Math & Computer Science

Course Descriptions

Algebra 1

Algebra 1 serves as an introductory course into the language and fundamental operations of mathematics. Students solidify skills in distinguishing classes of numbers and their properties, simplifying expressions, equation and inequality solving, and function applications. An exploration of linear, quadratic, exponential, rational, and radical equations and functions begins by cementing operational techniques and then developing graphing skills. In addition, methods such as factoring, completing the square, and the quadratic formula are introduced. This course is the basis of any future math course.

TEXT: Algebra 1, ISBN:0078651131

Geometry

Geometry is an introductory course in theoretical and analytical Euclidean geometry. Students advance their knowledge of geometric concepts such as planes, lines, triangles, circles, area, and volume. In addition, students learn basic trigonometry as well as coordinate geometry. Students complete geometrical proofs, which involve both deductive and inductive reasoning using theorems, definitions, and properties. Students also use algebraic techniques in equation solving, simplifying radicals, graphing, and formula based operations.

TEXT: Geometry, ISBN: 0395977274

Algebra 1/Geometry

Algebra 1/Geometry is an accelerated course, combining crucial algebraic concepts with a full year analysis of introductory Euclidean geometry. Students first begin by reviewing algebra, with an emphasis on factoring, simplifying radicals, linear and non linear equation solving, graphing, and word problem solving. Students then explore geometrical concepts such as planes, lines, triangles, circles, area, and volume. In addition, students are exposed to introductory trigonometry and coordinate geometry. Students complete geometrical proofs, which involve both deductive and inductive reasoning using theorems, definitions, and properties.

TEXTS: Algebra 1, ISBN:0078651131; Geometry, ISBN: 0395977274

Algebra 2

Algebra 2 is a continuation of concepts introduced in Algebra 1 with advanced applications. Emphasis is placed on analyzing linear and nonlinear functions, equations, and inequalities.  Students refine their abilities in solving systems of equations and inequalities, polynomial, rational, exponential, and radical equations and functions using the real and complex number systems. In addition, the course exposes students to concepts such as conic sections and logarithms and takes an in-depth approach to sequences, series, and probability.

TEXT: Algebra 2, ISBN: 0078279992

Algebra 2/Trigonometry

Algebra 2/Trigonometry is an accelerated course which algebraic concepts and trigonometric properties. There is a greater emphasis in analyzing linear and nonlinear functions, equations, and inequalities than in Algebra 2.  In addition to the Algebra 2 material covered, students thoroughly investigate trigonometric ratios with graphs and applications of the sine, cosine, tangent, secant, cosecant, and cotangent functions in both degree and radian measurements. Students will also work in rectangular, polar, and parametric forms. Trigonometric identities and non-right triangle applications are introduced.

TEXT: Algebra and Trigonometry, ISBN: 0321501128

Algebra 2/Trigonometry Honors

This course continues an exploration of algebra at greater depth and incorporates a rigorous introduction to analytical trigonometry.  Semester one primarily focuses on linear, quadratic, and rational functions as well as an introduction to exponential and logarithmic functions. Also, new concepts such as complex numbers, composition of functions, and behavior of polynomial functions are addressed. Semester two begins with trigonometry, extending right triangle applications and building a bridge into other trigonometric functions and their graphs. Identities, Law of Sines, Law of Cosinse, and complex numbers in trigonometric form, polar coordinates, and vectors are also included. The remainder of the course covers matrices, conic sections, sequences, series, probability, and combinatorics.

TEXT: Algebra and Trigonometry, ISBN: 0321501128

Pre-Calculus (Trigonometry/Math Analysis (college prep and honors), Introduction to Analysis and Calculus(IAC))

Pre-Calculus is a continuation of concepts introduced in Algebra 2 as well as a formal introduction to trigonometry.  Students analyze varying functions, emphasizing continuity, critical points, asymptotes, end behavior, domain, range, intervals of increasing and decreasing, and roots. Additionally, students investigate a great range of trigonometric concepts including secant, cosecant, and cotangent as well as solving non-right triangles. Emphasis is placed on graphing functions and their inverses.  Students work within the Cartesian coordinate system, the complex, and polar systems. Vectors, parametric equations, logarithms, conic sections, sequences, and series are also included. Students begin limits and basic differentiation as an introduction to calculus. 

TEXT: Precalculus, ISBN: 013227650X

Math Analysis Honors (Precalculus Honors)

Honors Math Analysis is an advanced, accelerated course designed to prepare students for AP Calculus BC. Students who take this course can earn honors credit towards his or her GPA.  Students review concepts such as linear and nonlinear applications, solving systems of equations and inequalities, matrices, and number properties before analyzing various functions. Trigonometric functions, along with vectors, parametric equations, logarithms, conic sections, sequences, series, and probability are addressed. In addition, students begin introductory differential calculus by analyzing limits using both theoretical and computational approaches. Students learn various differential techniques from the power, chain, quotient, and product rule and complete a rigorous study in application of derivatives. 

TEXTS: Precalculus, ISBN: 013227650X; Calculus of a Single Variable, ISBN: 0547212909

Calculus

Calculus introduces basic differential and integral applications, emphasizing a computational rather than theoretical approach. This class is designed to give students exposure to Calculus in preparation for future encounters with a college level course. Students are required to have a firm understanding of varying functions and behaviors, with an emphasis on domain, range, critical values, and graphing techniques. Furthermore, students learn to evaluate limits, implement differentiation techniques using the power, chain, quotient, and product rules, and integrate definite and indefinite functions.  Students delve into differential and integral applications such as optimization, related rates, motion, and area.

TEXT: Applied Calculus, ISBN: 0495384283

AP Calculus AB

AP Calculus AB is a collegiate-level introduction to single-variable differential and integral Calculus. Students analyze limits, differentiation, and integrals at theoretical, conceptual, and computational levels.  Basic techniques such as power, product, quotient, and chain rule are covered. Students practice the application of derivatives, learning key concepts such as the Mean Value Theorem and Rolle’s Theorem, as well as optimization and related rates. Further analysis of critical values, intervals of increasing/decreasing in functions, as well as concavity are included. In addition, students learn how to evaluate area underneath curves by a geometrical approach using the Midpoint, Upper/Lower, Trapezoidal, and Simpson’s Rule. Implementation of both the First and Second Fundamental Theorems of Calculus provide students with direct approaches for evaluating integrals. Students continue with integration techniques such as varying substitution methods, integration by parts, and partial fraction decomposition. Applications of integration are explored as students calculate area between curves, surface area, and volume generated by revolutions.

TEXT: Calculus of a Single Variable, ISBN: 0547212909

AP Calculus BC

AP Calculus BC is an accelerated collegiate-level introduction to single variable differentiation and integral Calculus. Students analyze limits, differentiation, and integrals at  theoretical, conceptual, and computational levels. Students investigate the meaning of limits and learn basic techniques of differentiation such as power, product, quotient, and chain rule. Students explore applications of derivatives while learning key concepts such as the Mean Value Theorem and Rolle’s Theorem, as well as optimization and related rates. Further analysis of critical values, intervals of increasing/ decreasing in functions, as well as concavity are covered. In addition, students learn how to evaluate area underneath curves by first a geometrical approach using the Midpoint, Upper/Lower, Trapezoidal, and Simpson’s Rule.  Implementation of both the First and Second Fundamental Theorems of Calculus provide students with direct approaches for evaluating integrals. Students learn further integration techniques for application, where exploration of area between curves, surface area, and volume generated by revolutions are interpreted. In addition, students analyze of sequence and series, investigating convergence and divergence. Parametric equations are included with emphasis on vectors and conic sections.

TEXT: Calculus of a Single Variable, ISBN: 0547212909

Statistics

The discipline of statistics offers perspective in calculating and interpreting uncertainty. This course develops an elementary level of statistical analysis. Students learn introductory probability, distinguishing populations versus samples, translating graphical data, random variables, probability distribution functions, Central Limit Theorem, test statistics, confidence intervals, hypothesis testing, paired sampling, analysis of variance, and regression. Students will learn to decipher numerical information and comprehend its widespread applications. 

TEXT: Elementary Statistics, ISBN: 0201775700

AP Statistics

AP Statistics is a collegiate-level introduction to the discipline of statistics.  Students learn introductory probability, distinguishing population versus sample, translating graphical data, random variables, probability distribution functions, Central Limit Theorem, test statistics, confidence intervals, hypothesis testing, paired sampling, analysis of variance, and regression. By the end of the course, students will have a strong basis in deciphering numerical information and comprehending the importance of real-world applications.

TEXT: The Practice of Statistics for AP, ISBN: 142924559X

Computer Science

Upon completion of this one year elective students should have a clear understanding of Java and have confidence in approaching and solving challenging problems while recognizing ethical and social implications of using and developing software.

Not a text-based course.

AP Computer Science A

The purpose of this course is to introduce the student to the object-oriented programming paradigm using the Java programming language. This course emphasizes programming methodology, procedural abstraction, an in-depth study of algorithms and data structures, and a detailed examination of a large case study program. Students have individual hands-on laboratory work that helps to reinforce new concepts. Instruction includes preparation for the AP Computer Science A exam. Upon completion of the course, the student should have a clear understanding of Java, have confidence in approaching and solving challenging problems, and recognizing ethical and social implications of using and developing software.

Not a text-based course.

AP Computer Science Principles

AP Computer Science Principles is an introductory college-level computing course that introduces students to the breadth of the field of computer science. Students learn to design and evaluate solutions and to apply computer science to solve problems through the development of algorithms and programs. They incorporate abstraction into programs and use data to discover new knowledge. Students also explain how computing innovations and computing systems—including the internet—work, explore their potential impacts, and contribute to a computing culture that is collaborative and ethical.

Not a text-based course.

Differential Equations

This course is designed to meet the needs of advanced math students considering engineering, physics, mathematics or any computational science course in college. Differential equations are fundamental to our understanding of the world as they form the substance of the language in which many laws (such as the laws of motion in mechanics) are written. This course will cover such topics as: the existence and uniqueness theorem, Euler’s method, Runge Kutta first and higher order equations, series solutions, method of undetermined coefficients, variation of parameters and the Laplace transform.

TEXT: A First Course in Differential Equations, ISBN: 0495108243

Linear Algebra

Linear Algebra is a full year elective course that introduces students to the basic theory of linear equations and matrices, real vector spaces, bases and dimension, rank, nullity, linear transformations as matrices, determinants, eigenvalues and eigenvectors, inner product spaces, and the diagonalization of symmetric matrices. This course enables high-school students to enter college with an advantage, as Linear Algebra is a requirement for mathematics and physics majors, and is highly recommended for majors in other applied sciences, such as computer science.

TEXT: Elementary Linear Algebra, ISBN: 0471669601

Discrete Mathematics

This course is designed to meet the needs of advanced students considering engineering, computer science or mathematics in college. Discrete mathematics deals with the mathematics of communicating with a computer as designer, programmer, or user.  This requires that many problem-solving strategies be applied to real-world applications. Critical thinking and reasoning procedures for problem solving are essential.  Problems involve situations in which students collaborate while developing verbal and written skills.  Also, discrete mathematics promotes mathematical connections within and across disciplines through a wide range of problem types. In this class, technology is typically used to gather, process, and analyze data. This course covers such topics as symbolic logic, mathematical induction, probability, generating functions, relations, graph theory, spanning trees and Boolean Algebra.

TEXT: Discrete Mathematics and its Applications, ISBN: 0072424346

Introduction to Complex Analysis

This yearlong course is an introduction to Complex Analysis. The course covers the basic principles of analytic complex-valued functions of a single variable. It will address the theory as well as the various applications of the subject. Topics include the complex number system, Cauchy-Riemann conditions, analytic and harmonic functions, linear fractional transformations, roots, logs, exponential, trigonometric and hyperbolic functions. We will also cover complex integration, Cauchy’s theorem, Taylor and Laurent series, the calculus of residues, Picard’s theorem, Morera’s theorem, Rouchés theorem and will prove the Fundamental Theorem of Algebra with use of Liouville’s theorem.

Text: Complex Variables and Applications. ISBN, 9780073383170

Introduction to Real Analysis Honors

This yearlong course is an introduction to Real Analysis. The setting is as concrete as possible, most of the time presenting the analysis of Euclidean Space. It includes properties of the Real number system, continuous functions, sequences of functions, point set topology, differentiable maps and integration. This course gives a deeper, more rigorous look into concepts learned in a calculus course. The student learns to prove a variety of facts about computing limits, derivatives, and integrals. Students examine and master precise definitions as there is an emphasis on deliberate communication and writing.

A major goal of this course is to have the student learn how to read, write and understand proofs. This is not a course about problem solving, but rather being able to explain and communicate results. Although this course would fall under a “pure mathematics” veil, it does have powerful applications to engineering and physical science, as it will provide important theories for topics in control theory and quantum mechanics.

Text: Elementary Classical Analysis, ISBN: 0716721058

Multivariable Calculus Honors

The purpose of this course is to provide advanced mathematics students who completed AP Calculus BC with an opportunity to further their knowledge beyond two-dimensional Real functions and foster a greater curiosity in the applications of mathematics.

The main focal points of the course will be on functions of several variables in the xy and xyz-plane, as well as vector, polar, and parametric function analysis. Students must be proficient in topics from previous calculus studies, such as limits, continuity, applications of differentiation and integration, power series, and Taylor polynomials. New topics such as geometric surfaces in three-dimensional lanes, partial differentiation, Lagrange multipliers, multiple integrals, and vector-value functions will be introduced along side their respective theorems, such as Green and Stokes’, as well as real-world applications.

Text: Calculus, 9th edition, ISBN: 9781337654449