Mathematics
From the Simple English Wikipedia, the free encyclopedia that anyone can change
Mathematics is the study of numbers, patterns, and shapes. People who are experts at mathematics are called mathematicians.
Mathematics is used to find practical solutions to real world problems. A common saying is "Do the math," meaning check the answer and see that it is right. For example, if we want to know whether or not a particular medicine will help to cure a disease, mathematics is used to answer that question.
The method mathematicians use to solve problems is called deduction. Deduction is the use of reason to discover new ideas from old. For example, from the simple idea of a triangle mathematicians discovered the Pythagorean theorem, that in a right triangle the sum of the squares of the two shorter sides is equal to the square of the longest side. Thus, if we know that the shorter sides of a right triangle are 3 inches and 4 inches, we can deduce that the longest side is 5 inches, because the square of 3 is 9, the square of 4 is 16, and the square of 5 is 25; and 9 + 16 = 25.
Mathematics is necessary in business, science, engineering, construction work, and in many other jobs.
Contents 
[change] About
Mathematics includes the study of:
 Number: how many things there are.
 Structure: how things are organized.
 Place: where things are and their arrangement.
 Change: how things become different over time.
Mathematics uses logic to study these things and to create general rules, which are an important part of mathematics. These rules leave out information that isn't important so that a single rule can cover many situations. By finding general rules, mathematics solves many problems at the same time.
A proof gives a reason why a rule in mathematics is correct. The reason can include using certain other rules that everyone agrees are correct, which are called axioms. A rule that has a proof is sometimes called a theorem. Experts in mathematics perform research to create new theorems.
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 considered simple or beautiful. Sometimes these ideas and rules are found in the real world after they are studied in mathematics. This has happened many times in the past. This means that studying the rules and ideas of mathematics can help us know the world better.
[change] Number
 Mathematics includes the study of number, or quantity.

Natural numbers Integers Rational numbers Real numbers complex numbers π Arithmetic Mathematical constant Ordinal number Cardinal number
[change] Structure
 Some areas of mathematics study the structure that an object possesses.

(()(()())) Number theory Abstract algebra Linear algebra Order theory Graph theory Operand theory
[change] Place
 Some areas of mathematics study the arrangement of things.

Topology Geometry Trigonometry Differential geometry Fractal geometry
[change] Change
 Ways to express and handle change in mathematical functions, at changes between numbers.

Calculus Vector calculus Analysis Differential equations Dynamical systems Chaos theory
[change] Discrete mathematics
 Discrete mathematics is about objects that can only be certain arrangements, called states, but cannot have any other arrangements:
Combinatorics  Naïve set theory  Theory of computation  Cryptography  Graph theory 
[change] Applied mathematics
 Applied mathematics uses mathematics to solve problems of other areas such as engineering and physics.
 Mechanics – Numerical analysis – Optimization – Probability – Statistics – Financial mathematics – Game theory – Mathematical biology – Cryptography – Information theory – Fluid dynamics – Quantum Physics
[change] Famous theorems
 See list of theorems, list of conjectures for more
These theorems have interested mathematicians and people who are not mathematicians.
 Pythagorean theorem – Fermat's last theorem – Goldbach's conjecture – Twin Prime Conjecture – Gödel's incompleteness theorems – Poincaré conjecture – Cantor's diagonal argument – Four color theorem – Zorn's lemma – Euler's Identity – ChurchTuring thesis
These are theorems and conjectures that have greatly changed mathematics.
 Riemann hypothesis – Continuum hypothesis – P=NP – Pythagorean theorem – Central limit theorem – Fundamental theorem of calculus – Fundamental theorem of algebra – Fundamental theorem of arithmetic – Fundamental theorem of projective geometry – classification theorems of surfaces – GaussBonnet theorem – Fermat's last theorem
[change] Foundations and methods
Progress in understanding the nature of mathematics also influences the way mathematicians study their subject.
 Philosophy of mathematics – Mathematical intuitionism – Mathematical constructivism – Foundations of mathematics – Set theory – Symbolic logic – Model theory – Category theory – Logic – Reverse Mathematics – Table of mathematical symbols
[change] History and the world of mathematicians
See also list of mathematics history topics
Mathematics in history, and the history of mathematics.
 History of mathematics – Timeline of mathematics – Mathematicians – Fields medal – Abel Prize – Millennium Prize Problems (Clay Math Prize) – International Mathematical Union – Mathematics competitions – Lateral thinking – Mathematical abilities and gender issues
[change] Name
The word "mathematics" comes from the Greek word "μάθημα" (máthema). The Greek word "μάθημα" means "science, knowledge, or learning".
Often, the word "mathematics" is made shorter into maths (in British English) or math (in American English). The short words math or maths are often used for arithmetic, geometry or simple algebra by young students and their schools.
[change] Awards in mathematics
There is no Nobel prize in mathematics. The most important awards a mathematician can receive are the Abel prize and the Fields medal.
The Clay mathematics institute has said they will give one million dollars to any mathematician who solves one of the Millennium Prize Problems
[change] Mathematical tools
 Tools that are used to do mathematics or find answers to mathematics problems.
Old:
 Abacus
 Napier's bones, Slide Rule
 Ruler and Compass
 Mental calculation
New:
 Calculators and computers
 Programming languages
 Computer algebra systems (listing)
 Internet shorthand notation
 statistical analysis software
 SPSS
 SAS programming language
 R programming language
[change] Notes