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Mathematics CoursesAn undeniable reason for studying mathematics is its application to fields and enterprises, such as engineering and economics, that are highly valued for their utility. In fact, entry into many of these fields is possible only to those who can demonstrate excellent achievement in a rigorous mathematics program. And so, it is very much in a student’s long-term interest to study mathematics in order to keep doors open to many fields that may later prove of interest. But beyond the practical reasons for studying mathematics, we hope that Loomis Chaffee students will come to share our deep appreciation of the abstract beauty of mathematics — a very human endeavor that grows out of the most careful thinking about the concepts that spring from our fundamental ideas concerning magnitude, quantity, shape, structure and reasoning itself.
- Advanced Placement Calculus AB
Following the Advanced Placement AB Calculus syllabus, this course
introduces differential and integral calculus. Rules of differentiation
for most of the common algebraic and transcendental functions are
introduced, and students learn applications of the derivative in graph
theory, motion problems, related rates of change and optimization
problems. The course introduces definite and indefinite integrals along
with the most common techniques of integration and applications to
area, volume, motion, and growth and decay. The calculus topics are
explored algebraically, numerically, verbally and graphically with the
aid of the TI-83 or TI-84 calculator. Read more
- Advanced Placement Calculus BC
Following the Advanced Placement BC Calculus syllabus, this course
offers a rigorous, college-level introduction to differential and
integral calculus. Topics include the theory and applications of
derivatives and integrals of common algebraic and transcendental
functions, offered in Calculus AB. Beyond the topics from 4085,
students work with the calculus concepts as they apply to vector
functions, parametrically defined functions and polar functions, and
also do significant work with sequences and series. The calculus topics
are explored algebraically, numerically, verbally and graphically with
the aid of the TI-83 or TI-84 calculator. Read more
- Advanced Placement Statistics
Equivalent to a one-semester, introductory, non-calculus-based college
statistics course, this course incorporates four themes: exploring
data, learning designs for data collection and experiments,
anticipating patterns in advance and drawing conclusions from data.
Computers and the TI-83 or TI-84 calculator are important tools for
completing data analysis and understanding more sophisticated
statistical concepts. This data-based approach involves group
activities and student-generated studies. The course emphasizes reading
and communicating statistical information accurately in real world
situations. Students enrolled in the spring term of this course are
required to take the Advanced Placement Examination. Read more
- Advanced Precalculus With Differential Calculus
This honors course is primarily for juniors who have done well in
Algebra II Advanced and Advanced Geometry or equivalent courses. It
covers more material than Precalculus 4065 at a more rapid pace and in
greater depth. It includes significant work in the concept of the limit
of a function and, in the spring term, an introduction to the
derivative in calculus. Students are prepared to continue in AP
Calculus BC. Read more
- Algebra I
This course is for freshmen who have had less than a full year of
algebra. It covers properties of the real number system, linear and
quadratic equations, with strong emphasis on word problems and
non-traditional problem solving. Students develop competence with the
graphs of linear and quadratic equations and master a number of
techniques for solving equations and simplifying algebraic expressions.
While the course emphasizes the development of algebraic skills, it
also introduces students to some of the numerical and graphical
solutions to problems made possible with the TI-83 or TI-84
calculators.
Read more
- Algebra II
This course reviews, strengthens and further develops the algebraic
concepts and techniques involving work with linear and quadratic
equations and inequalities. In this early work this course emphasizes
functions and the properties of their graphs. The course then explores
functions involving radical expressions and rational polynomials, and
finally considers logarithmic and exponential functions and their
applications. Beyond traditional algebraic techniques, students learn
numerical and graphical solution techniques with the guided use of the
TI-83 or TI-84 graphing calculators. Work with matrices, trigonometry,
complex numbers and sequences and series is introduced along the way. Read more
- Algebra II Advanced
This honors course is for interested and able students who have done
well in a full-year, in-depth, first-year algebra course. It covers at
a faster pace and in more detail the same material as Algebra II 4035,
as well as conic sections, rational functions and trigonometry. The
TI-83 or TI-84 graphing calculator is used extensively in class.
Placement for new students will be determined by the department. Read more
- Algebra II Essentials
A course primarily designed for juniors that covers selected topics
from Algebra II in order to strengthen algebraic knowledge and mastery
of basic topics from Algebra I and Algebra II. Unlike 4035, Algebra II
Essentials does not aim to prepare students to enter Precalculus
directly. Read more
- Calculus
This course introduces students to most of the theories, techniques and
applications of a first-year calculus course. Designed for students who
want to understand and work with the concepts of calculus, this course
also strengthens their precalculus skills. By mixing theory and
application, and by using both discrete and continuous examples, the
course offers students a solid foundation of the basic techniques of
differential and integral calculus and explores the utility of calculus
in a variety of fields. Although not covering the entire AP program of
AP Calculus AB, this course prepares students for a rigorous first-year
calculus course in college and enables them to use calculus concepts in
other disciplines. Read more
- Functions and Discrete Mathematics
This course is intended for juniors who wish to strengthen and widen
their mathematical background before taking Statistics 4057,
Precalculus 4065, or in rare cases Calculus 4070. It includes a brief
review of basic concepts as well as more advanced concepts using
functions, graphs and applications, techniques of equation solving,
combinations, probability, data analysis and other discrete mathematics
topics. Students become proficient in the use of the TI-83 or TI-84
graphing calculator. Read more
- Geometry
This standard mathematics course for sophomores deals with Euclidean
geometry of two and three dimensions. Construction with straight-edge
and compass and an introduction to right triangle trigonometry are
included. Where appropriate, students utilize technology to enhance the
learning process. The course’s emphasis on rigorous deductive reasoning
develops the skills needed to communicate more complex ideas
effectively. Read more
- Geometry Advanced
This honors course is for able students who have had two full years of
algebra. It covers the same topics as Geometry 4025, but at a faster
pace and in greater depth. It also includes a more thorough study of
trigonometry and coordinate geometry. Read more
- Independent Studies in Mathematics
A student who has exhausted the offerings of the Mathematics Department
or who desires to study a math-related topic not offered as a course
may propose an Independent Study Project for credit. The student must
arrange for a project adviser from within the department, submit a written proposal, and obtain approvals from the academic adviser, project adviser, department head and dean of faculty. Read more
- Introduction to Logic
Please see description under Philosophy, Psychology and Religion
offerings. Students interested in logical foundations of mathematics
and in greater sophistication in methods of proof may consider this
course. Read more
- Linear Algebra
Linear Algebra is an introduction to college mathematics for students
who have shown exceptional promise in their study of mathematics.
During the first half of the year, Linear Algebra covers the theory and
applications of systems of equations, matrices and matrix algebra, row
reduction, invertibility and determinants. The second half of the
course veers sharply towards the abstract. Topics such as vector spaces
and linear transformations serve as an introduction to conceptual
mathematical systems that will later create the foundation of college
level algebra. Throughout the course emphasis is placed on learning the
structure of formal mathematical proof writing. Linear Algebra is a
full-year course taught in a half-time block. Read more
- Mathematical Applications in Engineering
This course introduces students to typical projects across engineering
disciplines and develops the mathematical skills required to support
engineering projects. Students research engineering projects to
understand design concepts and to learn how to balance these against
practical and economic constraints. In addition, students hear guest
lecturers from several engineering disciplines: electrical, mechanical,
civil, computer, transportation, environmental and chemical. The
mathematics required to support engineering projects are presented in a
broad overview using as a guideline sample problems from the
Professional Engineering License course. Read more
- Multivariable Calculus
For able students who have completed AP Calculus BC, this course
extends the work of calculus to two- and three-dimensional vector
functions and functions of several variables. In the spring, advanced
topics are discussed such as linear, boolean and abstract algebra; set
theory; and foundationalism. Read more
- Precalculus
This course is for students who have done very strong work in Algebra
II or Functions and Discrete Mathematics, and who intend to take
calculus on the secondary or college level. The primary focus is a
rigorous study of algebraic and trigonometric functions. The course
offers a detailed study of the properties, graphs and applications of
each of the functions. Additional topics include sequences, series,
limits and probability. The TI-83 or TI-84 graphing calculator is used
extensively. Read more
- Statistics
This course offers a briefer and less demanding approach to the
material presented in AP Statistics 4055. The course emphasizes
problem-solving, student-generated studies and group work. The TI-83 or
TI-84 graphing calculator is used extensively. Students may elect
either the first term or both terms of the course. Read more
- Topics in Algebra
This one-term course for seniors deepens understanding of functions and increases mastery of algebraic skills. Read more
- Topics in Discrete Mathematics
This course explores a number of real-life mathematical applications.
Topics include combinatorics, finding optimal solutions through linear
programming and the Hungarian Algorithm, investigating the mathematics
of check digits embedded into various codes, and the mathematics of
election techniques and Congressional apportionment. The course is
designed for those who intend to take statistics in the winter and
spring terms but who do not need the algebra review of our 4051 Topics
in Algebra. It can serve equally well as a term elective for students
who are enrolled in a full-year math course such as 4065 Precalculus,
4055 AP Statistics or one of the calculus classes, but who additionally
would like this introduction to discrete math. Read more
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