34
Probability and Counting Techniques
If you recall that the classical probability of an event E S is given by
P (E ) =
n(E )
n(S )
where n(E ) and n(S ) denote the number of elements of E and S respectively.
Thus, nding P (E ) requires counting the elem
25
Integers: Addition and Subtraction
Whole numbers and their operations were developed as a direct result of
peoples need to count. But nowadays many quantitative needs aside from
counting require numbers other than whole numbers.
In this and the next se
26
Integers: Multiplication, Division, and Order
Integer multiplication and division are extensions of whole number multiplication and division. In multiplying and dividing integers, the one new issue is
whether the result is positive or negative. This se
28
Real Numbers
In the previous section we introduced the set of rational numbers. We have
seen that integers and fractions are rational numbers. Now, what about
decimal numbers? To answer this question we rst mention that a decimal
number can be terminat
29
Functions and their Graphs
The concept of a function was introduced and studied in Section 7 of these
notes. In this section we explore the graphs of functions. Of particular interest, we consider the graphs of linear functions, quadratic functions, cu
27
Rational Numbers
Integers such as 5 were important when solving the equation x +5 = 0. In a
similar way, fractions are important for solving equations like 2x = 1. What
about equations like 2x + 1 = 0? Equations of this type require numbers like
1 . I