Unit 1.11: Math Class

The Math Class

The Math class is part of the java.lang package, which is automatically imported into every Java program.

Static Utility Class

The Math class is a utility class that provides common mathematical functions. You never create an "instance" of Math; you simply call its static methods using the class name.

The Math class contains only static methods (class methods), meaning they are called using the class name: Math.methodName().

Key Math Methods

The following static methods are part of the Java Quick Reference and are required for the AP CSA exam:

Method Signature	Description	Result Example
`static int abs(int x)`	Returns the absolute value of an `int`.	`Math.abs(-5)` → `5`
`static double abs(double x)`	Returns the absolute value of a `double`.	`Math.abs(-5.5)` → `5.5`
`static double pow(double base, double exponent)`	Returns the value of the `base` raised to the power of the `exponent`.	`Math.pow(2, 3)` → `8.0`
`static double sqrt(double x)`	Returns the positive square root of a `double`.	`Math.sqrt(9.0)` → `3.0`
`static double random()`	Returns a `double` value in the range `[0.0, 1.0)` (inclusive of 0.0, exclusive of 1.0).	`Math.random()` → `0.453...`

Generating Random Numbers

By manipulating the result of Math.random(), you can generate random integers within a specific range.

Pseudorandomness

Math.random() returns a decimal between 0.0 and 0.999... By multiplying this value by a range and casting to int, you can generate random whole numbers.

Formula for a random integer between min and max (inclusive): int randomNum = (int) (Math.random() * range) + min;

range: The number of possible values, calculated as max - min + 1.
min: The starting value of your range.

Math Random Process

Examples

Using Math Methods

Task: Applying common Math library methods.

double power = Math.pow(10, 2); // Result: 100.0 (double)
double root = Math.sqrt(100);   // Result: 10.0 (double)
int val = Math.abs(-50);        // Result: 50 (int)

Random Integers

To generate a random number between 1 and 10 (inclusive):

Calculate the range: 10 (max) - 1 (min) + 1 = 10 total values.
Apply the formula:

Task: Generating a random integer within a specific range. java // Math.random() * 10 gives a value in [0.0, 10.0) // (int) converts it to an integer in [0, 9] // Adding 1 shifts the range to [1, 10] int rand = (int)(Math.random() * 10) + 1;