LEC3

Numbers and Mathematics

• Introduction to Programming: Covers numerical data types, operations, functions, and reading numbers from the console.

Announcements

• Assignment Deadlines:
  • Assignment 1: Due on April 9, 11:59 PM
  • Assignment 2: Released on April 9, Due April 16, 11:59 PM

Numerical Data Types

• Numerical Data Types in Java: Some common types include:
  • byte: Range: $[-128, 127]$, Storage: 8-bit signed
  • short: Range: $[-32768, 32767]$, Storage: 16-bit signed
  • int: Range: $[-2147483648, 2147483647]$, Storage: 32-bit signed
  • long: Range: $[-9223372036854775808, 9223372036854775807]$, Storage: 64-bit signed
  • float: Range: $[-3.4028235E+38, 3.4028235E+38]$, 32-bit IEEE 754
  • double: Range: $[-1.7976931348623157E+308, 1.7976931348623157E+308]$, 64-bit IEEE 754

Number Literals

• Definition: A constant value directly present in the program like int i = 34;
  • Common examples: 34, 1000000, 5.0

Integer Literals

• Integer Assignment Rules: An integer literal can be assigned to an integer variable if it fits the variable's range. E.g.,
  • byte b = 1000; causes a compilation error.
• Types:
  • Default is int unless specified as long using L or l (preferably L).

Floating-point Literals

• Characteristics: Written with a decimal point, treated as double by default.
  • To define a float, append f or F, for double, use d or D.
• Example: 100.2f for float, 100.2d for double.

Scientific Notation

• Utilization: Floating-point literals can also be in scientific notation, e.g.,
  • 1.23456e+2 is equivalent to ( 123.456 ) and 1.23456e-2 is equivalent to ( 0.0123456 ).

Numeric Operations

• Basic Operations Overview:
  • + : Addition
  • - : Subtraction
  • * : Multiplication
  • / : Division
  • % : Remainder

Accuracy in Floating-point Calculations

• Imprecision: Floating-point numbers are approximated leading to rounding errors:
  • Example: ( 1.0 - 0.1 - 0.1 - 0.1 - 0.1 - 0.1 ) yields ( 0.5000000000000001 )
• Integers: Stored precisely with exact results in operations.

Division and Remainder

• Integer Division Behavior: Truncates fractional parts.
  • Example: ( 5 / 2 ) results in 2.
• Remainder Operator Use: Allows checking even/odd.
  • Example: ( ext{day ext{(Saturday) }+ 10 ext{ days}} = (6 + 10) mod 7 = 2 )

Augmented Assignment Operators

• Common Operators:
  • += : i += 8 equivalent to i = i + 8
  • -= : i -= 8
  • *= : i *= 8
  • /= : i /= 8
  • %= : i %= 8

Increment & Decrement Operators

• Types:
  • Pre-decrement: --var
  • Post-decrement: var--
  • Pre-increment: ++var
  • Post-increment: var++
• Example:
  • int j = ++i; (j is 2, i is 2)

Type Conversion Rules

• Automatically: 1. If double, convert others to double; 2. If float, convert to float; 3. If long, convert to long; 4. Otherwise, to int.

Type Casting

• Implicit Casting: E.g., double d = 3; (widening).
• Explicit Casting: E.g., int i = (int)3.0;, truncates fractional part.

Operator Precedence

• Order of operations defined by:
  • Parentheses > Unary Operators > Type Casting >
  • Multiplication/Division/Remainder > Addition/Subtraction >
  • Relational > Equality > Logical > Assignment.

Operator Associativity

• Associativity: Determines order with same precedence, generally left-to-right except for assignment which is right-to-left.

Reading Numbers from the Console

• Creating Scanner: Scanner input = new Scanner(System.in);
• Methods for Reading:
  • nextByte(), nextShort(), nextInt(), nextLong(), nextFloat(), nextDouble().
• Example Usage:
  • double d = input.nextDouble();

Mathematical Functions

• Math Class Methods:
  • Constants: Math.PI, Math.E
  • Trigonometric Methods: Math.sin(), Math.cos(), etc.
  • Exponent Methods: Math.pow(), Math.sqrt(), etc.
  • Rounding Methods: Math.ceil(), Math.floor(), etc.
  • Miscellaneous: Math.min(), Math.max(), Math.abs(), and Math.random().

Next Topics Review

• Focus on characters and strings in the next lecture.