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 21^stcentury. 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. The Department encourages students to work both individually and collaboratively to solve real-world problems. Students are expected to use 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 skills 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: Game Theory, Graph Theory, Differential Equations, Chaos and Fractals, and Artificial Intelligence, to name just a few.

Students must successfully complete mathematics through the Fifth Form year or Precalculus, whichever comes later.

Accelerated Precalculus with Computer Programming (Y)

Prerequisites: Geometry and Algebra 2 with Trigonometry. This fast-paced course begins with an introduction to both differential and integral calculus. Using these concepts, we examine the same topics as those covered in Precalculus with Polar Coordinates with a particular emphasis on proofs and the application of vectors, polar coordinates, and complex numbers to the physical sciences. Students planning to enroll concurrently in AP Calculus BC and Advanced Physics: Mechanics are encouraged to consider taking this class instead of Precalculus with Polar Coordinates.

Students who enroll in Accelerated Precalculus with Computer Programming will learn to program in Java and will follow the curriculum for Computer Science: Object Oriented Programming (see the description for 2963). Students wishing to take Data Structures and Advanced Programming (2970) without first taking AP Computer Science should select this option.
Accelerated Precalculus with Discrete Mathematics (Y)

Prerequisites: Geometry and Algebra 2 with Trigonometry. This fast-paced course begins with an introduction to both differential and integral calculus. Using these concepts, we examine the same topics as those covered in Precalculus with Polar Coordinates with a particular emphasis on proofs and the application of vectors, polar coordinates and complex numbers to the physical sciences. Students planning to enroll concurrently in AP Calculus BC and Advanced Physics: Mechanics are encouraged to consider taking this class instead of Precalculus with Polar Coordinates.

Students who enroll in Accelerated Precalculus with Discrete Mathematics will round out their study of precalculus with an in-depth look at a single topic in discrete mathematics. Topics will vary from year-to-year. See the course description of Discrete Mathematics for details
Accelerated Precalculus with Vector Analysis (Y)

Prerequisites: Geometry and Algebra 2 with Trigonometry. This fast-paced course begins with an introduction to both differential and integral calculus. Using these concepts, we examine the same topics as those covered in Precalculus with Polar Coordinates with a particular emphasis on proofs and the application of vectors, polar coordinates, and complex numbers to the physical sciences. Students planning to enroll concurrently in AP Calculus BC and Advanced Physics: Mechanics are encouraged to consider taking this class instead of Precalculus with Polar Coordinates.

Students who enroll in Accelerated Precalculus with Linear Algebra will continue their study of vectors and matrices by considering challenging problems in 3D geometry and linear mapping.
Advanced Math Topics (F)

Open to Sixth, Fifth, and Fourth Formers. Prerequisite: AP Calculus AB or BC. The topic for fall 2024-25 is Mathematical Modeling. 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.
Advanced Math Topics (S)

Open to Sixth, Fifth, and Fourth Formers. The topic for spring is Mathematics in Literature & Art. We will use works from the literary arts and visual/performing arts to help us take a deep dive into a few fairly advanced mathematical fields. Starting with Borges’ short story The Library of Babel we will study the concept of infinity as well as transfinite numbers, advanced combinatorics, and be introduced to topology and graph theory. Other readings will include (but are not limited to) passages from Abbott’s Flatland, Melville’s Moby Dick, and Oulipo (a collective of writers and mathematicians among whom was Harry Matthews, Groton ‘47) with the intent of investigating dimensions higher than the three we live in, ‘strange’ curves, set theory, and number theory. In addition, we will look at visual/performance artists whose work has been in some way inspired by mathematics related to the topics mentioned: Sol LeWitt, Yoko Ono, Agnes Martin, Caroline Shaw, and others.
Advanced Math Topics (W)

Open to Sixth, Fifth, and Fourth Formers. Prerequisite: completion of any calculus course or concurrent enrollment in AP Calculus BC. The topic for winter 2024-25 is calculus-based statistics. This course uses the tools of calculus to examine basic probabilistic concepts of statistics in a mathematically rigorous way. Topics include: random variables and combinations of random variables; discrete and continuous distributions; unbiased estimators; significance and hypothesis testing; and some multivariate statistics. Unlike AP Statistics, this course will not focus on data or experimental design questions, turning instead to the theoretical.
Algebra 1 (Y)

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

Prerequisites: Algebra 1 and Geometry. This course involves reinforcing and building upon 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 transformations of functions are also presented. In addition, students will explore sequences and series and receive an introduction to statistics. Graphing calculators and Desmos are used as exploratory and computational tools. By the end of the year, students are expected to have a solid grasp of how to simplify, solve, and graph the elementary functions. After completing this course, students will be prepared to take Precalculus with Advanced Trigonometry.
Algebra 2 with Trigonometry (Y)

Prerequisites: Algebra 1 and Geometry. This course is for students who have already demonstrated proficiency with quadratic functions. In addition to the topics covered in Algebra 2 with Quadratics, this course expands upon the trigonometry students learned in Geometry with an in-depth exploration of trigonometric functions. Problem solving and a focus on real-world applications will be highlighted. By the end of the year, students are expected to have a solid grasp of how to simplify, solve, and graph the elementary and trigonometric functions. After completing this course, students will be prepared to take Precalculus with Polar Coordinates or Accelerated Precalculus.
AP Calculus AB (Y)

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

Prerequisite: Successful completion of Precalculus Honors Accelerated or permission of the department. This year-long course covers the material of AP Calculus AB 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.
AP Computer Science (Y)

Prerequisite: Geometry 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 Advanced Placement 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 CAS 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)

Prerequisite: Precalculus. This course introduces students to the big ideas and many applications of calculus. It covers most of the topics included in the AP Calculus AB syllabus, including limits, methods of differentiation, related rates, optimization, advanced graphing, Riemann sums, methods of integration, area, and volume, but it is not designed to prepare students for the AP Calculus exam. Throughout the course, the tools of calculus are applied to answer questions from physics, biology, chemistry, economics, and medicine. Technology (CAS, spreadsheets, and graphing tools) is utilized to help the focus remain on the ideas of calculus more than algebraic manipulation.
Computer Networks and the Internet (W)

Prerequisites: Geometry. In this course, students will explore what the internet is and how it works. Upon completing this course, students will have a solid understanding of what’s happening behind the scenes whenever they visit a website or send an email. We will learn about how computers store and transmit data, and we will consider cybersecurity questions that arise as we try to keep that data safe and private. We will study the basics of encryption and the algorithms that power modern search engines. Beyond technical details, we will examine the global impact that the internet has on society, the economy, and culture. This course is not primarily a programming course, but it will include several Python programming labs. Prior knowledge of a text-based programming language is recommended but not required.
Computer Science (F)

Prerequisites: Geometry 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 Python programming language, we will study concepts such as iteration, conditional code execution, and procedural decomposition. This will be a heavily project-based course, with students developing 4 larger programs throughout the term. Specifically, students will code a choose-your-own-adventure game, a chatbot, a random sentence generator, and a tic-tac-toe game (including a computer player that always plays optimally).
Computer Science: Object Oriented Programming (S)

Prerequisite: Computer Science. This course will cover the basics of Object Oriented Programming (OOP) through studying data structures that model objects in the real world. A Global Positioning System (GPS) is a radio navigation system that allows land, sea, and airborne users to determine their exact location, velocity, and time 24 hours a day, in all weather conditions, anywhere in the world. In order for such systems to work effectively they need to maintain
relationships with many different real world objects, and respond appropriately to human interaction. OOP allows the different components of this system to be designed independently and brought together, through event and data flow diagrams, to produce resilient, re-usable, and structurally sound software for the GPS program. This course will use the OOP language Processing to model OOP techniques. A general understanding of the basics of programming, as outlined in the Introduction to Computer Science course, is required.
Data Structures and Advanced Programming (Y)

Prerequisites: Either AP Computer Science or Algorithm Design and Analysis, or a demonstrated proficiency with textual programming language and permission of the department.

This course takes a project-based approach to learn 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. Prerequisite: completion of Algebra 2. The topic for fall 2024-25 is Sports Analytics. In this course, students will learn a variety of ways to represent team and player data. With those in hand, we’ll introduce regression tools that we can use to analyze that data, model past results, and build predictive models. Examples will come from a variety of sports, including basketball, football, hockey, and soccer. The goal will be for students to transition from being consumers of sports statistics and analytics created by others to producing their own analyses and predictive models. Students do not need any background in working with data (sports or otherwise), just curiosity about the topic.
Discrete Math (S)

Open to Sixth, Fifth, and Fourth Formers. Prerequisite: completion of Algebra 2. The topic for spring 2024-25 is Statistics for Social Justice. Can you spot misrepresentations of data in popular media? How does a neighborhood map of crime tell a different story than city-wide totals? How do statistical experts from each side of a college admissions discrimination lawsuit come to different conclusions from the same data? How do biases inherent in the design of systems like loan approvals and AI play out? How do politicians rearrange voting districts so that representation in government doesn’t accurately reflect the population they serve? What can we learn from the census? If you’re curious about these and/or similar questions, this course is for you. We’ll also explore what types of data are publicly available, what gets presented, and how the presentation of data tells a story.
Discrete Math (W)

Open to Sixth, Fifth, and Fourth Formers. Prerequisite: completion of Precalculus. The topic for winter 2024-25 is Game Theory. Game Theory is the study of how and why we make decisions and the outcomes based on the choices that are made in our interactions, outcomes which can often be counterintuitive and/or surprising. After spending a little time investigating games of chance, we will discuss and analyze some of the classic Game Theory problems; The Prisoner’s Dilemma, The Volunteer’s Dilemma, Kuhn Poker, and Blotto, to name a few. We will often do so in the hopes of learning something about morality and efficiency in choice making. A basic understanding of probability and a willingness to think critically in our game playing are the prerequisites for this course.
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 polyhedra, similarity, circles, the trigonometry of triangles, area, and volume. Students will explore these topics using both analytical and quantitative methods.

During the spring term students will study problems in applied geometry and modeling. Programming will be used as an exploratory and problem solving tool. 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 are placed in honors sections. Placement in the regular section puts no restriction on future math courses.
Geometry with Advanced Problem Solving (Y)

Prerequisite: Algebra 1 and permission of department. Geometry with Advanced Problem Solving is a full-year course covering all topics from Geometry but in more depth and breadth. The course will focus on problem-solving strategies and skills while developing mathematical communication and proofwriting. Additional topics include work with vectors, conic sections, graph theory, and algebraic representations of geometric objects. The department determines placement for this course.
Multivariable Calculus (Y)

Prerequisite: Successful completion of AP Calculus AB or AP Calculus BC. This yearlong 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 geometry and extrema 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, Green's Theorem, and Stokes' Theorem. If time allows, we will also study second-order differential equations and their applications.
Precalculus and Statistics (Y)

Prerequisites: Geometry and Algebra 2 (2340 or 2350). This course introduces students to foundational topics in trigonometry, intermediate algebra, probability, and statistics. As students learn to use mathematical concepts to model the real world, significant emphasis is placed on reviewing topics covered in previous courses. This class aims to prepare students for 2720 Applied Calculus. Students wishing to take an AP-level calculus course should enroll in Precalculus with Advanced Trigonometry, Precalculus with Polar Coordinates, or Accelerated Precalculus.
Precalculus with Polar Coordinates (Y)

Prerequisites: Geometry and Algebra 2 with Trigonometry. Designed for students who have already done significant work in trigonometry, this class supplements the curriculum for Precalculus with Advanced Trigonometry with an additional in-depth study of polar coordinates and complex numbers. After completing this course, students will be prepared to take either AP Calculus AB or AP Calculus BC.
Precalculus with Trigonometry (Y)

Prerequisites: Geometry and Algebra 2 (2340 or 2350). This full-year course introduces students to the advanced algebraic and trigonometric topics that serve as the basis for advanced courses in mathematics and physics. In particular, students will learn about sinusoidal functions, vectors, combinatorics, probability, and statistics. The course also includes a review of both infinite series and exponential functions, which collectively motivate a study of introductory calculus in the spring term. After completing this course, students will be prepared to take either Applied Calculus or AP Calculus AB.

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Our Faculty

Michael Gnozzio

Mathematics and Computer Science Department Co-Head

978-448-7383

mgnozzio@dgrzzx.com
Bio
Michael Gnozzio graduated from Groton in 2003 and returned to the Circle in the fall of 2017 to join the Department of Math and Computer Science. In the interim, he attended Williams College, earned a BA in Computer Science, and spent ten years working as a software engineer at Cogo Labs, a startup incubator that helped build some of the Boston area’s fastest growing Internet companies. His primary academic interests are in the areas of machine learning, parallel processing, and predictive modeling.

Outside the classroom, Michael helps coach the school’s Debating Society and enjoys discussing politics, religion, and philosophy—especially where those topics intersect with science and technology. He also coaches JV boys hockey. He lives with his husband Matthew and their two cats, Alex and Daphne.
Kristen LeRoy

Mathematics and Computer Science Department Co-Head

978-448-7591

kleroy@dgrzzx.com
Bio
Kristen LeRoy joined the Groton faculty in the fall of 2011. She received her B.S. from Gettysburg College in biology, minoring in math, and her master's degree from Harvard Extension School in mathematics for teaching. Kristen spent four years working in scientific research labs at Joslin Diabetes Center and Harvard Medical School before recognizing her calling as a secondary math educator. Kristen is the co-head of the Mathematics and Computer Science Department and has served in a variety of roles on campus, including dorm head and coach of the JV girls soccer, basketball, and lacrosse teams. She lives on campus with her husband, Tim, and their daughters, Linley and June.
Michaella Chung

Dorm Head

978-448-7570

mchung@dgrzzx.com
Bio
Michaella Chung teaches mathematics and environmental science. Before arriving at Groton, she earned a BS in civil engineering from Columbia University and a PhD in civil and environmental engineering from University of California, Berkeley. Michaella’s research focused on fusing together mathematics and emerging technologies to better understand watersheds and critical habitat, and she is excited to encourage her students to use mathematical theory and concepts to answer questions that they may have about the world.

Outside of the classroom, Michaella runs an Upper School girls' dorm and coaches girls cross country. She enjoys baking pies, rooting for the New York Mets, and catching up on the newest developments in the eco-hydrology world. After many years away from New England, she is excited to re-explore the region with her husband, Daniel.
Jon Creamer

978-448-7721

jcreamer@dgrzzx.com
Bio
Jon Creamer holds a B.Sc. in mathematics from Brown University and an MFA in photography from Bard College. Before arriving here in 2002, he taught at Cushing Academy and Lawrenceville.

At Groton, he teaches mathematics and supervises the Math Club. As time allows, he works on his photography and likes to travel by car or train; Wisconsin and North Dakota are the only two contiguous states he has not visited.

Jon is a 2011 recipient of the Presidential Scholars Teacher Recognition Award. His cats, Scout and Sammy, are well-known fixtures on campus.
Nishad Das

Dean of Globalism and Experiential Learning

978-448-7379

ndas@dgrzzx.com
Bio
Nishad Das began teaching mathematics at Groton in 1999, after having taught in England for nine years, at Cheltenham College and Caterham School. Both his BA, from St. Stephen’s College, Delhi University, and his MA, from Cambridge University, are in mathematics. During his years at Groton, he has taught a variety of courses ranging from Geometry, Algebra 1, and Algebra 2 to Computer Science, Precalculus Accelerated Honors, BC Calculus, Linear Algebra, and Cryptography.

Nishad chaired Groton’s Technology Committee from 2001 to 2004, a period in which the school introduced a laptop program and developed the all-school intranet. In 2004, Nishad became co-chair of the Mathematics Department, and in 2011 he dropped that position to become director of Global Education. In 2006, he received the Jonathan Choate Award for teaching and coaching.

As director of Global Education, Nishad has set up global partnerships for Groton’s GEOs (Global Education Opportunities), started an incoming and outgoing student exchange program, and worked with the Global Education student committee and Global Education student prefects to coordinate and organize various Global Education events during the academic year. He is a member of the GEBG (Global Education Benchmark Group), a group of some two hundred-plus independent schools committed to global education, and in April 2016 was elected to the GEBG board.

Outside the classroom, Nishad has coached cross country, field hockey, and was the girls varsity squash coach from 2004 to 2016. Also connected to the world of squash, Nishad chaired the Girls New England Inter-Scholastic Squash Association from 2006 to 2016. He lives on campus with his wife, Sravani Sen-Das, who chairs Groton's English Department, and their three children, the oldest of whom graduated from Groton in 2016. Nishad loves to spend time with his family in Maine, hiking kayaking, and playing board games.
Maximo Fernandez Scheinowitz

Math Fellow

mfernandezscheinowitz@dgrzzx.com
Julie Keeling

978-448-7639

jkeeling@dgrzzx.com
Bio
After being raised on her family’s Iowa dairy farm and finishing her schooling in Iowa, Julie Keeling worked in a variety of settings. Just prior to coming to Groton in 1987, she taught in Kenya, splitting her time between a rural school and a school in an impoverished section of Nairobi.

At Groton, Julie teaches mathematics courses ranging from Algebra 1 to Calculus. She has been a dormitory head, coached girls basketball, and served on numerous committees. Currently, she is an affiliate to an Upper School dorm and the advisor to the Fourth Form.

Julie has a BS from Iowa State University and an MA from the University of Iowa. She lives on campus with her two daughters, Emma and Marie. During the slower days of summer, she enjoys gardening, raising backyard chickens, reading, and traveling. Trips have included journeys to China, the birthplace of her children.
Katharine Leggat

Assistant Head for Academics, Mathematics and Computer Science, Thomas S. Williams Chair

978-448-7266

kleggat@dgrzzx.com
Bio
Katharine Leggat joined Groton after teaching at Northfield Mt. Hermon School from 1980-83. Her first job after graduating from college in 1978 was teaching in a tutorial school at Waterville Valley, a stint primarily intended to support her skiing “habit.” At Dartmouth College, Kathy majored in geography and played field hockey and ice hockey, a team she helped start her first year there.

Like many faculty at Groton, Kathy has worn numerous hats over the years: full-time mathematics teacher, dean of students, acting assistant head, dorm head, coach of varsity field hockey and girls ice hockey. She is currently the academic dean, teaches in the mathematics department, is a field hockey assistant coach, a dorm affiliate in the Lower School, and holds the Thomas S. Williams Chair.

When the School gives her time off, Kathy gardens, skis, reads, and spends time on the water. She lives on campus with her husband, fellow mathematician Jonathan Choate.
Tim LeRoy

Assistant Dean of Students, Director of Student Activities, Dorm Head

978-448-7698

tleroy@dgrzzx.com
Bio
Tim LeRoy joined the Groton faculty in 2013 after six years at Cardigan Mountain School, where he served in various roles, including math department head and head hockey coach. At Groton, Tim is the director of the Student Activities Committee (SAC), a member of the Mathematics and Computer Science Department, an Upper School boys dorm head, and a coach of girls varsity soccer, boys varsity hockey, and varsity baseball. In his free time, Tim enjoys golfing, fishing, and spending time in Maine. He lives on campus with his wife, Kristen, daughters Linley and June, and their dog, Bruschi.
Luke Tichi

Math Fellow

ltichi@dgrzzx.com
Nathaniel White

978-448-7592

NWhite@dgrzzx.com
Bio
Nat White joined the Groton faculty in 2018. He teaches math, coaches soccer and ice hockey, and serves as a dorm affiliate. A native of Milwaukee, Nat spent his undergraduate years at Williams College studying math and chemistry. Since then, he has pursued multiple passions and interests, both academic and athletic. Along the way, Nat earned an MA studying educational policy at the University of Michigan and an MS in mathematics at the University of Wisconsin-Milwaukee. He has taught math and coached at a private day school in Wisconsin and a boarding school in Connecticut. Nat is excited to work with Groton students and colleagues who demonstrate their talents and curiosity in multiple realms.

Nat lives on campus with his wife, Julie ’95, their two elementary school-aged children, and two cats. In addition to his teaching and coaching interests, Nat enjoys speedskating, cycling, hiking, camping, and reading.

Explore our Curriculum

Mathematics and Computer Science

Our Faculty