This foundational class covers modes of reasoning used in quantitative sciences and mathematics, using environmental questions for many classroom examples and projects. We will start by interrogating numbers and equations, applying problem-solving strategies, and gaining a deeper understanding of functions. We will apply these skills while learning the art of mathematical modeling, i.e. translating the physical systems/real-life situations into mathematics. This process involves isolating the essential variables and interactions, setting up equations that constitute a model, running the model on a computer (using the program R), analyzing and interpreting the results, and modifying the hypotheses and assumptions accordingly. This process is helpful in many areas of science and social science because it forces you to carefully understand your assumptions, allows you to test and more deeply understand basic conceptual theories and their implications for complex systems with multiple interactions, and can help identify targeted experiments to fill gaps in the current understanding of the system.
This course is not a repetition of high school mathematics; rather, it places high school mathematics in a larger context and concentrates on the applications of mathematical thinking to the sciences. You do not need to know about logarithms or trig functions to take the course – we will develop these from the beginning – but you should be comfortable with topics like elementary algebra and drawing simple graphs.
This class was formerly titled Introduction to Applied Mathematics and will count similarly toward course prerequisites.