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

Kristen LeRoy

Mathematics and Computer Science Department Head

978-448-7591

kleroy@groton.org
Bio
Kristen LeRoy joined the Groton faculty in 2011 after working for four years at Harvard Medical School in a scientific research lab. She received her B.S. from Gettysburg College in biology, minoring in math, and her master's degree from Harvard in mathematics for teaching. Kristen is a coach for JV girls soccer and JV girls basketball and lives on campus with her husband, Tim, daughter, Linley, and their dog, Bruschi.
Michaella Chung

Dorm Head

978-448-7570

MChung@groton.org
Bio
Michaella Chung teaches mathematics. 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 us e mathematical theory and concepts to answer questions that they may have about the world.

Outside of the classroom, Michaella is an affiliate in a Lower School dorm. 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@groton.org
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. He runs the second form boys dorm with the considerable help and care of the prefects and affiliates, coaches thirds boys soccer or basketball, depending on the year, and is a Choices leader. 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

Director of Global Education

978-448-7379

ndas@groton.org
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 seventeen 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.
Michael Gnozzio

978-448-7383

mgnozzio@groton.org
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.
Edward Harvey

978-448-7412

EHarvey@groton.org
Bio
Eddie Harvey joined the Groton faculty as a math teacher in 2018, after spending three years at Cambridge Associates, an investment advisory firm that serves a variety of endowments and foundations, including many private schools. Prior to working in finance, Eddie graduated cum laude from Dartmouth College with a major in economics and a minor in Spanish. There he co-captained the lightweight crew team, tutored econometrics, and led backpacking trips in the White Mountains with the Dartmouth Outing Club’s First Year Trips Program.

In addition to teaching a variety of math courses, Eddie coaches cross country in the fall and rowing in the spring, and serves as a dorm affiliate. He enjoys teaching statistics because it is an unloved branch of math that has many applications across STEM fields and the social sciences.

Eddie picked up endurance sports in high school and has followed these passions ever since. Depending on the season you will find him running on a road, gliding on a cross-country ski trail, rowing on a river, or hiking on a mountainside.
Julie Keeling

978-448-7639

jkeeling@groton.org
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

Academic Dean, Mathematics and Computer Science, Thomas S. Williams Chair

978-448-7266

kleggat@groton.org
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

Director of Student Activities, Dorm Head

978-448-7698

tleroy@groton.org
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 and boys varsity hockey. In his free time, Tim enjoys golfing, fishing, and spending time in Maine. He lives on campus with his wife, Kristen, daughter, Linley, and their dog, Bruschi.
Catherine Lincoln

Dorm Head, LuAnn S. Polk Coeducation Chair

978-448-7553

clincoln@groton.org
Bio
After graduating from Connecticut College in 1980, Catherine Lincoln joined Groton as a math intern, then was hired to be a full-time math teacher, coach, and dorm head. After serving as co-head of the Math Department for more than fifteen years, Cathy continues to teach but now devotes more time to crisis management and mitigation. She holds the LuAnn S. Polk Coeducation Chair.

After raising her children, Cathy moved back into the dormitory and now heads an Upper School dorm. Her dorm apartment has a huge fireplace, and she enjoys having the girls in for hot chocolate in front of a roaring fire. Over the years, Cathy has coached girls varsity and thirds soccer and girls varsity crew; currently, she times varsity basketball games.

Cathy is an EMT and a nationally certified firefighter for the Town of Groton, as well as mother to Alex ‘07 and Abigail ’10. She has a master’s from Dartmouth College. When she finds time, she can be found baking in her kitchen or working in her gardens.
Nathaniel White

978-448-7592

NWhite@groton.org
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.
Zara Williams-Nicholas

Mathematics Fellow

978-448-7384

zwilliams-nicholas@groton.org
Bio
Zara Williams-Nicholas is the 2019–20 Mathematics Teaching Fellow. They graduated from Swarthmore College in 2019 with a double major in mathematics and dance. At Swarthmore, Zara worked as a peer tutor for the Mathematics Department and choreographed for the school's Dance Department. In their free time, Zara also worked as a SAT mathematics tutor for Jamaican students.

Zara is originally from Jamaica and enjoys learning how to garden and farm. They can sometimes be found walking around their community, admiring the trees and flowers.