Mathematics

Math 2 builds on Math 1 by spiraling key concepts from algebra and functions while focusing on Euclidean geometry. Students explore geometric reasoning, congruence, similarity, and the properties of circles, polygons, and three-dimensional figures. Alongside geometry, the course introduces polynomial functions, right triangle trigonometry, vectors, and parametric equations, emphasizing connections between algebraic and geometric representations. Throughout, students engage in problem-based learning that integrates multiple strands of mathematics and develops both conceptual understanding and procedural fluency.

This course eschews the traditional lecture format. It revisits the families of functions studied in MA20 from a more sophisticated point of view and includes systematic study of trigonometric functions, with an emphasis on their transcendental nature. Additional topics include combinatorics, discrete probability, and sequences and series of numbers. Emphasis is placed on problem solving; students are regularly faced with having to solve problems that they have no prior experience with. In addition, students are expected to present their solutions to the class.

This course explores the mathematics of motion. It is an introduction to both differential and integral calculus, and their applications. The topics include the usual suspects: limits, computing instantaneous rates of change, optimization and other applications of the derivative, the definite integral, the Fundamental Theorems of Calculus, and basic techniques of anti-differentiation. Students who complete this course will be prepared to take the Advanced Placement Calculus AB exam.

This course combines the content of Calculus I and Calculus II into a single year, offering an intensive and fast-paced exploration of the mathematics of motion and change. Students begin with the foundational concepts of differential and integral calculus, including limits, instantaneous rates of change, optimization, the definite integral, and the Fundamental Theorems of Calculus. Building on these core ideas, the course moves into topics including techniques of integration, applications of definite integrals, improper integrals, sequences and series, and an introduction to differential equations. Throughout the course, emphasis is placed on conceptual understanding, analytical reasoning, and the application of calculus to real-world problems. Prerequisites: For returning students: An A or A- year-end grade in BUA MA60 Precalculus, along with approval from the mathematics department based on demonstrated readiness for an accelerated course. For new students: Placement is determined by the mathematics department, based on performance on BUA’s math placement test, in consultation with the admission team.

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.

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.