Algebra I

Algebra I is the first course of a two-year sequence in high school Algebra. The course develops algebraic skills through multiple perspectives: analytically, graphically, and numerically. Honors Algebra I also prepares students for the rigorous paces and expectations of our core mathematical courses. There is a focus on analyzing functions, particularly linear and quadratic functions, in a variety of contexts. Core skills are built for later math classes, including work with exponents, polynomials, and basic right triangle trigonometry. An emphasis is placed on algebraic problem-solving skills, conceptual understanding, and graphical analysis of functions. Students will gain facility with various technologies including graphing calculator software, spreadsheets, and various applications. Wherever possible, students work with data drawn from real world situations within the cross-curricular, thematic grade-level setting. Successful completion of Algebra I positions the student for the study of Geometry. Students who demonstrate clear mastery of algebraic fluency may be invited to complete a Geometry summer intensive to facilitate an advancement to Algebra II & Trigonometry the following year.

Prerequisite: Pre-Algebra or Equivalent Credit: MATH Period: Full Year

Geometry

Geometry seeks to build sterling algebra and spatial skills for later math classes. In a series of fast-paced units, we solidify Algebra I through study of linear systems, polynomials and factoring, exponents and radicals, and quadratic equations. Geometry covers a minimum of one semester of Geometry using more integrated and interdisciplinary methods for discovery. Students are expected to complete projects regularly, and group collaboration is one focus for this course. Geometry topics include points, lines and planes, triangles & similarity, right-angle trigonometry, circles, area and volume. An introduction to proof will be offered as time and class progress permits, and the proofs will be more algebraic and coordinate based instead of traditional proof writing. Students will gain facility with various technologies such as graphing calculators, graphing software, and spreadsheets. This is a non-honors course interspersed with opportunity to engage with higher order conceptual thinking and problem solving. Students demonstrating aptitude and a distinguished work record will be considered for Honors Algebra II & Trigonometry. Successful completion of Geometry prepares the student for the study of Algebra II.

Algebra I (Course Average: B or Higher)  with Faculty Recommendation Credit: MATH

Period: Full Year

Honors Geometry

Honors Geometry explores concepts at both a deeper and more theoretical level while also preparing students for the quick pacing of our more accelerated course offerings. It is intended for the student with a deep interest in mathematics who enjoys discovering connections. In addition to the study of core geometric concepts and relationships, the course centers on a rigorous examination of logic, conjecture, and proof.  Logical inference is a key skill across disciplines. By extending students’ primarily computational exposure to mathematics, the study of logic and proof in Euclidean Geometry lays the foundation for a more theoretical approach to high school mathematics. The class will further cover plane and solid geometry, transformations and coordinate geometry, congruence and similarity, right triangle trigonometry, and an introduction to the unit circle. Emphasis is placed on developing students’ critical thinking and collaborative skills. A solid foundation in Algebra I is a prerequisite in this accelerated class. Successful completion of Honors Geometry readies the student for the study of Honors Algebra II & Trigonometry.

Prerequisite: Honors Algebra I or Equivalent (Course Average: A- or Higher), Qualifying Score on Algebra Readiness Assessment, Faculty Recommendation Credit: MATH Period: Full Year

Algebra II 

Algebra II focuses on the analysis of functions and their applications while introducing students to a variety of topics in discrete mathematics. After exploring the algebraic, graphical, and numerical properties of general functions, specific types of functions will be examined from these perspectives. This course will develop an understanding and mastery of each of the following function families: linear, quadratic, polynomial, exponential, and logarithmic. Additional topics in discrete mathematics, such as statistics, combinatorics, and probability, will give students the tools to analyze interesting, highly relevant problems. Students learn to interpret data sets relating two variables, using linear regression and curve-fitting techniques. Real world applications and problem solving are central to each unit.

Prerequisite: Integrated Geometry Credit: MATH Period: Full Year

Honors Algebra II & Trigonometry

Honors Algebra II & Trigonometry explores concepts at both a deeper and more theoretical level. It is intended for the student capable of handling a faster pace who enjoys discovering connections. The course centers on a rigorous examination of the theory of polynomial algebra through the study of functions: linear, quadratic, polynomial, inverse functions and their transformations, a variety of equations and inequalities, polynomials, rational roots, root finding algorithms, and graphing techniques, exponential and logarithmic functions, introductory trigonometry, and if time permits, probability and combinatorics. We introduce practical applications and modeling problems through exploration and project designs. A major theme of this course is patterns in reasoning, including visual analysis, formal proof, and problem-solving. Oral and written communication concerning the logic of procedures and interpretation of results is central to our work. In the spring semester, students choose a capstone investigation: an exploration in which to dedicate themselves to their own learning and to that of the class at large. Examples of past deep-dives include algebraic topology, Pascal’s triangle, and projectile motion.

Prerequisite: Honors Geometry (Course Average: A- or Higher) or Geometry (Course Average: A+) with Faculty Recommendation Credit: MATH Period: Full Year

Introduction to Precalculus 

The focus of Intro to Precalculus is the use of functions as mathematical models. This precalculus course prepares the student for the study of statistics or calculus senior year. We work with functions that represent change – polynomial, rational, exponential and trigonometric functions. The course is taught from the point of view of the big picture ideas and project based applications of functions, so algebraic fluency and an in-depth understanding of polynomial, rational, and inverse functions from Algebra II is indispensable. This lays the foundation for cross-curricular investigations involving biological processes and sustainability. In the spring semester, our focus shifts to trigonometry, trigonometric equations, and the modeling of periodic phenomena. Topics necessary for success in either a calculus or statistics course (including conic sections, regression techniques, and sequences & series) will be studied if time permits. Students should anticipate some review of material from previous courses as a bridge towards more advanced understanding. 

Prerequisite: Algebra II Credit: MATH Period: Full Year

Precalculus 

Precalculus blends  project-based explorations with developing problem solving skills that require skill mastery in order to prepare students for Calculus senior year. The students use functions studied in their previous course in contexts arising in Precalculus. Polynomial, exponential and trigonometric functions will serve to model phenomena such as projectile motion, a vibrating string, bacterial growth. Conic sections are explored in applied contexts involving ellipses and parabolas. Integrated into the curriculum is the study of linear, exponential, and polynomial regressions, so that students may evaluate the effectiveness of various mathematical models by evaluating r-squared and plotting residuals. Students are introduced to sampling and surveying techniques. Data and research is collected from the physical sciences and social sciences, so there is a significant interdisciplinary component to the course. Intermediate algebra skills (solving quadratic, radical, exponential and logarithmic equations) are reviewed and secured in the process. A variety of pedagogical techniques will be employed to meet the needs of a diverse group of mathematical learners. If time permits, the course will further explore polar and parametric equations and sequences and series.

Prerequisite: Algebra II & Trigonometry  (Course Average: B or Higher) with Faculty Recommendation Credit: MATH

Period: Full Year

Honors Precalculus

This problem and inquiry based course focuses on the advanced study of a wide range of mathematical topics, including polynomial, exponential, logarithmic, power, and trigonometric functions, conic sections and analytic trigonometry, complex arithmetic and polar equations, and sequences and series. Additional topics such as parametric representation of functions, matrices, and vectors may be introduced as time permits. Honors Precalculus is intended for the student with a strong interest in mathematics who enjoys discovering connections. The course assignments are designed to promote and emphasize communication of mathematical ideas, persistence in solving challenging problems, self-reliance, resourcefulness, and collaboration. In the spring semester, Honors Precalculus students are expected to dedicate themselves to their own learning, and many major projects and explorations are often self directed. Examples of past deep dives are: the Golden Ratio in art and music, recursive functions in computer science, conic sections and planetary motion, Euler’s constant “e.” Deep dives encourage the student to reach beyond curricular boundaries. The pace is swift, and the student will need to have secured a solid foundation in intermediate algebra prior to this course, which means that little time is spent on review of Algebra II topics.

Prerequisite: Honors Algebra II & Trigonometry (Course Average: A- or Higher) with Faculty Recommendation or Algebra II & Trigonometry (Course Average: A+) with Faculty Recommendation Credit: MATH Period: Full Year

Statistics

Statistics is the art of using data to make numerical conjectures about problems. Descriptive statistics is the art of summarizing data. Topics include histograms, the average, the standard deviation, the normal curve, and correlation. Much statistical reasoning depends on the theory of probability: chance models, expected value, standard error, probability histograms, convergence to the normal curve. This introductory course in statistics aims at helping students see that math is part of everyday life. We will apply statistics to the worlds of politics, business, and sports. Students will be able to read and analyze statistical studies and articles. We introduce techniques of data gathering, designing and conducting surveys around their individual projects. The course is project-based and appropriate for students who enjoy a fresh take on math from a different angle than their previous algebra-based courses. Technology is integrated throughout.

Prerequisite: Introduction to Precalculus     Credit: MATH     Period: Full Year

Honors Calculus 

Calculus was developed some three hundred years ago to solve problems of change and motion. Two thousand years earlier, Greek minds puzzled over the paradox of instantaneous motion: can an arrow flying through the air be captured at any instant, as a still object suspended in mid-air? The course emphasizes an intuitive, geometric understanding of calculus concepts. We will focus on the big ideas underpinning calculus: derivatives, integrals and their connection in the Fundamental Theorem of Calculus. Working within contexts whenever possible, we will explore the meaning, use, and interpretation of the derivative; apply techniques of differentiation to solve optimization problems; use the definite integral in applications involving accumulation. Differential equations with slope fields are introduced as time permits. Physics students will relish solving problems involving distance, velocity, and acceleration.

Prerequisite: Honors Precalculus (Course Average of A- or Higher) with Faculty Recommendation Credit: MATH

Period: Full Year

Math Elective: Politics, Power, and Social Choice

This project based course introduces students to the mathematics of voting theory. We will also focus on understanding power, politics, and citizenship within the United States. Students will research another country’s voting methods and government philosophies. Collaboration and presentation permeate this course. We will analyze various methods besides “first past the post” and also gain an understanding of the complexity of and scoring of these various voting methods. After looking at alternative voting methods, students will explore the history of the Apportionment, along with finding data to perform the historical calculations, since the inception of the US Constitution. This naturally leads into the Electoral College debate and also an exploration of Gerrymandering, which serves as an excellent application of geometry and is the subject of controversy currently. Further topics include weighted voting, company and public company voting structures, power indexes to determine fairness, social choice functions, and game theoretical strategies for building a political strategy. The standards of this course are at the level of a semester college elective, and students should expect to spend time researching independently and within a group to complete the projects. We will also spend time analyzing some deeper philosophical ideas surrounding the ideas of democracy, dictatorship, and other political belief systems through the lens of mathematics. 

Prerequisite: Precalculus Credit: MATH Period: Semester

Diploma Credit: Engineering, Sustainability

Math Elective: Logic, Ethics, and Decision Making

This project based course introduces students to the mathematics of decision analysis. We will analyze the foundations of propositional logic and apply these ideas to understanding various philosophical ideas. With the advent and proliferation of Artificial Intelligence, this course also seeks to wrestle with the ethics surrounding A.I. and technology in society in general. We will spend time learning about probabilities, conditional and Baysian probability situations, and expectation from statistics. With these ideas, equipped with linearity, the main focus of the course is to develop and understand the mathematics behind decision trees and making choices independent of emotion. We will also wrestle with the ideas of regret and FOMO (fear of missing out)  in decision making. Students will have the opportunity to apply these ideas in economics, philosophy, or theology. This course is restricted to second semester seniors since we will be engaging with challenging ideas and themes. Students who enjoy big picture thinking, analytical writing, and discussions are encouraged to apply, and we encourage students who are worried about the mathematical requirements of this course to speak with the math program lead. Plenty of opportunities to demonstrate mastery beyond just math calculations will be focused on in this course. 

Prerequisite: Precalculus Credit: MATH Period: Semester

Diploma Credit: Engineering, Sustainability

AAM: Advanced Calculus

Advanced Calculus explores concepts at both a deeper and more theoretical level. Topics include limits and continuity, the derivative and its applications, the integral and its applications, the Fundamental Theorem of Calculus, differential equations with slope fields, and Taylor approximations. We will bring the graphical, numerical, and analytic methods developed throughout the course into multiple cross-curricular connections and applications. We will explore infinite sequences and series, definition and tests for convergence, Taylor series, and both polar and parametric equations. This course is equivalent to a robust college-level calculus I and II course and serves as a foundation for aspiring engineers and any student looking to take or earn credit for Calculus I and II in college.

Prerequisite: Honors Precalculus (Course Average: A or Higher) and Department Approval Credit: MATH

Period: Full Year

AAM: Multivariable Calculus

This course forms a bridge between calculus and theoretical, proof-based courses typically encountered in college. A brief introduction to proof aims at mastery of increased levels of rigor, dealing with mathematical notation, and learning how to write, present, and analyze proofs. We then extend the ideas of calculus to functions in more than one variable: lines and curves in 3D space, partial derivatives, level curves and gradients, line and surface integrals, and Lagrange multipliers. Throughout the course, we introduce Linear Algebra: the study of linear systems of equations, vector spaces, and linear transformations. Students come to understand a matrix as a linear transformation relative to a basis of a vector space. Eigenvalues, eigenvectors, and their applications in discrete dynamical systems will enable students to undertake projects in population dynamics and networking. Aspiring computer scientists will learn the underpinnings of graphics, image processing, cryptography, machine learning, and optimization. The capstone project for this course is students researching pieces of mathematical works and theorems and presenting them to a panel of STEM faculty at our mathematics colloquium.

Prerequisite: Advanced Calculus and Department Approval Credit: MATH Period: Full Year

AAM: Advanced Statistics

Advanced Statistics is intended for students with a strong mathematical background and an interest in exploring statistical inference. Statistical inference is the art of using samples to make conclusions about populations of interest. In class, we will leverage statistical concepts to explore topics that align with a typical first semester college stats course. Topics include descriptive statistics, data collection, central limit theorem, probability, expectation, confidence intervals, and hypothesis tests. The course requires creativity, logical thinking, and organization. Its objective is to provide students with pragmatic tools for assessing statistical claims and conducting their own statistical research. 

Prerequisite: Approval of Math Program Lead, Honors or Advanced Calculus, Department Approval Credit: MATH

Period: Full Year

AAM: Discrete Mathematics 

This year-long course provides a deeper study of finite systems through a survey of advanced, discrete mathematics topics that are required for further STEM research and theory. Discrete mathematics is the study of mathematical structures that are countable or otherwise distinct and separable. We work with discrete objects instead of continuous situations. Mathematically, we would work with the integer versus the irrational number. Frequently, situations in our world can be modeled with discrete mathematics. Some examples of discrete math topics include logic, counting, graph theory, networks, cryptography, game theory, decision analytics, trees, algorithms, integer programming, number theory, finance, computational complexity, and voting theory. In this course, we study the fundamental math concepts associated with these applications, which includes matrix algebra, probability and expectation, sequences and series, and counting along with a potpourri of applications to these areas of study. This course is heavily project based and requires the use of technology given the scope and size of the problems. Students should be able to draw connections to applications in engineering, computer science, and sustainability, and to demonstrate this mastery, students are expected to write and submit a thesis on a topic of their choice involving one of the topics and applications that we study. Students may propose their own topic of research for approval at the end of semester 1.

Prerequisite: Department Approval Credit: MATH, CAT Period: Full Year Diploma Credit: Engineering

*This course is cross-listed between the Math and Creative Applied Technologies programs. When registering, students must select the credit for which they would like the course to be registered. The title of the course will reflect the credit selected (e.g. "AAM: Discrete Mathematics" for Math credit). Students should consult with their advisor and review their graduation requirements. 

AAM: Advanced Seminar in Mathematics

Under the supervision of the faculty instructor, students taking this course will choose an area of mathematics to study based on their interests. The course will further develop each student's proof writing skills, techniques, and prose. Students are expected to research different theorems and applications of the theory on their own and then present their findings regularly. Some branches of mathematics that students may choose to study include Real Analysis, Complex Analysis, Differential Equations, Number Theory, or Graph Theory. The final project will consist of the students writing an exposition of a given set of theorems and applications and then presenting their results to a panel of STEM faculty, followed by a period of questioning from the panel. 

Prerequisite: Department Approval Credit: MATH Period: Full Year

AAM: Advanced Applied Math & Physics with Computer Science (CSX)

This course is an interdisciplinary offering from the computer science, physics, and math faculty. Student assignments will reflect concepts from all three disciplines including: projectile motion, orbitals, strings, particles, matrices, and area below a curve (Riemann). Simple graphics will be included as part of the course. Significant time outside of the classroom is expected. This course includes competitions in the American Computer Science League as well university-led competitions.

Prerequisite: Computer Science I and II, Precalculus, Physics, Department Approval Credit: SCI, MATH, or CAT

Period: Full Year Diploma Credit: Engineering

*This course is cross-listed between the Math, Science, and the Creative Applied Technologies programs. When registering, students must select the credit for which they would like the course to be registered. Students should consult with their advisor and review their graduation requirements.