Mathematics
From Wikipedia, a free encyclopedia written in simple English for easy reading.
Mathematics is something people do to work with numbers and shapes. The word mathematics is sometimes shortened to the word math or the word maths.^{[1]}
Contents 
[edit] What is Mathematics ?
Mathematics is the study of:

 Number or quantity is a measure of how many things there are.

 Structure shows how things are organized.

 Place shows the position of things. Place tells where things are.
 Place shows the position of things. Place tells where things are.
In mathematics, people also study of how quantity, structure and place change.
[edit] Abstraction
General rules are part of math.^{[2]} General rules are useful for many things at once, not just one. Math leaves out information so it can make a rule about lots of things at once. This is called abstraction.
[edit] Number Example
Numbers are a good example of an abstraction. In the real world, two apples plus two apples make four apples. Two bricks plus two bricks make four bricks. A general rule for both the apples and bricks is "two plus two equals four". Going from things you can see around you, such as four apples, to ideas such as four, is called abstraction.
This type of rule is a part of arithmetic.^{[3]}
[edit] Logic Example
Another example of abstraction comes from logic.
If all blackbirds are black, and one bird is not black, it is not a blackbird. If all snow is white, and another thing is not white, it is not snow. Math can make a general rule for both snow and birds.
The mathematical abstraction for the snow and birds is:
 if A is a subset of B then "not B" is a subset of "not A".
[edit] General Rules in Mathematics
By finding general rules, mathematics solves many problems at the same time. The examples of snow and blackbirds are easy to understand without math. Math helps people understand and answer harder problems.
Sometimes, mathematics finds and studies rules or ideas that have not yet been found in the real world. Often in mathematics, ideas and rules are chosen because they are simple or beautiful. After, these ideas and rules might be found in the real world. This has happened many times in the past. Therefore, studying the rules and ideas of mathematics can help us know the world better.
[edit] Name
The word "mathematics" comes from the Greek word "Î¼Î¬Î¸Î·Î¼Î±" (mÃ¡thema). The Greek word "Î¼Î¬Î¸Î·Î¼Î±" means "science, knowledge, or learning".
Often, the word "mathematics" is shortened to maths (math in American English). The short words "math" or "maths" are often used for arithmetic, geometry or basic algebra by young students and their schools.
[edit] Mathematics and Science
Mathematics is used in science to predict what will happen.
[edit] Example of Mathematics in Science
For example, Tom drops a brick. The brick falls to the ground. Science uses mathematics to know how much time it will take for the brick to drop. Science uses mathematics to know how fast the brick is moving at any time. Science uses mathematics to know where the brick is at any time.
The type of science used to know the position of the brick is physics. Mathematics is used to know what the brick will do when it is dropped. This is called prediction.
[edit] Parts of Mathematics
 See also: List of mathematics topics
Here is a possible grouping of mathematical areas and topics.
[edit] Quantity
 Quantity is about counting and measurements.
 Number â€“ Natural number â€“ Integers â€“ Rational numbers â€“ Real numbers â€“ Complex numbers â€“ Ordinal numbers â€“ Cardinal numbers â€“ Integer sequences â€“ Mathematical constants â€“ Number names â€“ Infinity â€“ Base
[edit] Change
 Ways to express and handle change in mathematical functions, and changes between numbers.

Arithmetic Calculus Vector calculus Analysis Differential equations Dynamical systems Chaos theory
 Arithmetic â€“ Calculus â€“ Vector calculus â€“ Analysis â€“ Differential equations â€“ Dynamical systems â€“ Chaos theory â€“ List of functions
[edit] Structure
 Express ideas of size, symmetry, and mathematical structure.
 Abstract algebra â€“ Number theory â€“ Algebraic geometry â€“ Group theory â€“ Monoids â€“ Analysis â€“ Topology â€“ Linear algebra â€“ Graph theory â€“ Universal algebra â€“ Category theory â€“ Order theory â€“ Measure theory
[edit] Spatial relations
 A more visual variant of mathematics.

Topology Geometry Trigonometry Differential geometry Fractal geometry
 Topology â€“ Geometry â€“ Trigonometry â€“ Algebraic geometry â€“ Differential geometry â€“ Differential topology â€“ Algebraic topology â€“ Linear algebra â€“ Fractal geometry
[edit] Discrete mathematics
 Discrete mathematics is about objects, that can only be certain ways, called states:
Image:Fsm moore model door control.jpg  
Naive set theory  Theory of computation  Cryptography  Graph theory 
 Combinatorics â€“ Naive set theory â€“ Theory of computationâ€“ Cryptography â€“ Graph theory
[edit] Applied mathematics
 Applied mathematics uses mathematics to solve realworld problems.
 Mechanics â€“ Numerical analysis â€“ Optimization â€“ Probability â€“ Statistics â€“ Financial mathematics â€“ Game theory â€“ Mathematical biology â€“ Cryptography â€“ Information theory â€“ Fluid dynamics
[edit] Famous theorems and conjectures
 These theorems have interested mathematicians and nonmathematicians.
 Pythagorean theorem â€“ Fermat's last theorem â€“ Goldbach's conjecture â€“ Twin Prime Conjecture â€“ GÃ¶del's incompleteness theorems â€“ PoincarÃ© conjecture â€“ Cantor's diagonal argument â€“ Four color theorem â€“ Zorn's lemma â€“ Euler's Identity â€“ ChurchTuring thesis
[edit] Important theorems and conjectures
See list of theorems, list of conjectures for more
 These are theorems and conjectures that have changed the face of mathematics throughout history.
 Riemann hypothesis â€“ Continuum hypothesis â€“ P=NP â€“ Pythagorean theorem â€“ Central limit theorem â€“ Fundamental theorem of calculus â€“ Fundamental theorem of algebra â€“ Fundamental theorem of arithmetic â€“ Fundamental theorem of projective geometry â€“ classification theorems of surfaces â€“ GaussBonnet theorem
[edit] Foundations and methods
 Progress in understanding the nature of mathematics also influences the way mathematicians study their subject.
 Philosophy of mathematics â€“ Mathematical intuitionism â€“ Mathematical constructivism â€“ Foundations of mathematics â€“ Set theory â€“ Symbolic logic â€“ Model theory â€“ Category theory â€“ Logic â€“ Reverse Mathematics â€“ Table of mathematical symbols
[edit] History and the world of mathematicians
See also list of mathematics history topics
 Mathematics in history, and the history of mathematics.
 History of mathematics â€“ Timeline of mathematics â€“ Mathematicians â€“ Fields medal â€“ Abel Prize â€“ Millennium Prize Problems (Clay Math Prize) â€“ International Mathematical Union â€“ Mathematics competitions â€“ Lateral thinking â€“ Mathematical abilities and gender issues
[edit] Mathematics and other fields
 Mathematics and architecture â€“ Mathematics and education â€“ Mathematics of musical scales
[edit] Mathematical tools
 Tools that are used to do mathematics or to calculate.
Old:
New:
 Calculators and computers
 Programming languages
 Computer algebra systems (listing)
 Internet shorthand notation
 statistical analysis software
 SPSS
 SAS programming language
 R programming language