Key Concepts in Mathematics

Natural Numbers (N): Positive integers (1, 2, 3, ...).
Whole Numbers (W): Natural numbers plus zero (0, 1, 2, ...).
Integers (Z): Whole numbers and their negatives (..., -3, -2, -1, 0, 1, 2, 3, ...).
Rational Numbers (Q): Numbers that can be expressed as a fraction (p/q, where p and q are integers, q ≠ 0).
Irrational Numbers: Numbers that cannot be expressed as a fraction (e.g., √2, π).

Variables: Symbols that represent numbers (e.g., x, y).
Expressions: Combinations of numbers, variables, and operations.
Equations: Statements that two expressions are equal (e.g., 2x + 3 = 7).
Polynomials: Expressions consisting of variables raised to whole number powers (e.g., 4x² + 3x - 5).

Basic Shapes:
- Triangle: 3 sides, sum of angles = 180°.
- Rectangle: Opposite sides equal, area = length × width.
- Circle: Area = πr², circumference = 2πr.
Theorems:
- Pythagorean Theorem: a² + b² = c² for right-angled triangles.
- Area and perimeter formulas for various shapes.

Functions: Sine (sin), Cosine (cos), Tangent (tan).
Relationships: In right triangles, the functions relate angles to side lengths.
Important Angles: 30°, 45°, 60°, and their corresponding sine and cosine values.

Limits: The value that a function approaches as the input approaches some value.
Derivatives: Measure of how a function changes as its input changes (slope of the tangent).
Integrals: Representation of the area under a curve.

Descriptive Statistics: Summarizes data through measures like mean, median, and mode.
Inferential Statistics: Makes predictions or inferences about a population based on sample data.
Probability: The study of randomness and uncertainty, ranging from 0 to 1.

Sets: Collections of distinct objects.
Graph Theory: Study of graphs, which are mathematical structures used to model pairwise relations.
Combinatorics: The study of counting, arrangements, and combinations.

Natural Numbers (N): Include all positive integers starting from 1 (1, 2, 3,...).
Whole Numbers (W): Extend natural numbers by adding 0 (0, 1, 2,...).
Integers (Z): Comprise whole numbers along with their negatives (..., -3, -2, -1, 0, 1, 2, 3,...).
Rational Numbers (Q): Represent numbers that can be expressed as fractions (p/q) with p and q as integers, and q not equal to 0.
Irrational Numbers: Cannot be expressed as simple fractions, examples include √2 and π.

Variables: Symbols (like x and y) that denote unknown values.
Expressions: Combinations of numbers and variables connected by operational signs.
Equations: Mathematical statements asserting that two expressions are equal (e.g., 2x + 3 = 7).
Polynomials: Formulas including variables raised to non-negative integer powers (e.g., 4x² + 3x - 5).

Basic Shapes:
- Triangle: Has three sides, with interior angles summing up to 180°.
- Rectangle: Includes two pairs of equal opposite sides, with area computed as length times width.
- Circle: Calculated area is π times the radius squared (A = πr²), while circumference equals 2π times the radius (C = 2πr).
Theorems:
- Pythagorean Theorem: In right triangles, the relation a² + b² = c² holds true.
- Various area and perimeter formulas for other geometric shapes.

Functions include Sine (sin), Cosine (cos), and Tangent (tan), essential for relating angles to side lengths in right triangles.
Important Angles: Common angles such as 30°, 45°, and 60° have specific sine and cosine values which are critical for calculations.

Limits: Establish the value that a function nears as its input approaches a given point.
Derivatives: Serve as a measure of how a function alters with respect to changes in its input, representing the slope of the tangent line.
Integrals: Utilize to determine the area beneath curves in a graphical representation.

Descriptive Statistics: Summarizes data through measures including mean, median, and mode.
Inferential Statistics: Enables predictions about populations when based on sample data.
Probability: Analyze randomness and uncertainty, ranging values from 0 (impossible) to 1 (certain).

Statements: Propositions that hold truth values of either true or false.
Logical Connectives: Operators such as AND, OR, NOT, used to forge compound propositions.
Quantifiers: Terms like universal (indicating "for all") and existential (indicating "there exists").

Sets: Defined as collections of distinct objects that can be classified by certain properties.
Graph Theory: Studies the mathematical frameworks of graphs, which depict pairwise relations.
Combinatorics: Explores arrangements, counting, and combinations of objects within a set.