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Math & Computer Science

The College Prep Mathematics program is problem-based and student-centered.
Using an approach that integrates the traditional areas of mathematics (algebra, geometry, trigonometry, and pre-calculus) throughout four sequential levels of study, students become independent learners who excel in reading, writing about, exploring, applying, and communicating mathematical concepts. The curriculum is structured around these principles:
  • Algebra is foundational as a modeling and problem-solving tool. 
  • Geometry in two and three dimensions is integrated across topics at all levels and includes coordinate and transformational approaches.
  • The study of vectors, matrices, counting, data analysis, and other topics from discrete mathematics is woven into core courses.
  • Computer-based and calculator-based activities are part of core courses.
  • Topics are explored visually, symbolically, and verbally.
  • The capacity to develop problem-solving strategies depends on an accumulated body of knowledge.
 
These principles are addressed in the integrated curricula of courses through level four. Placement
tests are used to determine the appropriate level math class for each incoming student. The program also offers opportunities for advanced work, including AP Calculus, AP Statistics, and Multivariable Calculus. Math Club, open to all interested students, meets regularly to share ideas and investigate problems beyond the scope of the normal curriculum. Math Club also provides opportunities for students to prepare for local and national mathematics competitions.

List of 8 items.

  • Math 1

    This course develops foundational problem solving skills, the translation of prose into mathematical equations and diagrams, oral and written presentations of mathematical processes, and deep mathematical intuition. Students learn to use graphing calculators as an effective problem-solving tool. Topics from algebra and geometry are integrated and include: conversions and rates, proportional reasoning, area and perimeter, linear and quadratic equations, inequalities, and coordinate geometry. 
  • Math 2

    In this course, topics include algebra, geometry, and trigonometry. Building a repertoire of skills as they progress, students learn techniques and theorems through problem-solving. Collaborative study helps students develop their ability to reflect on and explain mathematical processes clearly. Topics covered include: lines, polygons and vectors, circles and parabolas, and right triangle trigonometry. Similarity and congruence are studied through the lens of transformations. An investigation of linear motion leads to the use of parameters and consideration of optimal paths of travel.
  • Math 3 (AB and BC)

    This course explores nonlinear motion and nonlinear functions: circular motion and the functions that describe it, ellipses and hyperbolas, exponential and logarithmic functions, dot products and matrices, and geometry on the surface of the Earth. Logarithms are used to straighten nonlinear data and matrices are used to describe geometric transformations and various patterns of growth. This course is offered at two different levels.
  • Applied Math

    This lab-based course explores topics across a broad spectrum, including pre-calculus, calculus, economics, finance, and statistics. The emphasis is on applications of mathematics that are useful in diverse academic pursuits and in a variety of fields. The course provides a review and expansion of polynomial, rational, exponential and logarithmic functions, an introduction to limits, and an exploration of mathematical modeling. Tools from calculus are introduced in order to perform relevant analysis of functions as applied to real-world contexts. Further course topics include set theory and probability, sinusoidal modeling, financial math (interest, annuities, and amortization), statistics, and a further study of selected topics from calculus. 
  • Math 4 (AB and BC)

    This course builds on the foundation of function and trigonometry from earlier courses and continues into introductory calculus. Analysis topics include: sequences and series; vectors, matrices, and determinants; polar and parametric functions; and complex numbers. Topics from discrete math include matrices, combinatorics, and probability. Trigonometry topics include sum/difference formulas and trigonometric identities. Vector topics include the dot product, the cross product, and their applications. Calculus topics include limits, first and second derivatives of the basic functions, applications to maxima and minima, and rates of change. This course is offered at two different levels.
  • AP Calculus (AB and BC)

    These yearlong courses cover differential and integral calculus at the college level. Calculus AB is the basic course, covering techniques and applications of derivatives and integrals. It prepares students for the “AB” AP Calculus Exam. Calculus BC covers the same material, as well as other topics such as infinite series and multivariable calculus; this course prepares students for the “BC” AP Calculus Exam. The Math Department advises students on which course to take based on their previous math work at College Prep.
  • Multivariable Calculus

    This course extends the concepts of differentiation and integration, which are introduced in single variable calculus, to functions of more than one variable. Students study parametric curves, polar coordinates, vectors in 2- and 3-dimensions, partial derivatives, the gradient, optimization in more than one variable, line integrals, multiple integrals, and the theorems of Green, Stokes, and Gauss (the divergence theorem). There is a substantial amount of review of single-variable calculus and other topics, as necessary. To be eligible for this course, students must have completed AP Calculus AB or BC, have an insatiable love of math, and be willing to work very hard.
  • AP Statistics

    Statistics is the art and science of collecting, organizing, analyzing, and drawing conclusions from data. This course focusses on four major themes: exploratory data analysis, designing studies, probability models and simulation, and statistical inference. Students design, administer, and tabulate results from surveys and experiments. Sampling distributions provide the logical structure for confidence intervals and hypothesis tests. Students use a TI-83/84 graphing calculator, JMP statistical software, and web-based Java applets to investigate statistical concepts. This course is recommended for anyone who is interested in any field that uses data, including the sciences, engineering, social sciences, or business studies.

Computer Science

College Prep’s Computer Science offerings provide students a diverse set of opportunities to explore different aspects of Computer Science. Students who are new to CS may take two introductory courses. The first is a broad survey of software, hardware, and communications; the history, evolution, and latest developments in the field; computer science’s theoretical foundations and fields of study; and a light introduction to programming. The other introductory course is deep dive into programming, developing proficiency in a single language (Python) while also building a foundation in the general constructs of programming languages. In the department’s advanced-level project-based course, students apply their programming skills to build embedded system prototypes using microcontrollers such as Arduinos and Raspberry Pis, sensors, and other electronics.

List of 3 items.

  • Computer Programming with Python

    Using the Python programming language, this course focuses on fundamental concepts of computer programming: abstraction, algorithms, efficiency, and data manipulation. Its simplicity and readability makes Python an ideal first programming language, and its versatility makes it an excellent choice for a wide variety of applications. Topics include: the different variables used in programming and what each is used for; Boolean logic and the use of conditional statements to control the flow of a program; and loops and how to apply recursion to solve problems. Students use functions to perform tasks that break a complex problem into smaller pieces that are easier to solve. The course also introduces programming paradigms such as functional programming and imperative programming. Students use Unix commands to operate their computers like a pro “in the command line.”
  • Computer Science Foundations

    This course is an introduction to the four pillars of computer science: algorithms, computer programming, data structures, and computer architecture. The course begins with an exploration of how the digital revolution has impacted and transformed individuals, culture, and society. The web design unit uses themed projects to teach the following: HTML (markup), CSS (styling), JavaScript (programming), and SQL (databases & data management). Students try out various hardware input devices (VR headsets, biosensors, the Leap, and more) and explore websites and apps that facilitate the emerging “Internet of Things” movement. For the course’s final project, teams of students identify and envision a technology-based project that can “improve the human condition” in a local, national, or international community group. 
  • Interactive Computing and Electronics

    This project-based course uses the Arduino, a palm-sized microcontroller, to interface with various sensors and devices to create embedded systems that accomplish a given task. Students work on mini-projects that progress in complexity throughout the course, programming the Arduino to communicate with various input devices (e.g., switches, light sensors, temperature sensors, distance sensors, etc.) and output devices (e.g., motors, speakers, LEDs, LCDs, etc.). For their final team projects, students create a digital portfolio that showcases their original proposal, research, prototyping process, obstacles faced, refinements made, lessons learned, and a demo of their project. Past projects include using laser diodes to build a home security system, making a robot that can solve a maze, programming a game of pong on an LED matrix, and creating an interactive art exhibit. Students learn design concepts while accomplishing their goals within the project budget and timeline. The course concludes with a final presentation of the team projects to the College Prep community.

Math

List of 10 members.

The College Preparatory School

mens conscia recti

a mind aware of what is right
Photo Credit: Dan Battle, Mark Compton, Bosky Frederick, Polly Lockman, Richard Wheeler, and Jonathan Zucker.