Working with Math and Random Numbers

1. Using Math Class Methods

Method	Description
`Math.abs(x)`	Absolute value
`Math.max(a,b)` / `min(a,b)`	Comparison
`Math.pow(b, e)`	Power
`Math.sqrt(x)` / `cbrt(x)`	Roots
`Math.floorDiv(a,b)` / `floorMod(a,b)`	Floor division
`Math.signum(x)`	-1.0, 0.0, 1.0
`Math.addExact(a,b)`	Throws on overflow
`Math.PI` / `Math.E`	Constants

2. Working with Trigonometric Functions

Method	Input	Output
`sin/cos/tan`	Radians	double
`asin/acos/atan`	Ratio	Radians
`atan2(y, x)`	Coords	Angle to point
`toRadians(deg)` / `toDegrees(rad)`	Conversion	—
`sinh/cosh/tanh`	Hyperbolic	—

3. Using Exponential Functions

Method	Description
`Math.exp(x)`	e^x
`Math.log(x)`	Natural log
`Math.log10(x)`	Base-10 log
`Math.log1p(x)`	ln(1+x), accurate near 0
`Math.expm1(x)`	e^x - 1, accurate near 0

4. Rounding Numbers

Method	Result for 2.5	Result for -2.5
`Math.round(x)`	3	-2
`Math.floor(x)`	2.0	-3.0
`Math.ceil(x)`	3.0	-2.0
`Math.rint(x)`	2.0 (banker's)	-2.0

5. Generating Random Numbers

Method	Range
`Math.random()`	[0.0, 1.0)
`(int)(Math.random() * n)`	[0, n)
`ThreadLocalRandom.current().nextInt(min, max)`	[min, max)
`RandomGenerator.getDefault()` JAVA 17+	Modern factory API

6. Using Random Class

Example: Random

Random rng = new Random();              // unseeded
Random seeded = new Random(42L);
int dice = rng.nextInt(6) + 1;          // 1..6
double d = rng.nextDouble();            // [0,1)
boolean b = rng.nextBoolean();
rng.ints(10, 0, 100).forEach(System.out::println);

Method	Returns
`nextInt()`	Any int
`nextInt(bound)`	[0, bound)
`nextLong/nextDouble/nextFloat/nextBoolean`	Per-type
`nextGaussian()`	Normal distribution mean 0, sd 1
`ints/longs/doubles`	Stream of values

7. Using SecureRandom

Aspect	Detail
Class	`java.security.SecureRandom`
Use for	Tokens, passwords, crypto keys, salts
Algorithm	`SecureRandom.getInstanceStrong()`
API	Same as `Random` + `nextBytes(byte[])`

Warning: Never use Math.random() or Random for security-sensitive values.

8. Understanding Random Number Seeds

Behavior	Detail
Same seed	Same sequence (reproducible)
Default seed	System time + counter
Set after creation	`rng.setSeed(s)`

9. Working with BigInteger

Example: BigInteger

BigInteger a = new BigInteger("123456789012345678901234567890");
BigInteger b = BigInteger.TEN.pow(50);
BigInteger sum = a.add(b);
BigInteger gcd = a.gcd(b);
boolean prime = a.isProbablePrime(20);

Method	Description
`add/subtract/multiply/divide/mod`	Arithmetic (immutable)
`pow(int)`	Exponentiation
`modPow(e, m)`	Modular exponentiation
`gcd(b)`	Greatest common divisor
`compareTo(b)`	Order comparison
Constants	`ZERO, ONE, TWO, TEN`

10. Working with BigDecimal

Example: Money math

BigDecimal price = new BigDecimal("19.99");
BigDecimal qty = BigDecimal.valueOf(3);
BigDecimal total = price.multiply(qty)
    .setScale(2, RoundingMode.HALF_UP);  // 59.97

Method	Description
`new BigDecimal("0.1")`	String constructor (exact)
`BigDecimal.valueOf(d)`	Use this for double — avoids float artifacts
`add/subtract/multiply`	Exact arithmetic
`divide(b, scale, mode)`	Specify rounding
`setScale(s, RoundingMode)`	Decimal places
RoundingMode	`HALF_UP, HALF_EVEN, FLOOR, CEILING, UP, DOWN`

Warning: Never construct via new BigDecimal(0.1) — uses inexact double. Use string or valueOf.

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Working with Math and Random Numbers

1. Using Math Class Methods

2. Working with Trigonometric Functions

3. Using Exponential Functions

4. Rounding Numbers

5. Generating Random Numbers

6. Using Random Class

Example: Random

7. Using SecureRandom

8. Understanding Random Number Seeds

9. Working with BigInteger

Example: BigInteger

10. Working with BigDecimal

Example: Money math

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