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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 21st 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. 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 Machine Learning, to name just a few.
Students must successfully complete mathematics through the Fifth Form year or through Trigonometry (the first term of the Precalculus sequence), whichever comes later.
Open to Sixth, Fifth, and Fourth Formers. Prerequisite: Calculus A or Calculus B. The topic for fall 2021-22 is 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.
Open to Sixth, Fifth, and Fourth Formers. Prerequisite: Precalculus. The topic for spring 2021-22 is Advanced Topics in Geometry. Does the sum of the measures in a triangle have to equal 180 degrees? Who knew there are over 300 proofs of the Pythagorean Theorem. Or, that there are quite a few ways to find the area of a triangle or that circles have different types of radii. In this class, we will start by exploring some of Euclidean Geometry's great but overlooked Theorems before investigating some of the problems that led to the development of Taxicab Geometry, Spherical Geometry, and Hyperbolic Geometry.
Open to Sixth, Fifth, and Fourth Formers. Prerequisite: Calculus A or Calculus B. The topic for winter 2021-22 is Cryptography. Cryptography, the art of scrambling a message so that only the person with the right algorithm can decipher it, has played a crucial role in history. Wars have been won and lost, cities have been defended, monarchs have been executed and banks have been made more secure through the use of cryptography. The cryptanalysts, the people who intercept messages and try to break the cipher, have the harder task to tackle, but once a method for cracking a particular code has been established the secrecy around this solution can sometimes be kept for centuries. In this course, we move from Julius Caesar to Mary Queen of Scot, to Charles Babbage to Hitler and the Enigma machine and finally to RSA and modern day encryption as used on the internet. Besides learning to encrypt and decrypt messages you will also build tools in Python to crack certain ciphers, to simulate the Enigma machine.
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.
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 sequences and series, proof by induction, and learn a variety of problem solving techniques.
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 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.
Prerequisites: Geometry 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.
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.
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.
Open to Sixth and Fifth Form Students. 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.
Prerequisite: Honors Precalculus 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.
Prerequisite: Successful completion of Precalculus (H) 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.
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 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, teamwork, and abstraction in the programming process. As a capstone to this course, students will design and implement a significant programming project of their choice.
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 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.
Open to Sixth, Fifth, and Fourth Formers. Prerequisite: completion of Algebra 2. The topic for fall 2021-22 is Networks. Consider the famous Konigsberg bridge problem. In the Prussian city of Konigsberg, there are seven bridges that cross the river Pregel. The challenge for the citizens of Konigsberg is to take a walk crossing each bridge exactly once. Leonard Euler provided a solution to this problem and he used graph theory to solve it. Whether it is social networks, transport networks or utility networks, the study of networks is crucial to everyday life. What is the cheapest way of laying cable in a town? What is the shortest route for a traveling salesman to travel in order to visit as many towns as possible? What’s the best and cheapest route in a transport network system? Given constraints in a business model, what is the optimum way to adjust your resources to maximize profit? How do you efficiently sort large repositories of data? These discrete math problems have their roots in graph theory and are ones that we will study in this course.
Open to Sixth, Fifth, and Fourth Formers. Prerequisite: completion of Algebra 2. The topic for spring 2021-22 is Statistics for Social Justice. This elective course builds on the skills of data analysis to allow students to critically consider what statistical information is available and how data is presented. The course will explore how our worldview is influenced by data. Students will be given specific projects at the outset of the course, and then will research issues of equity and social justice of their choosing.
Open to Sixth, Fifth, and Fourth Formers. Prerequisite: completion of Precalculus. The topic for winter 2021-22 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. 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.
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.
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. 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.
Prerequisites: Geometry and Algebra 2H and permission of the department. This is a fast-track Precalculus honors course and consists of the following sequence of topics: trigonometry, vectors, polar coordinates, parametric equations, matrices, probability and combinatorics, 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, exponents and logarithms, and elementary geometry. Students also learn programming in Python and apply it to solving problems from the curriculum.
Prerequisites: Geometry and Algebra 2H and permission of the department. This course consists of the following sequence of topics: trigonometry, polar coordinates, parametric equations, vectors, matrices, probability and combinatorics, 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, logarithms and exponents, and elementary geometry. 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).
Prerequisites: Geometry and Algebra 2. This course consists of the following sequence of topics: trigonometry, statistics, sequences and series, and a review of the functions studied thus far. This review of functions is algebraic, graphical, and includes modeling various mathematical situations. 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: 2411 Precalculus (F), 2412 Precalculus (W), 2413 Precalculus (S).
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 Extension School in mathematics for teaching. Kristen is the 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, daughters Linley and June, and their beagle rescue pup, Bruschi.
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.
Ida Cortez is joining the Groton community as a mathematics teaching fellow, coming from Bowdoin College in Maine. She graduated in 2020 with a double major in mathematics and history. She will be teaching Honors Precalculus this year. Her favorite activities include reading and walking in the beautiful Groton area, and she is looking forward to adopting a kitten!
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 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.
Louisa Ebby is one of Groton's 2020–21 math teaching fellows. She graduated from Williams College in 2020 with a B.A. in mathematics and environmental studies. While at Williams, she was captain of the women’s lacrosse team, a math teaching assistant, and helped run nature education programs in the local community. She also spent a semester in Denmark studying sustainability. Originally from Philadelphia, she enjoys running, hiking, and pretty much anything that allows her to be outside.
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.
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.
Assistant Director of Admission, Mathematics and Computer Science
Katie Kreider is an assistant director of Admission and teaches in the Mathematics and Computer Science Department. Prior to coming to Groton, she taught mathematics for the last two years at the Christchurch School in Virginia, after graduating from Hamilton College with a B.A. in psychology.
At Hamilton, Katie played soccer and participated in numerous community service opportunities. In addition to her work in admissions and teaching math at Groton, Katie coaches girls soccer, basketball, and tennis and serves as a dorm affiliate.
Katie has a deep love for learning and education, is passionate about living an active and healthy lifestyle, and enjoys reading and traveling with her friends and family. She loves exploring Groton and the surrounding area with her dog, Missy.
Academic Dean, Mathematics and Computer Science, Thomas S. Williams Chair
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 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.
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.
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 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.