Mathematics

From Wikipedia, the free encyclopedia

Mathematics, or math (sometimes also shortened as "maths"), is the study of numbers, shapes and patterns. Mathematicians are people whose job is to learn and discover such things in mathematics. The biggest part of mathematics is useful for solving problems that occur in the real world, so many people besides mathematicians study and use these parts of mathematics. Today in many kinds of jobs -- in business, science, engineering, and construction, for example -- knowledge about certain aspects of mathematics is needed.

Mathematicians solve problems by using logic. Mathematicians often use deduction. Deduction is a special way of thinking to discover and prove new truths using old truths. To a mathematician, the reasons you know something is true are just as important as the fact that it is true. Using deduction is what makes mathematical thinking different from normal thinking.

[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. This is done by 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 experts find an idea that they think is a theorem but can not find a proof for it. That idea is called a conjecture until they find a proof.

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.

$1, 2, 3, \ldots$	$\ldots, -1, 0, 1, \ldots$	$\frac{1}{2}, \frac{2}{3}, 0.125,\ldots$	$\pi, e, \sqrt{2},\ldots$	$1+i, 2e^{i\pi/3},\ldots$
Natural numbers	Integers	Rational numbers	Real numbers	complex numbers
$+,-,\times,\div$	$π, e$	$\omega, \omega + 1, \ldots, 2\omega, \ldots$	$\aleph_0$
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.

		$\int 1_S\,d\mu=\mu(S)$
Calculus	Vector calculus	Analysis
$\frac{d^2}{dx^2} y = \frac{d}{dx} y + c$
Differential equations	Dynamical systems	Chaos theory

[change] Applied mathematics

Applied mathematics uses mathematics to solve problems of other areas such as engineering and physics.

Numerical analysis – Optimization – Probability theory – Statistics – Mathematical finance – Game theory – Mathematical physics – Fluid dynamics

[change] Famous theorems

See list of theorems, list of conjectures for more

These theorems have interested mathematicians and people who are not mathematicians.^{[needs proving]}

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 – Church-Turing 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 – Gauss-Bonnet 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

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 – Maths and gender

[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. Mathematicians can receive the Abel prize and the Fields Medal for important works.

The Clay Mathematics Institute have said they will give one million dollars to anyone 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:

New:

Mathematics

From Wikipedia, the free encyclopedia

Contents

[change] About

[change] Number

[change] Structure

[change] Place

[change] Change

[change] Applied mathematics

[change] Famous theorems

[change] Foundations and methods

[change] History and the world of mathematicians

[change] Name

[change] Awards in mathematics

[change] Mathematical tools

Views

Personal tools

Search

Getting around

Print/export

Toolbox

In other languages