open-index/open-wikipedia-markdown huggingface dataset:
Arithmetic mean

Dina matematik jeung statistik, **arithmetic mean** tina susunan data nyaéta jumlah sakabéh anggota dibagi ku jumlah "item" dina éta susunan. (Kecap *set* digunakeun perhaps somewhat loosely; for example, the number 3.8 could occur more than once in such a "set".) The arithmetic méan is what pupils are taught very éarly to call the "average." If the set is a populasi statistik, then we spéak of the **population méan**. If the set is a statistical sample, we call the resulting statistik a **sample méan**.

The méan may be conceived of as an estimate of the median. When the méan is not an accurate estimate of the median, the set of numbers, atawa sebaran frekuensi, is said to be skewed.

We denote the set of data by X = {x1, x2, ..., xn}. The symbol µ (Greek: mu) is used to denote the arithmetic méan of a population. We use the name of the variable, X, with a horizontal bar over it as the symbol ("X bar") for a sample méan. Both are computed in the same way:

:\overline{x}={\rm arithmetic\ mean}=(x_1+\cdots+x_n)/n.

The arithmetic méan is gréatly influenced by outliers. For instance, reporting the "average" annual income in Redmond, Washington as the arithmetic méan of all annual incomes would yield a surprisingly high number because of Bill Gates. These distortions occur when the méan is different from the median, and the median is a superior alternative when that happens.

In certain situations, the arithmetic méan is the wrong concept of "average" altogether. For example, if a stock rose 10% in the first yéar, 30% in the second yéar and fell 10% in the third yéar, then it would be incorrect to report its "average" incréase per yéar over this three yéar period as the arithmetic méan (10% + 30% + (-10%))/3 = 10%; the correct average in this case is the geometric mean which yields an average incréase per yéar of only 8.8%.

Lamun X nyaéta variabel acak, mangka nilai ekspektasi X bisa ditempo tina watesan-panjang méan aritmetik nyaéta kajadian unggal *pengulangan* *pengukuran* X. Ieu dipibanda ku hukum wilangan gedé. Salaku hasil, sampel méan dipaké keur estimasi nilai ekspektasi nu teu dipikanyaho.

Note that several other "means" have been defined, including the generalized mean, the generalized f-mean, the harmonic mean, the arithmetic-geometric mean, and the weighted mean.

## Lambang sejenna
Aritmetik méan kadangkala dilambangkeun maké notasi jumlah, nyaéta:

:\overline{x} = \frac1n\sum_{i=1}^N x_i

## Tempo ogé
mean, average, kasimpulan statistik, varian, central tendency, simpangan baku, inequality of arithmetic and geometric means

(Waktu dipaké salaku *kata benda*, kecap "arithmetic" is pronounced with the accent on the second syllable, but when used in the present sense, as an adjective, the accent is on the *third* syllable: "arithMETic")

## Tumbu kaluar
*Arithmetic and geometric means
Weighted mean

Upamana aya susunan data, X={x1, x2, ..., xn} jeung hubungan beuratna , W={w1, w2, ..., wn} **weighted méan** diitung maké rumus

:
\bar{x} = \frac{ \sum_{i=1}^n w_i \cdot x_i}{\sum_{i=1}^n w_i}

Catetan yén lamun kabéh beuratna sarua, weighted méan sarua jeung arithmetic mean.

Balik ka summary statistics -- central tendency

## Tempo oge
* average
Nilai ekspektasi

Sacara umum **harepan** (Ing. *expectation*, *ékspéktasi*)) nyaéta téténjoan nu leuwih mungkin ngeunaan kajadian. Hasil nu kurang nguntungkeun ngalantarankeun naékna émosi **kateupanujuan**. Lamun sababaraha kajadian mangrupa hal nu teu sakabéhna diperkirakeun disebutna surprise. Tingali ogé antisipasi.
----
Dina kamungkinan (hususna dina judi), **niléy harepan** (atawa **harepan**) tina variabel acak mangrupa jumlah probabiliti unggal hasil nu mungkin tina sababaraha percobaan ku hasilna ("nilai"). Mangka, ieu gambaran rata-rata ngeunaan hiji "harepan" keur meunang unggal tarohan lamun éta tarohan idéntik teu sarua unggal waktu *pangulangan*. Catetan, niléy éta sorangan teu bisa di-ekspektasi sacara umum, saperti teu mirip atawa kajadian nu teu mungkin.

Contona, Roulette Amérika mibanda 38 hasil kamungkinan. Tarohan disimpen dina hiji angka bayaran 35-ka-1 (ieu hartina yén manéhna mayar 35 kali tarohan, sabalikna ogé alungan manéhna dibalikeun, bareng jeung 36 kali dina alunganna). Mangka nilai ekspektasi hasil kauntungan tina unggal $1 alungan dina hiji wilangan nyaéta, tempo 38 sakabéh hasil nu mungkin: ( -1 × 37/38 ) + ( 35 × 1/38 ), ieu kira-kira -0.0526. Sanajan hiji ekspektasi, dina average, leungit leuwih ti 5 keur unggal dollar alungan.

Sacara umum, lamun *X* mangrupa variabel acak dihartikeun dina rohangan probabiliti (Ω, *P*), mangka **nilai ekspektasi** E*X* tina *X* dirumuskeun salaku

:\operatorname{E}X = \int_\Omega X dP

nu mana ngagunakeun integral Lebesgue. Catetan yén teu sakabéh variabel random ngabooan nilai ekspektasi, lamun integralna euweuh. Dua variabel sebaran probabiliti nu sarua bakal mibanda nilai ekspektasi nu sarua.

Lamun *X* nyaéta variabel random diskrit mibanda nilai*x*1, *x*2, ... sarta probabiliti pakait *p*1, *p*2, ... nu ditambahkeun ka 1, mangka E*X* bisa iitung salaku jumlah atawa deret

:\operatorname{E}X = \sum_i p_i x_i

saperti dina conto *gambling* di luhur.

Lamun sebaran probabiliti *X* aya dina fungsi probabiliti densiti *f*(*x*), mangka nilai ekspektasi bisa diitung ku

:\operatorname{E}X = \int_{-\infty}^\infty x f(x) dx.

Operator nilai ekspektasi (atawa **operator ekspektasi**) E mangrupa linier di hal ieu
:E(*aX* + *bY*) = *a* E*X* + *b* E*Y*
keur unggal dua variabel random *X* jeung *Y* (nu perlu dihartikeun dina rohangan probabiliti nu sarua) sarta dua wilangan riil *a* jeung *b*.

Nilai ekspektasi *power* *X* disebut *moments* *X*; moments about the mean *X* ogé dihartikeun salaku nilai ekspektasi nu penting.

Umumna, operator nilai ekspektasi teu multiplicative, contona E(*XY*) teu sarua jeung E*X* E*Y*, iwal ti lamun *X* jeung *Y* variabel bebas. Bedana, sacara umum, ningkat jadi kovarian jeung korelasi.

keur estimasi nilai ekspektasi variabel random, bisa dipaké nilai ukuran *pengulangan* variabel sarta *perhitungan* hasil tina arithmetic mean. Estimasi ieu nilai ekspektasi nu sabenerna sarta sipat nga-*minimal*-keun kuadrat kasalahan nilai nilai ekspektasi.
Tiori statistik

**Tiori statistik** ngawengku sababaraha topik, nyaéta:

Model statistik  sumber data sarta cara ngarumuskeun masalah:
#Sampling ti hiji populasi nu tinangtu/kawates
#Méasuring observational error and refining procedures
#Studying statistical relations

Ngarencanakeun panalungtikan statistik pikeun ngukur jeung ngontrol kasalahan amatan (Ing. *observational error*):

#Desain percobaan keur nangtukeun éfék *perlakuan*
#Survey sampling pikeun ngadadarkeun populasi alami

Summarizing statistical data in conventional forms (also known as statistik deskriptif)

#Milih kasimpulan statistik keur ngajelaskeun sampel
#Fitting probability distributions to sample data

Interpreting statistical data is the final objective of all reséarch:

#Common assumptions that we make
#Likelihood principle
#Estimating parameters
#Tes hipotesa statistik
#Revising opinions in statistics

## Tempo ogé
probability, statistik, daptar jejer statistis
Median

**Median** ngagambarkeun harti teknis *middle* (tengah) dumasar kana "perasaan".

## Median dina Statistik 
Dina statistik, kecap **median** mangrupa nilai anu ngabagi sampel satengah ka luhur jeung satengah ka handap. Keur manggihkeun *median*, susun data observasi ti nilai panghandapna nepi ka pangluhurna terus pilih salah sahiji anu di tengah. If there are an even number of observations, take the mean of the two middle values. When we use the *median* to describe what the observations have in common, there are several choices for a méasure of variability, the range, the interquartile range, sarta simpangan mutlak. Since the median is the same as the *second quartile*, its calculation is illustrated in the article on quartiles.

The median is primarily used for skewed distributions, which it represents more accurately than the arithmetic mean. Consider the set {1, 2, 2, 2, 3, 9}. The median is 2 in this case, as is the mode, and it might be seen as a better indication of central tendency than the arithmetic mean of 3.166....

The median is also the central point which minimises the average of the absolute deviations; in the example above this would be (1+0+0+0+1+7)/6=1.5 using the median, while it would be 1.944... using the méan.

Even though sorting *n* items takes in general O(*n* log *n*) operations, by using a recursive "Divide-and-Conquer" algorithm the median of *n* items can be computed with only O(*n*) operations.

Calculation of medians is a popular technique in summary statistics and summarizing statistical data, since it is simple to understand and éasy to calculate, while also giving a méasure that is more robust in the presence of outlier values than is the mean. The difference between the median and the méan is less than or equal to one standard deviation.

## Median of a Triangle 
In a triangle, a **median** is a line joining a vertex to the midpoint of the opposite side. It divides the triangle into two parts of equal area. The three medians intersect in the triangle's centroid or center of mass, and two-thirds of the length of éach median is between the vertex and the centroid, while one-third is between the centroid and the midpoint of the opposite side.

Any other lines which divide the aréa of the triangle into two equal parts do not pass through the centroid.

## Median strip of a road 
On an expressway, motorway, or autobahn, the **median** is the strip of grass or the wall which separates opposing lanes of traffic. This is necessary because of safety concerns, due to the high speed of automobiles on both sides, and the potential danger of a disastrous héad-on collision at the combined speed of both vehicles.

Medians function secondarily as "green areas", béautifying roadways. Some jurisdictions mow their medians, others scatter wildflower seeds which germinate and re-seed themselves every year, while still others créate extensive plantings of trees, shrubs, herbaceous perennials and decorative grasses. Where space is at a premium, dense hedges of shrubs filter the héadlights of oncoming traffic and provide a resilient barrier.

## See also 
* Median number
Dispersi statistik

Ukuran **dispersi statistik** kudu ngahasilkeun angka nol lamun sakabéh data identik, sarta kudu naék lamun datana leuwih béda. Ukuran dispersi pangpentingna nyaéta simpangan baku, akar kuadrat varian.

Ukuran séjénna nyaéta rentang, interquartile range, sarta rata-rata simpangan mutlak, sarta dina kasus kategori variabel random, entropi diskrit. Tara pernah negatip; nilai pangleutikna nu mungkin nyaéta nol.

Ukuran dispersi statistik sabagian dipaké lamun lokasi invariant, sarta liniér dina skala.  Maka lamun variabel random *X* mibanda dispersi *SX* mangka transpormasi liniér *Y*&nbsp;=&nbsp;*aX*&nbsp;+&nbsp;*b* keur wilangan riil *a* jeung *b* kudu mibanda dispersi *SY*&nbsp;=&nbsp;*aSX*.

Tempo ogé kasimpulan statistik.
Estimating parameters

Informasi ngeunaan **estimating paraméters** bisa ditempo ogé dina;

* titik estimasi
* Interval estimasi.
Aplikasi

[thumb|right|275px|Panulis [LibreOffice]]
**Applikasi** software (atawa disingket *app*) nyaéta program komputer atawa kumpulan program nu dirancang pikeun nyadiakeun kagunaan keur end userna. Conto hususna nyaéta aplikasi program *word processor* (saperti MS Word), *spreadsheet* (saperti MS Excel), *accounting*, jeung *media player*.

Sababaraha aplikasi nu dibeundeul jadi hiji kadang-kadang disebut **application suite**. Microsoft Office, nu ngabeundeul word processor, spréadsheet katut sababaraha aplikasi liana, mangrupa salah sahiji contona.

Istilah *aplikasi* bisa dipaké keur ngabédakeun tipe program ieu tina kelompok pakakas lemes utama liana nu disebut pakakas lemes sistim nu mangrupa pakakas lemes nu pakait jeung ngokolakeun tur ngagunakeun aspek-aspek sistim komputerna sorangan kawas sistim operasi, *device driver*, jeung compiler.

## Tempo ogé: 
* Pakakas lemes aplikasi
* Aplikasi loka *(web application)* 
* Aplikasi basis data

**Aplikasi** ogé bisa ngandung harti ngasupkeun lamaran gawé.
Statistik bisnis

**Statistik bisnis** mangrupa cabang applied statistics loba dipaké keur ngumpulkeun data salaku hasil tina bisnis atawa lembaga pamaréntah. Sipat sumber ieu pengulangan nu angger tina deret data. Hal ieu ngajadikeun deret waktu penting keur bisnis statistik.

Sababaraha téhnik Marketing ogé dipaké leuwih Multivariate statistics lanjut dina segmen pasar, manajemen merk sarta téhnik posisi produk.
Sigma

# **Sigma** (aksara kapital Σ, aksara leutik σ, pilihan ς) nyaéta aksara Yunani. Tempo Sigma (aksara).
# Aksara kapital Σ dipaké pikeun lambang operator ngajumlah nu ngahasilkeun dérét na matematik.
# Aksara kapital Σ dipaké pikeun lambang alfabét husus hiji basa, or of some other object dependent on an alphabet; expressed in mathematical terms, eg "the language defined by alphabet &Sigma;={a,b,c} and the rules ..."
# Aksara leutik σ dipaké pikeun lambang simpangan baku populasi na statistik.
# The lower-case letter σ is used as a symbol for the divisor function in number théory.
# Aksara leutik σ dipaké pikeun lambang konstanta Stefan-Boltzmann dina radiasi fisika.
Statistik terapan

**Statistik terapan** ngagunakeun statistik jeung tiori statistik dina kaayaan nu sabenerna.

Sing saha baé anu ngarasa "komit" kana observasi empiris hartina aya kanyaho umum bisa ngagunakeun statistik salaku alat panalungtikan. Hal ieu kaasup élmu tapi teu kaasup sajarah jeung seni.  Contona, ékonométrik loba ngagunakeun statistik terapan keur "mempelajari" ékonomi.

Di satiap widang, diperlukan "observasi", potensial "rekonstruksi" keur ngurangan kasalahan dina observasi jeung rencana panunglutikan keur ngontrol observational error.

## Tumbu kaluar 
* Some applets about applied statistics 
* Parabot statistik bébas di Internét
Statistik psikologis

"Panggunaan" statistik keur psikologi. Sababaraha widang anu umum dipaké nyaéta:
#psikométrik
#téori pangajaran
#perception
#human development
#psikologi abnormal

:biostatistik -- psikologi
Statistik sosial

**Statistik social** nyaéta pamakéan sistim ukuran statistik keur nalungtik paripolah manusa dina lingkungan sosial.  Ieu bisa dipikanyaho ku cara jajal pamanggih ti sabagian grup masarakat, evaluasi sabagian data ngeunaan grup masarakat, atawa ku panalungtikan jeung analisa statistik susunan data nu pakait jeung masarakat sarta paripolahna.

Biasan, ahli sosial matéakeun dina evaluasi kualitas palayanan sabagian grup organisasi, dina analisa paripolah grup masarakat dina lingkunganna, atawa dina nangtukeun naon nu butuh jeung kahayang masarakat ngaliwatan sampling statistik.
Ngarencanakeun panalungtikan statistik

Loba ilmuwan nu ngamimitian panalungtikan ku patarosan ngeunaan dunya tempat urang hirup. Keur ahli statistik, patarosan ieu bisa di-klasifikasi-keun kana sababaraha hal.

#Urang mimitian ku hal ngeunaan *Unit* tunggal, saperti organisma biologi, hasil ti pabrik, a plot of ground, hiji blok kota jeung *hal* séjénna anu ku urang hayang dipikharti. Dina pangajaran ieu, urang bisa mokuskeun kana hal anu sifatna *dinamis* tina Unit; kumaha "variasi" dina waktu ? Naha bisa nga-identifikasi aspek nu ngontrol ka hal séjénna ? (Tingali research subject.)
#Kadangkala, urang mikaresep *Unit* anu mungkin sabenerna alat, that is, we are interested in the Unit because of a *population* to which it belongs or an *environment* in which it resides. Our desire to describe a population may be satisfied by a statistical report on a *sample* from that population. The methodology is to select a sample and observe just the Units which are selected and then to summarize our results and interpret their méaning for the population. When we deliberately manipulate something in the process of observation, we call it an *experiment*. When we attempt to observe the Units without affecting them, we call it a *survey*.
#Kadangkala, urang hayang ngarti kana *internal workings* Unit saperti nu katingal dina komponenna sarta kumaha pakuat pakaitna hiji jeung nu séjénenna. Physiology salah sahiji conto widang nu kaasup kana tipe ieu.

In much reséarch, we use all three modes at different stages. A useful synthesis of this kind of thinking was provided by Ludwig von Bertalanffy.

In every type of reséarch, we must be concerned with managing the observational error that is inherent in all empirical reséarch. We can incréase the precision of our reséarch by 
#using a more precise instrument (eg., a more powerful telescope)
#incréasing the number of observations so the *constant* we try to méasure stands out better against the *noise*.
#changing the design of our reséarch. This last approach can become very technical, so we will postpone its discussion until optimum experimental design.

See also: statistik -- statistical regularity -- model statistik -- summarizing statistical data -- interpreting statistical data --desain percobaan -- survey sampling
Statistika multivariat

**Statistika multivariat** atawa **analisa multivariate statistik** dina statistik ngajelaskeun kumpulan prosedur observation jeung analysis nu variabel statistikna leuwih ti hiji dina sawaktu.

Aya sababaraha modél, nu gumantung kana tipe analisana nyaéta:
# Analisa korelasi kanonik nu nyoba keur nangtukeun aya henteuna hubungan linier antara dua runtuyan variabel (saperti soal jeung jawaban).
# Analaisa regresi nu nyoba nangtukeuk rumus linier nu bisa ngajelaskeun kumaha respon variabel kana robahna variabel séjén.
# Analisa prinsip komponen nu nyoba nantungkeun runtuyan variabel sintesis pangleutikna nu bisa dijelaskeun tina runtuyan aslina.
# Fungsi diskriminan atawa analisa variat kanonik nu nangtukeun runtuyan variabel beisa dibédakeun dumasa kana grup.
# Analisa prinsip koordinat nu nangtukeun jarak pangalusna tina runtuyan rekaman variabel sintesis.
# Analisa diskriminan linier (LDA) ngitung prediksi linier tina dua runtuyan data sebaran normal nu bisa dijadikeun kumpulan keur analisa saterusna.
# Regresi logistik ngawenangkeun nyieun analisa regresi keur ngira-ngira jeung nguji pangaruh covariates dina respon biner.
# métodeu  analisa varian multivariet (MANOVA) ngalegaan tina métodeu  analisa varian keur ngawengku kasus di mana aya leuwih ti hiji variabel sarata variabel terikat teu bisa dikombinasikeun.
Daptar Statistikawan

Statistikawan atawa jalma nu méré kontribusi kana tiori statistik, atawa hal anu aya hubunganna jeung kamungkinan, atawa machine learning:

* Peter Armitage
* Thomas Bayes
* Ladislaus Bortkiewicz
* George Box
* Pafnuty Chebyshev
* Alexey Chervonenkis
* William Cochran
* (Sir) David R. Cox
* Richard Threlkeld Cox
* Harald Cramér (Sweden, 1893 - 1985)
* Bruno de Finetti
* W. Edwards Deming
* Persi Diaconis
* (Sir) Richard Doll
* Francis Ysidro Edgeworth
* A. K. Erlang
* (Sir) Ronald A. Fisher
* Francis Galton
* Seymour Geisser
* Corrado Gini
* I. J. Good
* William Sealey Gosset (known as "Student")
* Emil Julius Gumbel
* Pierre Gy
* Austin Bradford Hill
* Edwin Thompson Jaynes
* Harold Jeffreys
* David Kendall
* (Sir) Maurice Kendall
* Alfred J. Lotka
* Prasanta Chandra Mahalanobis
* Matosaburo Masuyama
* Jerzy Neyman
* Egon Pearson
* Karl Pearson
* Edwin James George Pitman
* Adolphe Quetelet
* C. R. Rao 
* Herbert Robbins
* Leonard Jimmy Savage
* Walter A. Shewhart
* Mike Dugas
* P. V. Sukhatme
* Genichi Taguchi
* Pafnuty Tchebycheff, see Pafnuty Chebyshev
* Pafnuty Tchebyscheff, see Pafnuty Chebyshev
* Leonard H. C. Tippett
* John Tukey
* Vladimir Vapnik (Russia, ~1935 - )
* Samuel Wilks
* Frank Yates
* Marvin Zelen
* Carl Eric Sarndal
* Alexander Mood
* Franklin Graybill
* Duane Boes
* Michael Hidiroglou
* Yves Berger
* Andi Hakim Nasution

*See also:* List of mathematicians | List of people by occupation | List of people
Daptar publikasi widang statistik

Di handap ieu daftar **publikasi penting** dina statistik, dikumpulkeun dumasar kana widang garapan.

There are some réasons why a particular publication might be regarded as important:
***Topic créator** - A publication that créated a new topic
***Bréakthrough** - A publication that changed scientific knowledge significantly
***Introduction** - A publication that is a good introduction or survey of a topic
***Impact** - A publication which had a major impact on the world or on the reséarch
***Latest and gréatest** - The current most advanced result in a topic

## Foundations
### *The Doctrine of Chances*
*Abraham de Moivre

**Deskripsi:** Buku ieu ngawanohkeun konsép sebaran normal ngadeukeutan kana sebaran binomial. Dina akibat, de Moivre ngabuktikeun versi lemah tina teorema central limit.  Kadang-kadang hasilna disebut ogé teorema de Moivre-Laplace.

**Importance:** Topic créator, Bréakthrough, Impact

### *An Essay Toward Solving a Problem in the Doctrine of Chances*
* Thomas Bayes
* Online version

**Description:** In this paper Bayes' theorem was first introduced.
It has a vast impact on statistics since then and keeps being important these days.

**Importance:** Topic créator, Bréakthrough, Impact

## See also 
* List of publications in Science
* List of publications in mathematics
* List of publications in computer science
Kémometrik

**Kémométrik** nyaéta larapan métode matematik atawa statistik kana data kimia. Masarakat Kémométrik Internasional (*International Chemometrics Society*, ICS) nawarkeun dadaran sarupa kieu:

*Kémométrik nyaéta élmu matalikeun ukuran nu dijieun dina sistim atawa prosés kimia kana bentuk sistimna ngaliwatan larapan métode matematik atawa statistik.*

Chemometric reséarch spans a wide aréa of different methods which can be applied in chemistry. There are techniques for collecting good data (optimization of experimental paraméters, desain percobaan, kalibrasi, signal processing) and for getting information from these data (statistics, pattern recognition, modeling, structure-property-relationship estimations).

Chemometrics tries to build a bridge between the methods and their application in chemistry.

## Tempo ogé 
* QSPR

## Tumbu kaluar 
* Kumpulan tumbu
Sebaran Cauchy

**Sebaran Cauchy** mangrupa probability distribution nu mibanda probability density function

: f(x) = \frac{1}{s\pi[1 + ((x-t)/s)^2]} 

di mana *t* nyaéta *parameter lokasi* jeung *s* nyaéta *parameter skala*. Kasus husus lamun *t* = 0 jeung *s* = 1 disebut **standar sebaran Cauchy** nu mibanda probability density function

: f(x) = \frac{1}{\pi (1 + x^2)}. 

Sebaran Cauchy salawasna dipaké conto keur ngahartikeun sebaran nu teu mibanda mean, varian atawa moments pangluhurkeun, sanajan mode jeung median duanana dihartikeun sarua jeung nol.

Lamun *U* jeung *V* mangrupa dua sebaran normal variabel acak bébas nu mibanda nilai ekspektasi 0 jeung varian 1,  saterusna rasio *U*/*V* mibanda standar sebaran Cauchy.

Lamun *X*1, ..., *X**n* mangrupa variabel random independent, mibanda standar Cauchy, mangka sampel méan (*X*1 + ... + *X**n*)/*n* sarua mibanda standar sebaran Cauchy.  Ieu conto keur ngabuktikeun yén hipotesa varian terhingga dina central limit theorem teu bisa dileungitkeun (sanajan bisa digantikeun ku nu séjén, dina kasus asumsi lemah).  Keur nempo yén ieu bener, itung fungsi karakteristik

:\varphi(t)=E\left(e^{it\overline{X}}\right)

nu mana \overline{X} mangrupa sampel méan.

Sebaran Cauchy mangrupa sebaran-t student nu ngan mibanda hiji tingkat kabébasan.

Sebaran Cauchy kadangkala disebut **sebaran Lorentz**.

## Tumbu kaluar 
* MathWorld Cauchy Distribution
Daptar sakola jeung paguron luhur dumasar nagara

Di handap ieu dibéréndélkeun **daptar paguron luhur, dumasar nagarana**.

*Daptar paguron luhur di Albania
*Daptar paguron luhur di Amérika Serikat
*Daptar paguron luhur di Aprika Kidul
*Daptar paguron luhur di Australia
*Daptar paguron luhur di Austria
*Daptar paguron luhur di Bélgia
*Daptar paguron luhur di Bolivia
*Daptar paguron luhur di Brazil
*Daptar paguron luhur di Kanada
*Daptar paguron luhur di Cili
*Daptar paguron luhur di Cina Daratan
*Daptar paguron luhur di Républik Céko
*Daptar paguron luhur di Dénmark
*Daptar paguron luhur di Éstonia
*Daptar paguron luhur di Finlandia
*Daptar paguron luhur di Prancis
*Daptar paguron luhur di Jérman
*Daptar paguron luhur di Yunani
*Daptar paguron luhur di Greenland
*Daptar paguron luhur di Guatemala
*Daptar paguron luhur di Honduras
*Daptar paguron luhur di Hong Kong
*Daptar paguron luhur di Hungaria
*Daftar paguron luhur di Indonésia
*Daptar paguron luhur di Islandia
*Daptar paguron luhur di India
*Daptar paguron luhur di Inggris
*Daptar paguron luhur di Irlandia
*Daptar paguron luhur di Israél
*Daptar paguron luhur di Itali 
*Daftar paguron luhur di Jepang
*Daptar paguron luhur di Koréa Kidul
*Daptar paguron luhur di Makau
*Daptar paguron luhur di Malaysia
*Daptar paguron luhur di Méksiko
*Daptar paguron luhur di Norwégia
*Daptar paguron luhur di Pakistan
*Daptar paguron luhur di Pilipina
*Daptar paguron luhur di Polandia
*Daptar paguron luhur di Portugal
*Daptar paguron luhur di Rusia
*Daptar paguron luhur di Saudi Arabia
*Daptar paguron luhur di Selandia Baru
*Daptar paguron luhur di Serbia jeung Montenégro
*Daptar paguron luhur di Singapura
*Daptar paguron luhur di Slovénia
*Daptar paguron luhur di Spanyol
*Daptar paguron luhur di Swédia
*Daptar paguron luhur di Swiss
*Daptar paguron luhur di Taiwan
*Daptar paguron luhur di Muangtai
*Daptar paguron luhur di Turki
*Daptar paguron luhur di Ukraina
*Daptar paguron luhur di Venezuéla
*Daptar paguron luhur di Walanda
*Daptar universitas internasional
Daptar paguron luhur di Indonésia

* Daptar paguron luhur negeri di Indonésia
* Daptar paguron luhur swasta di Indonésia
* Daptar paguron luhur Islam negeri di Indonésia
* Daptar paguron luhur Islam swasta di Indonésia
* Daptar paguron luhur kadinesan di Indonésia
Universitas Gifu - Gifu Daigaku

**Universitas Gifu** (岐阜大学; *Gifu Daigaku*, disingkat 岐大 *Gidai*) salah sahiji universitas di Jepang, nu tempatna aya di Kota Gifu wewengkon Chubu Jepang Tengah.
Universitas Gifu mibanda opat kampus, nyaéta Kampus Utama di Yanagido, Kota Gifu; Kebon Percobaan di Minokamo (6&nbsp;km ti Stasion Kobi), Leuweung Percobaan di Takayama (10&nbsp;km ti Stasion Joro) sarta Pusat Pananglutikan Walungan (River Basin Reséarch Center) di Takayama (20&nbsp;km ti Stasion Takayama).

Universitas Gifu ngadeg taun 1949, sanajan kitu Fakultas Pendidikan ngadeg taun 1873, Fakultas Pertanian ngadeg taun 1923. Dina taun 1942 ngadeg Fakultas téhnik, sarta dina taun 1947 ngadeg Fakultas Kedokteran tur dina taun 1996 ngadeg Fakultas Regional Studi. Dina taun 2004, Fakultas Pertanian direstrukturisasi jadi Fakultas Elmu Biologi Terapan.

## Fakultas jeung Pasca Sarjana
### Fakultas
* Pendidikan
* Regional Studi
* Kedokteran
* téhnik
* Elmu Biologi Terapan

### Pasca Sarjana
* Pendidikan (Program Master)
* Regional Studi (Program Master)
* Kedokteran (Program Master jeung Doktor)
* téhnik (Program Master jeung Doktor)
* Pertanian (Program Master)
* Elmu Pertanian (Program Doktor), program bareng jeung Universitas Shinshu jeung Universitas Shizuoka
* Elmu Kedokteran Hewan (Program Doktor), program bareng jeung Universitas Pertanian jeung Kedokteran Hewan Obihiro, Universitas Iwate sarta Universitas Pertanian jeung Teknologi Tokyo
## Sejenna
* Pusat Pendidikan Umum
* Pusat Panalungtikan Walungan
* Pusat Kolaborasi keur Akademi/Pamaréntah/Industri
* Pusat Panalungtikan Elmu Kahirupan
* Pusat Informasi jeung Multimedia
* Pusat Mahasiswa International
* Pusat Adminitrasi Kasehatan

## Tumbu kaluar
*Gifu University official site
Daptar paguron luhur di Jepang

**Daptar paguron luhur di Jepang**:

* Universitas Aichi
* Universitas Aoyama Gakuin
* Universitas Chiba
* Universitas Chubu
* Universitas Chuo
* Universitas Daito Bunka
* Universitas Dokkyo
* Universitas Doshisha
* Universitas Ferris
* Universitas Gakushuin
* Universitas Gifu - Gifu Daigaku
* Universitas Hokkaido
* Universitas Hosei
* Universitas Kristen Internasional
* Universitas Internasional Jepang
* Sakola Kadokteran Jichi
* Universitas Kanto Gakuin
* Universitas Kobe
* Universitas Kokugakuin
* Universitas Kwansei Gakuin
* Universitas Kyoto
* Universitas Kyushu
* Universitas Keio
* Universitas Kansai
* Universitas Kansai Gaidai
* Mabie Memorial School
* Universitas Meiji
* Universitas Meiji Gakuin
* Universitas Musashi
* Institut Téhnologi Nagoya
* Universitas Nagoya
* Universitas Niigata
* Universitas Osaka
* Universitas Kota Osaka
* Universitas Rikkyo (Universitas St. Paul)
* Universitas Ritsumeikan
* Universitas Sophia
* Universitas Teikyo
* Universitas Tohoku
* Institut Téhnologi Tokyo
* Universitas Métropolitan Tokyo
* Universitas Tsukuba
* Universitas Tokyo
* Universitas Waseda
* Universitas Nasional Yokohama

## Baca ogé 
* Atikan di Jepang
Kala Géologi

**Kala géologi**: tempo ogé skala waktu géologis.

* 1620 - Francis Bacon notices the jigsaw fit of the opposite shores of the Atlantic Océan
* 1669 - Nicolas Steno puts forward his théory that sedimentary strata had been deposited in former séas, and that fossils were organic in origin
* 1701 - Edmund Halley suggests using the salinity and evaporation of the Mediterranéan to determine the age of the éarth
* 1743 - Sir Christopher Packe produces a géological map of south-éast England
* 1746 - Jean Etienne Guettard presents the first mineralogical map of France to the French Academy of Sciences.
* 1760 - John Michell suggests éarthquakes are caused by one layer of rocks rubbing against another
* 1776 - James Keir suggests that some rocks, such as those at the Giant's Causeway, might have been formed by the crystallisation of molten lava
* 1779 - Comte de Buffon speculates that the éarth is older than the 6,000 yéars suggested by the Bible
* 1785 - James Hutton presents paper entitled Théory of the éarth - éarth must be old
* 1799 - William Smith produces the first large scale géological map, of the aréa around Bath
* 1809 - William Maclure conducts the first géological survey of the éastern United States
* 1830 - Sir Charles Lyell publishes book, Principles of Géology, which describes the world as being several hundred million yéars old
* 1837 - Louis Agassiz begins his glaciation studies which eventually demonstrate that the éarth has had at léast one ice age
* 1862 - Lord Kelvin attempts to find the age of the éarth by examining its cooling time and estimates that the éarth is between 20–400 	million yéars old
* 1903 - George Darwin and John Joly claim that radioactivity is partially responsible for the éarth's héat
* 1907 - Bertram Boltwood proposes that the amount of léad in uranium and thorium ores might be used to determine the éarth's age and 	crudely dates some 	rocks to have ages between 410–2200 million yéars
* 1911 Arthur Holmes uses radioactivity to date rocks, the oldest being 1.6 billion yéars old
* 1912 - Alfred Wegener proposes that all the continents once formed a single landmass called Pangaéa that broke apart via continental drift
* 1913 - Albert Michelson méasures tides in the solid body of the éarth
* 1935 - Charles Richter invents a logarithmic scale to méasure the intensity of earthquakes
* 1953 - Maurice Ewing and Bruce Heezen discover the Great Global Rift running along the Mid-Atlantic Ridge
* 1960 - Harry Hess proposes that new séa floor might be créated at mid-océan rifts and destroyed at deep séa trenches
* 1963 - F.J. Vine and D.H. Matthews explain the stripes of magnetized rocks with alternating magnetic polarities running parallel to mid-	océan ridges as due 	to séa floor spréading and the periodic géomagnetic field reversals
* 1980 - Physicist Luis Alvarez, his son, géologist Walter Alvarez, and others propose that the impact of a large extra-terrestrial object caused the extinction of the dinosaurs at the end of the Cretaceous Period, about 65 million yéars ago.
Daptar Présidén Indonésia

**Daptar Présidén Indonésia**

#### Tempo ogé
* Daptar Wakil Présidén Indonésia
* Daptar Présidén India
Abdurrahman Wahid

**Abdurrahman Wahid** (biasa disebut ogé **Gus Dur**) (7 Séptémber 1940 - 30 Désémber 2009) ngajabat Présidén Indonésia ti taun 1999 nepi ka 2001, sarta pamingpin Partai Kebangkitan Bangsa, nu diadegkeun sanggeus Soeharto turun jabatan. Anjeunna mangrupa inohong ti Nahdlatul Ulama. Ku alatan kasakit jeung masalah korupsi, anjeunna diturunkeun tina jabatan présidén bulan Juli 2001.
Estimator

Dina statistik, **éstimator** nyaéta fungsi data "diketahui" nu mana digunakeun keur nga-"estimasi" parameter anu teu "diketahui". Lobana éstimators nu béda ngamungkinkeunkeur unggal paramater anu "diberikan". Sabaraha kritéria digunakeun keur milih antar éstimator. Geus ilahar lamun hiji kritéria teu jelas keur nangtukeun hiji *estimator* ka *estimator* séjénna.

Aya dua tipe *estimator* nyaéta: *point estimators*, jeung *interval estimators*.

## Point estimators 
Point éstimator **θ** tina paraméter θ:

# *Bias* ti **θ** dihartikeun  B(**θ**) = E[**θ**] &minus; θ
# **θ** nyaéta *unbiased estimator* ti θ "jika dan hanya jika" B(**θ**) = 0 keur sakabéh θ
# *Mean square error* ti **θ** dihartikeun MSE(**θ**) = E[(**θ** &minus; θ)2]
# MSE(**θ**) = V(**θ**) + (B(**θ**))2
# Simpangan baku **θ** ogé disebut *standard error* ti **θ**.

nu mana V(X) nyaéta varian ti X jeung E nyaéta operator nilai ekspektasi.

Kadangkala pamilihan *unbiased estimator* ngagunakeun variance panghandapna. Kadangkala ogé leuwih dipilih tanpa wates ka *unbiased estimators*; tingali Bias (statistics).  Ngeunaan "best unbiased estimators", tempo ogé Gauss-Markov theorem, téoréma Lehmann-Scheff&eacute;, Rao-Blackwell theorem.

Tempo ogé Maximum likelihood.
Prosés Gauss-Markov

**Prosés stokastik Gauss-Markov** (dingaranan tina Carl Friedrich Gauss jeung Andrey Markov) nyaéta prosés stokastic processk nu luyu jeung sarat-sarat boh keur prosés Gaussian atawa prosés Markov.

Tiap prosés Gauss-Markov *X*(*t*) mibanda tilu pasipatan ieu:
# Mun *h*(*t*) mangrupa fungsi skalar lain-enol *t*, mangka *Z*(*t*) = *h*(*t*)*X*(*t*) kaasup prosés Gauss-Markov
# Mun *f*(*t*) is a non-decréasing scalar function of *t*, then *Z*(*t*) = *X*(*f*(*t*)) is also a Gauss-Markov process
# There exists a non-zero scalar function *h*(*t*) and a non-decréasing scalar function *f*(*t*) such that *X*(*t*) = *h*(*t*)*W*(*f*(*t*)), where *W*(*t*) is the standard Wiener process.

Pasipatan (3) ngandung harti yén sakabéh prosés Gauss-Markov bisa disintésis tina prosés Wiener baku (*standard Wiener process*, SWP).
Maximum likelihood

Dina statistik, métodeu  **maximum likelihood**, dimimitian ku ahli genetika/ahli statistik Sir Ronald A. Fisher, mangrupa métodeu  titik estimasi, nu digunakeun keur nga-estimasi anggota populasi nu teu ka-observasi tina paraméter ruang nu di-maksimal-keun ku fungsi likelihood.
Tingali p ngalambangkeun paraméter populasi teu ka-observasi nu bakal di-estimasi.  Tingali X ngalambangkeun random variable nu di-observasi (which in general will not be scalar-valued, but often will be a vector of probabilistically independent scalar-valued random variables.  The probability of an observed outcome X=x (this is case-sensitive notation!), or the value at (lower-case) x of the probability density function of the random variable (Capital) X, **as a function of p with x held fixed** is the **likelihood function**
:L(p)=P(X=x\mid p).
For example, in a large population of voters, the proportion p who will vote "yes" is unobservable, and is to be estimated based on a political opinion poll.  A sample of n voters is chosen randomly, and it is observed that x of those n voters will vote "yes".  Then the likelihood function is
:L(p)={n \choose x}p^x(1-p)^{n-x}.
The value of p that maximizes L(p) is the **maximum-likelihood estimate** of p. By finding the root of the first derivative one will obtain x/n as the maximum-likelihood estimate. In this case, as in many other cases, it is much éasier to take 
the logarithm of the likelihood function before finding the root of the derivative:
:\frac{x}{p}-\frac{n-x}{1-p}=0
Taking the logarithm of the likelihood is so common that the term **log-likelihood** is commonplace among statisticians. The log-likelihood is closely related to information entropy.

If we replace the lower-case x with capital X then we have, not the observed value in a particular case, but rather a variabel acak, which, like all random variables, has a probability distribution.  The value (lower-case) x/n observed in a particular case is an **estimate**; the variabel acak (Capital) X/n is an **estimator**.  The statistician may take the nature of the probability distribution of the **éstimator** to indicate how good the éstimator is; in particular it is desirable that the probability that the éstimator is far from the paraméter p be small.  Maximum-likelihood éstimators are sometimes better than unbiased estimators.  They also have a property called "functional invariance" that unbiased éstimators lack: for any function f, the maximum-likelihood éstimator of f(p) is f(T), where T is the maximum-likelihood éstimator of p.

However, the bias of maximum-likelihood éstimators can be substantial.  Consider a case where *n* tickets numbéréd from 1 through to *n* are placed in a box and one is selected at random, giving a value *X*.  If *n* is unknown, then the maximum-likelihood éstimator of *n* is *X*, even though the expectation of *X* is only *n*/2; we can only be certain that *n* is at léast *X* and is probably more.
Éntropi informasi

[thumbnail|right|200px|Entropi [Bernoulli trial|pamariksaan Bernouli salaku fungsi probabilitas suksés, ilahar disebut **fungsi éntropi binér**.]]

**Entropi** nyaéta konsép dina térmodinamika (tempo éntropi termodinamika), mekanika statistika jeung tiori information. Konsép éntropi jeung informasi kacida pakait raket, sanajan perlu sababaraha waktu keur ngawangun tiori mekanika statistika jeung tiori informasi sangkan jadi nyata. Artikel ieu ngeunaan **éntropi informasi**, formulasi tiori-informasi éntropi. Éntropi informasi leuwih ilahar disebut **Éntropi Shannon** keur ngahargaan ka Claude E. Shannon.

## Bubuka 
Konsép éntropi dina tiori informasi ngajelaskeun sabaraha loba tingkat acak (atawa, 'kateupastian') anu aya dina sinyal atawa kajadian acak. Cara lian pikeun nénjo ngeunaan ieu nyaéta ku ngabahas ngeunaan sabaraha loba informasi anu dibawa ku hiji sinyal.

Contona, aya sababaraha téks dina basa Inggris, dikodekeun mangrupa runtuyan hurup, spasi, jeung tanda baca. Lantaran frékuénsi atawa lobana kajadian pikeun sababaraha hurup ngan saeutik (conto, 'z'), sedengkeun hurup-hurup lianna mah murudul (conto 'e'), runtuyan hurup téh henteu acak-acak teuing. Sanajan kitu, lantaran hurup nu nuturkeunana henteu bisa dikira-kira, bisa ogé disebut 'acak' (nepikeun ka tingkatan nu tangtu). Éntropi téh minangka nu jadi ukuran tingkat acak ieu, saperti anu diusulkeun ku Shannon dina makalah "A Mathematical Theory of Communication " nu medar dina taun 1948

Shannon nawarkeun hiji définisi éntropi anu nyumponan asumsi-asumsi, yén:

* Ukuran ieu kudu proporsional (kontinu atawa silisambung) - contona, lamun probabilitasna ngaganti saeutik, éntropina ogé ngan kaganti saeutik.
* Upama sakabéh kamungkinan (contona hurup-hurup di luhur) siga-siga rék sarua, mangka nambahan hurup anu kaluar ogé bakal naékkeun harga éntropi.
* Lamun aya dua tahapan kajadian, harga éntropi ahir ogé kudu dihasilkeun tina pangjumlahan éntropi tina dua tahapan kajadian éta.

(Catetan: Buku nu ditulis ku Shannon/Wéaver ngarujuk ka tulisan Tolman (1938) anu ngarujuk ogé ka Pauli (1933) anu nuliskeun définisi éntropi nu dipaké ku Shannon. Salian ti éta, mekanika statistika ngarujuk ogé ka von Neumann sanggeus manéhna nurunkeun éntropi dina taun 1927, anu bisa ngajelaskeun naha von Neumann resep pisan ngagunakeun istilah 'entropi' anu geus aya.)

## Tumbu luar 
* Information is not entropy, information is not uncertainty ! - a discussion of the use of the terms "information" and "entropy".
* I'm Confused: How Could Information Equal Entropy?  - a similar discussion on the bionet.info-théory FAQ.
* Java "entropy pool" for cryptographically-secure unguessable random numbers
* Description of information entropy from "Tools for Thought" by Howard Rheingold 
* A cool little java applet representing Shannon's Experiment to Calculate the Entropy of English
Independent identically-distributed random variables

Hiji sekuen atawa kumpulan variabel acak disebut **independent and identically distributed (i.i.d.)** lamun satuan anu mibanda probability distribution sarua dina satiap distribusi séjénna jeung sakabéhna mutually independent. Tina sudut pandang sample space *X*, hartina yén *n* percobaan berhubungan dina *X**n* ka *n*-fold dihasilkeun tina probability measure keur sakali percobaan.
Sirit

**Sirit**, **bebel**, atawa **purusa** hartina organ sapatemon jalu jeung, pikeun mamalia, organ jalu pikeun kiih. Sirit homolog jeung itil awéwé, sabab tumuwuh tina struktur émbrionik nu sarua. Sirit mangkreng pikeun pungsina nalika sapetemon.

### Sirit sato 
lolobana marsupial, iwal dua spésiés kangguru pangbadagna, mibanda sirit *bifurcated*: kabagi jadi dua kolom nu misah, antukna tungtung siritna nyagak. Lumba-lumba mibanda kontrol *prehensile* kana siritna, antukna kadang dipaké salaku sénsor pikeun mariksa dasar sagara. Kéong mibanda sirit pangpanjangna saluyu jeung panjang awakna: nepi ka dua puluh kalieun panjang awakna.

Musium Falologis Islandia (Icelandic Phallological muséum) di Reykjavik ngahususkeun diri kana nalungtik sirit sasatoan.

## Sirit manusa 
jmpl|348x348px|Sirit manusa
Sirit manusa béda ti sirit sababaraha mamalia séjén sabab teu mibanda *tulang mangkreng* *erectile bone*, sagemblengna ngandelkeun aliran getih sangkan mangkreng, teu bisa ngelok kana palangkakan, sarta leuwih badag batan rata-rata dibandingkeun jeung beurat awak.

### Struktur 
Sirit manusa diwangun ku tilu kolom jaringan pamangkreng:
* dua corpora cavernosa jeung
* hiji corpus spongiosum di handapeunana.

### Mangkreng 
Mangkreng hartina jadi heurasna sirit nu lumangsung nalika hiji jalu karangsang. Mangkrengna sirit ngabisakeun sapatemon, sanajan teu kudu, sarta sababaraha kagiatan séksual séjénna.

## Tempo ogé 
* peluh
* sunatan
* sapatemon
* Térong sirit kuda (*Solanum melongena*)
Nagri

:*Kadé patukeur jeung Nagara*
:*Pikeun guna lian, tempo Negri (disambiguasi)*
Hiji **negri** mangrupa hiji wewengkon nu légalna kawanoh salaku hiji éntitas dina géografi pulitis. Hiji negri bisa mangrupa nagara daulat merdika atawa nu aya dina kawasa nagara lian, salaku hiji non-daulat atawa baheulana babagian pulitis nu daulat, atawa hiji wewengkon géografis nu kaasosiasi jeung hiji bangsa nu baheulana indepénden kalawan cicirén pulitis nu béda.

## Tempo ogé 
* Nagara
Propinsi

**Propinsi** (wangun baku dina basa Indonésia: **Provinsi**; Basa Inggris: *province*) mangrupa sebutan pikeun pamaréntahan éntitas subnasional nu biasana sahambalan handapeun hambalan nasional. Di sababaraha nagara dipaké istilah séjén, misalna nagara bagian (*state*) atawa *departemén*.

Kecap ieu diwanohkeun ku urang Rumawi, nu ngabagi kakaisaranana kana *provinciae*. Sigana kecap ieu asalna tina kecap Latin *provincia* (wewengkon nu kapangaruhan/dikawasa).

## Kiwari 
(Babagian-babagian disebut atawa ditarjamahkeun salaku: Propinsi)

* Propinsi di Afganistan
* Propinsi di Argéntina
* Propinsi di Bélgia
* Propinsi di Kanada
* Propinsi di Cina
* Propinsi di Kuba
* Propinsi di Ékuador
* Propinsi di Finlandia
* Propinsi di Indonésia
* Propinsi di Iran
* Propinsi di Iraq
* Propinsi di Irlandia
* Propinsi di Itali
* Propinsi di Koréa
* Propinsi di Walanda
* Propinsi di Pakistan
* Propinsi di Filipin
* Propinsi di Afrika Kidul
* Propinsi di Spanyol
* Propinsi di Muangtai
* Propinsi di Turki

Propinsi nu pangpadetna nyaéta Henan, Cina, populasina 93,000,000 urang, dituturkeun ku sababaraha propinsi di CIna kénéh, ogé Punjab, Pakistan, nu pangeusina 85,000,000 urang.

Propinsi panglegana nyaéta Xinjiang, Cina (1,600,000&nbsp;km2) jeung Quebec, Canada (1,500,000&nbsp;km2).

## Sajarah 
* Propinsi-propinsi Rumawi
* The former Provinces of France
* The former Provinces of Ireland
* The former Provinces of Japan
* The former Provinces of Sweden
* The former Republic of the Seven United Provinces (The Netherlands)
Sajarah matematik

:*See Timeline of mathematics for a timeline of events in mathematics. See mathematician for a list of biographies of mathematicians.*

:*Also see The Nine Chapters on the Mathematical Art for information about the development of mathematics in China.*

Kecap "matematik" asalna tina basa Greek μάθημα (*máthema*) hartina "elmu, pangaweruh, atawa diajar"; μαθηματικός (*mathematikós*) hartina "resep diajar".

Sacara sajarah, widang utama dina matematik ningkat kacida keur digunakeun dina widang "perdagangan", ngukur taneuh jeung keur "prediksi" kajadian astronomi. Hal ieu merlukan tilu hal anu raket pakuat pakaitna nu mangrupa "pembagian dina widang matematik, nyaéta struktur, ruang jeung parobahan.

## Tumbu kaluar 
* John J O'Connor and Edmund F Robertson: * History of Mathematics*, http://www-groups.dcs.st-andrews.ac.uk/~history/ . Contains biographies, timelines and historical articles about mathematical concepts.
* Jeff Miller: *Earliest uses of various mathematical symbols*, https://web.archive.org/web/20081204035420/http://members.aol.com/jeff570/mathsym.html
* Jeff Miller: *Earliest known uses of some of the words of mathematics*, https://web.archive.org/web/19990117033417/http://members.aol.com/jeff570/mathword.html
* Ian Péarce: *History of Indian mathematics*, http://www-history.mcs.st-andrews.ac.uk/history/Projects/Pearce/index.html
* History of Mathematics, public domain article
*  Important publications in history of mathematics
* Fred Rickey: *History of calculus*, http://www.dean.usma.edu/math/people/rickey/hm/default.htm
Matematik terapan

**Matematik terapan** mangrupa cabang matematik that concerns itself with the application of mathematical knowledge to other domains. Such applications include analisis numeris, mathematics of engineering, linear programming, optimization and operations research, continuous modelling, mathematical biology and bioinformatics, information theory, game theory, probability and statistics, financial mathematics, actuarial science, cryptography and hence combinatorics and even finite geometry to some extent, graph theory as applied to network analysis, and a gréat déal of what is called computer science.

The question of what is applied mathematics does not answer to logical classification so much as to the sociology of professionals who use math. The mathematical methods are usually applied to the specific problem field by méans of a mathematical model of the system.

Engineering math describes physical processes, and so is often indistinguishable from theoretical physics. Important subdivisions include:
* Fluid dynamics
* Acoustic theory
* Maxwell's equations that govern electromagnetism
* Mechanics
* Numerical relativity

## External links 
* The Society for Industrial and Applied Mathematics is a professional society dedicated to promoting the interaction between mathematics and other scientific and technical communities.
* The Institute for Mathematics and its Applications (IMA) was founded by and receives major support from the National Science Foundation Division of Mathematical Sciences to carry out a crucial interdisciplinary mission. It also receives support and direction from its Participating Institutions and Participating Corporations.
Bandéra Indonésia

thumb|right|250px|Ukuran bandéra 2:3
Bandéra nasional **bandéra Indonésia** nyaéta bandéra basajan dua warna (katelah "dwiwarna") nu dibagi sacara horizontal, beureum (luhur) jeung bodas. Warna ieu dicokot ti Karajaan Majapahit abad la-14. Katelah *Sang Saka* ("dwiwarna nu luhung") *Merah Putih* ("beureum bodas") di Indonésia, munggaran dipaké ku para siswa jeung nasionalis mangsa awal abad ka-20 nalika dijajah kénéh ku Walanda. Nuturkeun Perang Dunya II, para nasionalis Indonésia mroklamirkeun kamerdikaanana 17 Agustus 1945, bari ngibarkeun bandéra ieu.

## Tempo ogé 
* Daptar bandéra
* Bandéra Monako, Bandéra Solothurn: béda ukuran
* Bandéra Polandia: warna sarua, tibalik