This foundational class covers modes of reasoning used in all quantitative sciences and mathematics. We will start by interrogating numbers and equations, applying problem solving strategies, and practicing effective communication of mathematics. We will then apply these skills while learning the art of 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 (we will use R: http://www.r-project.org/), and modifying the hypotheses in response to the models behavior. 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 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.