Through studying mathematics at Putney, students learn the skills necessary for academic and personal success while building deep conceptual understanding through projects, rich problems, and explorations. Our math courses cover fundamentals for college preparation while encouraging our students to explore the beauty of mathematics and its connection with other subjects.
Advanced Topics in Computer Science
Not Currently Offered
In Advanced Topics in Computer Science students build on their work from Computer Science 2. During the course of this class, students will design and build projects of their choosing in any programming language they choose. The in-class discussions will expand upon object-oriented programming and will introduce the basics of programming efficiency and runtime calculations. Prerequisite: Computer Science 1 & 2. *
* Denotes classes that combine work with a teacher (1 blocks per week) with independent, student work (3 blocks per week.) These courses require motivated students and permission from the instructor.
Advanced Topics in Mathematics
0.5 - 1.0 credit Prerequisite: Calculus 2
Advanced Topics students study mathematical topics not typically covered in a traditional secondary school mathematics sequence. In addition to building understanding about these topics, students further their ability to write about sophisticated mathematical concepts. Students also strengthen their abilities to use technology as tools for analysis and exploration. Mathematical literacy and writing are emphasized to prepare students for advanced study at the university level. Mathematical topics vary from year to year based on the interests and backgrounds of the students. In recent years, topics have included the study of satellite motion using computer models of differential equations, the science of passwords and encryption, and multivariable calculus. The anticipated focus for 2020-2021 is the intersection of calculus, probability and statistics. Depending on staffing and enrollment, this may be offered as a 1 or 2 trimester course.
Algebra students focus on how to represent, model, and analyze the world they live in using mathematics. Students examine the motion of objects, population growth, climate change, and games of chance. Representation is a major thrust of the course; students regularly use tables, graphs, algebraic symbols, and verbal descriptions to represent patterns and relations. Mathematical topics include probability, linear functions, quadratic functions, and exponential functions. Computer-based technology, including graphing software, spreadsheets, and programming, is used extensively as a tool for analysis and exploration.
In Algebra 2, students continue learning to use mathematics to recognize, generalize, and represent patterns in our world and to make predictions based on those patterns. The main theme of the course is understanding functions and building mathematical models for input-output relationships that are ubiquitous in everyday life. Students examine projectile motion, population growth, compound interest, and common logarithmic scales such as pH to learn about different ways that variables are used in linear, quadratic, higher-degree polynomial, rational, exponential, and logarithmic functions. Students increase their fluency with graphing programs and analytical software, use basic principles of statistics to analyze real-world data, and advance their skills in trigonometry.
Students in Calculus 1 learn methods for determining how a dynamical system is changing, and how to work from a description of a changing system to a complete model of the system.
Physical examples include objects moving in space, populations growing or shrinking, objects heating or cooling, and many others. The course introduces students to the basic methods of using derivatives and integrals to investigate these systems, using a conceptual understanding of limits. We emphasize a solid physical understanding of derivatives and integrals and their connection via the Fundamental Theorem of Calculus. We leverage technology extensively in this course to assist our problem solving, system visualization, and conceptual mastery. Students also develop their ability to read mathematical writing, learning skills for understanding dense and abstract text. Please note that The Putney School does not teach to the AP curriculum and that this course is not intended to prepare students for the AP exam.
Students in Calculus 2 develop a strong understanding of techniques of integration, including integration by parts, trigonometric integration, trigonometric substitution, integration of rational functions by partial fractions, and manipulations of the integrand. If time allows, students may also get an introduction to fluid mechanics and/or simple differential equations. Activities include applications of Calculus 2 content to science and engineering scenarios to demonstrate utility as well as develop problem-solving skills. The Putney School does not teach to the AP curriculum and this course is not intended to prepare students for the AP exam.
Computer Science 1
Computer Science 2
In Computer Science 2 students build on their work from Computer Science 1. Students use Python to build more complex projects. The course introduces object-oriented programming including modularity, scope, and recursion. Students set up development environments including installing external libraries and using text editors to build and run Python projects. To culminate the trimester, students will apply these new skills in an independent coding project.
In Geometry, students learn how the mathematical concepts of proof and logical reasoning are used to build models of relationships among geometric figures, both real and abstract. The course draws examples from the physical campus at the Putney School and incorporates elements of art and design in real-world applications. Students develop a stronger understanding of the properties of polygons, parallel lines, and circles, as well as a beginning understanding of trigonometry. Technology, including geometric modeling software and computer programming, is used extensively as are pencil and paper techniques. More broadly, students strengthen their ability to use mathematical thinking to analyze a wide variety of situations, gather information about them, manipulate that information, and move toward finding elegant solutions to problems using both creativity and logic.
Precalculus students expand their earlier understanding of functions to model a larger set of nonlinear situations. Students analyze how the amount of sunlight varies cyclically throughout the year, how the levels of greenhouse gasses in our atmosphere are growing, and many examples of circular motion ranging from Ferris wheels to gears and engines. Function transformations are used extensively as a method for calibrating mathematical models to given data sets. Specific mathematical content includes sinusoidal functions, exponential and logarithmic change, vectors, sequences and series, and probability and combinatorics.
In this one-trimester introduction to statistics, students learn a variety of mathematical methods to manage and understand variability in data. Many scientific, social, and economic contexts will be used to motivate different techniques. We begin with ways of summarizing data quantitatively and graphically and then turn to using statistical methods to draw conclusions in the presence of variability. Our primary technology will be spreadsheets, but we will use other tools as appropriate. Topics will include linear regression, confidence intervals, and hypothesis testing. Prerequisite: Algebra 2.