What's the big deal about functions?

We assume that you're acquainted with the idea of a function (although you may be a little rusty). In society you're expected to deal with functions: for example,

Anything funny about this representation of a function?

Informally: a relationship between two or more quantities ("variables").

Formally: One quantity (the dependent variable) is uniquely determined given one or more underlying quantities (the independent variables).

For example, your grade in a course could be determined by your grades on the final, the hour exams, the quizzes, and the homework. We then might write

G(F,E,Q,H)

or

G=g(F,E,Q,H)

to indicate that your grade G is a function of these four "sub-grades". This is called a multivariate function, since G is a function of multiple (more than one) variables (F, E, Q, and H).

By the way, notation is frequently one of the biggest stumbling blocks to understanding of mathematics. Why do we have two different, completely acceptible ways of writing the same thing? Should we?

In this class we'll more frequently encounter functions of a single variable (univariate functions). Are the following statements true in a formal or informal sense, or just plain false?

• "Student happiness is a function of student grades."
• "The state of the economy is a function of the Gross Domestic Product."
• "The area of a square is a function of the side length."

We'll spend some time looking at important real data, that should be represented by functions, but which may quite complicated -- and yet very important -- such as the Keeling Curve.