Explore our Curriculum

Mathematics and Computer Science

The goal of the Groton School math and computer science program is to provide students with quantitative information, problem solving techniques, and the analytical skills required by the changing landscape of the twenty-first century. Through student-centered discussions, technology-based explorations, discovery exercises, and lectures, we encourage students to investigate and analyze a variety of mathematical models. By exposing students to questions that emphasize theory as well as real-world applications, we instill the ability to reason quantitatively and to arrive at solutions in an organized, detailed, and concise way. Students are expected to work individually and collaboratively, using a range of technological tools, including CAS graphing calculators, graphing software, spreadsheets, geometric modeling software, and computer programming to analyze and solve challenging problems. To meet the demands of a rapidly changing world, the department seeks to provide students with essential mathematical and technological skills.
 
We place students in courses and sections relevant to their skill level. We offer courses that are designed to provide students with skill in a range of topics in algebra, geometry, probability, statistics, calculus, discrete mathematics, and computer science. Students who complete the math program through Advanced Math Topics are encouraged to pursue the study of more advanced topics on a self-selected tutorial basis. Some notable past tutorials include Linear Algebra, Multivariable Calculus, Game Theory, Chaos and Fractals, and Object Oriented Programming.
 
Students must successfully complete mathematics through the Fifth Form year or through Trigonometry (the first term of the Precalculus sequence), whichever comes later.
  • Advanced Math Topics (F)

    Open to Sixth, Fifth, and Fourth Formers. For the 2019-20 schoolyear, AMT (F) with be Mathematical Modeling. Prerequisite: Calculus A or Calculus B. In this course we will learn how to use discrete dynamical systems and occasionally differential equations to solve advanced counting and probability problems, as well as to model and analyze situations one finds in the physical and social sciences.  In addition, we will look at how the body absorbs and eliminates medicines, various models for how populations grow, the economics of harvesting, why one should think twice before playing roulette, and the basics of genetics.
  • Algebra 1 (Y)

    This course is a thorough introduction to algebraic techniques and their applications. Basic algebraic skills will be emphasized, with some use of the graphing calculator. Topics include linear, exponential, and quadratic functions, along with polynomials, factoring and radicals. Technological tools such as graphing calculators and Desmos will be used to investigate various relationships and functions.
     
  • Algebra 2 (H) (Y)

    Prerequisites: Algebra 1 and Geometry. The department determines which students get placed in the honors section. This course will cover everything covered in the Algebra 2 regular course but with added depth and rigor. In addition, students will study the binomial theorem, sequences and series, combinatorics, and probability.
  • Algebra 2 (Y)

    Prerequisites: Algebra 1 and Geometry. This course involves reinforcement and expansion of the skills
    and concepts presented in Algebra 1. Topics include linear, quadratic, exponential and logarithmic
    functions, with emphasis placed on modeling of real-life situations. Polynomial functions, rational and
    irrational functions, and conic sections are also presented. Graphing calculators are used as an
    exploratory and computational tool. By the end of the year, students are expected to have a solid grasp
    of the elementary functions.
     
     
  • Algorithm Design and Analysis (S)

    Prerequisites: Algebra 2 and permission of the department.  No prior programming experience is required. This course introduces students to the Java programming language and the basics of procedural programming.  We will study Java’s type system, why it exists, and how it helps programmers write code that is both correct and efficient.  Students will learn techniques for analyzing programming problems and breaking them into simple parts.  We will discuss what makes a problem computationally difficult and will examine the limits of what a computer can and cannot accomplish.  Additionally, students will master debugging skills and will learn how to reduce redundancy in their code.  In short, this course aims to give students the tools they need to become successful programmers.  Students wishing to take the AP Computer Science A exam are strongly encouraged to enroll in this course the year before they wish to take the AP exam.
  • AP Computer Science (Y)

    Prerequisite: Algebra 2 and permission from the department.  Collectively, courses 2951, 2955, and 2956 constitute the equivalent of a one-semester college level course in computer science.  Students wishing to take them in sequence may opt to take them as a year long course under the AP designation. Students enrolled in AP Computer Science will be required to take the AP Computer Science Principles exam in May.
  • AP Statistics (Y)

    Prerequisite: Algebra 2 and permission of the department. The topics of study will include exploratory analysis, planning a study, probability, and statistical inference. The topics within each theme emphasize statistical thinking and minimize computational procedures. Students will utilize the powerful statistical package in the TI-NSpire graphing calculator. In all that they study, students will be required to write accurate conclusions that are supported by statistical analysis. Students will be required to take the Advanced Placement examination in May.
  • Applied Calculus (Y)

    Open to Sixth and Fifth Form Students.  Prerequisite: Precalculus. This course aims to provide students with the foundations of calculus in conjunction with its application to calculus-based physics.  Combining the theories of both calculus and physics into one course gives students the unique opportunity to make strong connections between math and science in a way that parallel courses may not always allow.  Topics likely to be covered include the basic fundamental ideas of calculus (derivatives, integrals, volumes, and basic differential equations) and physics (especially projectile motion, kinetics, and center of mass).
  • Calculus A (Y)

    Prerequisite: Honors Precalculus and permission of the department. This is a year course covering differential and integral calculus. Students will be required to take the Advanced Placement Calculus AB examination in May.  
  • Calculus B (Y)

    Prerequisite: Successful completion of Precalculus Accelerated or permission of the department. This year-long course covers the material of Calculus A as well as polar coordinates, parametric functions, Taylor and Maclaurin series, and advanced integration techniques, among other topics. Students will be required to take the Advanced Placement Calculus BC examination in May.
  • Computer Science (F)

    Prerequisites: Algebra 2 and permission of the department.  No prior programming experience is required. This is a first course in computer science and introduces students to the fundamentals of computer programming.  Using the Snap! visual programming language (UC Berkeley’s version of Scratch), students will program several classic computer games including pong, hangman, and a platformer.  Through these projects, students will learn about programming concepts such as variables, conditional statements, loops, arrays, and functions. Particular emphasis will be placed on iterative design principles and the roles of creativity and abstraction in the the programming process.  As a capstone to this course, students will design and implement a significant programming project of their choice.
  • Computer Science Game Design (W)

    Learning How to Design and Implement Video Games. Prerequisite: Algebra 2. Covering a brief history of games, as well as designing and programming a digital game, this class will require a knowledge of and ability to implement Object Oriented Programming. Not Game Theory. Game design is the process of learning how to design a game whether digital or physical.  During this class, we will learn not only how to design games in the physical realm (also referred to as “meat space”) but also design digital games.
  • Data Structures and Advanced Programming (Y)

    Prerequisites: Algorithm Design and Analysis or a demonstrated proficiency with Java and permission of the department.  (For the 2019-2020 school year, successful completion of either Introduction to Computer Science or Precalculus Honors Accelerated will be considered sufficient preparation for enrollment in this course.)

    This course takes a project-based approach to learning advanced programming techniques.  Using the Java programming language, we will study object-oriented design and other software engineering principles.  We will program Conway’s Game of Life to study the behavior of cellular automata and emergent behaviors; we will puzzle over the Towers of Hanoi and contemplate the running time of programs; and we will dabble in artificial intelligence as we code Martin Gardner’s game of Hexapawn (a simplified version of chess).  Along the way, we will encounter data structures such as stacks, queues and trees — and we will learn about how to use them to solve various programming challenges. Students who do well in this course will be encouraged to take the AP Computer Science A exam in May, but this course will also address additional topics that go beyond the scope of the AP curriculum.  
     
  • Discrete Math (F)

    Open to Sixth, Fifth, and Fourth Formers. For the 2019-29 schoolyear, Discrete Math (F) will be Iteration. Prerequisite: completion of Algebra 2. Iteration is the repetition of a process. We’ll use it as a tool to help understand the math behind modeling a wide variety of real-world situations, including but not limited to: your body’s processing of a drug; saving for retirement; spreading rumors; measuring messy coastlines/borders; and the lifespan of salmon. Along the way, we’ll meet new uses for and gain comfort with sequences and series; exponential, logarithmic, and logistic functions; matrices; fractal geometry; and chaos.  
  • Geometry (Y)

    Prerequisite: Algebra 1. Geometry is a full year course with the fall and winter terms focusing on Euclidean geometry. Topics covered in the first two terms include fundamentals of Euclidean geometry, congruence and proof, parallel lines, quadrilaterals, polygons and polyhedral, similarity, the trigonometry of triangles, circles, area, and volume. Students will explore these topics using both analytical and quantitative methods. Students will do extensive work with technological tools such as GeoGebra, Geometer’s Sketchpad, SketchUp,and graphing calculators. During the spring term students will study problems in applied geometry and modeling. Topics may include measuring the area of the Circle with Google Earth and surveying tools, creating parabolic ovens, or applying topics studied in previous terms of the course. Students will use programming and other tools to solve applied problems in geometry. This course will have an honors section that will cover all of the above topics, but in greater depth and with greater emphasis on problem solving. The department will determine which students get placed in the honors sections. Placement in the regular section puts no restriction on future math courses.
     
  • Linear Algebra and Multivariable Calculus (Y)

    Prerequisites: Calculus A or Calculus B and permission of the department. This course is year-long. Half of the course will focus on linear algebra, on matrix theory and linear algebra that will be useful in other disciplines, including systems of equations, the geometry of 3 space, linear transformations, vector spaces, determinants, eigenvalues, similarity, and positive definite matrices. Many applications will be introduced including how Google’s Page Algorithm works and how many social media sites helps one find friends. Extensive use will be made of Mathematica, a computer algebra and graphics system. The second half of the course will cover differential, integral and vector calculus for functions of more than one variable. Topics covered will include but not be limited to the following: the extrema and geometry of three dimensional surfaces, calculus based probability models, finding the area of regions and volumes of solids using double and triple integrals in a variety of coordinate systems, line integrals and their applications, and Green’s Theorem.  These mathematical tools and methods are used extensively in the physical sciences, engineering, economics and computer graphics.
  • Precalculus (H) (Acc) (Y)

    Prerequisites: Geometry and Algebra 2H and permission of the department. This is a fast-track Precalculus honors course and consists of the following sequence:  trigonometry, vectors, polar coordinates, parametric equations, matrices, transformations in 2D, complex analysis, limits, continuity, and other introductory calculus topics. During the year, there will be an ongoing cumulative review. Students will review topics from previous courses such as functions, probability and combinatorics, and elementary geometry. Students also learn programming in Python and apply it to solving problems from the curriculum. At the end of the course, students are encouraged to take the SAT Subject Test: Mathematics, Level 2. This sequence will be a year course for all students except Sixth Formers, who must complete the Fall Term but can then take the next two terms on an elective basis.
  • Precalculus (H) (Y)

    Prerequisites: Geometry and Algebra 2H and permission of the department. This year-long course consists of the following sequence of topics:  trigonometry, polar coordinates, vectors, matrices, statistics, and introductory calculus topics. During the year, there will be an ongoing cumulative review.  Students will review topics from previous courses such as functions, combinatorics and probability, logarithms and exponents, and elementary geometry. At the end of the course, students are encouraged to take the SAT Subject Test: Mathematics, Level 2. This will be a year-long course for all students except Sixth Formers, who must complete the Fall Term but can then take the next two terms on an elective basis. Sixth Formers may use the following course sequence: 2451 Precalculus (H) (F), 2452 Precalculus (H) (W), 2453 Precalculus (H) (S).
  • Precalculus (Y)

    Prerequisites: Geometry and Algebra 2. This year-long course consists of the following sequence of topics: trigonometry, probability and statistics, sequences and series, and a review of the functions studied thus far. This review of functions is algebraic and graphical, as well as for use in modeling various mathematical situations. This sequence will be a year-long course for all students except Sixth Formers, who must complete the Fall Term but can then take the next two terms on an elective basis.

    Sixth Formers may use the following course sequence:
    2411 Precalculus (F)
    2412 Precalculus (W)
    2413 Precalculus (S)
  • Statistics (Y)

    Statistics is the science of collecting, organizing, and interpreting data. With this in mind, students in this course learn how to design experiments and to interpret data. The topics include exploratory data analysis, probability and sampling distribution, survey and experimental design, making valid inferences based on data, and detecting misleading uses of statistics. Students will participate in several projects, at least one of which may involve collecting and analyzing data for a local business. Emphasis is placed on writing valid conclusions, in such a way that statisticians and non-statisticians can understand the conclusions that are being drawn. Students use technology (the TI-89 graphing calculator and/or Fathom™ software) throughout the course.

Our Faculty

  • Photo of Kristen LeRoy

    Kristen LeRoy

    Mathematics and Computer Science Department Head
    978-448-7591
    Bio
  • Photo of Michaella Chung

    Michaella Chung

    Dorm Head
    978-448-7570
    Bio
  • Photo of Jon Creamer

    Jon Creamer

    978-448-7721
    Bio
  • Photo of Nishad Das

    Nishad Das

    Director of Global Education
    978-448-7379
    Bio
  • Photo of Michael Gnozzio

    Michael Gnozzio

    978-448-7383
    Bio
  • Photo of Edward Harvey

    Edward Harvey

    978-448-7412
    Bio
  • Photo of Julie Keeling

    Julie Keeling

    978-448-7639
    Bio
  • Photo of Katharine Leggat

    Katharine Leggat

    Academic Dean, Mathematics and Computer Science, Thomas S. Williams Chair
    978-448-7266
    Bio
  • Photo of Tim LeRoy

    Tim LeRoy

    Director of Student Activities, Dorm Head
    978-448-7698
    Bio
  • Photo of Catherine Lincoln

    Catherine Lincoln

    Dorm Head, LuAnn S. Polk Coeducation Chair
    978-448-7553
    Bio
  • Photo of Nathaniel White

    Nathaniel White

    978-448-7592
    Bio
  • Photo of Zara Williams-Nicholas

    Zara Williams-Nicholas

    Mathematics Fellow
    978-448-7384
    Bio