Key Concepts in Math

Natural Numbers: Positive integers (1, 2, 3, ...)
Whole Numbers: Natural numbers including zero (0, 1, 2, 3, ...)
Integers: Whole numbers and their negatives (..., -3, -2, -1, 0, 1, 2, 3, ...)
Rational Numbers: Numbers that can be expressed as the quotient of two integers (e.g., 1/2, -3, 4.5)
Irrational Numbers: Numbers that cannot be expressed as fractions (e.g., √2, π)

Variables: Symbols (often letters) that represent unknown values.
Expressions: Combinations of numbers, variables, and operations (e.g., 3x + 2).
Equations: Statements that two expressions are equal (e.g., 2x + 3 = 7).

Shapes: Basic shapes include circles, triangles, squares, rectangles.
Perimeter: The distance around a shape.
Area: The space contained within a shape (e.g., Area of a rectangle = length × width).
Volume: The amount of space occupied by a 3D object.

Sine, Cosine, Tangent: Functions related to the angles of triangles.
Pythagorean Theorem: In right triangles, a² + b² = c², where c is the hypotenuse.

Limits: The value a function approaches as the input approaches some value.
Derivatives: Measure the rate of change of a function.
Integrals: Represent the accumulation of quantities, often area under curves.

Mean: Average of a set of numbers.
Median: Middle value in a sorted set of numbers.
Mode: The value that appears most frequently in a data set.
Standard Deviation: Measure of the amount of variation or dispersion in a set of values.

Science: Used for data analysis, modeling, and experiments.
Finance: Involves calculations for budgeting, investing, and financial analysis.
Engineering: Critical for design, construction, and analysis of structures.
Computer Science: Algorithms, data structures, and computational theory rely heavily on mathematical principles.

Natural Numbers: The sequence of positive integers starting from 1.
Whole Numbers: The set of natural numbers including zero, beginning at 0.
Integers: All whole numbers, both positive and negative, along with zero.
Rational Numbers: Any number that can be represented as a fraction, including integers and finite decimals.
Irrational Numbers: Numbers that cannot be expressed as a fraction, featuring non-repeating decimals, e.g., √2 and π.

Addition (+): The process of combining values to yield a sum.
Subtraction (−): Determining the difference between two values.
Multiplication (×): Repeatedly adding a number to itself a specified number of times.
Division (÷): Distributing a number into equal parts or determining how many times one number is contained within another.

Variables: Symbols, often letters, that symbolize unknown quantities or values.
Expressions: Mathematical phrases combining numbers, variables, and operations (e.g., 3x + 2 is an expression).
Equations: Mathematical statements asserting that two expressions are equivalent (e.g., 2x + 3 = 7 illustrates an equation).

Shapes: Foundational geometric forms include circles, triangles, squares, and rectangles.
Perimeter: The total length around a geometric figure, calculated by summing all sides.
Area: The measure of space within a shape, for instance, a rectangle's area is calculated as length multiplied by width.
Volume: The amount of three-dimensional space occupied by an object, such as a cube or sphere.

Sine, Cosine, Tangent: Fundamental trigonometric functions that describe relationships between angles and sides in triangles.
Pythagorean Theorem: A cornerstone of geometry stating that in a right triangle, the square of the length of the hypotenuse equals the sum of the squares of the lengths of the other two sides (a² + b² = c²).

Limits: Assess the value a function nears as the input approaches a certain point.
Derivatives: A tool for expressing the rate of change of a function regarding its variable.
Integrals: Represents the accumulation of quantities, commonly used to calculate areas under curves.

Mean: The arithmetic average calculated by dividing the sum of all values in a data set by the count of the values.
Median: The middle number when a data set is ordered from least to greatest.
Mode: The value that occurs most frequently in a given data set.
Standard Deviation: A metric that measures the spread or dispersion of a set of numbers relative to their mean.

Probability: A quantitative measure of the likelihood of an event occurring, ranging from 0 (impossible) to 1 (certain).
Sample Space: The complete set of all possible outcomes of a probability experiment.
Events: Specific collections of outcomes from a probability experiment.

Science: Mathematics is integral for performing data analysis, creating models, and conducting experiments.
Finance: Essential for budgeting, investment calculations, and financial metrics.
Engineering: Mathematics is foundational for the design, construction, and assessment of structures and systems.
Computer Science: Advances in this field are driven by mathematical concepts, such as algorithms and data structures.