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In this course, you will learn some new mathematical techniques and some new facts about biology, but the course is primarily intended to improve your ability to understand and construct mathematical models as they are used in biology.
For most biologists, mathematics is a foriegn language. To learn a foriegn language takes time and practise -- which we'll do a lot of in this class. In the end, what matters most is not that you have any particular formulae memorized but rather that you are proficient in the language of mathematics. That means that you are able to understand what is meant by a mathematical formula used in a biological context and that if you don't know how to solve something, you know where to look.
A large proportion of the mathematics used in biology is simply algebra and very basic calculus, which all of you will have had. In addition, matrix algebra, probability theory, and statistics are commonly used. This course will introduce you to some matrix theory and some probability theory, but we will not deal with statistical issues; Biology 300 should be taken to give you the statistical background that you will need.
As biologists, we are very fortunate to live in the age of computers. It is no longer necessary to be math wizs to solve fairly sophisticated mathematical models. For those models that cannot be solved, one can always run simulations and I encourage you to learn a programming language. In this class, however, we will use a software package called "Mathematica", which is able to do pretty much all the math that you have ever done in your lives and much more.
The advantage of using a software package like Mathematica is that it frees us up -- for instance, we no longer have to memorize tables of integrals. Mathematica is able to solve many of the functions that can be solved. Instead we can concentrate on what mathematics we want to do: posing a question, constructing a model, and analysing specific mathematical equations. Our task in this class is to practise doing just that.
As an example, we'll discuss how colleagues and I have been using models to better understand the dynamics and evolution of COVID-19 (Download lecture or maxima code).