Boston University Academy’s mathematics offerings have the broad goal of improving students’ comprehension of concepts, procedural fluency, capacity for logical thought and justification, as well as their inclination to see mathematics as sensible and useful. Along the way, we hope students will experience the elegance and beauty inherent to mathematics. In addition to mathematical concepts and skills, there is a strong emphasis on problem solving and effective and elegant written and oral communication. BUA teachers strive to inspire the kind of intellectual excitement that leads to discovery and genuine problem solving.
MA25A: Advanced Algebra
This course develops students’ algebraic skills through the study of standard families of functions, including linear, quadratic, general polynomial, exponential, and logarithmic functions. Special topics include mathematics needed for the study of Newtonian mechanics, some basic number theory, and logic. Students are expected to present, critique, and discuss mathematical arguments.
This course leads students through a guided discovery and proof of many classical Euclidean theorems. Students propose, refute, or accept conjectures and formulate rigorous, discursive proofs to confirm their conjectures. At the beginning of the course, some number theory is used as a vehicle to develop and justify basic proof techniques (such as direct, contradiction, contraposition, and induction proofs).
This course eschews the traditional lecture format. It revisits the families of functions studied in MA25A 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.
MA80: Calculus I
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.
MA90: Calculus II (Fall Semester)
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.
MA95: Multivariable Calculus (Spring Semester)
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.