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Noble and Greenough School is a rigorous academic community dedicated to inspiring leadership for the public good. Through mentoring relationships, we motivate students to achieve their highest potential and to lead lives characterized by service to others.

Mathematics

Upper School Academics

For its utilitarian role in the natural and social sciences, mathematics needs to be studied and understood by anyone with an interest in such subjects as biology, chemistry, physics, economics, linguistics and computer science, to name but a few. Equally important, however, is the aesthetic quality of mathematics, including the many patterns, structures, and interconnections between various subjects in the discipline. The study of mathematics fosters logical thinking, emphasizes precision in language and notation, improves pattern recognition, encourages multiple ways of looking at a particular problem, and increases one's ability to understand the complex world in which we live.

Students at Nobles will be exposed to a variety of technology in their math courses including, but not limited to, graphing calculators and interactive whiteboards.
 

Algebra I | Full Year
Full Credit
Open to: III, IV
Prerequisites: Pre-algebra

This course covers the most fundamental and, therefore, most important skills in secondary school mathematics. Included in the course are a study of the rational and irrational numbers, extensive work with equations and inequalities, graphing of linear and quadratic functions, solving systems of equations, polynomial algebra, rational expressions and equations, and a variety of word problems. Use of the TI-84 graphing calculator will begin with the study of linear functions, and therefore is a required tool for the course.

Geometry | Full Year
Full Credit
Open to: III, IV
Prerequisites: Algebra I

This year-long course has three main objectives: first, to impart an understanding and mastery of basic Euclidean geometric facts; second, to improve the student's ability to perceive problems visually and to improve his or her use of perception, intuition, and pattern-recognition in problem-solving; and third, to introduce the student to a basic formal deductive mathematical system in which definitions and postulates lead to the discovery and proof of theorems. The year will be devoted to topics traditionally included in a high school geometry course: points, lines, planes, triangles, quadrilaterals, circles, parallelism, congruence, similarity, area, general polygons, and surface area and volume of solids.

 

Honors Geometry | Full Year
Full Credit
Open to: III, IV
Prerequisites: Algebra I and permission of the department

While covering essentially the same syllabus as the regular geometry course, students in Honors Geometry will move at a faster pace, cover topics in greater depth, and be required to do significantly more formal proof-writing. A student must demonstrate strong interest and background in mathematics and high achievement in a comprehensive Algebra I course to earn consideration from the Department for honors placement.

 

Algebra II - Foundations | Full Year
Full Credit
Open to: II, III, IV
Prerequisites: Algebra I and Geometry, by recommendation of the department

This year-long course builds on the foundations studied in Algebra I, and it will examine and analyze algebraic concepts at a pace that allows additional time for mastery.  It is a course designed to improve skills and confidence as well as to study the traditional topics of Algebra II:  factoring techniques; properties of exponents and logarithms; functions (polynomial, logarithmic, and exponential); elementary trigonometry.

 

Algebra II | Full Year
Full Credit
Open to: II, III, IV
Prerequisites: Algebra I, Geometry, and permission of the department

This year-long course builds on the foundations studied in Algebra I. Specifically, it includes coverage of: polynomial functions, equations, and inequalities; conic sections; the complex number system; advanced factoring techniques and binomial expansion; elementary trigonometry; properties of exponents and an introduction to logarithms.

Honors Algebra II | Full Year
Full Credit
Open to: II, III, IV
Prerequisites: Algebra I, Geometry, and permission of the department

Because of the faster pace possible in an honors section, Honors Algebra II affords coverage which goes deeper into the underlying theory and unifying connections between topics than do the regular sections of Algebra II, where more emphasis is given to exposure than to depth.

 

Precalculus FY | Full Year
Full Credit
Open to: I, II
Prerequisites: Algebra II Foundations or Algebra II by recommendation of the department

This year-long Precalculus course revisits many topics learned in an Algebra II course; polynomial, exponential, logarithmic, and trigonometric functions. This course places greater emphasis on solving advanced equations and analysis. Functions will be examined graphically, numerically, algebraically, and verbally in order to give students the benefit of alternate presentations.
 

Statistics | Fall Only
Full Credit
Open to: I, II, III
Prerequisites: Algebra II

This course includes the collection, evaluation and organization of data, probability distributions, sampling, hypothesis testing, correlation, and linear regression. The emphasis is on developing a working knowledge of these tools rather than mastering the complete theory behind the methods.

Precalculus | Spring Only
Full Credit
Open to: I, II, III
Prerequisites: Algebra II and permission of the department

Precalculus revisits many of the topics studied in Algebra II but places more emphasis on abstract thinking. Students are asked to apply concepts more generally and to make more connections between topics. As its name suggests, this course prepares the student for the eventual study of calculus. Topics to be covered include: formal definitions of function, domain, and range; composition and inversion of functions; techniques of graphing; triangle and circle trigonometry; sequences and series; exponential and logarithmic functions.

Honors Precalculus with Differential Calculus | Full Year
Full Credit
Open to: II, III
Prerequisites: Honors Algebra II and permission of the department

This two-semester course is offered to the strongest Algebra II Honors students. This course covers all of the topics of Precalculus, followed by BC Calculus topics, specifically the theory of limits, the derivative, techniques of differentiation, and applications of derivatives. The pace of this course is rapid and therefore the course is open by invitation only to those students who, in the opinion of the math department, have demonstrated strong interest and performed at a consistently high level in their previous mathematics courses.

 
Discrete Mathematics | Full Year
Full Credit
Open to: I, II
Prerequisites: Precalculus or permission of the department

This year-long course is designed to extend students’ mathematical maturity and ability to deal with abstraction. The fall semester focuses on statistical analysis. It covers counting theory (permutations and combinations), probability, and descriptive statistics with many practical applications. The spring semester focuses on decision algorithms and social choice. In particular, we will examine graph theory, voting theory, apportionment, taxes, savings options, loans, and the realities of monthly expenses.

 

Calculus | Full Year
Full Credit
Open to: I
Prerequisites: Precalculus and permission of the department

This two-semester course provides an introduction to calculus, but is not intended to prepare the student for either the AB or the BC Advanced Placement examination. The first semester deals primarily with the properties of limits and differential calculus and the second semester with those of integral calculus.

Advanced Placement (AP) AB Calculus | Full Year
Full Credit
Open to: I, II
Prerequisites: Precalculus and permission of the department

This is a two-semester Advanced Placement sequence in calculus, which gives a thorough introduction to the fundamentals of differential and integral calculus. The fall semester is primarily devoted to the development of differential calculus and covers limits, the derivative, methods of differentiation, and applications of the derivative. The spring semester begins with the fundamental theorem of integral calculus and studies the integral, its methods and its applications, including a brief introduction to differential equations and slope fields.This course prepares students for the College Board's AP exam in Calculus AB.

Advanced Placement (AP) BC Calculus | Full Year
Full Credit
Open to: I, II
Prerequisites: Honors Precalculus with Differential Calculus and permission of the department

BC Calculus is a full-year, AP course that offers the second and third semesters of this three-semester advanced calculus sequence. Topics covered during these two semesters are the integral, its methods and applications, the calculus of transcendental functions, vector functions, polar coordinates, infinite series, and differential equations. this course prepares students for the College Board's AP exam in Calculus BC.

Multivariable Calculus | Fall Only
Full Credit
Open to: I, II
Prerequisites: BC Calculus and permission of the department

This course is an extension to the principles and techniques of the integration and differentiation learned in single-variable calculus (BC Calculus). Topics include functions of 2 or more variables, vectors, integration with multiple variables, optimization in several variables, partial derivatives and gradient. We will use a 3-D grapher to help visualize these functions.
 

Advanced Placement (AP) Statistics | Spring Only
Full Credit
Prerequisites: Statistics or Honors Precalculus and permission of the department

This fast-paced, one-semester course, which prepares students for the AP Exam, is available to students who have taken our introductory Statistics course and also advanced, motivated students who have never had a formal course in statistics. The topics for AP Statistics will emphasize four areas: (1) exploring data, (2) planning a study, (3) anticipating patterns in advance (probability), and (4) statistical inference. This course does not replace Precalculus in fulfilling the mathematics requirement and will not be offered if enrollment is inadequate.

Advanced Topics in Mathematics A | Fall Only
Full Credit
Open to: I, II
Prerequisites: AB or BC Calculus and permission of the department

Advanced Topics in Mathematics A is a one-semester elective offered periodically in the fall semester to students who have completed either AB or BC Calculus prior to Class I. Depending on the mutual interests of the class and the instructor, such topics might include: additional topics from integral calculus; an introduction to Linear Algebra (the theory and applications of matrices, determinants, vectors, vector spaces, and subspaces); probability theory; combinatorics; famous problems and theorems of mathematics; methods of problem-solving.

Not offered 2017-18

Advanced Topics in Mathematics B | Spring Only
Full Credit
Open to: I, II
Prerequisites: BC Calculus and permission of the math department

Advanced Topics in Mathematics B is a one-semester elective offered periodically in the spring semester. It is a continuation of the topic presented in the fall semester and is open to students who have completed Advanced Topics in Mathematics A. Greater emphasis will be placed on solving advanced problems in geometry, algebra, number theory, statistics, probability theory, and combinatorics. There will be some preparation for national mathematics competitions.

Not offered 2017-18

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