MATH 192/450: Spring 2012
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Professor: Dr. Talitha M. Washington Contact: Office: 218 Academic Support Building B; Phone: (202) 806-6834; E-mail:
[email protected]; Web: http://talithawashington.com Office hours: MWF 2:10-3:00 pm; and by appointment Class Time: Class meets from 11:10 am to 12:00 pm, MWF Course Website: Blackboard, http://www.howard.edu/blackboard/ Texts: Main: L. Edelstein-Keshet, Mathematical Models in Biology. http://ec-securehost.com/SIAM/CL46.html Supplement: G. de Vries, T. Hillen, M. Lewis, J.Muller, and B. Schoenfisch, A Course in Mathematical Biology: Quantitative Modelling with Mathematical and Computational Methods. http://www.ecsecurehost.com/SIAM/MM12.html Additional material will be posted on the course website Course Description: MATH 192/450 Topics in Applied Mathematics (3): A course in mathematical biology. The course covers applications of difference equations, differential equations, and dynamical systems theory to biological problems. Topics include population dynamics, reaction kinetics, diseases, and cellular dynamics. Prereq.: MATH 159. Course Learning Objectives: The main objective will be to have a clear understanding of the interplay between mathematics and biology. This includes developing and analyzing mathematical models that accurately describe biological processes. Specifically, this course strives to help you: acquire methods to solve biological problems mathematically learn to analyze and interpret models apply course material using the software package MATLAB/OCTAVE for analysis and presentation of data Nature of the Class: All students should be comfortable with differential equations. Introductory material on biology and mathematics will be introduced as needed. Graduate students enrolled will have higher-level materials that are not required for the undergraduate. Grading: The weights in determining your final grade are as follows: Homework - 70% Final Project - 30% Course requirements and policies: a. Computing: The assignments and final project may require the use of MATLAB/OCTAVE and LaTeX MATLAB can be purchased for $99 at www.mathworks.com/store. OCTAVE is free and can be downloaded at http://www.gnu.org/software/octave/. Note that OCTAVE binaries for Windows and Mac OS X is located at: http://octave.sourceforge.net/ . LaTeX is free and can be downloaded at http://www.latex-project.org/ b. Attendance: You are expected to attend class on time every day. However, if you miss a day, it is up to you (not me, or your classmates) to catch up and learn what you have missed. c. Homework: Assignments will be posted on the class website. Assignments must be turned in at the start of class on the day that they are due. Late homework will be accepted to a point, but will be subject to a penalty. d. Final Project: The final project will involve writing a paper and giving a presentation on a reading in mathematical biology. The topic must be approved by the instructor. Guidelines for the paper and presentation will be given out at a later date.
MATH 192/450: Spring 2012
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e. Submitted Work: Take care in writing up your solutions for the homework assignments and exams. If critical steps in the solution of a problem are missing, expect to lose points. In general, be sure to show your work. All written solutions must be clear, concise and correct. Even if your solution is correct, expect to lose points if it is difficult to read and understand. This includes solutions that are confused, incomprehensible, unnecessarily complicated, verbose, illegible or incomplete. f. Honor Code: It is expected that students are familiar with and will comply with the terms of the University's Academic Code of Student Conduct on academic cheating, plagiarism, and copy infringement. Note that collaboration on homework is allowed and encouraged, but the work you submit must be your own. g. Accessibility: Please let me know immediately if you have a learning or physical disability requiring accommodation. For more information, contact the Dr. Barbara Williams, Dean for Special Student Services, at (202) 238-2420.
Tentative Course Outline Introduction to Mathematical Biology (dV 1.2) Introduction to MATLAB Linear Difference Equations (EK Ch 1) Nonlinear Difference Equation (EK Ch 2; dV 2.1, 2.2) Applications of Nonlinear Difference Equations (EK Ch 3; dV 2.3) Continuous Models (EK Ch 4; dV 3.1-3.3) Qualitative Analysis (EK Ch 5; dV 3.4) Population and Disease Dynamics (EK Ch 6) Cellular/Molecular Events (EK Ch 7) Models of Neurons (EK Ch 8) Introduction to Partial Differential Equations (EK Ch 9) Partial Differential Equation Models (EK Ch 10) Development and Spatial Patterns (EK Ch 11) Note: (EK) denotes L. Edelstein-Keshet and (dV) denotes de Vries
Have a great semester!
