Math Fundamentals: Numbers and Algebra

Numbers

• Types of numbers:
  • Natural numbers (1, 2, 3, ...)
  • Whole numbers (0, 1, 2, 3, ...)
  • Integers (...,-3, -2, -1, 0, 1, 2, 3, ...)
  • Rational numbers (fractions, decimals)
  • Irrational numbers (π, e, ...)
  • Real numbers (all rational and irrational numbers)
  • Complex numbers (with imaginary parts)

Algebra

• Variables and expressions:
  • Variables: letters or symbols representing unknown values
  • Expressions: combinations of variables, constants, and operations
• Equations and inequalities:
  • Equations: statements with equal signs (=)
  • Inequalities: statements with greater than (>), less than (<), etc.
• Functions:
  • Domain: set of input values
  • Range: set of output values
  • Notation: f(x) = ...

Geometry

• Points, lines, and planes:
  • Points: locations in space (x, y, z coordinates)
  • Lines: sets of points extending infinitely in two directions
  • Planes: flat surfaces extending infinitely in all directions
• Angles and measurements:
  • Degrees: units of angle measurement
  • Types of angles: acute, right, obtuse, straight, reflex
• Shapes and figures:
  • 2D: triangles, quadrilaterals, polygons, circles
  • 3D: pyramids, prisms, spheres, cones, cylinders

Calculus

• Limits:
  • Concept of approaching a value
  • Notation: lim x→a f(x) = ...
• Derivatives:
  • Rate of change of a function
  • Notation: f'(x) = ...
• Integrals:
  • Accumulation of a function
  • Notation: ∫f(x)dx = ...

Statistics and Probability

• Data analysis:
  • Types of data: qualitative, quantitative
  • Measures of central tendency: mean, median, mode
  • Measures of variability: range, variance, standard deviation
• Probability:
  • Events: outcomes of an experiment
  • Probability measures: 0 to 1, or 0% to 100%
  • Rules of probability: addition, multiplication, complement

Numbers

• Natural numbers are a set of positive integers starting from 1, such as 1, 2, 3, and so on.
• Whole numbers are a set of non-negative integers, including 0, such as 0, 1, 2, 3, and so on.
• Integers are a set of whole numbers and their negative counterparts, such as ..., -3, -2, -1, 0, 1, 2, 3, and so on.
• Rational numbers are fractions or decimals that can be expressed as a ratio of two integers, such as 3/4 or 0.5.
• Irrational numbers are decimal numbers that cannot be expressed as a ratio of two integers, such as π (pi) or e (Euler's number).
• Real numbers are a set of all rational and irrational numbers, including decimal numbers.
• Complex numbers are numbers that have both real and imaginary parts, such as 3 + 4i.

Algebra

• Variables are letters or symbols used to represent unknown values or quantities.
• Expressions are combinations of variables, constants, and mathematical operations, such as 2x + 5.
• Equations are statements with equal signs (=), used to express the equality of two expressions, such as 2x + 5 = 11.
• Inequalities are statements with greater than (>), less than (<), or other comparison operators, used to express a relationship between two expressions, such as 2x + 5 > 11.