Jeffrey Barton

This course introduces students to fundamental calculus concepts via rich applied contexts. The course prioritizes mathematical thinking, experimentation, and clear communication while de-emphasizing symbolic manipulation and rote exercises. We will apply the ideas of calculus such as derivatives, differential equations, and integrals in a variety of contexts including epidemiology, ecology, and environmental sustainability. Students will use computers routinely to carry out calculations, experiment with parameter choices, and create informative graphs. Coding experience is not assumed, but some comfort with coding will be a plus. While there are no formal mathematical prerequisites, students should be comfortable with college level algebra. Keywords:Calculus, mathematics, modeling, differential equations

This course introduces students to fundamental topics in linear algebra. We will use Python to visualize concepts, implement algorithms, and perform calculations that would be intractable by hand. No prior Python experience is required. The focus of the course will be on applications in a variety of contexts, though there will be some theory as well. Topics will include systems of equations, vectors, matrix algebra, linear independence, eigenvalues and eigenvectors, and matrix factorization. While the course has no formal prerequisites in terms of mathematics or coding, it will require some mathematical maturity and/or comfort with programming. Keywords:Linear algebra, eigenvalues, matrices, vectors

In this course, students will engage with mathematical modeling in two important ways: by learning to use existing models as powerful problem-solving tools and by developing their skills in creating their own models. The kind of models we examine are known as discrete dynamical systems, which are just models that specify mathematically how a quantity changes from one time step to the next. We develop such models in a variety of important contexts including populations and sustainability, infectious diseases, blood alcohol concentration, and ranking systems for sports teams or web searches. We only introduce the mathematics necessary for answering important questions in each context, and we will use Microsoft Office Excel as our modeling software throughout the course. Some mathematical concepts we will cover include exponential growth, equilibrium values, and stability. No prior college-level mathematics or experience with Excel is assumed. Keywords:Modeling, equilibrium values, Excel, math

This course introduces students to foundational topics in probability through applications to games, puzzles, paradoxes, and problems. Included will be discussions of independence, discrete and continuous random variables, conditional probability, Bayes' Theorem, random walks, and the Law of Large Numbers. Along the way we will discover the important role that calculus plays in probability (though no knowledge of calculus is assumed), and we will see glimpses of more advanced topics such as the existence of different sizes of infinity and measure theory. Keywords:Probability, randomness, chance, games, math