Mathematics

Mathematics at BUA is more than numbers, symbols, and memorized formulae. In keeping with the Academy’s classically based curriculum, mathematics is placed in a historical context, and students explore its connections to history, science, English, language, art, and music. In addition to mathematical concepts and skills, there is a strong emphasis on problem solving and the effective written and oral communication of technical information. Academy teachers generate the kind of intellectual excitement that leads to discovery and progress. In doing so, students learn to see mathematics as a powerful tool for discovering and understanding the world around them and to relish the challenge difficult problems present.

 

This course is a rigorous study of algebra and trigonometry with an emphasis on variable manipulation, problem solving, equations and inequalities, sequences and functions, order of operations, exponents, and the use of tables and graphs. Both skills and concepts are stressed. Students learn concrete, informal, and formal methods of solving linear and quadratic equations. Students apply algebraic methods to solve a variety of both theoretical and real-world problems. Frequent group work enhances understanding of the math concepts and generates excitement during periods of discovery. Text used: Algebra, Form and Function, McCallum et al.

This course focuses on plane and solid Euclidean geometry, with a secondary emphasis on number theory and algebra. A balanced emphasis is placed on numerical and algebraic problems, informal proofs, and formal proofs. Students learn congruence; similarity; constructions; parallel and perpendicular lines and planes; triangles; quadrilaterals; polygons; polyhedra; the Pythagorean theorem; circles; area and volume; prime numbers; and factoring. Both deductive and inductive reasoning are stressed. Students begin to develop their technical writing skills and are frequently asked to write on topics relevant to the course. Text used: Elementary Geometry for College Students, Alexander and Koeberlein.

This course broadens student’s earlier study of algebra to include complex numbers; a consideration of polynomial, exponential, logarithmic, rational and trigonometric functions; conic sections; and an introduction to sequences and series and limits. Emphasis is placed on transformations of functions; their graphs; conversions from one form to another; domain and range; inverses; and composition of functions. Students use computers as well as graphing calculators to investigate and compare the behaviors of functions, to represent and analyze data, and to simulate experiments. Text used: Functions Modeling Change: A Preparation for Calculus, Connally et. al..

Students in this course must have demonstrated a thorough knowledge of elementary and advanced algebra and trigonometry, and have completed pre-calculus. The course focuses on the fundamentals of both differential and integral calculus, with an equal emphasis on understanding the conceptual foundations of calculus, on procedural fluency, and on applications. Students who complete MA80 will be prepared for Calculus II (MA90 or CASMA124). It is expected that students will complete this course by the time they graduate from the Academy. Text used: Calculus: Single and Multivariable, Hughes-Hallett et al.

This course begins with a brief review of differential calculus and the basics of definite and indefinite integrals. From there, the course covers improper integrals, applications of definite integrals, sequences and series, ordinary first-order and second-order differential equations, and systems of differential equations. Students who complete this course will be prepared to take the Advanced Placement Calculus BC exam. Text used: Calculus: Single and Multivariable, Hughes-Hallett et al.

This course extends the ideas covered in MA80 and MA90 to functions of two and three variables. After introducing functions of more than one variable, the course covers differentiation and integration of these functions, including optimization; parameterizations and vector fields; line and flux integrals; and calculus of vector fields. Text used: Calculus: Single and Multivariable, Hughes-Hallett et al.