This three credit course will be an introduction to the interplay of mathematics with biology. This course will introduce math majors to biological modeling and wet lab work, and will provide biology majors with an opportunity to increase their mathematical maturity in preparation for 200 level (3rd and 4th year) courses. It will be taught within the context of Systems Approach to Mathematical Modeling in Biology. Students will have hands-on exposure to software tools and symbolic manipulators, and will conduct both wet and dry lab experiments to compare model predictions with experimental data.

Description:

Discrete processes in Biology, nonlinear difference equations. Continuous processes and ordinary differential equations, phase plane methods and quantitative solutions, applications to population dynamics and epidemiology. Michaelis-Menten kinetic model, and autocatalysis. Huxley’s model for muscle contraction. Diffusion in biology.

Learning Objectives: 

1.      Master Population and ecological level modeling

(i)         Elementary discrete and ordinary differential equations in population biology

(ii)        Integration techniques and density dependent problems

(iii)       Graphs and software tools for prototype models

2.      Master aspects of Molecular, cellular and chemical level modeling

(i)        Algebraic manipulation and solution of equations for reactions and systems

(ii)        Formulation of mass action kinetics

(iii)       Graphs and software tools for prototype models

3.      Master aspects of modeling at the Physiological level

(i)         Compartmental systems and differential equations

(ii)        Muscle mechanics and differential equations

(iii)       Graphs and software tools for prototype models

4.      Master modeling concepts from Developmental Biology

(i)         Diffusion in Biology and Ecology

(ii)        Pattern formation and differential equations

(iii)       Graphs and software tools for prototype models

Topics:

1. Manipulation of matrices, eigenvectors and eigenvalues using linear algebra
2. Basic computer algebra and numerical analysis
3. Graphing functions (in one, two and three dimensions)
4. Algebraic manipulation of functions and parameters to quantify behaviors
5. Application of integral and differential calculus to scalar and vector fields
6. Discrete, Ordinary and partial differential equations
7. Exposure to probability distributions and statistics.

Dry Lab: Assignments using Symbolic manipulators, such as Matlab and Mathematica

Wet Lab: Location: 114 Marsh Life Science Bldg

Course Expectation & Conduct: The purpose of our class meetings is to help you to obtain the core material that will allow you to learn through your own work outside the classroom. Therefore, an essential part of your {positive} learning process is to look for additional information from the library and other sources (namely, my office hours).

All rules including student class conduct, cheating, attendance, etc. will be handled as required by the student code of conduct currently in effect. Should you miss a quiz or test due to illness or an emergency, you will be required to give advance notice or provide a doctor's excuse in order to be allowed to make-up on the tests and quizzes. Students who require special accommodation must have a formal letter from Specialized Student Services and must also formally notify me of this need early in the term.

Students with Special Needs: Students with documented learning disabilities are entitled by law to certain “reasonable accommodations.” If you have a documented reason for special accommodations, you must provide written evidence of this as soon as possible from the appropriate office. No accommodations can or will be given without the documentation. Each time special accommodations are requested, the request must be submitted, in writing, at least one week before the event.

Homework: Homework problems will be assigned regularly. Occasionally, you will be required to hand in your homework assignments for grading.