Number Theory and Algebra Concepts

Definition: Study of integers and their properties.
Key Concepts:
- Prime Numbers: Numbers greater than 1 that have no positive divisors other than 1 and themselves.
- Composite Numbers: Numbers that have more than two positive divisors.
- Greatest Common Divisor (GCD): Largest integer that divides two or more integers without leaving a remainder.
- Least Common Multiple (LCM): Smallest multiple that is exactly divisible by two or more integers.
- Divisibility Rules: Guidelines to determine if one number is divisible by another (e.g., even numbers are divisible by 2).
- Modular Arithmetic: A system of arithmetic for integers, where numbers wrap around upon reaching a certain value (modulus).

Definition: Branch of mathematics dealing with symbols and the rules for manipulating those symbols.
Key Concepts:
- Variables: Symbols used to represent numbers in expressions or equations.
- Expressions: Combinations of variables, numbers, and operations (e.g., 3x + 2).
- Equations: Mathematical statements that assert the equality of two expressions (e.g., 2x + 3 = 7).
- Functions: Relationships where each input has a single output (e.g., f(x) = 2x + 3).
- Quadratic Equations: Polynomial equations of the form ax² + bx + c = 0; solutions can be found using factoring, completing the square, or the quadratic formula.
- Inequalities: Expressions that show the relationship of one quantity being greater than or less than another (e.g., x + 2 > 5).

Definition: A polygon with three edges and three vertices.
Types of Triangles:
- By Sides:
  - Equilateral: All sides are equal; all angles are 60°.
  - Isosceles: Two sides are equal; angles opposite the equal sides are equal.
  - Scalene: All sides and angles are different.
- By Angles:
  - Acute: All angles are less than 90°.
  - Right: One angle is exactly 90°.
  - Obtuse: One angle is greater than 90°.
Key Properties:
- Sum of Angles: The sum of the interior angles of a triangle is always 180°.
- Pythagorean Theorem: In a right triangle, a² + b² = c² (where c is the hypotenuse).
- Area Calculation: Area = 1/2 × base × height.
- Perimeter Calculation: Perimeter = sum of the lengths of all sides.

Study of integers and their properties.
Prime Numbers: Defined as numbers greater than 1 with no positive divisors other than 1 and themselves.
Composite Numbers: Defined as numbers that possess more than two positive divisors.
Greatest Common Divisor (GCD): Identified as the largest integer that divides two or more integers without a remainder, important for simplifying fractions.
Least Common Multiple (LCM): Recognized as the smallest multiple that is divisible by two or more integers, often used in finding common denominators.
Divisibility Rules: Set of guidelines to determine whether one number can be evenly divided by another, e.g., all even numbers are divisible by 2.
Modular Arithmetic: System of arithmetic where numbers wrap around after reaching a specified value or modulus, essential in computer science and cryptography.

Branch of mathematics focused on symbols and their manipulation.
Variables: Symbols representing unknown numbers in mathematical expressions or equations.
Expressions: Combinations of variables, constants, and operations, such as 3x + 2, which can be simplified or evaluated.
Equations: Mathematical statements asserting the equality of two expressions, e.g., 2x + 3 = 7, requiring solutions to find unknowns.
Functions: Relationships connecting each input to a single output, denoted as f(x) = 2x + 3, illustrating dependency of one variable on another.
Quadratic Equations: Polynomial equations formatted as ax² + bx + c = 0, solvable by factoring, completing the square, or employing the quadratic formula.
Inequalities: Mathematical expressions indicating the comparative size of quantities, such as x + 2 > 5, which identifies value ranges rather than exact solutions.

Defined as a polygon consisting of three edges and three vertices.
Types by Sides:
- Equilateral: All sides equal, and all angles measure 60°.
- Isosceles: Two equal sides with equal opposite angles.
- Scalene: No equal sides or angles, all differing from one another.
Types by Angles:
- Acute: All angles are less than 90°.
- Right: Contains one angle that is exactly 90°.
- Obtuse: Features one angle greater than 90°.
Key Properties:
- Sum of Angles: Interior angles always sum up to 180°.
- Pythagorean Theorem: In right triangles, the relation a² + b² = c² holds, where c denotes the hypotenuse.
- Area Calculation: Determined using the formula Area = 1/2 × base × height.
- Perimeter Calculation: Found by summing the lengths of all three sides.