Course One

From Numbers to Functions

Real Numbers
An introduction to the real line, fractions and their multiple representations, classroom applications and use of numbers in modeling.

From Numbers to Functions
An introduction to functions: the intuitive idea of function, its use as assignments and as a constraint between two types of quantities, the formal definition of function. Composition of functions. The vertical line criteria. Use of functions in modeling. Examples  include simple arithmetic operations (addition, product) and also functions on objects other than numbers. Special attention to multiple representations of functions (verbal, arrows, tables, algebraic expressions and graphs).

Examples of Functions
An expansion of the previous unit focused mostly on examples of functions of one real variable, especially those examples that appear commonly in mathematics and science: linear functions, absolute value, monomials, exponentials and step functions. Some examples of compound functions like those obtained from the simpler pieces by composition, addition or product.

The various interpretations and applications of division. Functional approach to ratio and proportion. Division with remainder, decimals and decimal representation of rational numbers. A basic introduction to divisibility for integers and decomposition into product of powers of primes.