Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of topics such as quantity (numbers), structure, space, time, motion, change, and measurement.
(TO DO: expand, organize, cross-reference, illustrate.)
Contents
Definition
There is a range of views among mathematicians and philosophers as to the exact scope and definition of mathematics.
See ... TO DO.
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 syntax
- Abstract syntax tree
- Abstraction (mathematics)
- Algebra
- Algorithm
- Analysis
- Argument of a function
- Arithmetic
- Axiom
- Binomial
- Calculus
- Cellular automaton
- Citizen Maths
- Complex dynamics
- Complex number
- Computation
- Conjecture
- Constant (mathematics)
- Control theory
- Covering space
- Discrete mathematics
- Dynamical systems
- Equation
- Euler angles
- Fibonacci coding
- Fibonacci sequence
- Fixed-point theorem
- Formal language
- Formal grammar
- Foundations of mathematics
- Fractal
- Function (mathematics)
- Geometry
- Graph theory
- Hexadecimal
- How to Solve It
- Idempotence
- Integer
- Julia set
- Lambda calculus
- Large cardinal
- Logic
- Mandelbrot set
- Mathematical analysis
- Mathematical logic
- Mathematical notation
- Mathematical object
- Mathematical proof
- Mathematician
- Morse theory
- Morse–Smale system
- Music theory
- Natural number
- Newton's method
- Number
- Number theory
- Numeral system
- Permutation
- Pi
- Polar coordinate system
- Power of two
- Real number
- Recursion
- Rounding
- Round-off error
- Scaling (geometry)
- Self-reference
- Signal
- Signal processing
- Simplicial complex
- The Unreasonable Effectiveness of Mathematics in the Natural Sciences
- Tuple
- Turing machine
- Variable (mathematics)
- Undecidable problem
External links
- Mathematics @ Wikipedia
