• A mathematical model is a representation of a real system
• A good mathematical model is simple in design and exhibits the basic properties of the real system
• The model should be testable against empirical data
• The comparisons of the model to the real system should lead to improved mathematical models
• The model may suggest improved experiments
• Often there is not an exact answer, differing from K-12 training in mathematics

Growth of a Culture of Yeast

• In 1913, Carlson [1] studied a growing culture of yeast
• Below is a table of the population for these yeast at one hour intervals
• Want to develop a mathematical model to describe the growth of this culture
   

Link to Excel sheet of yeast culture.

References

[1] T. Carlson Über Geschwindigkeit und Grösse der Hefevermehrung in Würze. Biochem. Z. 57: 313-334, 1913.

Link to Lynx and Hare data.

Modeling with Differential Equations

Link to data for S. cerevisiae and S. Kephir growing in culture - Basic Malthusian and Logistic growth models.

Lecture for the mixed culture.