Mathematics

Math Courses

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Pre-Algebra Hide

Pre-Algebra is designed to give boys a strong background in basic mathematical concepts and skills. Students study arithmetic operations with fractions, decimals, and signed numbers as well as examining percents, ratio, proportion, and divisibility rules. The course also covers fundamental geometric concepts including perimeter, area, and volume. Basic probability and statistics are taught as well. Finally, in preparation for Algebra 1, students learn to solve elementary equations and word problems. The text for the course is Dolciani, Pre-Algebra, An Accelerated Course, supplemented by Bridgess, Exercises in Basic Mathematics.

Algebra 1 Hide

Algebra 1 presents a comprehensive overview of the fundamentals of algebra. The course emphasizes algebraic techniques, particularly factoring, solving equations, and analyzing linear functions. Strategies for solving problems form an important component of the course, and an assortment of word problems are taught throughout the year. Other topics covered include real numbers, operations with polynomials and algebraic fractions, variation, inequalities, systems of equations, radical expressions, and quadratic functions. The text for the course is Brown, Dolciani, Sorgenfrey, and Cole, Algebra Book 1.

Algebra 2 Hide

Algebra 2 extends the foundation in algebra begun in Algebra 1. Students explore the classic elementary functions, namely polynomial, rational, exponential, and logarithmic functions. Other topics studied include conics, sequences and series, and basic trigonometry. Students also become much more adept at using the numerical, graphing, and programming capabilities of their calculators. The text for the course is Brown, Dolciani, Sorgenfrey, and Kane, Algebra Book 2.

Geometry Hide

Geometry begins with a look at Euclid’s postulates and definitions, upon which students build a framework to prove deductively other geometry relationships. Point, line, and plan properties lead to those of angles, triangles, circles, quadrilaterals, and so on. Students also learn the importance and applications of logic, congruence, similarity, and area/volume. The text for all sections is Brown, Jurgenson, and Jurgenson, Geometry.

Trigonometry Hide

Trigonometry builds on the geometric study of circles and right triangles. Students move beyond simple sine/cosine/tangent calculations to the study of periodic functions. They rely heavily on graphing calculators for much of the analysis and discovery part of the course. This leads to relationships between the functions and then algebraic proofs of identities. Further topics studied may include polar coordinates and vectors. Students investigate a wide array of real-world applications. The text consists of relevant chapters from Brown, Advanced Mathematics.

Analysis Hide

Analysis continues the development of topics studied in Algebra 2. Exponential, logarithmic, polynomial, and rational functions are revisited in greater depth. Students have by now become proficient with their calculators, which aid them in their study of these functions and their graphs. Other topics include sequences and series, probability, and conic sections. The text is relevant chapters from Brown, Advanced Mathematics. Upon completion of this course, students are prepared to take the Mathematics Level-2 SAT Subject Test.

Statistics Hide

Statistics is the science of collecting, analyzing, and drawing conclusions from data. Both the Advanced Placement and regular Statistics courses cover four major topics: exploratory data analysis, in which students use graphs and numbers to describe and analyze data; experimental and sampling design, in which students discover the proper ways to collect data via sampling and controlled experiments; probability, in which students learn fundamental principles of random variables and sampling distributions; and statistical inference, in which students draw conclusions from data using confidence intervals and tests of significance. The text is Bock, Velleman, and Deveaux, Stats: Modeling the World.

Calculus Hide

Calculus is one of the masterpieces of mathematics. In this course students extend the concepts of slope and area to all the nonlinear functions they have studied. This advanced placement course is offered at two levels: AB and BC Calculus. Both sections study the derivative and integral in depth, covering topics such as tangent lines, curve sketching, related rates, implicit differentiation, slope fields, Euler’s Method, optimization problems, areas, volumes, and differential equations. The BC Calculus class also covers advanced integration techniques and Taylor series. The text for the course is Finney, Demana, Waits, and Kennedy, Calculus: Graphical, Numerical, Algebraic or Larson and Hostetler, Calculus.

Advanced Topics in Physics and Mathematics Hide

Advanced Topics in Physics and Mathematics is offered jointly with the Science Department. Students study topics in physics and mathematics chosen by the instructor after consultation with students. Physics topics examined in past years include Einstein’s special relativity, properties of elementary particles, astrophysics, aerodynamics, electronic circuits, and mechanics and electromagnetism developed with calculus and mathematics. Math topics examined in past years include multivariable calculus, differential equations, linear algebra, and number theory. Other topics may include general relativity (Einstein’s theory of gravity), symmetry, and group theory. We expect to focus on a few topics so that students may achieve a significant depth of understanding. Calculus is not a prerequisite.