Math 235, Spring 2015: Comments on Report 2

After grading (most of) the second round of reports, I have the following comments:

• While it is necessary to state the methods being used to analyze a system (such as linearizing about an equilibrium), it is not necessary to explain the theory behind the method, or to show all the details. Rather, it is better to tell the reader what method is being used and then to report the result. If the method is long or complicated, you might show the result of an intermediate step.

For example, if you linearize about an equilibrium and find that it is a saddle point, you might report what the eigenvalues are.
One consequence is that most of the math work you do won’t actually get typed up.

• In general, the reports needed to include more interpretation and less computational details.
• Further, it is important to remember that it is the model that is being interpreted. In this case, the model is an “idealized predator-prey model.” While the introduction can motivate such a model by mentioning specific predatory-prey situations, you are not analyzing a specific situation. Rather, you are analyzing the model. This has two important consequences:
• The mechanisms which cause/explain behavior are mathematical, not biological. That is, the reason variable $x$ tends to zero is not because some species isn’t getting enough food, but because the differential equation governing $x$ is pushing the value down.
• If a mathematical statement is made (such as $x$ decreases to zero) this needs to be justified mathematically. A biological interpretation or rationale is neither sufficient nor appropriate.
• It is important to make good choices of windows / ranges when making plots!
• Do not make value judgements. Statements like “this value of $\alpha$ is too large” should be avoided. What is more appropriate is something like “if $\alpha$ is large, then $x$ tends to zero very quickly.”
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