# Mathematics

We believe that inquiry and the construction of knowledge are essential elements of each student’s educational experience. Park’s mathematics program provides opportunities for students to become more mathematically aware, capable, and confident.

Mathematics enables students to develop a better understanding of our world, to create and discover patterns and ideas, and to appreciate a compelling form of inquiry and argument. Making connections between different areas of mathematics is a major component of our department’s program. We believe the study of mathematics is a unified body of knowledge that emphasizes problem solving and generalization. Applications will engage students and promote their ability to communicate and reason mathematically.

To these ends, all Park students take courses that allow them to become better problem-solvers. Students learn algebra, geometry, trigonometry, and other topics through a discovery process and are routinely expected to apply these concepts in novel situations.

Requirements

Two years of mathematics are required for graduation. However, most Park students complete mathematics for all four of their years in the Upper School. Students cover the material on the SAT Subject Test in mathematics by the end of 11th grade.

Students are placed in appropriate mathematics classes by the Mathematics Department and are encouraged to visit the Mathematics/Science Office for assistance from faculty members at any time; peer tutors are also available.

A TI-83+ or TI-84+ graphing calculator is required for all classes.

**Note: **Our goal is for students to take the math courses most appropriate for them. Each level within the core curriculum in grades 9, 10, and 11 will appear as Math 9, Math 10, and Math 11 on student transcripts.

**Math 9Grade 9** •

**Required**

This course is required at one of four levels: Math 9-1, Math 9-2, Math 9-3, or Math 9-4.

**Math 9-1Grade: 9**This course explores advanced algebraic and geometric content through an emphasis on problem solving, reasoning, and proof. Topics include graph theory, laws of exponents and radicals, the algebra of rational expressions, quadratic equations, Euclidean and coordinate geometry, and unit-circle trigonometry.

**Math 9-2, Math 9-3, and Math 9-4Grade: 9**These courses explore algebra, geometry, and the connections between the two, with an emphasis on developing students’ ability to solve problems through a variety of approaches. Topics include algebra, coordinate geometry, systems of equations, trigonometry, quadratic functions, and combinatorics, with a consistent focus throughout on reasoning and proof.

**Math 10Grade 10** •

**Required**

This course is required at one of four levels: Math 10-1, Math 10-2, Math 10-3, or Math 10-4.

**Math 10-1Grade: 10**

Students expand upon the understanding of algebra and geometry gained in Math 9-1. They explore exponential and logarithmic functions, combinatorics, sequences and series, graphical transformations, polynomials and rational functions, circular motion and the trigonometric functions, trigonometric identities, complex numbers, and begin the study of infinitesimal processes.

**Math 10-2, Math 10-3, and Math 10-4Grade: 10**

These courses examine algebra, geometry, and discrete mathematics, but in greater depth than the previous year, with a continuing emphasis on developing students’ ability to solve problems through a variety of approaches. Topics may include graph theory, geometric sequences and series, radicals and laws of exponents, the algebra of rational expressions, exponential functions, further study of quadratic equations, polynomial functions and complex numbers, statistics, and Euclidean geometry.

**Math 11-2, Math 11-3, and Math 11-4Grade: 11**

These courses emphasize applications of mathematics and may include the following areas: algorithms, exponential functions, logarithms, trigonometric functions, transformations of functions, polynomial functions, trigonometric identities, combinatorics and probability, and further topics in geometry.

**Calculus (Accelerated)Grades: 11-12**

Concepts and applications of differential and integral calculus are presented. For juniors, a month-long final project, requiring considerable independent work, concludes the course. Students who complete the course successfully are prepared to take the Advanced Placement Calculus AB exam.

*Prerequisite: Math 10-1 or permission of current math teacher.*

**Advanced Calculus (Accelerated)Grade: 12**

In Calculus, students are introduced to the concept of limits, and learn how they can be applied to develop the theory of differentiation (rates of change) and integration (accumulation), which culminates with the fundamental theorems of calculus. Advanced Calculus further develops the techniques of differentiation and integration, and serves as a foundation for classes like differential equations, multivariable calculus, and linear algebra. The curriculum is designed to include the following: indeterminate forms; logarithmic and implicit differentiation; related rates; integration by parts; partial fraction decomposition; improper integrals; parametric and polar equations; vector calculus as it applies to position, velocity, and acceleration; differential equations and population models; sequences; Taylor and power series. These topics cover all of the material found on the Advanced Placement (AP) Calculus BC exam, and will provide a strong foundation for students interested in taking the test. In addition to the core topics previously mentioned, the class may take occasional tangents into other areas of higher mathematical study. These topics may include different number systems; the “sizes” of infinity; mathematical physics and relativity; multivariable calculus and geometry; and Fourier series.

*Prerequisite: Calculus*

**Symmetry: Groups and Rings: An Introduction to Abstract Algebra (Accelerated) Grades: 9-12**

Mathematics is often described as the science of symmetry, and yet we often don’t see the relevance of this description in most precalculus and calculus classes – even when we’ve studied plane geometry. Look at the table of contents of any text on abstract algebra: after some basic review of operations and other tools from elementary algebra, the topics sound really strange! The definition of a Group! Finite or Infinite Groups; Abelian Groups; Dihedral Groups; Integral Domains; Rings – and so much more. This is not your little sib’s algebra any more.

Students who love the structure and elegance of language are likely to enjoy abstract algebra. Students who love calculating, computing, and problem solving are likely to enjoy abstract algebra. Students who love visualizing technical ideas will likely enjoy abstract algebra. This class is fully on par with the difficulty level of the Advanced Calculus course and is viewed as such by colleges.

Students will learn abstract definitions, how these definitions help them develop a mathematically precise notion of symmetry, how to write good mathematics, how to write proofs, how to use abstract mathematics to describe the structures of crystals and other examples, and how to use all of the mathematical habits of mind to deepen their mathematical maturity and confidence. *Prerequisite: Permission of department.*

**Calculus 1Grade: 12**

Students will begin the course by considering the “tangent line problem” and go on to study limits and develop a definition of the derivative. Students will then learn to interpret the derivative in context and explore ideas of continuity and differentiability, understanding when derivatives do and do not exist. Before applying the derivative to real-life problems, students will learn a variety of techniques for taking derivatives of advanced functions while strengthening their skills with algebra and modeling physical and social phenomenon using mathematical functions.

*Prerequisite: Math 11-2 or permission of the department.*

**Discrete Mathematics 1Grades: 10-12**

Discrete Mathematics is a contemporary branch of mathematics that focuses on various problems, topics, and algorithms that often have whole-number outcomes. The topics are grounded in real applications. This course focuses on the mathematical perspective of fairness, value, and individual perception. Students study a wide variety of voting methods and examine “fair division” algorithms through the lens of entitlement to estates, apportionment for governing bodies, and an array of continuous cases.

**Statistics 1Grades: 10-12**

Students study topics in descriptive statistics: displaying data, describing data sets according to center, shape, and spread, correlation, experimental design, sampling techniques, sampling bias, and probability.

**Calculus 2Grade: 12**

Students will continue to use the lens of calculus to study functions and their graphs. Topics may include implicit differentiation, optimization problems, related rate problems, the area under a curve, the definition of an integral, and the Fundamental Theorem of Calculus.

*Prerequisite: Calculus 1*

**Discrete Mathematics 2Grades: 10-12**

Discrete Mathematics 2 will focus primarily on applications that can be analyzed with the help of matrices. After a quick study of what matrices are, and how they work, students will use them as tools to study a variety of applications. The class will model and predict population growths, take an introductory study into cryptography, and study expected probabilities through chance-based board game construction.

*Note:**Discrete Mathematics 1 is not a prerequisite.*

**Statistics 2Grades: 11-12**

Topics may include the normal distribution, sampling techniques, simulations, confidence intervals, hypothesis testing, probability, and expected value. Note that Statistics 1 is a prerequisite for this course.

*Prerequisite: Statistics 1*