Mathematics

Algebra I is a formal introduction to the notation, skills, and conceptual framework of the foundational principles of algebra. Students review simplifying algebraic expressions before becoming fluent in solving one-variable equations and inequalities. The course then progresses to the study of linear equations and inequalities in two variables. Emphasis is placed on the multiple representations of a linear equation, including a table of values, graph on a coordinate plane, and symbolic notation. Systems of linear equations are solved via graphical and algebraic methods. The course also includes properties of exponents, polynomial expressions, factoring, and an introduction to simplifying radical expressions. Students will develop fluency with abstract algebraic reasoning through the use of concrete and pictorial models (e.g, bar models, algebra tiles, and other manipulatives).

This course will further explore the ideas of linear and quadratic equations and graphs that were built in Algebra I while introducing the idea of functions. It will then go on to investigate new functions including both exponential and radical. The course will use a graphing calculator to help to see the relationship between the graphs of functions and their equations. In addition, calculators will be used to model real-world data and predict outcomes based on different regression analyses. Students finish the year with an introductory study of probability and statistics.

 

Focused on exploring functions both algebraically and graphically, this course builds upon students’ previous understanding of linear and quadratic functions while introducing absolute value, radical, exponential and logarithmic functions. Students will use TI-84 graphing calculators to enhance their understanding of the relationship between the graphs of functions and their equations. In addition, calculators will be used to model real-world data and predict outcomes based on different regression analyses. Students finish the year with an introductory study of probability and statistics.

The focus of this course is the study of mathematical functions both algebraically and graphically. The algebra portion of the course develops the concept of a function through the study and graphing of relations, the language of sets , functions as special relations, properties of functions, and operations on functions. This course builds upon students’ previous understanding of linear and quadratic functions while introducing absolute value, radical, exponential and logarithmic functions. Students will use TI-84 graphing calculators to enhance their understanding of the relationship between the graphs of functions and their equations. In addition, calculators will be used to model real-world data and predict outcomes based on different regression analyses. Students finish the year with an introductory study of probability and statistics.

This course approaches the study of Euclidean and coordinate geometry from both intuitive and structured perspectives. The study of logical principles, geometric transformations and constructions form the foundation for an exploration of the geometric properties of parallel lines, triangles and quadrilaterals. Congruence principles are used to prove selected properties of quadrilaterals. Unit circle trigonometry, dilations and similarity are developed using coordinate geometry approaches. Other topics include the study of polygons, angles related to circles, special right triangles, right triangle trigonometry, area and volume formulas.

This course explores topics in Euclidean geometry and coordinate geometry with an emphasis on problem solving and proof. Beginning with an introduction to logical principles, the deductive organization of geometry is developed through a combination of intuitive and rigorous investigations. The course is designed to give students a range of skills associated with this branch of mathematics and to continue their preparation for the study of precalculus mathematics. The course includes logic, isometries, geometric constructions, congruence proofs, properties of geometric figures, coordinate geometry, a study of dilations and similarity, areas of polygons, and volumes of polyhedra

This course involves a study of geometric concepts using a variety of methods, formalizing the geometric ideas first learned in lower and middle school. Concepts are explored using constructions, algebraic models, and theorems. Euclidean proof strategies are used during the study of congruence, polygons, angles related to polygons and circles, similarity, and applications of the Pythagorean Theorem. Proofs are rigorous and multi-step, preparing students to prove more complex problems. Understanding the concepts of area in two-dimensional objects and surface area and volume of three-dimensional objects finishes the year. In Honors Geometry, the focus is on rigor and precision, allowing students to begin to see the importance of notation and the universal language of mathematics.

This course reviews topics from previous algebra courses as needed through the solution of linear, quadratic, and rational equations. Advanced topics will include polynomial functions, rational functions, trigonometric functions, solution of triangles, trigonometric identities, solving trigonometric equations, circular functions and their graphs, complex numbers, conic sections and sequences and series.

This course is a preparation for advanced mathematics courses including calculus. The major topics covered in the course include the algebra of functions, analysis of polynomial functions, complex numbers, inequalities, systems of equations, exponential and logarithmic functions, analytic geometry of the conic sections, sequences and series, and mathematical induction. Students use graphing calculators for solving equations and inequalities, solving systems of equations, and envisioning mathematical models

This course is a preparation for advanced mathematics courses including calculus. Polynomials, polynomial functions, rational functions, polar and parametric equations are studied using analytical techniques and a graphing calculator. The study of complex numbers includes polar forms and roots of complex numbers. Other topics include order in the real number system, principles of exponents and radicals, operations on functions, exponential and logarithmic functions, proofs by mathematical induction, curve fitting and the analytic geometry of the conic sections.

This is a one-semester course designed to be both an introduction to statistics and a preparation for the Topics in Data Science course which is taught in the Spring semester. To that end, we will spend about half of this semester learning the basic structure and functionality of the statistical software and data analysis package R, after which we will use R to learn basic probability and statistics, including descriptive statistics, statistical visualization, and linear regression.

Topics in Data Science is an interdisciplinary course which combines ideas and concepts of Statistics and Computer Science. In this course, the students will learn how to extract data from cyberspace (or more specifically from the internet), learn how to organize the data, and learn how to understand various aspects of the re-organized data. The main tool we will use for the course is the open-source statistical software R. Most of the first half of the course will be spent teaching aspects of R which will be used in the rest of the course. An introductory knowledge of R gained through the prerequisite course options is expected of students entering the course. All students will complete a project using a real-world data set.

This course, which uses a college-level text, covers an advanced treatment of elementary functions, limits, continuity, derivatives, integration, calculus of the transcendental functions, and techniques of integration. The course is appropriate for students who wish to maintain proficiency in mathematics and who wish to explore additional mainstream mathematics for later work in science, social science, business or medicine. This course may be used as preparation for the Calculus AB Advanced Placement Examination

This course may be taken either independently of or in sequence with Advanced Probability and Statistics II. The course is designed for students who have completed a precalculus course and wish to investigate a wide variety of applications of statistical concepts. This course may be taken simultaneously with a calculus course.

Topics covered include descriptive statistics, probability, the basics of combinatorial mathematics, random variables, and experimental design. Students are introduced to R, a statistics software program that enables them to summarize data and make statistical plots.

This course extends the concepts studied in Advanced Probability and Statistics I. It may be taken simultaneously with a calculus course.

Topics covered include inference tests for proportions and means, two proportions or two means, regression, chi-squared tests, and F-tests. Students continue to use R, a statistics software program that was introduced in the first semester of the sequence. Students who take both semesters of Advanced Probability and Statistics will be prepared to take the Advanced Placement exam in Statistics.

This course, which uses a college-level text, offers an accelerated study of a rigorous undergraduate calculus curriculum. It includes a comprehensive investigation of single-variable differentiation and integration, including several applications. Units on techniques of integration, sequences and series, and differential equations are included.

This class, with guidance from the instructor, may be used as preparation for either the Calculus AB or Calculus BC Advanced Placement exam.

Linear Algebra is a one-semester course using a college-level textbook. The topics covered will include: solving linear equations using matrices, an introduction to linear transformations, general matrix algebra, the theory and applications of determinants, general vector spaces, and eigenvalues and eigenvectors. If there is time we will discuss orthogonality and least-squares problems. We will use graphing calculators for some basic computations, but we will extensively use computer algebra systems for numerical computations.

Combinatorics and Graph Theory is a one-semester course using a college-level textbook. The topics covered will include: introductory counting principles including permutations and combinations, general principles of graphs and trees, Eulerian and Hamiltonian graphs, graph coloring, and matrix applications to graphs. If we have time we will discuss other applications of graph algorithms. We will use graphing calculators for some basic computations, but we will extensively use computer algebra systems for numerical computations.

Discrete Dynamical Systems is a one-semester course using a college-level textbook. Discrete dynamical systems are studied with an emphasis on the dynamics of the quadratic map. Included in the topics covered are formal and informal approaches to periodicity and chaos; fractals; and dynamical systems including the computer code to produce Julia Sets.

Multi-variable is a one-semester course using a college-level textbook. The topics covered will include: parametric and polar curves and parametric surfaces; equations and representations of lines, planes and surfaces in three-dimensions; differentiability of multivariable functions and partial derivatives; optimization of multivariable functions, including Lagrange multipliers for constrained problems; and multiple integrals. We will use graphing calculators for some basic computations, but we will extensively use computer algebra systems for numerical computations and visualization.