Overview of Mathematics

Definition: The study of numbers, quantities, shapes, and patterns.
Branches:
- Arithmetic: Basic operations (addition, subtraction, multiplication, division).
- Algebra: Use of symbols and letters to represent numbers in equations.
- Geometry: Study of shapes, sizes, and properties of space.
- Calculus: Study of change, involving derivatives and integrals.
- Statistics: Analysis and interpretation of numerical data.
- Probability: Study of chance and uncertainty.

Numbers:
- Natural Numbers: Counting numbers (1, 2, 3, ...).
- Integers: Whole numbers including negatives (..., -2, -1, 0, 1, 2, ...).
- Rational Numbers: Fractions or ratios of integers.
- Irrational Numbers: Numbers that cannot be expressed as a fraction (e.g., √2, π).
- Real Numbers: All rational and irrational numbers.
Operations:
- Addition (+), Subtraction (-), Multiplication (×), Division (÷).
- Order of operations: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction (PEMDAS).

Variables: Symbols used to represent unknown values.
Equations: Mathematical statements that assert the equality of two expressions.
Functions: Relations where each input has a single output.
Linear Equations: Equations of the first degree (e.g., y = mx + b).

Points, Lines, and Angles: Basic building blocks of geometric shapes.
Shapes:
- 2D Shapes: Circles, triangles, squares, rectangles.
- 3D Shapes: Spheres, cubes, cylinders, cones.
Theorems: Pythagorean theorem, properties of triangles, area, and volume calculations.

Mean, Median, Mode: Measures of central tendency.
Standard Deviation: Measure of the dispersion of a set of data points.
Probability Rules: Addition and multiplication rules, independent vs. dependent events.

Understand the Problem: Read carefully and determine what is being asked.
Devise a Plan: Choose a strategy (e.g., drawing a diagram, creating an equation).
Carry Out the Plan: Execute the chosen strategy methodically.
Review/Reflect: Check the solution and revisit the problem if necessary.

Types of Numbers:
- Natural Numbers: Counting numbers beginning from 1 (e.g., 1, 2, 3).
- Integers: Entire number set, including negative and positive values (e.g., -2, -1, 0, 1, 2).
- Rational Numbers: Numbers expressible as fractions or ratios (e.g., 1/2, 3/4).
- Irrational Numbers: Cannot be represented as fractions (e.g., √2, π).
- Real Numbers: Combination of rational and irrational numbers.
Mathematical Operations:
- Includes addition (+), subtraction (-), multiplication (×), and division (÷).
- Order of operations follows PEMDAS (Parentheses, Exponents, Multiplication/Division, Addition/Subtraction).

Variables: Symbols denoting unknown values.
Equations: Establish equality between two expressions.
Functions: Relationships where each input corresponds to a single output.
Linear Equations: First-degree equations represented as y = mx + b, where m is the slope and b is the y-intercept.

Fundamental Elements: Points, lines, and angles serve as the foundational components of geometry.
Shapes:
- 2D Shapes: Include figures like circles, triangles, squares, and rectangles.
- 3D Shapes: Comprise objects such as spheres, cubes, cylinders, and cones.
Important Theorems: Include the Pythagorean theorem and formulas for calculating area and volume for various shapes.

Limits: Describes the behavior of functions as inputs approach specific values.
Derivatives: Quantify how a function's output changes with variations in input.
Integrals: Relate to the total accumulation of quantities; often used to calculate areas.

Measures of Central Tendency: Includes mean (average), median (middle value), and mode (most frequent value).
Standard Deviation: Indicates how much data varies from the mean.
Probability Rules: Cover addition and multiplication rules, distinguishing between independent and dependent events.

Understand the Problem: Carefully analyze the question to grasp what is required.
Devise a Plan: Formulate a strategy, which could involve drawing a diagram or outlining an equation.
Carry Out the Plan: Implement the chosen strategy in an organized manner.
Review/Reflect: Reassess the solution for correctness, considering restating the problem if needed.