Difference between revisions of "Mathematics"
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Revision as of 14:03, 20 February 2016
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of topics such as quantity (numbers), structure, space, time, motion, change, and measurement.
Contents
Definition
There is a range of views among mathematicians and philosophers as to the exact scope and definition of mathematics.
Patterns and conjectures
Mathematicians seek out patterns and use them to formulate new conjectures.
Mathematical proof
Mathematicians resolve the truth or falsity of conjectures by mathematical proof.
Physics
When mathematical structures are good models of real phenomena, then mathematical reasoning can provide insight or predictions about nature.
See Physics.
Fundamental principles
Through the use of abstraction and logic, mathematics developed from:
- Counting
- Calculation
- Measurement
- The systematic study of the shapes and motions of physical objects
History
Practical mathematics has been a human activity for as far back as written records exist.
Effort required
The research required to solve mathematical problems can take years or even centuries of sustained inquiry.
See also
- Abstract algebra
- Abstract syntax
- Abstract syntax tree
- Abstraction (mathematics)
- Algebra
- Algorithm
- Analysis
- Analytic geometry
- Antiderivative
- Approximation
- Argument of a function
- Arithmetic
- Axiom
- Base
- Binomial
- Boolean algebra
- Boolean function
- Calculus
- Canonical form
- Category theory
- Cellular automaton
- Citizen Maths
- Complex dynamics
- Complex number
- Complex system
- Computable analysis
- Computation
- Conjecture
- Constant (mathematics)
- Constraint (mathematics)
- Constructive analysis
- Constructive mathematics
- Control theory
- Covering space
- Descriptive geometry
- Differential equation
- Differential geometry
- Differential geometry of surfaces
- Differential topology
- Dimensionless quantity
- Discrete mathematics
- Dynamical systems
- Element (mathematics)
- Engineering
- Equation
- Euler angles
- Euler method
- Expression (mathematics)
- Feasible set
- Fibonacci coding
- Fibonacci sequence
- Fixed-point theorem
- Formal language
- Formal grammar
- Foundations of mathematics
- Fractal
- Function (mathematics)
- Functional completeness
- Geodesic
- Geometry
- Graph theory
- Hexadecimal
- Higman's embedding theorem
- How to Solve It
- Idempotence
- Indecomposability
- Indecomposable continuum
- Integer
- Julia set
- Lakes of Wada
- Lambda calculus
- Large cardinal
- Local analysis
- Logic
- Logarithm
- Mandelbrot set
- Mathematical analysis
- Mathematical logic
- Mathematical notation
- Mathematical object
- Mathematical optimization
- Mathematical proof
- Mathematician
- Morse theory
- Morse–Smale system
- Music theory
- Natural logarithm
- Natural number
- Newton's method
- Nonzero-rule
- Normalization
- Number
- Number theory
- Numeral system]]
- Ordinary differential equation
- Permutation
- Philosophy of mathematics
- Pi
- Poincaré section
- Polar coordinate system
- Power of two
- Radix
- Real number
- Recursion
- Recursive definition
- Rewriting
- Rounding
- Round-off error
- Scaling (geometry)
- Search space
- Self-reference
- Signal
- Signal processing
- Simplicial complex
- Solution space
- The Unreasonable Effectiveness of Mathematics in the Natural Sciences
- Topology
- Tuple
- Turing completeness
- Turing machine
- Variable (mathematics)
- Undecidable problem
- Zero
- Zero-based numbering
External links
- Mathematics @ Wikipedia
