ALGEBRA 1
This course is an introduction to the principles of elementary algebra. Topics include simplification and evaluation of algebraic expressions including algebraic functions, exponential and radical expressions; solution of concrete and linear equations of the first and second degree, of absolute value equations and inequalities, and two-variable systems of equations; graphing of linear and quadratic equations and inequalities; factoring and division of polynomials; function notation; and solution of word problems by algebraic technique.

GEOMETRY
This is an introduction to a deductive system of logic—the presentation of an axiomatic system in which general principles are derived from a limited group of postulates. The course follows the traditional development of Euclidean geometry with an emphasis on proofs and deductive reasoning, visual intuition and problem solving strategies. The elements of algebra are reviewed in relation to some topics, particularly the section on coordinate geometry, presented both as an analytic representation of geometric principles and as a tool for proof. Constructions, rotations, reflections, symmetry, and elementary trigonometry may be included. Prerequisite: Algebra 1

ALGEBRA 2
Algebra 2 is devoted to simplifying, problem solving, and graphing n th degree polynomial functions. We review the basic concepts of algebra, including the study of the real number system and the accompanying axioms; solving equations and inequalities with an emphasis on word problems, absolute value, and linear functions. Moving ahead, we study the characteristics of polynomial and rational algebraic expressions and their practical applications. Irrational and imaginary expressions are explored; and other topics such as logarithms and exponential functions, conic sections, and inverse functions are investigated. Matrices, determinants and probability may be encountered. Prerequisite: Algebra 1

ELECTIVES

TRIGONOMETRY
Beginning with trigonometric functions and triangle solutions, we move on to identities, equations, angle formulae, and the practical applications thereof. Last, we cover the graphs of all the trigonometric functions including inverses and period, amplitude, and phase shifts. Prerequisite: Algebra 2

TRIGONOMETRY/ANALYSIS
This is a rigorous approach to polynomial, trigonometric, and exponential functions: sequences and series; vectors; and some analytic geometry. Emphasis is on the mastery of proofs and creative applications to practical problems. This course is a prerequisite for calculus. Text: Dolciani et al., Modern Introduction to Analysis. Prerequisite: Algebra 2

CALCULUS 1
This is a college-level calculus course, with heavy emphasis on proofs, derivations, and creative applications. Limits, differentiation and integration, and applications thereof are covered. Transcendental functions are also explored. The course is intended for the serious mathematics student. Prerequisite: Trigonometry/Analysis

CALCULUS 2
Calculus 2 is a continuation and expansion of the techniques of Calculus 1. It includes a review and a proof of the fundamental theorem of Calculus, further methods of integration with application to physical problems, alternative coordinate systems, series and sequences, vector functions, and differential equations. Prerequisites: Calculus 1 and departmental recommendation

ADVANCED PROBLEM SOLVING
This course is designed for students on the Junior and Senior Math Teams. We work on past AMC and AIME Exams along with the six-question NYC IML exams. Topics in number theory, probability, algebra, geometry, and trigonometry are explored as they arise in problem solving. Students also have the opportunity to conduct independent research and present their discoveries at an in-school math fair.

PROBABILITY AND GAMES OF CHANCE
Counting techniques, the laws of probability, and the principle of mathematical expectation are used to analyze the lottery, craps, poker, backgammon and other games. A game theoretic model is employed to develop an optimal strategy for bluffing.

APPLICABLE MATH
This course is for anyone who has ever asked, “When would I ever use this?” Students explore how mathematics is used in fields such as computer science, engineering, and government. The first semester focuses on information technology with topics such as cryptology, circuitry logic, and voting theory. Projects may include creating and decrypting original codes and building a simple calculator. The second semester consists of engineering projects that may include building a trebuchet and a structurally sound bridge. Students may enroll in this course for a single semester or a full year. Prerequisite: Algebra 1

DISCRETE MATHEMATICS
This class asks a variety of questions and then uses techniques from many areas of mathematics to answer them. How many possible chess games are there? What’s the probability that a monkey will type Hamlet? What’s the maximum distance a volleyball can travel? Often we spend a while learning the ins and outs of a game—Set, Chess, Go, Monopoly—before constructing mathematical models and testing them. Students are encouraged to ask their own questions and refer the class to games/puzzles/questions from science or economics that interest them. Prerequisite: Algebra 2

FORMAL LOGIC
Formal logic, a discipline created by Aristotle, has applications in a variety of disciplines including philosophy, mathematics, physics, computer science and linguistics. One might in fact argue that logic is relevant to any endeavor that involves reasoning. This course begins with a consideration of arguments of English and the question, What constitutes a good argument? We then focus on the symbolic system known as sentential logic and the more powerful symbolic system known as predicate logic. In both cases, students learn to translate arguments of English into symbolic arguments and to evaluate such arguments using the aforementioned systems. This is a proof intensive class. Prerequisite: Geometry

NON-EUCLIDEAN GEOMETRY
One of the postulates of Euclidean geometry states that through a point not on a given line there is exactly one line parallel to the given line. This postulate, known as the parallel postulate, seems intuitively unassailable. For what would it mean to say that the parallel postulate is false—either that there are no parallels to a line from an external point, or there are multiple parallels? And both of these options seem, at least at first glance, patently absurd. As it turns out, however, these alternatives to the parallel postulate do not lead to absurdity but to different and completely consistent geometries. This course begins with a close look at the Euclidean parallel postulate and then turns its focus to some of the main ideas of the two general types of non-Euclidean geometry: hyperbolic geometry (in which, by the way, the sum of the angles of a triangle is always less than 180 E ) and elliptic geometry (in which the sum of the angles of a triangle is always greater than 180 E ). Discussion of the philosophical consequences of non-Euclidean geometries is certainly a part of this course. Prerequisite: Geometry

MICROECONOMICS
This course is an introduction to the principles and applications of microeconomics. Topics to be covered include the theory of supply and demand, market equilibrium, consumer behavior, the behavior of firms, and perfect and imperfect competition. Social issues such as pollution, income distribution, and welfare are analyzed within an economic framework. Prerequisite: Algebra 2

MACROECONOMICS
This course is an introduction to the principles and applications of macroeconomics. Topics to be covered include the Keynesian and classical models of equilibrium, national income, inflation, unemployment, fiscal and monetary policy, investment and the banking system, international trade, and economic growth. Prerequisite: Algebra 2; microeconomics is not a prerequisite for this course.

INDEPENDENT STUDY IN MATHEMATICS
Topics to be determined by interest and inclination of individual student and teacher.

WHAT IS MATHEMATICS?
AN INTRODUCTION TO PURE MATHEMATICS
What do mathematicians do, and why do they do it? This class examines the art of mathematics from both the philosophical and aesthetic points of view, and provides a broad overview of the subject. Mathematics is about exploring our imaginations, finding beautiful patterns, and searching for explanations. Along the way we discover infinite numbers, the transcendence of pi, and the symmetry of knotted space. And we might just learn to see in four dimensions... The course features a survey of important unsolved problems that motivate modern research, as well as a “studio” where you will create and critique your own works of mathematical art. The purpose of the course is to help you develop your mathematical intuition and taste, and in the process blow your mind to pieces. No previous mathematical experience is necessary, but permission of the instructor is required.

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