Math

Students taking this course will continue previous work in translating and evaluating expressions, translating and solving equations and inequalities, exploring the meanings of variables and growth rates of equations and inequalities, and working with exponents.  Students will work to build and grow a variety of mathematical skills including but not limited to polynomial operations and factoring, translating and solving equations and inequalities with absolute values and radicals, simplifying and performing operations on exponents and radicals, solving systems of equations and inequalities, and examining both explicit and recursive equations.  In addition, students are formally introduced to the concept of a function, and the concepts of range and domain.  Introductory work with functions focuses on linear functions, studied in a variety of forms (graphs, equations, tables of values), but will also explore geometric functions as well.  The key ideas of slope as a meaningful rate of change and y-intercepts as initial values will be discussed in detail as students learn to write linear equations modeling real-world data.

Students will investigate properties of functions, which can be modeled by piecewise, absolute value, constant, polynomial (linear and quadratic), exponential, and logarithmic functions through experiences and activities.  Properties will include, but not be limited to:  domain, range, inverses, increasing/decreasing intervals, intercepts, critical points, extreme values, slope, and end behavior.  Students will understand relationships between the graph of a function and its corresponding equation.  Throughout the course, students will expand their critical thinking skills.  These skills include, but are not limited to, analysis, confidence in reasoning, clarifying conclusions, generating and assessing solutions, distinguishing relevant from irrelevant facts, and recognizing contradictions.

Students will continue to develop a sense of functions by exploring properties of trigonometric, cyclical, vector, and polar functions. Students will continue to investigate logarithmic and exponential functions. The course will emphasize the following properties of functions:  even or oddness, rates of change, inverses, domain and range and their relevant restrictions, end behavior, asymptotic behavior, period and amplitude (where applicable), increasing and decreasing intervals, concavity, and limits. Throughout the course, students are expected to think critically, reason logically and develop the ability to communicate mathematics effectively, so there is a strong emphasis on vocabulary.

This course will provide opportunities for students to further investigate and analyze the properties and applications of higher degree polynomial functions in addition to ongoing work with rational functions as well as exponential, logarithmic, and trigonometric functions. Students will work more with word problems and also be re-introduced to recursive equations and functions, and introduced to parametric functions and conic sections. They will continue to develop their modeling skills by working with compositions and combinations as needed to address applications of students’ interest. Students will also explore sequences and series and be introduced to the foundations of calculus work including, but not limited to, limits and derivatives of functions. With ongoing studies of the foundations of calculus the course provides a reasonable balance between theory and real-world modeling applications.

This college-level course offers a rigorous introduction to Calculus. The pace of the course is structured such that students are exposed to all of the material emphasized on the AP Calculus AB exam. Topics include limits, continuity, the derivative and application problems involving derivatives, methods of integration, solving differential equations, and revolutions of solids. These skills will be applied to polynomial, piecewise, absolute-value, rational, exponential, logarithmic, and trigonometric functions.

This course is primarily a course in Real-valued multivariable calculus aimed to teach the student differentiation and integration techniques in spaces of 2 or more dimensions.  In addition to these standard methods students will evaluate the progress of the foundations of Standard Calculus since its inception and attempt to cultivate a contemporary perspective on the current tools and applications of analysis.  The course also covers introductory and intermediate work with series and sequences and introductory work with Vector Algebra and Vector Calculus, with other topics added as per student interest.

This course is primarily a course in Real-valued multivariable calculus aimed to teach the student differentiation and integration techniques in spaces of 2 or more dimensions.  In addition to these standard methods students will evaluate the progress of the foundations of Standard Calculus since its inception and attempt to cultivate a contemporary perspective on the current tools and applications of analysis.  The course also covers introductory and intermediate work with series and sequences and introductory work with Vector Algebra and Vector Calculus, with other topics added as per student interest.

The aim of this semester-long course is to introduce students to the computing processes underlying the technologies of Machine Learning, or Artificial Intelligence as typified by GPT platforms and their equivalents, together with understanding the implications of these technologies and how we ought to develop our relationships to this new class of machines. The mathematical studies are interwoven with topics in the Physical Sciences including an introduction to machine Circuitry and Signal Analysis as well as studies of how signals are processed in the Human Brain ranging from quantum to cellular architectures. This course offers students the opportunity to explore mathematical models of, reason, intuition, intent, and cognition from a wide variety of frameworks. From neural networks to artificial networks to natural networks, or natural intelligence, the language of mathematics is all-pervasive and necessary for a proper understanding of our current technological revolution.

In this course, students will have the opportunity to explore the foundations of statistical inferencing through active, hands-on experimentation. By first learning best practices to collect and sort data, students will investigate the patterns and order that arise. To that end, students will examine univariate, bivariate, and multivariate data, and the distributions that help more uniformly describe them. Students will also get a chance to take a deeper look at probability, as well as the elements of experimental design, both of which have applications of immense value in the real world. Full-year statistics students have the option of taking this class for college credit.