Fundamental Concepts of Mathematics

Fundamental Concepts

• Mathematics is a branch of science that deals with numbers, quantities, and shapes.
• It encompasses various fields, including arithmetic, algebra, geometry, calculus, and statistics.
• Mathematics provides a framework for understanding and modeling the world around us.
• It involves logical reasoning, problem-solving, and pattern recognition.
• Mathematical concepts are fundamental to many other disciplines, like physics, engineering, and computer science.

Number Systems

• Natural numbers (counting numbers): 1, 2, 3,...
• Whole numbers: 0, 1, 2, 3,...
• Integers:..., -3, -2, -1, 0, 1, 2, 3,...
• Rational numbers: numbers that can be expressed as a fraction p/q, where p and q are integers and q ≠ 0.
• Irrational numbers: numbers that cannot be expressed as a fraction of two integers. Examples include √2 and π.
• Real numbers: the set of all rational and irrational numbers.
• Imaginary numbers: numbers involving the square root of -1 (represented by 'i').
• Complex numbers: numbers that can be expressed in the form a + bi, where a and b are real numbers.

Arithmetic Operations

• Addition (+): combining two or more numbers to find a sum.
• Subtraction (-): finding the difference between two numbers.
• Multiplication (× or ⋅): repeated addition of a number.
• Division (÷ or /): splitting a number into equal parts.
• Order of operations (PEMDAS/BODMAS): a set of rules for evaluating expressions involving multiple operations in a specific sequence (Parentheses/Brackets, Exponents/Orders, Multiplication and Division, Addition and Subtraction).

Algebra

• Variables: symbols (like x, y, z) representing unknown values.
• Equations: statements showing the equality of two expressions.
• Inequalities: statements showing the relationship between two expressions (e.g., >, <, ≥, ≤).