Mathematics Fundamentals

Numbers and Operations

• Real Numbers: Include all rational and irrational numbers, can be expressed as decimal expansions
• Integer: Whole numbers, either positive, negative, or zero
• Rational Numbers: Can be expressed as a ratio of integers (e.g., 3/4)
• Irrational Numbers: Cannot be expressed as a ratio of integers (e.g., pi, e)
• Complex Numbers: Combine real and imaginary parts (e.g., 3 + 4i)

Algebra

• Variables: Letters or symbols representing unknown values
• Constants: Numbers that do not change value
• Expressions: Combinations of variables, constants, and operations
• Equations: Statements asserting equality between expressions
• Inequalities: Statements asserting a relationship between expressions (e.g., >, <, ≥, ≤)

Geometry

• Points: Locations in space, represented by coordinates (x, y, z)
• Lines: Sets of points extending infinitely in two directions
• Line Segments: Parts of lines with definite starting and ending points
• Rays: Lines with one endpoint and extending infinitely in one direction
• Angles: Formed by two rays sharing a common endpoint (vertex)
• Triangles: Three-sided polygons with three vertices and three sides
• Quadrilaterals: Four-sided polygons with four vertices and four sides

Calculus

• Limits: The value a function approaches as the input gets arbitrarily close to a certain point
• Derivatives: Measures of how a function changes as its input changes
• Integrals: Measures of the accumulation of a function over a given interval
• Multivariable Calculus: Deals with functions of multiple variables and their limits, derivatives, and integrals

Graph Theory

• Graphs: Collections of vertices (nodes) connected by edges
• Vertices: Points in a graph, may have multiple edges connected to them
• Edges: Connections between vertices
• Paths: Sequences of vertices connected by edges
• Cycles: Paths that start and end at the same vertex

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