Kathryn Montovan 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….

# Category: Mathematics

## Partial Differential Equations and Fourier Series

Andrew McIntyre Many of the laws of physics and engineering may be expressed in terms of partial differential equations. These include the laws of heat conduction, wave motion, electromagnetism, fluid mechanics, quantum mechanics, and statics. This course will cover these key linear partial differential equations and the methods of solution through Fourier series. Fourier series…

## Calculus B

Carly Briggs This course is a sequel to Calculus A. While Calculus A covers a broad range of concepts, Calculus B focuses on the techniques to put those concepts into practice, and the various problems to which those techniques may be applied. There will be applications to physics, chemistry, biology, environmental studies, economics, and other…

## Advanced Linear Algebra, Group Theory, and Geometry II

Andrew McIntyre This advanced class combines a traditional abstract algebra curriculum with topics in linear algebra and geometry. Topics include: introductory group theory; Sylow theorems; isometries of the Euclidean plane; symmetries of wallpaper patterns; isometries of the hyperbolic plane and Kleinian groups; elementary Lie groups and their discrete subgroups; Lie algebras; spectral theorems and decomposition…

## Conjecture and Proof in Discrete Mathematics

Steven Morics Using concepts from combinatorial mathematics and computer science, this course is an introduction to the nature and process of doing mathematics; playing around with patterns, making conjectures, and then stating and proving theorems. The course revolves around a large collection of open-ended problems, concerning topics from graph theory, game theory, set theory, combinatorics,…

## Does Your Vote Matter? A Mathematical Look at Politics and Social Choice

Steven Morics Mathematics and the natural sciences have a long history together, but recently, mathematicians have begun using the tools of their trade on a collection of problems from the social sciences. Is it right that, as a Californian, my vote counted much less than yours did in the last presidential election? If a business…

## Geometry and Physics

Andrew McIntyre This is an introductory course on modern geometry and its relationship to physics. We will be looking at how space might have more than three dimensions, or be combined with time, or be closed in on itself in different ways (such as the surface of a sphere or a donut), or be curved…

## Calculus: Principles and Concepts

Andrew McIntyre Calculus is the mathematics of quantities that are infinitely small or infinitely many in number. For example, in physics, the curved trajectory of a planet can be understood by splitting it into infinitely many, infinitely short straight line pieces. An area can be computed by splitting the shape into infinitely many, infinitely small…

## Multivariable Calculus and Differential Geometry

Andrew McIntyre This class will cover multivariable calculus at an advanced level: vector spaces, div, grad and curl, differential forms, and Stokesâ€™ theorems. The coverage will be at the level of Loomis and Sternbergâ€™s Advanced Calculus. The course will also provide an introduction to the rudiments of differential geometry: connections, curvature, and the Gauss-Bonnet theorem….

## The Art of Mathematics

Andrew McIntyre; Kathryn Montovan Are you interested in the interplay between art and mathematics? In this class, we will explore striking visual and spatial concepts that arise in sophisticated modern mathematics. We will do so without assuming any mathematical prerequisites. Topics include the structure of Moebius strips and solids; topology (the stretching and bending of…