A private coeducational school for grades 5-12 in Buffalo, NY.

# Mathematics

We offer more levels of mathematics courses at each grade than in any other course of study at the Upper School because we recognize that students need to be appropriately challenged and supported in the study of mathematics. The study of mathematics provides the foundation for logical thought and critical analysis of the abundant information with which we are presented each day.

From Algebra I to Multivariable Calculus, our math curriculum fosters a passion for problem solving and allows opportunity for study at the highest levels. • Algebra I: This first course in algebra promotes the understanding of a variable while teaching students to express and solve problems using equations. Students develop computational skills including graphing, manipulating fractions, factoring, working with polynomials, and solving first degree equations and inequalities. The course typically includes and introduction to quadratic equations. Order of operations, graphical representation, and proportional reasoning are emphasized throughout the course.
• Integrated Geometry and Algebra I: This full year course provides and introductory geometry course integrated with an intensive review of elementary algebra. Intended for students whose background in algebra needs additional support, this course covers many of the concepts of a traditional geometry course, however, it places less emphasis on formal proof in favor of algebraic computation and manipulation.
• Geometry: Geometry explores congruency, similarity, transformations, convex polygons, area, and volume. Students are also introduced to the presentation of ideas in the format of formal and informal proof. In order to cement skills studied in Algebra I, the course utilizes the coordinate plane and algebraic descriptions of geometric properties. At all levels, the course employs exploration and discovery in addition to traditional lecture. The Honors and Advanced sections presume greater proficiency with elementary algebra; these sections study vectors and transformations with greater depth and rigor.

• Algebra II: Algebra II develops computational proficiency while studying absolute value, linear and quadratic equations and expressions, systems of equations and inequalities. Function notation is introduced. Utilizing equations to model real world applications is emphasized. The Advanced and Honors sections study additional topics including polynomial, rational, power and root equations.
• Integrated Geometry and Algebra II: Integrated Geometry and Algebra II continues the exploration of the principles of plane and solid geometry through the lens of algebraic problem solving. The course gives students the opportunity to cement fundamentals from an introductory algebra course while advancing their command of geometric reasoning. The course also introduces several algebraic techniques typically studied in a second year algebra course.

• Functions and Trigonometry: This course utilizes the fundamental concepts and mechanical algebraic skills developed in Algebra II to study Analytical Trigonometry and advanced algebraic concepts. Topics include polynomial, rational, trigonometric, exponential, and logarithmic functions. As time permits, additional topics of study include matrices, polar coordinates, parametric equations, vectors, sequences, series, probability, and analytic geometry.
• Algebra and Trigonometry: This full course advances students' understanding and facility with algebraic methods of problem solving while preparing students to study more abstract topics in mathematics. The course includes an intensive review of trigonometry in triangles and also introduces the study of analytic trigonometry. This third course in the integrated sequence continues to emphasize concrete applications of mathematical concepts.

*Completion of Functions or Algebra and Trigonometry satisfies the graduation requirement in Mathematical Sciences.

## Mathematics Electives

• Introduction to Computer Programming: A computer program is a set of instructions that tells a computer how to accomplish a given task. Computer programming is the art and science of planning and implementing computer programs. This course is designed as an introduction to both hardware and software programming. The course begins with basic components of a computer, machine representation of data, number systems, and an introduction to digital electronics through logic gates. The course also introduces the syntax and style of a high level programming language such as C++ or Java. The course stresses the nature and design of algorithms, top-down and object-oriented design, and coding and debugging skills. Topics include data types, file and screen input and output, conditional statements, iterations, recursion, subroutines, arrays, and if time permits pointers and data structures. Students who do well in mathematics and have a possible interest in pursuing careers in any math or science area should consider taking this course. Prerequisites: An interest in computers, logic, and digital electronics with completion of Geometry with a Grade of C or better and permission from the Department.
• AP Statistics: AP Statistics introduces students to the major concepts and tools for collecting, analyzing, and drawing conclusions from data. Students are exposed to four broad conceptual themes: i.) Exploring data: observing patterns and departures from patterns ii.) Planning a study: deciding what and how to measure iii.) Anticipating patterns: producing models using probability theory and simulation iv). Statistical inference: confirming models. Prerequisites: Completion of Algebra II with a Grade of C+ or better and permission from the Department. The AP exam is a requirement of the course.
• AP Computer Science A: This second course in computer programming is intended for students who have successfully completed the Introduction to Computer Programming course and wish to continue their studies. The language focus for the second year course is Java. At the completion of the course, students have sufficient programming experience in Java and computer science knowledge to take the Advanced Placement A examination in Computer Science. Prerequisite: Introduction to Computer Programming. The AP exam is a requirement of the course.
• Data Structures and Topics: This third course is a continuation of study in computer science. The intention of the course is not only to study certain data structures and their associated algorithms, but also to study topics that are of student interest, such as GUI and applets. Prerequisite: AP Computer Science A.

## Senior Mathematics Electives

Registration for VI Form electives requires completion of Functions and Trigonometry with a grade of C+ or better. Students whose grades do not support further study in mathematics may be required to do summer work if they wish to register for a mathematics elective.

• Foundations of Precalculus: This full year course cements student understanding of more abstract concepts introduced in earlier coursework with the goal of preparing students for the study of mathematics at the collegiate level. Through both applications and more formal study, this course underscores the important multiple representations of mathematical concepts. Students are encouraged to employ algebraic, graphical, and technological skills to formulate and solve mathematical problems.
• Differential Calculus: While promoting a deeper understanding of the abstract notion of Function, this course concurrently introduces the fundamentals of Differential Calculus including Limits, the Difference quotient, the Derivative and its applications. The course is organized around families of function with particular attention to polynomial, exponential, logarithmic and trigonometric functions. Prerequisites: Completion of Functions and Trigonometry and permission of the Department.
• Honors Differential and Integral Calculus: This full year course introduces qualified students to the fundamentals of calculus. Topics from differential calculus include slopes of secant and tangent lines, the definition and interpretation of the derivative, application of the derivative including related rates, optimization and linearization. Topics from the integral calculus include techniques of integration and utilizing integration to find area, distance, and volume. Prerequisites: Completion of Honors Functions and permission of the Department.
• AP Calculus AB: AP Calculus AB covers all the material presented in Calculus, however it is studied in greater depth and with more emphasis on theory as opposed to computation. Additional topics covered include Mean Value Theorem, volumes by known cross-section, slope fields and differential equations. Prerequisites: Completion of Honors Functions and permission of the Department. The AP exam is a requirement of the course.
• AP Calculus BC: AP Calculus BC covers all the topics in AP Calculus AB but in greater depth. Additionally, students in BC also study Rolle's Theorem, Taylor series, L'hopital's rule, polar coordinates, arc length, surface area, vectors, and parametric equations. Prerequisites: Completion of Advanced Functions or Advanced Algebra II and permission of the Department. The AP exam is a requirement of the course.
• Multivariable Calculus: This introductory course in multivariable calculus focuses on functions of two and three variables. Students apply techniques of calculus to analyze the geometry of curves and surfaces in three-dimensional space. Topics include parametric equations and polar coordinates, vector functions, vectors in 2 and 3 dimensions, partial derivatives, and multiple integrals. Prerequisite: successful completion of AP Calculus BC or AP Calculus AB and permission of the Department.

## Faculty

Titles: US Math

Titles: US Math

### Erin Habelt

Titles: IV Form Dean

Titles: MS Math

Titles: US Math

Titles: MS Math

Titles: MS Math