Milton’s mathematics curriculum is designed to encourage students to develop their understanding of a rich variety of mathematical concepts, to recognize the spatial and quantitative dimensions of the world in which they live, and to appreciate the logical principles that inform those concepts. The department’s program of study acknowledges students’ varying aptitudes for this discipline. Therefore, the department offers different levels in several courses, and placement in a specific level requires the permission of the department. Honors level courses have an expectation of depth, extension, abstraction and independence in problem-solving that lends itself to identifying connections across topics. Some aspects of the course move more quickly than regular or foundations courses. Regular level courses include a structured approach to problem-solving and exploration that builds connections across topics, and allows time to consider many concepts in a real-world context. Foundations level courses provide adequate time for additional skills practice and application. Successful completion of Geometry and Algebra 2 fulfills the diploma requirement.
Students are expected to have a graphing calculator (beginning in Algebra II). The department supports the TI-83 or TI-84.
Math 1G—Algebra 1 with Geometry
This course is designed for students who have not taken a full-year algebra course, or who need to strengthen their algebra skills. The course also helps students to learn the fundamentals of geometry. This course will use geometric and graphing software to explore the key concepts, which include: linear, quadratic, exponential, and absolute value functions and equations; parallel lines, triangles, polygons, congruent and similar figures; and circles, area and volume. Upon successful completion of this course, students will proceed to Algebra 2. Enrollment in this course is limited and is granted by permission of the department.
Students come to this course with a substantial store of information about geometric relationships gained in previous coursework and through informal experiences. This course formalizes and extends their knowledge by emphasizing an axiomatic development of these relationships. Through explorations using software programs that allow the user to construct dynamic geometric models, students make conjectures about, and then investigate and prove, geometric relationships. Topics covered in this course include parallel lines, triangles, polygons, congruent and similar figures, circles, triangle trigonometry, coordinate geometry, area and volume, and a basic introduction to computer programming.
Math 3—Algebra 2
This course builds upon the foundation developed in Algebra 1 and extends students’ knowledge and understanding of algebraic concepts. The course emphasizes visual and symbolic analyses of linear, quadratic and exponential functions, as well as exponents, logarithms, sequences and series, optimization, transformations and triangle trigonometry. Other topics may include introductions to data analysis, conic sections and the properties of real and complex numbers. (Prerequisite: Geometry)
Math 4—Precalculus: Functions with Mathematical Modeling
This course examines the structure, application and connections between polynomial, exponential, logarithmic and trigonometric functions, along with rational functions and limits. The course also considers some discrete math topics, including combinatorics, probability and an introduction to statistics. Projects will allow students to pursue particular interests and see real-world connections. Goals of this course include building critical thinking and mathematical communication skills. (Prerequisite: Algebra II)
In this course students use limits of infinite processes to develop differential and integral calculus; they then use these concepts to create mathematical models. The abstract properties of elementary functions are re-examined in light of these new techniques; problems drawn from the natural and social sciences provide opportunities to apply these new concepts. (Prerequisite: Precalculus.)
Calculus and Applied Economics (Honors)
This class will introduce students to the essentials of single variable calculus and the principles of economics. Students will explore the central concepts of calculus: limits, derivatives, integrals and the Fundamental Theorem while emphasizing applications to economics. The course will also illuminate the central concepts of economics, particularly microeconomics. Economics is the study of the way consumers and producers interact in markets, and the economic way of thinking centers on cost-benefit analysis. The course will use the tools of calculus to model consumer and producer behavior and to analyze the social welfare effects of government policies. (Prerequisite: Precalculus.)
This course uses limits of infinite processes to study rates of change and areas under curves. We will then reexamine abstract properties of elementary functions in light of these new techniques. Problems drawn from the natural and social sciences provide opportunities to apply these concepts. Additional topics include infinite series, parametric equations, vector analysis, and an introduction to differential equations. (Prerequisite: Precalculus Honors and permission of the department.)
Statistics is the science of collecting, organizing and interpreting data. Students in this course learn how to analyze data from existing data sources as well as data collected from student-designed surveys and experiments. Students will also learn the importance of randomization in the collection of data and critique the validity of third-party data. This course investigates the underpinnings of probability theory, random variables and probability distributions as the basis for inferential statistics. Finally, students will apply all of these techniques to real-world and self-designed studies. Students gain mastery using a variety of technologies, including, but not limited to: MyStatLab, StatCrunch, spreadsheets and the calculator. (Prerequisite: Precalculus or permission of the department.)
Advanced Calculus and Mathematical Statistics (Honors)
This course is a calculus-based introduction to mathematical statistics. The course will cover basic probability, random variables, probability distributions, the central limit theorem and statistical inference, including parameter estimation and hypothesis testing. There are three main goals of this course: to learn the language of probability, to improve statistical intuition, and to use calculus to express and prove random concepts. Set theory, limits, sequences and series, additional methods of integration, multiple integrals and elementary differential equations will be covered. (Prerequisite: Calculus.)
This course will cover topics in multivariable calculus, including vectors, vector functions, partial derivatives, multiple integrals and vector calculus. Additional advanced topics may be included, at the discretion of the instructor. (Enrollment by permission of the department. With departmental permission, this course may be taken concurrently with Advanced Calculus and Mathematical Statistics (Honors) or Abstract Algebra and Group Theory.)
Abstract Algebra and Group Theory
This course is a proof-oriented introduction to the study of concrete categories such as sets, groups, abelian groups, fields, and vector spaces, focusing on the morphisms (functions), sub-structures, quotients, and actions within each category. Within Group Theory, topics include Lagrange’s Theorem, Cayley’s Theorem, The Isomorphism Theorems, and possibly Sylow’s Theorems. Within Linear Algebra, the course will focus on coordinate vectors, dimension, matrix representations of linear transformations, change of basis, determinants, and possibly eigenvectors. In the spring term, Linear Algebra will be applied to the study of Differential Equations. If time permits, rings, modules and topologies may also be considered. Specific attention will be given to the interplay between categories, which may involve the study of diagrams and functors. (Enrollment by permission of the department. With departmental permission, this course may be taken concurrently with any course beyond Precalculus.)
Advanced Topics in Mathematics
(Semester 1, Semester 2)
This course permits students to pursue explorations in the field of mathematics at an advanced level, for students who have already studied calculus and statistics. Topics may include number theory, topology, combinatorics, field theory, game theory or graph theory. Designed to meet the needs of the students with mathematical ideas they wish to explore in depth, this course is a seminar-style exploration of a particular field. Note: When there is a need, and staffing permits, this course may be offered as a half course. (Prerequisite: Calculus and Statistics and permission of the department.)