Mathematics - Do Not Use

MAT110/120/130: ALGEBRA
These courses develop facility in working with numbers, tables, equations, inequalities, and graphs. The focus is on solving word problems and reading carefully, and thus the building of algebra skills stems from the need to solve problems in a context, rather than from drill and practice for its own sake. Students learn how to use the graphing calculator appropriately as an effective problem-solving tool. In addition, students do a number of hands-on labs that require them to collect data, make conjectures, and draw conclusions. Topics covered include equations and graphs that are linear and quadratic, distinguishing linear versus non-linear data, inequalities, the basic rules of exponents, simple exponential growth and decay, and other traditional Algebra I topics.

MAT210/220/230: INTEGRATED MATHEMATICS
The 200-level courses are geometry courses tied to algebraic processes. Students investigate lines, polygons, and vectors, in both two and three dimensions. Right-triangle trigonometry is introduced, as are circles and parabolas, the latter viewed from a focus-directrix definition. Linear motion is explored, leading to the use of parameters to describe that motion and to an ongoing investigation of optimal paths of travel, an exploration motivating the frequent use of graphing calculators. A dynamic vision of geometry is further encouraged by viewing similarity and congruence through transformations. A study of the concurrence of special lines in a triangle allows for linear data analysis by the use of median-median lines.

MAT310/320/330/340: ADVANCED INTEGRATED MATHEMATICS
The purpose of the 300-level courses is to enable students to expand their view of algebra and geometry to include non-linear motion and non-linear functions. The investigation encompasses circular motion and the ensuing trigonometric functions, ellipses and hyperbolas, exponential and logarithmic functions, dot products and matrices, and geometry on the surface of the Earth. In particular, logs are used to straighten non-linear data; and matrices, to describe geometric transformations and various patterns of growth. In preparation for 400-level mathematics, two other strands are introduced: first, combinatorics and recursion, leading to the binomial theorem; second, infinitesimal behavior, especially instantaneous rates of change and slopes of non-linear graphs.

MAT311/321/331: ADVANCED INTEGRATED MATHEMATICS—ENRICHED
These courses cover the material of MAT310/320/330/340 in greater depth and at an accelerated pace. Prerequisite: Permission of the department.

MAT410: INTRODUCTION TO CALCULUS
Amidst a rich interplay of precalculus concepts, the study of calculus officially begins. Topics include probability, complex numbers, spirals, polar coordinates, expected value, recursion, functional notation, slope, velocity, asymptotes, the fundamental constant e, the Euler identity, and applications of the preceding. Prerequisite: MAT340 or its equivalent.

MAT411: INTRODUCTION TO CALCULUS—ENRICHED
These courses cover the material of MAT410 in greater depth and at an accelerated pace.

MAT420/430/440/450: CALCULUS
This four-term sequence presents a comprehensive and inductive approach to calculus. Working within contexts whenever possible, key concepts are developed with applications in mind. Students learn to read the language of differential equations, and to appreciate that the two principal divisions of calculus—differential (rate problems) and integral (accumulation problems)—are unified by the Fundamental Theorem of Calculus. Students who are enrolled in 430 or higher in the spring will be prepared to take the AB Advanced Placement examination. Students who are enrolled in 450 will be prepared for the BC examination. In preparation for these examinations, classes in the spring term may meet five times per week prior to the test and three times per week after.Prerequisite: MAT410 or permission of the chair of the department. MAT440 and 450 will be offered when numbers permit.

MAT421/431/441/451: CALCULUS—ENRICHED
This four-term sequence covers all the material of the 420/430/440/450 courses, with additional applications and explorations, and in greater depth.  Working within contexts whenever possible, key concepts are developed with applications in mind.  Students learn to read the language of differential equations, and to appreciate that the two principal divisions of calculus—differential (rate problems) and integral (accumulation problems)—are unified by the Fundamental Theorem of Calculus.  Students enrolled in 431 or higher in the spring will be prepared for the AB exam; students in 451 will be prepared for the BC test.  In preparation for these examinations, classes in the spring term may meet five times per week prior to the test and three times per week after. Prerequisite: Permission of the department.

MAT41D: TOPICS IN MODERN DISCRETE MATHEMATICS
The topics for this course depend on the interests of the instructor, and are usually drawn from everyday experience. They have included fair-division problems, such as apportioning the House of Representatives; network problems, such as map-coloring, scheduling, minimal-cost spanning trees, and the traveling salesman; various methods for extracting group preferences from election data; and quantifying the effect that coalitions have on voting power. Prerequisite: MAT330 or its equivalent. Offered: Fall and Winter Terms.

MAT41H: HISTORY OF MATHEMATICS
This will be a one-trimester course focusing on the historical development of mathematical ideas, the role of individual character and culture in the advancement of mathematics, and the historical context of major discoveries and changes of viewpoint. Major themes of the course include: the development of mathematics in non-Western cultures, the development of geometry and number theory, the Platonic/Pythagorean synthesis and the study of harmony, the algebraic synthesis of geometry and the early development of algebra, the arithmetization of analysis and the development of the number concept from ancient to modern times. Both mathematics and writing will be utilized in this course and each student will choose a topic for a written paper. Prerequisite: MAT 330. Offered: Spring Term.

MAT41M: MATHEMATICAL MODELING AND APPLICATIONS
In this course, the students explore the potential of mathematics for formulating, analyzing, and interpreting models in order to solve problems. They study and create models, analyze the assumptions in setting up these models, and test the models against real-world data. Students use computers as a tool, although no special computer experience is necessary. Data analysis, graphs, spreadsheets, computer models, and geometry are some of the modeling tools that are utilized. In the fall term, students will have an opportunity to participate in the High School Mathematical Contest in Modeling.  For this national competition, teams of students work on a real-world problem for a concentrated period of time and submit a written summary of their result. Prerequisite: MAT330 or its equivalent. Offered: Fall and Winter Terms.

MAT40S: INTRODUCTION TO STATISTICS
This one-term course provides an overview of the questions addressed by statisticians.  Students will discuss where data comes from, such as polls, surveys and experiments; they will study how to organize data and infer relationships between variables.  Students will study enough probability to be able to discuss the role of chance and randomness in outcomes.  In addition, they will decide how closely the results of polls actually mirror reality and how far the results of experiments can be extrapolated to the wider world.  There will be many activities in class, and students will use the computer and calculator to display and analyze the data. Prerequisite: MAT330 or permission of the department. Offered in Spring Term only. Preference will be given to seniors.

MAT41S: DESCRIPTIVE STATISTICS AND PROBABILITY
This course covers the basic principles of descriptive statistics. One-variable topics include graphical representations of data, measures of central tendency, and measures of variability. Two-variable data analysis is based on linear regression. Other topics include probability distributions, sampling techniques, binomial distributions, and experimental design. We emphasize the application of statistical techniques to real-world situations. Both the computer and the calculator are integral to the course. During the spring, the course also looks at the principles of hypothesis testing, including non-parametric methods used in the social sciences.Prerequisite: MAT330 or equivalent. Offered: Fall Term.

MAT42S: INFERENTIAL STATISTICS
This course extends MAT41S by covering topics in inferential statistics, including confidence intervals, tests of significance, and statistics in decision-making. We draw problems from the biological and physical sciences, political science, and sociology. Prerequisite: MAT41S. Offered: Winter Term.

MAT43S: ADVANCED STATISTICS AND PROBABILITY
This course builds on the principles of MAT41S and 42S, including more in-depth studies of probability theory. Student-designed projects, based on the statistical procedures learned in the previous courses, constitute important components of the course. Studying this course completes the students’ preparation for the Advanced Placement Examination in Statistics.  In preparation for this examination, classes will meet five times per week before the test and three times per week after. Prerequisite: MAT42S. Offered: Spring Term.

MAT510/520: MULTIVARIABLE CALCULUS
This two-term sequence includes vector analysis of the plane, geometry in space, the cross product, cylindrical and spherical coordinates, partial derivatives, gradients, directional derivatives, and double and triple integrals. Prerequisite: MAT450 or permission of the chair of the department.

MAT540/560/570: LINEAR ALGEBRA AND DIFFERENTIAL EQUATIONS
Math 540 and 560 are independent courses; Math 570 is a direct continuation of 560 and also requires 540.  Math 540 is an introduction to the theory of linear algebra, the study of systems of linear equations and their solutions.  The interplay between algebra and geometry affords powerful and quite different insights into the subject.  Topics include:  Gaussian elimination, matrices and geometric transformations, eigenvectors and eigenvalues, diagonalization, and discrete dynamical systems. Although there are some applications, this course is quite abstract. Math 560 and 570 cover the modern dynamical approach to differential equations. Math 560 covers the one-dimensional case, while Math 570 covers the case of higher (mostly two) dimensional systems. Differential equations are used to model the motion of the planets, the movement of a pendulum, and the growth and decay of animal populations. Calculus-based techniques are used to solve the simple (usually linear) systems explicitly. However, the main emphasis is on a qualitative understanding of solutions through the use of slope fields, direction fields, the phase line, the phase plane, and trajectories. Topics to be studied include: populations (exponential and logistic models, various models with harvesting, and predator-prey systems), harmonic oscillators, the Lorenz equations, stable and unstable equilibria, the classification of all two-dimensional linear systems, and chaos. Prerequisite: MAT450 or permission of the chair of the department.

MAT600: FOUNDATIONS OF ABSTRACT MATHEMATICS
This course constitutes an introduction to proof and formal mathematics with the idea of preparing students for higher-level mathematics. The emphasis is on understanding and mastering increased levels of rigor, dealing with mathematical notation, learning how to do proofs and how to assess the logical status of proposed proofs. Students will be expected to submit written work on a regular basis.  Course content may vary in given terms but will include exposure to the following: axiomatic structures and proofs; the principle of mathematical induction; proof by contradiction; existence principles; mathematical logic; elementary set theory; countable and uncountable sets; bijections between sets; elementary combinatorics; concepts of abstract structure and isomorphism. Prerequisites: Math 450 or permission of the chair of the department. Offered: Fall and Spring Terms.

MAT650: SELECTED TOPICS
The topics for these courses are dependent upon the interests and backgrounds of the students involved. In the past, topics have included group theory, topics in real and complex analysis, point set topology, knot theory, dynamic fractals, and advanced topics in geometry. Prerequisite: MAT600 or permission of the chair of the department.

Transition Mathematics
In order to merge new students as seamlessly as possible into our mathematics program, we offer a series of transition courses, which we deem necessary for these reasons: Our precalculus offerings are integrated across the standard boundaries of algebra, geometry and trigonometry; Word problems are the settings for all of our problems; Mathematics is done seminar-style, around a Harkness table; Much of the fundamental content of our courses is non-traditional; An introductory course gives both students and instructors an opportunity to determine the best placement for all incoming students. Typically, the transition courses last for one term, but some extend for two, or even three, terms.


MATTR1: TRANSITION ONE MATHEMATICS
This transition course is for students with one or more years of algebra, but little background in geometry. Students with a secure grasp of algebra promote to MAT210 after one term; others take an extra term to enhance their algebra skills and start MAT210 in the spring. Students with an especially strong algebra background may be placed immediately in MAT210 in the fall term. Offered: Fall Term.


MATTR2: TRANSITION TWO MATHEMATICS
This transition course is for students with one or more years of algebra and one full year of geometry. Students in the course usually promote to MAT230 in the winter. An accelerated section will promote to MAT311 in the winter term. Offered: Fall Term.


MATTR3: TRANSITION THREE MATHEMATICS
This is a two-term transition for students with three full years of high-school mathematics. Students in the course usually promote to MAT330 in the spring term. An accelerated section will promote to MAT331 in the spring. Offered: Fall and Winter Terms.


MATTR4: TRANSITION FOUR MATHEMATICS
This is a year-long course for students who have finished four years of high-school mathematics, and its goal is to review and reinforce the precalculus mathematics that students have previously seen, with the intention of preparing the students for the study of calculus in college. It will cover topics explored in MAT210 through MAT410. An accelerated section will cover, in greater depth, topics through MAT420.