High School Courses

Mathematics

The math department aims to develop each student's intellectual independence, creativity, and sense of community responsibility through the study of Algebra, Geometry, Calculus, and in math courses beyond the standard high school curriculum. Within each course, we seek to find the proper balance between the following:
  • the preparation necessary for college-level mathematics work,
  • the study of mathematics that is relevant and illuminating,
  • the application of mathematics in social and scientific contexts.

REQUIREMENTS FOR GRADUATION
Successful completion of three years of mathematics (3 credits).

LEVELS AND PLACEMENT
In order to meet each student's interests, abilities, and needs, the math department offers courses at different levels in every subject. Courses at different levels take different approaches to the study of mathematics. In general, Foundations and Standard courses focus on the applications of mathematics while '1A' and '2A' courses emphasize the study of mathematical theory.

Dalton students vary greatly in their attitudes towards math, and the math department hopes to support every student in finding a course that sparks interest and joy in mathematics while providing an appropriate level of challenge. When selecting a course, students should consider their interest level, their preparation, and their anticipated schedule of academic and co-curricular responsibilities. A student's placement at each level is based on their expressed interest, academic record, and teacher recommendation.

CURRICULUM OUTLINE
Courses in the Mathematics Department are structured as follows, with Math Team available at all levels:

9th grade
Foundations of Algebra
Algebra 2
Algebra 2 - '1A’
Algebra 2 - '2A’

10th grade
Foundations of Geometry
Geometry
Geometry ‘1A’
Geometry ‘2A’

11th grade
Foundations of Precalculus
Precalculus
Precalculus '1A’
Precalculus '2A’

12th grade
Calculus
Calculus '1A’
Calculus '2A’
Statistics
Statistics ‘A’
[NEW COURSE] Linear Algebra ‘2A’
Collaborative Problem Solving (offerred through Interschool)
Game Theory (offerred through Interschool)
  • Algebra 2

    This class is designed with all students at Dalton in mind. Algebra 2 continues the study of functions from 8th grade Algebra and incorporates the application of those functions to mathematical models. Students will become proficient working with a set of functions that have broad applications. This course prepares students for future study in math, science, and engineering.

    Full Year Course, 1.0 credit
  • Algebra 2

    This class is designed with all students at Dalton in mind. Algebra 2 continues the study of functions from 8th grade Algebra and incorporates the application of those functions to mathematical models. Students will become proficient working with a set of functions that have broad applications. This course prepares students for future study in math, science, and engineering.

    Full Year Course, 1.0 credit
  • Algebra 2 Accelerated ‘1A’

    This honors class is designed for students who seek a challenging experience in math. Students are expected to become comfortable engaging with novel problems and creating mathematical models to represent real world situations. This course covers the standard Algebra 2 curriculum in greater theoretical depth.
     
    Requires Preapproval
    Minimum requirements: completion of 8th grade Algebra (conceptual) or department approval
    Full Year Course, 1.0 credit
  • Algebra 2 Accelerated '1A'

    This honors class is designed for students who seek a challenging experience in math. Students are expected to become comfortable engaging with novel problems and creating mathematical models to represent real world situations. This course covers the standard Algebra 2 curriculum in greater theoretical depth.
     
    Minimum requirements: grade of A in 8th grade Algebra (standard) or completion of 8th grade Algebra (conceptual)

    Full Year Course, 1.0 credit

    Requires Preapproval
  • Algebra 2 - '2A’

    This high honors class is designed for students who seek the highest level of challenge in Algebra offered by the math department. Students are expected to complete demanding work and maintain a quick pace. Each topic is given a formal and rigorous treatment. In addition to the standard Algebra 2 curriculum, students will study the complex plane, conic sections, and trigonometry.

    Minimum requirements: completion of 8th grade Algebra (conceptual) with department approval
    Full Year Course, 1.0 credit    

    Requires Preapproval
  • Algebra 2 and Precalculus ‘2A’

    This high honors class is designed for students who seek the highest level of challenge in Algebra offered by the math department. Students are expected to complete demanding work and maintain a quick pace. Each topic is given a formal and rigorous treatment. In addition to the standard Algebra 2 curriculum, students will study the complex plane, conic sections, and trigonometry.

    Requires Preapproval
    Minimum requirements: completion of 8th grade Algebra (conceptual) with department approval
    Full Year Course, 1.0 credit
  • Algebra 2 and Precalculus '2A'

    This high honors class is designed for students who seek the highest level of challenge in Algebra offered by the math department. Students are expected to complete demanding work and maintain a quick pace. Each topic is given a formal and rigorous treatment. In addition to the standard Algebra 2 curriculum, students will study the complex plane, conic sections, and trigonometry.

    Minimum requirements: grade of A in 8th grade Algebra (conceptual)
    Full Year Course, 1.0 credit
    Requires Preapproval
  • Geometry

    This class is designed with all students at Dalton in mind. Geometry is the study of points, lines, planes, and two- and three-dimensional figures. Through the standard Geometry curriculum, students will become proficient in proof-writing and logical reasoning. The units on right triangle trigonometry and coordinate geometry connect the study of Geometry with that of Precalculus.
     
    Requires Preapproval
    Minimum requirements: completion of Algebra 2 (or equivalent).
    Full Year Course, 1.0 credit    
  • Geometry ‘1A’

    This honors class is designed for students who seek a challenging experience in math. Students are expected to become comfortable with developing their own conjectures about geometric objects and proving or disproving them through logical reasoning. This course follows the standard Geometry curriculum and gives each topic an extended and enriched treatment.

    Requires Preapproval
    Minimum requirements: satisfactory completion of  Algebra 2-‘1A’ or department approval
    Full Year Course, 1.0 credit
  • Geometry ‘2A’

    This high honors class is designed for students who seek the highest level of challenge in Geometry offered by the math department. Students are expected to complete demanding work and maintain a quick pace. Each topic is given a formal and rigorous treatment. In addition to the standard Geometry curriculum, students will study cyclic quadrilaterals, Menelaus’s and Ceva’s theorems, homothety, and the nine-point circle.
     
    Requires Preapproval
    Minimum requirements: satisfactory completion of Algebra 2-‘2A’.
    Full Year Course, 1.0 credit    
  • Precalculus

    This class is designed with all students at Dalton in mind. Students are expected to become proficient in the skills and concepts necessary for the study of Calculus. In addition to a review of major topics from Algebra 2, this course covers the applications of conic sections, trigonometric functions, and sequences and series. The course will introduce limits in preparation for Calculus.

    Requires Preapproval
    Minimum requirements: completion of Algebra 2 and Geometry
    Full Year Course, 1.0 credit    

    Requires Preapproval

  • Precalculus '1A'

    This honors class is designed for students who seek a challenging experience and who may be interested in future study of math, science, computer science, or engineering. Students are expected to become comfortable engaging with novel problems. The course covers the standard Precalculus curriculum both in theory and in how those topics are applied in science and engineering. Students will complete the first topic of Calculus – limits – by the end of the year.

    Requires Preapproval
    Minimum requirements: satisfactory completion of Algebra 2-‘1A’ and Geometry ‘1A’
    Full Year Course, 1.0 credit    
  • Precalculus '2A'

    This high honors class is designed for students who seek the highest level of challenge in Precalculus offered by the math department and who may be interested in future study of math. Students are expected to complete demanding work and maintain a quick pace. In addition to the standard Precalculus topics, students study combinatorics, recursion, and induction. Each topic is given a formal and rigorous treatment. The course covers most of the first semester of a standard Calculus curriculum by the end of the school year.

    Requires Preapproval
    Minimum requirements: satisfactory completion of Algebra 2-`2A’ and Geometry `2A’ (or equivalent) 
    Full Year Course, 1.0 credit
  • Calculus

    This course is designed with all students at Dalton in mind. Students will become proficient in the methods and concepts of Calculus. This includes methods for finding the slopes of curves and the area under and beneath curves along with their applications in science and engineering. Calculus serves as a capstone of the high school math curriculum, incorporating ideas from each previous year of study.

    Requires Preapproval
    Minimum requirements: completion of Precalculus
    Full Year Course, 1.0 credit
  • Calculus '1A'

    This honors class is designed for students who seek a challenging experience and who may be interested in future study of math, science, computer science, or engineering. Students are expected to be comfortable engaging with novel problems. This year-long course is equivalent to a one-semester college course in Calculus, and topics are explored both in theory and in how they are applied in science and engineering.

    Requires Preapproval
    Minimum requirements: satisfactory completion of Precalculus ‘1A’.
    Full Year Course, 1.0 credit
  • Calculus '2A'

    This high honors class is designed for students who seek the highest level of challenge offered by the math department and who may be interested in future study of math. Students are expected to complete demanding work and maintain a quick pace. Each topic is given a formal and rigorous treatment. This year-long course is equivalent to a two-semester college sequence in Calculus.

    Requires Preapproval
    Minimum requirements: satisfactory completion of  Precalculus ‘2A’
    Full Year Course, 1.0 credit
  • Statistics

    This class is designed for students who are interested in how math is applied. This course covers methods of data analysis, the design of surveys and experiments, topics in probability, and methods for drawing sound inferences from data. Students will collect data from a variety of sources, complete independent and group projects, discuss contemporary issues through a statistical lens, and create models using statistical software.

    Prerequisite: completion of Precalculus.
    Full Year Course, 1.0 credit    
  • Statistics 'A'

    This honors class is designed for students who are interested in how math is applied and who seek a challenging experience. Students are expected to engage with statistical concepts with more mathematical sophistication. This course follows the standard Statistics curriculum and gives each topic an extended and enriched treatment.

    Minimum requirements: grade of A in Precalculus or grade of B in Precalculus ‘1A’ or completion of Precalculus ‘2A’.
    Full Year Course, 1.0 credit
  • Linear Algebra '2A'

    This high honors class is designed for students who seek the highest level of challenge offered by the math department and who may be interested in future study of math. In Linear Algebra, students explore linear equations and their representations as matrices and vectors. This course is central to many areas of math, science, and engineering and is equivalent to a one-semester college course. It is an important step for future math majors. Students are expected to complete demanding work in a rigorous and formal context.

    Requires Preapproval
    Minimum requirements: grade of A in Calculus ‘1A’ or completion of Calculus ‘2A’.
    Seniors may take Linear Algebra concurrently with Calculus ‘1A’ or Calculus ‘2A’ with department approval.
    Full Year Course, 1.0 credit
  • Math Team

    The Dalton Math Team participates in math contests at the city, state, and national levels. Math contests provide an engaging challenge for students who enjoy solving novel problems. While only knowledge of Algebra and Geometry is required, math contest problems require inventive thinking. Through math team participation, students develop better problem solving skills that can be applied in their core academic courses and beyond.

    Full Year Course, 0.25 or 0.5 credits
  • IS: Math

    Independent studies are opportunities for 10th, 11th, and 12th grade students to pursue ideas and passions not covered by current course work.  

    Students must complete this form to apply for preapproval.

    Requires Preapproval
    Graded Pass/Fail
    Fall or Spring Semester Course, 0.25 credits
  • Chaos Theory and Fractals

    Chaos theory, a cutting-edge field of math that took off with the advent of modern computing, has applications in everything from meteorology to the stock market and beyond. In this course, we will study fundamental ideas in chaos theory and the mathematical discipline of dynamical systems, an area of math focused on systems that change over time. Starting with the idea of iteration, we will explore how small changes in initial conditions can produce big differences in outcomes. We will come to understand a hallmark of chaos theory and dynamics: even the most simple and deterministic systems can produce unpredictable behavior and even the most complex systems can reveal some kind of order. Finally, we will see how these ideas apply to the beautiful world of fractals, including the Julia sets and the Mandelbrot set.

    This course is offered by Interschool (at Spence) once a week in the evening.
    Full Year Course, 0.5 credits
  • Collaborative Problem Solving

    In this elective course students work together, in an informal atmosphere, to solve challenging math problems. Problems are taken from a variety of topics, including algebra, geometry, combinatorics, probability, and number theory. Problems are chosen for their interest, they are sometimes discussed for fairly long periods of time, and they are tackled collaboratively. The class should be of interest to students who love math and want to learn more, and to students who want to become better problem solvers. 

    This course is offered by Interschool (at Dalton) once a week in the evening.

    Full Year Course, 0.5 credits
  • Game Theory

    Game Theory is the mathematical analysis of conflict and cooperation, where “players" can include individuals, corporations, governments, or even nature. The theory attempts to predict, explain or recommend courses of action in situations where one player's success depends on the decisions of all players. The theoretical analysis of such situations is taught through applications in economics, politics, business, evolutionary biology, religion, philosophy, military strategy, computer science, and sports, as well as through games such as poker and chess.  Students will develop quantitative models for strategic situations, and analysis will include optimization and graphical analysis.

    This course is offered by Interschool (at Dalton) once a week in the evening.

    Full Year Course, 0.5 credits
  • Linear Algebra

    This high honors class is designed for students who seek the highest level of challenge offered by the math department and who may be interested in future study of math. In Linear Algebra, students explore linear equations and their representations as matrices and vectors. This course is central to many areas of math, science, and engineering and is equivalent to a one-semester college course. It is an important step for future math majors. Students are expected to complete demanding work in a rigorous and formal context.

    Requires Preapproval
    Minimum requirements: grade of A in Calculus ‘1A’ or completion of Calculus ‘2A’.
    Seniors may take Linear Algebra concurrently with Calculus ‘1A’ or Calculus ‘2A’ with department approval.
    Full Year Course, 1.0 credit
  • Multivariable Calculus

    In this course, students learn to differentiate and integrate functions of several variables. We extend the Fundamental Theorem of Calculus to multiple dimensions and the course will culminate in Green's, Stokes' and Gauss' Theorems. The course opens with a unit on vectors, which introduces students to this critical component of advanced calculus. We then move on to study partial derivatives, double and triple integrals, and vector calculus in both two and three dimensions. Students are expected to develop fluency with vector and matrix operations. Understanding parametric curve as a trajectory described by a position vector is an essential concept, and this allows us to break free from one-dimensional calculus and investigate paths, velocities, and other applications of science that exist in three-dimensional space. We study derivatives in multiple dimensions and use the ideas of the gradient and partial derivatives to explore optimization problems with multiple variables as well as consider constrained optimization problems using Lagrangians. After our study of differentials in multiple dimensions, we move to integral calculus. We use line and surface integrals to calculate physical quantities especially relevant to mechanics, electricity and magnetism, such as work and flux. We will employ volume integrals for calculations of mass and moments of inertia and conclude with the major theorems (Green's, Stokes', Gauss') of the course, applying each to some physical applications that commonly appear in calculus-based physics. Prerequisite: The equivalent of a college year of single-variable calculus, including integration techniques, such as trigonometric substitution, integration by parts, and partial fractions. Completion of the AP Calculus BC curriculum with a score of 4 or 5 on the AP Exam would be considered adequate preparation.

    This course is offered through our partnership with Global Online Academy (GOA).
    Full Year Course, 1.0 credits

    Requires Preapproval
  • Multivariable Calculus '2A'

    This high honors class is designed for students who seek the highest level of challenge offered by the math department and who may be interested in future study of math. In Multivariable Calculus, students extend what they learned in Calculus ‘2A’ to higher dimensions. This one year course is equivalent to the last traditional semester of college Calculus.  Students will study vector algebra and functions, matrices, curves in space, arc length and curvature, and velocity and acceleration.

    Minimum requirements: grade of A in Calculus ‘1A’ or completion of Calculus ‘2A’.
    Seniors may take Multivariable Calculus concurrently with Linear Algebra with department approval.
    Full Year Course, 1.0 credit    
    Requires Preapproval
  • Number Theory

    Once thought of as the purest but least applicable part of mathematics, number theory is now by far the most commonly applied: every one of the millions of secure internet transmissions occurring each second is encrypted using ideas from number theory. This course covers the fundamentals of this classical, elegant, yet supremely relevant subject. It provides a foundation for further study of number theory, but even more, it develops the skills of mathematical reasoning and proof in a concrete and intuitive way and is necessary preparation for any future course in upper-level college mathematics or theoretical computer science. We progressively develop the tools needed to understand the RSA algorithm, the most common encryption scheme used worldwide. Along the way we invent some encryption schemes of our own and discover how to play games using number theory. We also get a taste of the history of the subject, which involves the most famous mathematicians from antiquity to the present day, and we see parts of the story of Fermat’s Last Theorem, a 350-year-old statement that was fully proven only twenty years ago. While most calculations will be simple enough to do by hand, we will sometimes use the computer to see how the fundamental ideas can be applied to the huge numbers needed for modern applications. Prerequisite: A strong background in precalculus and above, as well as a desire to do rigorous mathematics and proofs. 
     
    This course is offered through our partnership with Global Online Academy (GOA).
    One Semester Course, Fall and Spring, 0.50 credits

    Requires Preapproval
  • Transformational Geometry 'A'

    This course is designed for the advanced student who has demonstrated a certain ease and facility with mathematical thinking as determined by individual evaluation.  It is an HONORS COURSE and presents the topics of transformational geometry in a rigorous manner.  Topics include: the four isometries in the plane and their role in the theory of congruence; geometry of the circle; the plane shear as an area preserving mapping and its application to orthogonal projections; the similarity transformation and an overall look at the concepts of co linearity and concurrency.  The course concludes with a full introduction to solid geometry.
     
    Prerequisite: strong completion of algebra 2A and placement by the math department

    Full Year Course, 1.0 credit
    Requires Preapproval

Faculty

  • Photo of Tao Wang
    Tao Wang
    High School Math Teacher and Department Chair
    Columbia University School of Engineering and Applied Science - B.S.
    Teachers College, Columbia University - M.A.
    Georgia Institute of Technology - M.S.
  • Photo of Jasmine Bensky
    Jasmine Bensky
    High School Mathematics Teacher
    University of Michigan - B.A.
    Teachers College, Columbia University - M.S.
  • Photo of Lisa Borenstein
    Lisa Borenstein
    High School Mathematics Teacher
    Massachusetts Institute of Technology - B.S.
    M.I.T. - M.S.
    Hunter College - M.A.
  • Photo of Daniel Cohen
    Daniel Cohen
    Mathematics Teacher
    University of Michigan - B.G.S.
  • Photo of Jennifer Collins
    Jennifer Collins
    HS Math Extension Teacher (T3)
    Columbia University School of General Studies - B.A.
    Columbia University, Teachers College - M.A.
  • Photo of David Gomprecht
    David Gomprecht
    High School Mathematics Teacher
    Wesleyan University - B.A.
    University of California at Berkeley - Ph.D.
  • Photo of Katherine Kim
    Katherine Kim
    HS Math Teacher
    University of Toronto - H.B.S.
    University of Toronto - M.T.
  • Photo of Guy Manuel
    Guy Manuel
    High School Mathematics Teacher
    Ecole Nationale des Ponts et Chaussees - M.S.
    MIT - Ph.D.
    Harvard University - M.B.A.
  • Photo of Ezra Nelson
    Ezra Nelson
    HS Math Faculty
    Brown University - B.A.
    Yale School of Management - M.B.A.
  • Photo of Megan Preis
    Megan Preis
    HS Math Teacher
    Bennington College - B.A.
    Johns Hopkins University School of Education - M.S.
(Grades K-3) 53 East 91st Street
New York, NY 10128
General: (212) 423-5200 | Admissions: (212) 423-5463
General: info@dalton.org | Admissions: fpadmissions@dalton.org

(Gr. 4 Dalton East & PE Center) 200 East 87th Street
New York, NY 10128
General: (212) 423-5200 | Admissions: (212) 423-5262
General: info@dalton.org | Admissions: admissionsmshs@dalton.org

(Grade 5-12) 108 East 89th Street
New York, NY 10128
General: (212) 423-5200 | Admissions: (212) 423-5262
General: info@dalton.org | Admissions: admissionsmshs@dalton.org