2025-26 Course Descriptions - Catalog - Page 13
SINGLE VARIABLE CALCULUS
In the world around us, one of the only constants
is change. While this statement may seem
oxymoronic, its message is at the heart of the study
of Calculus. In Single-Variable Calculus, students
explore the nature and applications of change
through numerical and analytical methods. By
delving deeper into questions related to the nature
of variation, students synthesize their previouslydeveloped analytical skills in order to discover
and use the rules of Calculus. The class studies
limits as a means to prove derivative functions.
Through the development of a common vocabulary
and set of structures, students use derivatives to
analyze curves, optimize theoretical and practical
models, and relate multiple changing variables to
one another in context. These studies are focused
on instantaneous rates of change for various
functions. The class also explores integrals as a
means to calculate and understand net change for
non-constant rates. Clear connections in Calculus
topics are made with other areas such as Biology,
Physics, and Geometry. Throughout the year,
students collaborate to problem solve and hone
their mathematical communications. Ultimately,
students use their new skills in order to create a
deeper understanding of how change is modeled in
our everyday lives.
Prerequisite: Analytical Precalculus or department
chair approval
MATH SEMINAR: ADVANCED TOPICS
Calculus is the culminating math course for many
high school students at The Field School and
elsewhere. We know, however, that the 昀椀eld of
mathematics extends vastly beyond the topics
that are typically taught in high school. What
does higher-level math look like? How is it used
to answer interesting questions about the world?
What kinds of problems are other branches of
math being used to solve? This course is designed
to challenge and prepare students who are
interested in these questions and may pursue
further study of, or careers in, math. Unit topics
are focused primarily on additional topics in
calculus including differential equations, volumes
of rotation, advanced integration techniques, and
sequences and series, with additional opportunities
to learn about number theory, graph theory,
topology, etc. As they work through this material,
students develop their voices as mathematicians,
focusing on precision in both written and verbal
communication of mathematical ideas. Excitement,
curiosity, and readiness to explore challenges
are encouraged mindsets as students confront
rigorous concepts and problems. In this course,
students move between the abstract and analytical
to the concrete, frequently asking: how can we
apply abstract topics to concrete scenarios?
Prerequisite: Single Variable Calculus or
department chair approval
