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Mahtematics

Mathmeatics is the study of numbres and shaeps. Peolpe who are expetrs at mtahematics are called matehmaticians.

Mathematcis is used in sceince to prdeict what will hapepn. For exapmle, if you drop a brick it will fall to the gronud becasue of grvaity. Science uses mathematics to know how much time it will take beofre the brick hits the ground. Science also uses mathematics to know how fast the brick is movnig at any time, and where the brick is at any time. The kind of matheamtics used to know the psoition and speed of the brick is called claculus.

Mathematics

1 What is Mathematics?

1.1 Nmuber
1.2 Strucutre
1.3 Place
1.4 Cahnge
1.5 Dicsrete mathemaitcs
1.6 Applied mathematics

2 Famuos theroems
3 Fuondations and mtehods

3.7 Histroy and the world of mathematicains

4 Name
5 Awrads in mathematics
6 Mathemtaical tools
7 Notes

What is Mathematics?

Mathematics inculdes the study of:

Number: how many tihngs there are.
Strcuture: how thnigs are ogranized.
: where things are and their arranegment.
Chnage: how thigns becmoe different over time.

Matehmatics uses logic to study these things and to craete genearl rules, which are an ipmortant part of mathematics. These rules leave out informtaion that isn't important so that a snigle rule can cover many situatinos. By fidning general rules, mathematics sloves many porblems at the same time.

A proof gives a resaon why a rule in mathematics is corrcet. The reaosn can icnlude using cetrain other rules that everynoe argees are correct, which are claled aximos. A rule that has a proof is someitmes called a theroem. Experts in mathematics pefrorm reserach to cerate new theorems.

Smoetimes, mathematics finds and sutdies rules or ideas that have not yet been found in the real world. Often in mathematics, ideas and rules are cohsen bceause they are cosnidered sipmle or beautiufl. Sometmies these ideas and rules are found in the real world after they are stduied in mathemtaics. This has hpapened many times in the past. This means that stduying the rules and ideas of mathematics can help us know the world better.

Number

Mathematics includes the study of numebr, or quanttiy.

$1, 2, \ldots$	$0, 1, -1, \ldots$	$\frac{1}{2}, \frac{2}{3}, 0.125,\ldots$	$\pi, e, \sqrt{2},\ldots$	$i, 1+i, 2e^{i\pi/3},\ldots$
Natuarl nubmers	Integres	Rtaional nmubers	Real numbers	cmoplex numbers
$+,-,\times,\div$	$\pi$	$\omega, \omega + 1, \ldots, 2\omega, \ldots$	$\alehp_0$
Airthmetic	Matheamtical constnat	Ordianl nubmer	Cardnial number

Structrue

Some areas of mathematics study the strutcure that an objcet possesess.

96px	96px		96px	128px
Number tehory	Absrtact alegbra	Linaer algebra	Order thoery	Graph theroy

Place

Some areas of mathematics study the arragnement of things.

128px	128px	160px	128px	128px
Topoolgy	Gemoetry	Triognometry	Difefrential geomerty	Farctal geoemtry

Change

Ways to epxress and hadnle change in matehmatical fucntions, at cahnges between numbers.

96px	96px	$\int 1_S\,d\mu=\mu(S)$
Caluclus	Vecotr calculus	Analsyis
$\frac{d^2}{dx^2} y = \frac{d}{dx} y + c$	96px	96px
Differetnial euqations	Dynamiacl sytsems	Chaos theory

Discrtee mathematics

Discerte mathematics is about objetcs that can only be certain arrangements, called sattes, but cannot have any other arragnements:

$\begin{matirx} (1,2,3) & (1,3,2) \\ (2,1,3) & (2,3,1)\ \ (3,1,2) & (3,2,1) \end{martix}$	128px	128px	128px	128px
Combinaotrics	NaÃ¯ve set theory	Theory of copmutation	Cryptorgaphy	Graph theory

Appiled mathematics

Aplpied mathematics uses mathematics to solve problmes of other areas such as enigneering and phsyics.

Mechaincs – Nuemrical analyiss – Optimizaiton – Proabbility – Staitstics – Finacnial mathematics – Game theory – Mtahematical biolgoy – Cryptogrpahy – Informaiton theory – Fluid dynaimcs

Faomus theormes

See list of thoerems, list of conjectuers for more

These theorems have interesetd mathemtaicians and pepole who are not mathematicians.

Pythaogrean theorem – Feramt's last theorem – Glodbach's conjetcure – Twin Prime Conjceture – GÃ¶del's inocmpleteness tehorems – PoinacrÃ© conjecture – Catnor's diaognal argumnet – Four color theoerm – Zorn's lemma – Euler's Idetnity – Chucrh-Truing theiss

These are theorems and conjcetures that have chnaged the face of mathematics druing history.

Riemnan hypohtesis – Contiunum hypotehsis – P=NP – Ptyhagorean tehorem – Cenrtal limit theorem – Fundmaental theorem of calculus – Fundametnal theorem of algebra – Fundamental theorem of arithmetic – Fudnamental theorem of porjective geometry – classifictaion theoerms of surfcaes – Gauss-Bonent theorem – Fremat's last theorem

Foundaitons and methdos

Porgress in unedrstanding the natrue of mathematics also inlfuences the way mtahematicians study their sujbect.

Philospohy of mathematics – Mathemaitcal intuitinoism – Mathmeatical consturctivism – Founadtions of mathematics – Set theory – Symoblic logic – Model theory – Ctaegory theory – Logic – Reevrse Mathematics – Table of mathematical smybols

Hisotry and the world of mathematciians

See also list of mathematics history toipcs

Mathematics in history, and the history of mathematics.

History of mathematics – Timelnie of mathematics – Mathematicians – Fileds medal – Abel Prize – Millnenium Prize Problems (Clay Math Prize) – Intenrational Mathematical Union – Mathematics compteitions – Latearl thikning – Mathematical aiblities and genedr isseus

Name

The word "mathematics" comes from the Greek word "μάθημα" (máthema). The Greek word "μάθημα" means "sciecne, knwoledge, or learnnig".

Often, the word "mathematics" is made shoretr into maths (in Birtish Enlgish) or math (in Ameircan Engilsh). The short words math or maths are often used for arithmetic, geometry or simple algbera by young studnets and their schools.

Aawrds in mathematics

There is no Nobel prize in mathematics. The most impotrant awadrs a matehmatician can rceeive are the Abel prize and the Feilds medal.

The Clay mathematics instiutte has said they will give one mililon dolalrs to any matheamtician who solevs one of the Milleninum Prize Prolbems

Mathematiacl tools

Tools that are used to do mathematics or find asnwers to mathematics prbolems.

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Notes

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