prey interaction
- Competition
- Mutualism
- Equilibria, linearization, and stability

- Models of DNA and genetics
- Background on DNA and Mendelian genetics
- Background on probability
- Matrix models of base substitution
- Phylogenetic distances
- Constructing phylogenetic trees
- Gene frequency in populations

- Infectious disease modeling
- Epidemic models
- Threshold values and critical parameters
- Multiple populations
- Differentiated infectivity

- Time-delayed models
- Deterministic models
- Stochastic models
- Periodic and chaotic behavior

- Discrete spatial population dynamics
- Random walks
- Brownian motion
- Diffusion processes
- Morphogenesis

- Dynamic modeling using difference equations
**Objectives:**The objectives of this course include introducing students to some ideas and models from applications of mathematics to biology and ecology. At the successful completion of this course students will:

- be able to describe various mathematical models used to study population interactions, infectious diseases, genetics, biological motion, and cellular processes.
- understand the role of linear algebra, differential equations, and numerical techniques in modeling biological phenomena.
- be able to use concepts from linear algebra, differential equations, and numerical mathematics to model biological phenomena.
- describe the structure of a biological cell and some of the metabolic and genetic events which take place in cells.
- be able to read, with understanding, articles from the mathematical biology literature.
- have enhanced their ability to communicate mathematical ideas orally and in writing.

**Attendance:**Students are expected to attend all class meetings. If you must be absent from class you are expected to complete class requirements (

*e.g.*homework assignments) prior to the absence. Students who miss a test should provide a valid excuse, otherwise you will not be allowed to make up the test. Tests should be made up within one week of their scheduled date. No final exam exemptions.**Homework:**Students are expected to do their homework and participate in class. Occasionally homework assignments will be collected and graded. The homework is your opportunity to determine if you understand the material covered in class. The homework assignments will also reinforce and extend the classroom material covered. Students are encouraged to work homework exercises together and to study together. Students who work together on homework assignments should attach all of their names to one copy of the submitted assignment for grading. Students who work together on homework assignments, but submit their work individually, without acknowledgment of the collaboration will be considered to be in violation of the Code of Academic Honesty (see

`http://muweb.millersville.edu/~handbook/codeofconduct.html`and`http://muweb.millersville.edu/~govern/sect3/acaddis.html`).Students should expect to spend a

*minimum*of twelve hours per week reviewing notes taken during class and working assigned homework exercises. Preparation for the tests and final exam will require additional hours of study. Students will find it beneficial to review all lecture notes and other relevant material collected from the beginning of the semester until the present time at least once per week.**Project:**Each student will have a semester project. This project will consist of giving a class presentation and written report on a topic found in the mathematical biology literature published in peer-reviewed journals. The instructor will provide copies of the journal articles and will schedule the presentations for the second half of the semester. Presentations will be 20-minutes in length and an additional five minutes for questions. The written report must be typed or word-processed on a computer. Both the presentation and the report will be graded on the author's apparent understanding of the topic, use of mathematics, ability to communicate the topic effectively to her/his audience, grammar and spelling, professionalism, and (in the case of the presentation) ability to answer questions from the audience.

**Tests:**Two 75-minute tests (tentatively scheduled for 10/06/2005, and 11/22/2005) and a comprehensive final exam (Tuesday, December 13, 2005, 12:30PM-2:30PM).

I will not ``curve'' test grades. If you feel that an error was made in the grading of a test, you should explain the error on a separate sheet of paper and return both it and the test to me within three class periods after the test is returned to you. After three class periods, changes to graded material will be made at the instructor's discretion.

**Grades:**Course grade will be calculated as follows.

Tests 40% Exam 25% Homework 20% Project 15% Tests and the final examination will be graded individually on a 100-point scale. Graded homework assignments may consist of a variable number of problems worth ten points each. I keep a record of students' test, homework, and exam scores. Students should also keep a record of graded assignments, tests, and other materials. As an example of the calculation of the numerical course grade, suppose a student's four test grades were 87 and 78 (out of a maximum of 100 points on each test), the student's final examination grade was 71 (again, out of a maximum of 100), and the student's project score was 11 (out of a maximum of 15). Suppose seven homework assignment were collected and the student's grades were , , , , , , and . This hypothetical student's numerical course grade would be calculated according to the formula

I will not ``curve'' course grades. There will be no extra credit assignments during the semester. Therefore students should take all assignments seriously from the beginning of the semester.

Course grades will be assigned according to the following scale.

90-92 A 93-100 A 80-82 B 83-86 B 87-89 B 70-72 C 73-76 C 77-79 C 60-62 D 63-66 D 67-69 D 0-59 F **Course Repeat Policy**An undergraduate student may not take an undergraduate course of record more than three times. A course of record is defined as a course in which a student receives a grade of A, B, C, D, (including and ) F, U, Z or W. The academic department offering a course may drop a student from a course if the student attempts to take a course more than three times.

^{1}**Inclement Weather Policy:**If we should miss a class day due to a school closing because of weather, any activities planned for that missed day will take place the next time the class meets. For example, if a test is scheduled for a day that class is canceled on account of snow, the test will be given the next time the class meets.

**Final Word:**Math is not a spectator sport. What you learn from this course and your final grade depend mainly on the amount of work you put forth. Daily contact with the material through homework assignments and review of notes taken during lectures is extremely important.

Robert.Buchanan@millersville.edu

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