Mathematical Methods

Mathematical models are a core component of the natural and social sciences. This program is centered around several fields of mathematics that are frequently used to build these models. The concepts and theorems that emerge from studying these areas of applied mathematics capture core insights into underlying patterns in the world. We will supplement our core mathematical topics of Differential Equations, Linear Algebra, and Multivariable and Vector Calculus with a weekly reading and seminar discussion exploring the nature of mathematical thinking, including model-building, philosophical questions, and the role of theorems and proofs. Each of these four areas represents a 4-credit thread within the program as a whole.

This program is designed for students who have completed a year of Calculus and are interested in going deeper into mathematics. For students whose studies focus on natural or social sciences, the mathematics we learn will help to engage with quantitative models in those fields. For students whose studies focus on mathematics, this program will cover core areas of intermediate mathematics and provide a solid background for Mathematical Systems, a winter/spring program focusing on pure mathematics. Taking the full-year sequence (Mathematical Methods followed by Mathematical Systems) will provide a solid background for students interested in careers in mathematics, math education, and sciences, as well as those who are simply interested in gaining deep insight into the nature of mathematical thinking.

Program activities will include lectures, workshops, seminar discussions and essays, weekly homework assignments, and regular quizzes and exams in each area of study. The material will be challenging and will require a very substantial time commitment outside of class in addition to consistent in-class participation. Students will be expected to complete several substantial homework assignments each week and to bring that learning to the classroom through active engagement with classmates. A strong emphasis will be placed on developing an inclusive learning community which fosters mutual support and success.