# Mathematics

“Mathematical imagination and imagery, closely linked, provide the vision that allows us to see the hidden but exquisite structure below the surface.”

- Robert Osserman, *Poetry of the Universe*

School for Advanced Studies offers two mathematics courses for our students. Those students ready for more advanced mathematics will access Miami Dade College courses.

## Honors Pre-Calculus (typically for incoming juniors)

**COURSE DESCRIPTION**

The central theme of this course is functions that can be grouped into families and used as models for real-life behavior. The goal of this class is to have students:

- work with and understand the connections among functions represented graphically, numerically, analytically, and/or verbally.
- communicate mathematics both orally and in well-written sentences and should be able to explain solutions to problems
- model a written description of a physical situation with a function
- use graphing calculators to help solve problems, interpret results, and verify conclusions
- determine the reasonableness of solutions, including sign, size, relative accuracy, and units of measurement

## Advanced Placement Calculus AB

**COURSE DESCRIPTION**

This course is an introduction to the sometimes called “mathematics of change”. It is the branch of mathematics that examines, analyzes, and describes the precise way in which changes in one variable relate to changes in another. The goal of this class is to have students

- work with and understand the connections among functions represented graphically, numerically, analytically, and/or verbally.
- understand the meaning of the derivative in terms of a rate of change and local linear approximation
- understand the meaning of the definite integral both as a limit of Riemann sums and as the net accumulation of a rate of change
- understand the relationship between the derivative and the definite integral as expressed in both parts of the Fundamental Theorem of Calculus
- communicate mathematics both orally and in well-written sentences and should be able to explain solutions to problems
- model a written description of a physical situation with a function, a differential equation, or an integral
- use graphing calculators to help solve problems, interpret results, and verify conclusions
- determine the reasonableness of solutions, including sign, size, relative accuracy, and units of measurement

For more details about AP Calculus, please visit: http://apcentral.collegeboard.com/apc/public/repository/ap-calculus-course-description.pdf