Mathematics and Computer Science (Cont.)

Precalculus (1 credit, full year)

Prerequisite: Algebra 2/Trig

10th, 11th, 12th

This course is designed to bridge the connection from Algebra to Calculus. Topics and concepts learned in prior Algebra classes are reinforced, and new topics are introduced. The goal is to deepen mathematical understanding and the ability to synthesize concepts. Topics include functions (polynomial, rational, exponential, and logarithmic), conic sections (circles, ellipses, hyperbolas, and parabolas), and trigonometry (solving equations, graphing functions, and verifying identities). Familiarity with the following topics is expected: solving systems of equations, graphing linear equations, ratios, and proportions, and solving quadratic equations by factoring. Basic understanding of trigonometry including: Sine, Cosine, and Tangent.

Honors Precalculus (1 credit, full year)

Prerequisite: Algebra 2/Trig,Honors Algebra 2/Trig, Department Permission Required 9th, 10th, 11th

This course studies the real and complex number systems and analysis of functions (polynomial, rational, circular, trigonometric, exponential, logarithmic, and logistic). It introduces and reinforces the study of vectors in two and three dimensions, parametric functions, analytic geometry, and polar functions. The course introduces calculus through optimization, asymptotic behavior, and limits. Students are expected to apply skills and concepts learned in various novel and challenging ways throughout the course. Familiarity with the following topics is expected: solving systems of equations, graphing linear equations, ratios, and proportions, and solving quadratic equations by factoring. Basic understanding of trigonometry including: Sine, Cosine, and Tangent.

Calculus (1 credit, full year)

Prerequisite: Precalculus

11th, 12th

This course explores topics in differential calculus and simultaneously reinforces algebraic skills. Understanding and mastery of intermediate skills in algebra and precalculus are expected. Topics include limits, continuity, differential and introductory integral calculus and their applications, including problems in the area of physics, and the role of calculus as a tool for problem-solving is emphasized. This course is open to all students who have completed Precalculus or Honors Precalculus. Familiarity with the following topics is expected: solving quadratic equations by factoring, identifying parent functions & their properties, identifying & solving polynomial, logarithmic, exponential, rational, & radical equations, familiarity with basic trigonometry & physics.

Advanced Calculus AB (1 credit,

full year)

Prerequisite: Precalculus, Honors Precalculus, Department Permission Required

10th, 11th, 12th

This course mirrors a college-level Calculus course that covers limit, differential, and integral calculus. A strong understanding of algebraic skills and Precalculus functions is expected and needed to find success. Students will need to apply skills and concepts learned in various ways. All topics in this course fall under the AP Calculus AB curriculum, though additional study and preparation are advised for those wishing to take the AP exam. Familiarity with the following topics is expected: solving quadratic equations by factoring, identifying parent functions & their properties, identifying & solving polynomial, logarithmic, exponential, rational, & radical equations, familiarity with basic trigonometry & physics.

Advanced Calculus BC (1 credit, full year)

Prerequisite: Honors Precalculus, Department permission required 10th, 11th, 12th

This course mirrors a college-level Calculus course that covers limit, differential, integral polar, parametric, and vector calculus, as well as sequences and series. This course has greater breadth, pace, and depth than AB Calculus. Students are expected to apply skills and concepts learned in various novel and challenging ways throughout the course. This course prepares students to take the AP Calculus BC Exam. Familiarity with the following topics is expected: solving quadratic equations by factoring, identifying parent functions & their properties, identifying & solving polynomial, logarithmic, exponential, rational, & radical equations, familiarity with basic trigonometry & physics.

Advanced Multivariable/Vector Calculus (1 credit, full year)

Prerequisite: Advanced Calculus AB/BC, Department permission required 11th, 12th

An undergraduate-level exploration of topics in Multivariable Calculus, including multivariable functions, vectors and vector fields, differentiation and integration in multiple variables, line integrals, flux, curl, and Stokes’ Theorem. Students should expect both traditional summative assessments and collaborative problem sets and projects. This course is designed for students who have completed single variable Calculus and are excited to pursue challenging higher level topics in mathematics. It is appropriate for students interested in majoring in math, engineering, or computer science. Familiarity with the following topics is expected: derivative Calculus, integration, Taylor series, and basic vector operations.

Advanced Linear Algebra (1 credit, full year)

Prerequisite: Advanced Calculus AB/BC, Department permission required 11th, 12th

An undergraduate-level exploration of topics in Linear Algebra, including matrix Algebra, vector spaces, linear transformations, determinants, eigenvectors, and orthogonality. Students should expect both traditional summative assessments as well as collaborative problem sets and projects exploring applications in Calculus, statistics, probability, and computer science. Students will also develop rudimentary programming skills using MatLab. This course is designed for students who have completed single variable Calculus and are excited to pursue challenging higher level topics in mathematics. It is appropriate for students interested in majoring in math, engineering, or computer science. Familiarity with the following topics is expected: derivative Calculus, integration, Taylor series, and basic vector operations.