Clay Sherman of the NJ DEP discussed a flood mitigation project along the Hudson River.

# Mathematics

The mathematics program at Pingry guides students in developing critical thinking and problem solving skills through the application of mathematical concepts. Students develop an appreciation and an understanding of mathematics as they engage in exploration, collaboration, conjecture, and proof. The curriculum is based on solving problems as not only a desired outcome but as a part of the learning process.

In teaching mathematics we aim to help students:

develop a strong conceptual understanding of various essential topics in mathematics. This includes such concepts as number, operation, equation, function, relation, congruence, and similarity;

practice pattern recognition and critical thinking;

collaborate with peers to explore new concepts, discover models and patterns, and engage in solving difficult problems;

develop oral and written communication skills such as asking useful questions, developing convincing arguments, and justifying one’s own reasoning;

use technology to explore mathematics and assess when and where individual tools will be most effectively employed.

A Pingry graduate should be able to understand how to convey mathematical logic using symbols, graphical representations, written language, and oral expression. This fosters the ability to adapt to dynamic environments in college and beyond.

## Mathematics Courses: Intermediate Algebra through Geometry

- Intermediate Algebra (#13327)
- Intermediate Algebra & Geometry (#13307)
- Geometry (#13427)
- GEOMETRY HONORS (#13428)

## Intermediate Algebra (#13327)

*Major year course. 3 credits. Form III. *

The goal of this course is to develop and strengthen algebraic skills, focusing on the second half of a traditional algebra sequence. The course emphasizes the relevance of algebra in the real world and our everyday lives. It begins with the study of functions and linear equations and continues through statistics, inequalities, exponential equations, quadratics, and factoring.

## Intermediate Algebra & Geometry (#13307)

*Major year course. 3 credits. Form III. Prerequisite: Departmental permission.*

This course covers material found in Intermediate Algebra at an accelerated pace, while also introducing the foundations of Geometry. The Intermediate Algebra topics focus on basic properties of functions and how they apply to linear, exponential, and quadratic functions. The Geometry topics introduce key definitions and theorems and how to apply them in formal deductive reasoning proofs. The next course in this sequence is Geometry and Advanced Algebra.

## Geometry (#13427)

*Major year course. 3 credits. Forms III-IV. Prerequisite: Intermediate Algebra.*

Geometry is a course in plane and solid geometry with an introduction to both logic and the methods of proof and an emphasis on algebraic application of geometric properties and theorems. Discovery is a central pillar of the course. Students are guided in an exploration of shapes and taught how to create conjectures about their properties and relationships. Upon developing a conjecture, students use gathered information to validate them with formal proof. These theorems are then used in a variety of problem solving scenarios, including the formation of new theorems. Although the discussion of formal postulates and the proof of various theorems are thoroughly explored, focus is on the construction of new proofs and application of theorems rather than memorization.

This course covers the traditional postulates and theorems discussed in Euclidean geometry. In addition, coordinate geometry is explored in depth. Considerable time will also be spent reviewing and applying skills developed in algebra.

## GEOMETRY HONORS (#13428)

*Major year course. 3 credits. Forms III-IV. *

*Prerequisite: Intermediate Algebra.*

Geometry Honors is a course in plane and solid geometry with considerable focus placed on logic and methods of proof. Discovery is a central pillar of the course. Students learn to independently explore the relationships between objects to develop conjectures about their properties and relationships. Upon developing a conjecture, students use gathered information to validate it with formal proof. These theorems are then used in a variety of problem solving scenarios, including the formation of new theorems. Although the discussion of formal postulates and the proof of various theorems are thoroughly explored, focus is on the construction of new proofs, not on the memorization of theorems.

This course covers the traditional postulates and theorems discussed in Euclidean geometry. In addition, coordinate geometry is explored in depth. Considerable skill in algebra is necessary for success.

*Note to all students taking Advanced Algebra or above: The Mathematics Department has incorporated the use of graphing calculators into its courses. The TI-83 or TI-84 is recommended and should be acquired by all students.*

## Mathematics Courses: Advanced Algebra & Above

- Advanced Algebra & Trigonometry (#13308)
- ADVANCED ALGEBRA & TRIGONOMETRY HONORS (#13310)
- Geometry & Advanced Algebra (#13425)
- Pre-Calculus (#13535)
- Pre-Calculus Honors (#13537)
- Analysis (#13617)
- A.P. Calculus AB (#13619)
- A.P. Calculus BC (#13629)
- Calculus (#13618)
- Math 6: Mathematics Seminar (#13640)
- Discrete Mathematics (#13656)
- Number Theory (#13655)
- A.P. Statistics (#13641)

## Advanced Algebra & Trigonometry (#13308)

*Major year course. 3 credits. Forms IV-V. Prerequisites: Geometry. *

The goal of the Advanced Algebra and Trigonometry course is to develop students’ ability to think about and apply algebraic models. The focus is on justification and support of mathematical reasoning. The learning environment emphasizes collaborative problem solving, through group inquiry and project-based explorations. Additionally, the use of various computer graphing programs allow students the opportunity to explore the work from different perspectives. Topics covered include a continuation of previously learned algebraic functions and a survey of trigonometric functions.

## ADVANCED ALGEBRA & TRIGONOMETRY HONORS (#13310)

*Major year course. 3 credits. Forms IV-V. Prerequisite: Geometry Honors or departmental permission.*

The Honors course is designed to develop higher order thinking and problem solving skills that are required to be successful in Advanced Placement courses and college mathematics. The course focuses on not only solving, but justifying and supporting conclusions with mathematical reasoning. Students will work individually and collaboratively to expand their algebraic fluency, while incorporating technology as a tool for exploration.

Topics covered include a continuation of previous learned algebraic functions, an in-depth analysis of trigonometric functions, statistics and probability. Additional topics will be included to prepare students for the rigors of future Advanced Placement courses.

## Geometry & Advanced Algebra (#13425)

*Major year course. 3 credits. Form IV. Prerequisite: Intermediate Algebra and Geometry or departmental permission.*

This course is the second year of a three-year program leading to Calculus as a senior. This course covers the second half of the material covered in plane and solid geometry. It then covers the material in Advanced Algebra up to but not including trigonometry.

## Pre-Calculus (#13535)

*Major year course. 3 credits. Form V. Prerequisite: Geometry & Advanced Algebra or *

*departmental permission*

*.*

Pre-Calculus is an integrated course in advanced algebra and trigonometry, whose unifying link is the concept of function. The work strengthens students’ conceptual understanding of problems and mathematical reasoning is emphasized throughout. To prepare students to continue their studies with calculus, the course emphasizes graphing and curve-sketching, with extensive use of technology. Students work through an advanced analysis of polynomial, rational, exponential and logarithmic functions. In addition, all trigonometric functions and properties are covered extensively, while elements of limits and differential calculus are introduced.

## Pre-Calculus Honors (#13537)

*Major year course. 3 credits. Form V. Prerequisite: Advanced Algebra & Trigonometry Honors *or departmental permission.

This course is designed for students who plan to study A.P. Calculus. The concepts of algebraic functions, exponential and logarithmic functions, numbers and number systems, trigonometric functions, analytic geometry, limits of functions, limits of series and sequences, and vectors are some of the topics covered. The concepts of differential calculus are covered in detail including applications such as optimization problems, related rate problems, and curve sketching.

## Analysis (#13617)

*Major year course. 3 credits. Form VI. Prerequisite: Advanced Algebra & Trigonometry. *

This course prepares students for further study of mathematics in college. The concepts of function, numbers and number systems, trigonometric functions, analytic geometry, limits of functions, series and sequences, and combinatorics are some of the topics covered in Analysis. Early concepts of differential calculus are covered, including curve sketching of rational functions.

## A.P. Calculus AB (#13619)

*Major year course. 3 credits. Form VI. Prerequisite: Pre-Calculus Honors or Pre-Calculus and **departmental permission**. **A minimum average of B+/A– is expected.*

This course is equivalent to a one-semester college freshman course in calculus. Course content follows the A.P. outline for AB Calculus. Students are required to sit for the AB Calculus A.P. exam in May.

## A.P. Calculus BC (#13629)

*Major year course. 3 credits. Form VI. Prerequisite: Pre-Calculus Honors** and **departmental permission**. **A minimum average of A/A+ is expected.*

This course is equivalent to a full-year college freshman course in calculus. Course content follows the A.P. outline for BC Calculus. Students are required to sit for the BC Calculus A.P. exam in May. This course is very rigorous and suited for students who wish to pursue math or science in college.

## Calculus (#13618)

*Major year course. 3 credits. Form VI.*

*Prerequisite: Pre-Calculus Honors or Pre-Calculus.*

This course begins with a thorough exploration of functions and limits of functions before moving into topics in differential and integral calculus. The focus of the course is on the calculus of polynomial and rational functions with some exploration of exponential and trigonometric functions. Applications such as related rates of change, optimization problems, curve-sketching, and area under a curve will be included. This course does not prepare students for Advanced Placement.

## Math 6: Mathematics Seminar (#13640)

*Major year course. 3 credits. Honors. Form VI. Open to students who have successfully completed BC Calculus and who have demonstrated a high level of ability in mathematics with **departmental permission**.*

This course starts as a third-semester college calculus course and then explores other selected topics, including higher-order differential equations, volumes and areas related to curved surfaces, linear algebra, and computer programming for all topics. A full discussion of mathematical statistics is also included.

## Discrete Mathematics (#13656)

*Major semester course. Offered in fall. 1.5 credits. Honors. Open to students who have completed A.P. Calculus or by **departmental permission**. Discrete Mathematics may not be taken concurrently with Math 6.*

This course introduces discrete mathematical structures such as propositions, sets, graphs and trees. It uses a formal approach to discuss the language used in mathematical reasoning, and the basic concepts, properties and relationships among the discrete objects. Students will be introduced to the idea of mathematical thinking with different methods of proofs, and they will learn to recognize and express the mathematical ideas graphically, numerically, symbolically, and in writing. Real world applications of these discrete objects such as logic gates in computers, traffic routing and scheduling will also be covered in this course. No previous computer science experience is required.

## Number Theory (#13655)

*Major semester course. Offered in spring. 1.5 credits. Honors. Open to students who have completed A.P. Calculus or by **departmental permission**. Number Theory may not be taken concurrently with Math 6.*

Number theory is the study of the set of natural numbers, from which all other numbers are based. A closer look at this seemingly simple set of numbers reveals that there is more to the natural numbers than meets the eye. Students will explore the rules of operations in this set of numbers and build higher levels of conceptual awareness through the exploration of algorithms and modular arithmetic. While exploring these concepts, students will develop an understanding of the various proof techniques in mathematics and build proofs of their own. Students will also explore applications of number theory, including applications of modern-day cryptography, and how they stem from the core concepts in number theory.

## A.P. Statistics (#13641)

*Major year course. 3 credits. Form V-VI. Prerequisites: B+ or better in Pre-Calculus Honors, A- or better in Pre-Calculus, or *

*departmental permission*

*.*

This course introduces students to the tools and concepts of exploring data, planning a statistical study, producing models using statistics and probability, normal distributions, sampling distributions, and statistical inference. A.P. Statistics is the equivalent of a one-semester college-level introductory statistics course and meets the requirements outlined by the College Board. Students enrolled in the course must take the Advanced Placement exam in May.

## Economics Courses

- Economics - Principles & Issues (#11779F for fall, #11779 for full year)
- A.P. Macroeconomics & Microeconomics (#11777)

## Economics - Principles & Issues (#11779F for fall, #11779 for full year)

*Major year course (3 credits). Forms V-VI.*

This two-semester course is an introduction to basic economic concepts and principles. Students will learn to apply these concepts and principles to current economic issues and global events. Some of the major areas of focus are Federal Reserve policies in the past and present, current economic goals, externalities, globalization, and what makes an economy function to the best of its ability. Students are introduced to supply and demand analysis, fiscal and monetary policy, and trade. Students who complete this course may wish to further their study of economics through enrollment in A.P. Economics in their senior year; however, this course is not a prerequisite nor a guarantee for admission to the A.P. course.

## A.P. Macroeconomics & Microeconomics (#11777)

*Major year course. 3 credits. Form VI. Prerequisite: Departmental permission (past performance in history, mathematics, and other disciplines is taken into account).*

This course is the equivalent of two semesters of college-level economics. The course will cover macroeconomic principles such as supply and demand, inflation, unemployment, and fiscal and monetary policy, as well as microeconomic topics including the nature and function of product markets, price determination, perfect and imperfect competition, efficiency, equity, stability, growth, and the role of government. Assessments include final tests covering microeconomics and macroeconomics.