Erin Carmody

Undergraduate Discipline

Mathematics

Undergraduate Courses 2021-2022

Mathematics

Calculus I: The Study of Motion and Change

Open, Seminar—Fall and Spring

Our existence lies in a perpetual state of change. An apple falls from a tree; clouds move across expansive farmland, blocking out the sun for days; meanwhile, satellites zip around the Earth, transmitting and receiving signals to our cell phones. The calculus was invented to develop a language to accurately describe and study the change that we see. The ancient Greeks began a detailed study of change but were scared to wrestle with the infinite; so it was not until the 17th century that Isaac Newton and Gottfried Leibniz, among others, tamed the infinite and gave birth to this extremely successful branch of mathematics. Though just a few hundred years old, the calculus has become an indispensable research tool in both the natural and social sciences. Our study begins with the central concept of the limit and proceeds to explore the dual topics of differentiation and integration. Numerous applications of the theory will be examined. For conference work, students may choose to undertake a deeper investigation of a single topic or application of the calculus or conduct a study in some other branch of mathematics. This seminar is intended for students interested in advanced study in mathematics or science, students preparing for careers in the health sciences or engineering, and any student wishing to broaden and enrich the life of the mind.

Faculty

Calculus II: Further Study of Motion and Change

Open, Seminar—Spring

This course continues the thread of mathematical inquiry, following an initial study of the dual topics of differentiation and integration (see Calculus I course description). Topics to be explored in this course include the calculus of exponential and logarithmic functions, applications of integration theory to geometry, alternative coordinate systems, infinite series, and power series representations of functions. For conference work, students may choose to undertake a deeper investigation of a single topic or application of the calculus or conduct a study of some other mathematically-related topic. This seminar is intended for students interested in advanced study in mathematics or science, for those preparing for careers in the health sciences or engineering, or for any simply wishing to broaden and enrich the life of the mind.

Faculty