User:Daniel5127/Mathematics

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This is my own page for Mathematics, but I copied this from User:Ta bu shi da yu/Math structure. I am interested in Mathematics, and involved in Mathematics Project in Wikipedia.

Contents

[edit] History

  1. History of Mathematics

[edit] Number

  1. Zero
  2. One
  3. Quantity
  4. Natural numbers
    1. Whole numbers
    2. Negative and non-negative numbers
    3. Number line
    4. Decimal
  5. Real numbers
    1. Rational number
    2. Irrational number
  6. Fraction
    1. Vulgar fraction
    2. Irreducible fraction
    3. Proper fraction
    4. Improper fraction
    5. Unit fraction
    6. Egyptian fraction
    7. Decimal fraction
    8. Dyadic rational
    9. Mixed fraction
    10. Continued fraction
    11. Compound fraction
    12. Partial fraction

[edit] Arithmetic

  1. Addition
    1. Counting
    2. Addition of natural numbers
    3. Commutative operation
    4. Associativity
    5. Absolute value
  2. Subtraction
  3. Plus and minus signs
  4. Multiplication
  5. Division
    1. Long division
    2. Division by zero
  6. Percent
  7. Square root
  8. Exponentiation
  9. Logarithm
  10. Order of operations

[edit] Algebra

[edit] Elementary algebra

  1. Variable
  2. Equation
  3. Function (mathematics)
  4. Polynomial
    1. Linear equation / Linear function
    2. Quadratic equation
    3. Cubic equation

[edit] Set theory

[edit] Naive set theory

  1. Set
  2. Element
  3. Empty set
  4. Cardinal number
  5. Subset
  6. Union
  7. Intersection
  8. Complement
  9. Russell's paradox
  10. Algebra of sets
  11. Relation

[edit] Functions

  1. Domain
  2. Codomain
  3. Range
  4. Multivalued function
  5. Partial function
  6. Types:
    1. Injective function
    2. Surjective function
    3. Bijective function
  7. Image & Preimage or Inverse image

[edit] Axiomatic set theory

  1. Axiom of extensionality
  2. Axiom of empty set
  3. Axiom of pairing
  4. Axiom of union
  5. Axiom of infinity
  6. Axiom schema of specification
  7. Axiom schema of replacement
  8. Axiom of power set
  9. Axiom of regularity
  10. Axiom of choice

[edit] Abstract algebra

  1. Algebraic structure

[edit] Graphing

  1. Coordinate system
  2. Coordinates (elementary mathematics)
    1. Cartesian coordinate system
    2. Polar coordinates
    3. Circular coordinates
    4. Cylindrical coordinates
    5. Spherical coordinates
  3. Graph of a function

[edit] Geometry

[edit] Euclidean geometry

  1. Point
  2. Line
    1. Ray
    2. Line segment
    3. Curve
  3. Plane
  4. Angle
  5. Parallel
  6. Perpendicular
  7. Congruency
  8. Similarity
  9. Polygon
    1. Triangle
      1. Congruent triangles
      2. Similar triangles
    2. Pentagon
    3. Hexagon
    4. Heptagon
    5. Octagon
    6. Enneagon
    7. Decagon
    8. Hendecagon
    9. Dodecagon
    10. Quadrilateral
      1. Trapezoid
      2. Isosceles trapezium
      3. Parallelogram
        1. Rhombus
          1. Kite
        2. Rectangle
        3. Square
  10. Circle
    1. Circumference
    2. Diameter
    3. Radius
    4. Secant
    5. Chord
    6. Arc
    7. Tangent
    8. Segment

[edit] Two and three-dimensional geometry

  1. Perimeter
  2. Arclength
  3. Area
  4. Volume
  5. Pythagorean Theorem
  6. Ellipse
  7. Polyhedron
  8. Ellipsoid
  9. Sphere

[edit] Traditional geometry

  1. Topology
  2. Erlangen program
  3. Hyperbolic geometry
  4. Elliptic geometry
  5. Affine geometry
  6. Projective geometry
  7. Inversive geometry

[edit] Modern geometry

  1. Algebraic geometry
  2. Differential geometry
  3. Noncommutative geometry

[edit] Trigonometry

[edit] Basic concepts

  1. Radian
  2. Degree
  3. Unit circle
  4. Trigonometric functions
  5. Sine wave
  6. Simple harmonic motion
  7. Exact trigonometric constants
  8. Generating trigonometric tables

[edit] Analytical trigonometry

  1. Trigonometric identity
  2. Sum and difference formula (trigonometry)

[edit] Calculus

[edit] Other

  1. Law of sines
  2. Law of cosines