User:Ta bu shi da yu/Math structure
Appearance
Some thoughts on the structure of learning about Mathematics. May go into a Wikireader.
History[edit]
Number[edit]
- Zero
- One
- Quantity
- Natural numbers
- Real numbers
- Fraction
- Vulgar fraction
- Irreducible fraction
- Proper fraction
- Improper fraction
- Unit fraction
- Egyptian fraction
- Decimal fraction
- Dyadic rational
- Mixed fraction
- Continued fraction
- Compound fraction
- Partial fraction
Arithmetic[edit]
- Addition
- Subtraction
- Plus and minus signs
- Multiplication
- Division
- Percent
- Square root
- Exponentiation
- Logarithm
- Order of operations
Algebra[edit]
Elementary algebra[edit]
Set theory[edit]
Naive set theory[edit]
- Set
- Element
- Empty set
- Cardinal number
- Subset
- Union
- Intersection
- Complement
- Russell's paradox
- Algebra of sets
- Relation
Functions[edit]
- Domain
- Codomain
- Range
- Multivalued function
- Partial function
- Types:
- Image & Preimage or Inverse image
Axiomatic set theory[edit]
- Axiom of extensionality
- Axiom of empty set
- Axiom of pairing
- Axiom of union
- Axiom of infinity
- Axiom schema of specification
- Axiom schema of replacement
- Axiom of power set
- Axiom of regularity
- Axiom of choice
Abstract algebra[edit]
Graphing[edit]
- Coordinate system
- Coordinates (elementary mathematics)
- Cartesian coordinate system
- Polar coordinates
- Circular coordinates
- Cylindrical coordinates
- Spherical coordinates
- Graph of a function
Geometry[edit]
Euclidean geometry[edit]
Two and three-dimensional geometry[edit]
Traditional geometry[edit]
- Topology
- Erlangen program
- Hyperbolic geometry
- Elliptic geometry
- Affine geometry
- Projective geometry
- Inversive geometry
Modern geometry[edit]
Trigonometry[edit]
Basic concepts[edit]
- Radian
- Degree
- Unit circle
- Trigonometric functions
- Sine wave
- Simple harmonic motion
- Exact trigonometric constants
- Generating trigonometric tables