User:Ta bu shi da yu/Math structure

Some thoughts on the structure of learning about Mathematics. May go into a Wikireader.

History

 * 1) History of Mathematics

Number

 * 1) Zero
 * 2) One
 * 3) Quantity
 * 4) Natural numbers
 * 5) Whole numbers
 * 6) Negative and non-negative numbers
 * 7) Number line
 * 8) Decimal
 * 9) Real numbers
 * 10) Rational number
 * 11) Irrational number
 * 12) Fraction
 * 13) Vulgar fraction
 * 14) Irreducible fraction
 * 15) Proper fraction
 * 16) Improper fraction
 * 17) Unit fraction
 * 18) Egyptian fraction
 * 19) Decimal fraction
 * 20) Dyadic rational
 * 21) Mixed fraction
 * 22) Continued fraction
 * 23) Compound fraction
 * 24) Partial fraction

Arithmetic

 * 1) Addition
 * 2) Counting
 * 3) Addition of natural numbers
 * 4) Commutative operation
 * 5) Associativity
 * 6) Absolute value
 * 7) Subtraction
 * 8) Plus and minus signs
 * 9) Multiplication
 * 10) Division
 * 11) Long division
 * 12) Division by zero
 * 13) Percent
 * 14) Square root
 * 15) Exponentiation
 * 16) Logarithm
 * 17) Order of operations

Elementary algebra

 * 1) Variable
 * 2) Equation
 * 3) Function (mathematics)
 * 4) Polynomial
 * 5) Linear equation / Linear function
 * 6) Quadratic equation
 * 7) Cubic equation

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

Functions

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

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

Abstract algebra

 * 1) Algebraic structure

Graphing

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

Euclidean geometry

 * 1) Point
 * 2) Line
 * 3) Ray
 * 4) Line segment
 * 5) Curve
 * 6) Plane
 * 7) Angle
 * 8) Parallel
 * 9) Perpendicular
 * 10) Congruency
 * 11) Similarity
 * 12) Polygon
 * 13) Triangle
 * 14) Congruent triangles
 * 15) Similar triangles
 * 16) Pentagon
 * 17) Hexagon
 * 18) Heptagon
 * 19) Octagon
 * 20) Enneagon
 * 21) Decagon
 * 22) Hendecagon
 * 23) Dodecagon
 * 24) Quadrilateral
 * 25) Trapezoid
 * 26) Isosceles trapezium
 * 27) Parallelogram
 * 28) Rhombus
 * 29) Kite
 * 30) Rectangle
 * 31) Square
 * 32) Circle
 * 33) Circumference
 * 34) Diameter
 * 35) Radius
 * 36) Secant
 * 37) Chord
 * 38) Arc
 * 39) Tangent
 * 40) Segment

Two and three-dimensional geometry

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

Traditional geometry

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

Modern geometry

 * 1) Algebraic geometry
 * 2) Differential geometry
 * 3) Noncommutative geometry

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

Analytical trigonometry

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

Other

 * 1) Law of sines
 * 2) Law of cosines