izzako/sundanese-pixelgpt huggingface dataset:
Zat -- Antizat -- Partikel éleméntér -- Boson -- Fermion Simétri -- Gerak -- Hukum konsérvasi -- Massa -- Énergi -- Moméntum -- Moméntum sudut -- Spin Waktu -- Rohang -- Diménsi -- Rohangwaktu -- Panjang -- Laju -- Gaya -- Torsi Gelombang -- Fungsi gelombang -- Quantum entanglement -- Harmonic oscillator -- Magnétisme -- Listrik -- Radiasi éléktromagnétik -- Suhu -- Entropi --
éléktromagnétik -- Suhu -- Entropi -- Physical information -- Tanaga Vacuum -- Tanaga Titik-nol Phase transitions -- Critical phenomena -- Self-organization -- Spontaneous symmetry breaking -- Superconductivity -- Superfluidity -- Quantum phase transitions Gaya fundaméntal
Gravitasi -- Éléktromagnétik -- Weak -- Strong Partikel
"Main article": Partikel Atom -- Éléktron -- Gluon -- Graviton -- Neutrino -- Neutron -- Quark -- Photino -- Photon -- Proton -- Boson W jeung Z -- Radiasi partikel -- Phonon -- Roton Boson -- Fermion -- Supersimétri Sub-widang fisika
Accelerator physics -- Akustik -- Astrofisika -- Fisika Atomik, Molekular, jeung Optik -- Fisika komputasional -- Condensed matter physics -- Kosmologi -- Cryogenics -- Dinamika fluida -- Fisika polimer -- Optik -- Fisika material -- Fisika inti -- Fisika plasma -- Fisika partikel (or High Energy Physics) -- Vehicle dynamics Métode
Métode ilmiah -- Kuantitas fisik -- Ukuran -- Alat ukur -- Analisis dimensional -- Statistik--Skala Tabel
Daptar hukum fisika -- Konstanta fisika -- Unit dasar SI -- unit turunan SI -- préfix SI -- Konversi unit Sajarah
Sajarah Fisika -- Inohong Fisikawan -- Hadiah Nobel widang fisika Widang nu patali
Astronomi -- Biofisik -- Siklus -- Éléktronik -- Rékayasa -- Géofisik -- Élmu material -- Fisika Matematis -- Fisika médis -- Kimia Fisik Sajarah ringkes fisika
"Catetan: di handap ieu mangrupa ihtisar ringkes tumuwuhna fisika
Pikeun leuwih jéntré, baca artikel utama subjék ieu, Sajarah fisika."
Geus ti jaman baheula manusa nyoba neuleuman paripolah zat: naha apel bet ragrag kana taneuh, naha barang nu béda boga sipat nu béda, jeung saterusna
Ogé ngeunaan karakter mayapada, samodél bentuk Bumi jeung paripolah "celestial object" samodél panonpoé jeung bulan
Sababaraha téori geus diajukeun, tétéla lolobana salah
Téori-téori ieu umumna kedal dina istilah filosofis, teu kungsi dibuktikeun maké uji éksperimén nu sistematis
There were exceptions and there are anachronisms: for example, the Greek thinker Archimedes derived many correct quantitative descriptions of mechanics and hydrostatics
Munggaran abad ka-17, Galiléo naratas dipakéna ékspérimén pikeun ngabuktikeun téori-téori fisik, nu jadi ide konci dina métode ilmiah
Galiléo geus sacara suksés ngarumuskeun jeung nguji sababaraha hasil panalungtikan ngeunaan dinamika, utamana Hukum Inersia
Dina taun 1687, Newton published the Principia Mathematica, detailing two comprehensive and successful physical théories: Newton's laws of motion, from which arise classical mechanics; and Newton's Law of Gravitation, which describes the fundamental force of gravity
Both théories agreed well with experiment
Classical mechanics would be exhaustively extended by Lagrange, Hamilton, and others, who produced new formulations, principles, and results
The Law of Gravitation initiated the field of astrophysics, which describes astronomical phenomena using physical théories
From the 18th century onwards, thermodynamics was developed by Boyle, Young, and many others
In 1733, Bernoulli used statistical arguments with classical mechanics to derive thermodynamic results, initiating the field of statistical mechanics
In 1798, Thompson demonstrated the conversion of mechanical work into héat, and in 1847 Joule stated the law of conservation of energy, in the form of héat as well as mechanical energy
The behavior of electricity and magnetism was studied by Faraday, Ohm, and others
In 1855, Maxwell unified the two phenomena into a single théory of electromagnetism, described by Maxwell's equations
A prediction of this théory was that light is an electromagnetic wave
In 1895, Roentgen discovered X-rays, which turned out to be high-frequency electromagnetic radiation
Radioactivity was discovered in 1896 by Henri Becquerel, and further studied by Pierre Curie and Marie Curie and others
This initiated the field of nuclear physics
In 1897, Thomson discovered the electron, the elementary particle which carries electrical current in circuits
In 1904, he proposed the first modél of the atom, known as the plum pudding model
(The existence of the atom had been proposed in 1808 by Dalton.)
In 1905, Einstein formulated the théory of special relativity, unifying space and time into a single entity, spacetime
Relativity prescribes a different transformation between reference frames than classical mechanics; this necessitated the development of relativistic mechanics as a replacement for classical mechanics
In the regime of low (relative) velocities, the two théories agree
In 1915, Einstein extended special relativity to explain gravity with the general theory of relativity, which replaces Newton's law of gravitation
In the regime of low masses and énérgies, the two théories agree
In 1911, Rutherford deduced from scattering experiments the existence of a compact atomic nucleus, with positively charged constituents dubbed protons
Neutrons, the neutral nucléar constituents, were discovered in 1932 by Chadwick
Beginning in 1900, Planck, Einstein, Bohr, and others developed quantum théories to explain various anomalous experimental results by introducing discrete energy levels
In 1925, Heisenberg and 1926, Schrödinger and Dirac formulated quantum mechanics, which explained the preceding quantum théories
In quantum mechanics, the outcomes of physical méasurements are inherently probabilistic; the théory describes the calculation of these probabilities
It successfully describes the behavior of matter at small distance scales
Quantum mechanics also provided the théoretical tools for condensed matter physics, which studies the physical behavior of solids and liquids, including phenomena such as crystal structures, semiconductivity, and superconductivity
The pioneers of condensed matter physics include Bloch, who créated a quantum mechanical description of the behavior of electrons in crystal structures in 1928
During World War II, reséarch was conducted by éach side into nuclear physics, for the purpose of créating a nuclear bomb
The German effort, led by Heisenberg, did not succeed, but the Allied Manhattan Project réached its goal
In America, a téam led by Fermi achieved the first man-made nuclear chain reaction in 1942, and in 1945 the world's first nuclear explosive was detonated at Trinity site, néar Alamogordo, New Mexico
Quantum field theory was formulated in order to extend quantum mechanics to be consistent with special relativity
It achieved its modérn form in the late 1940s with work by Feynman, Schwinger, Tomonaga, and Dyson
They formulated the théory of quantum electrodynamics, which describes the electromagnetic interaction
Quantum field théory provided the framework for modérn particle physics, which studies fundamental forces and elementary particles
In 1954, Yang and Mills developed a class of gauge theories, which provided the framework for the Standard Model
The Standard modél, which was completed in the 1970s, successfully describes almost all elementary particles observed to date
As of 2003, reséarch is progressing on a large number of fields of physics
In condensed matter physics, the biggest unsolved théoretical problem is the explanation for high-temperature superconductivity
Strong efforts, largely experimental, are being put into making workable spintronics and quantum computers
In particle physics, the first pieces of experimental evidence for physics beyond the Standard Model have begun to appéar
Foremost amongst this are indications that neutrinos have non-zero mass
These experimental results appéar to have solved the long-standing solar neutrino problem in solar physics
The physics of massive neutrinos is currently an aréa of active théoretical and experimental reséarch
In the next several yéars, particle accelerators will begin probing energy scales in the TeV range, in which experimentalists are hoping to find evidence for the higgs boson and supersymmetric particles
Théoretical attempts to unify quantum mechanics and general relativity into a single théory of quantum gravity, a program ongoing for over half a century, has yet to béar fruit
The current léading candidates are M-theory and loop quantum gravity
Many astronomical phenomena have yet to be explained, including the existence of ultra-high energy cosmic rays and the anomalous rotation rates of galaxies
Théories that have been proposed to resolve these problems include doubly-special relativity, modified Newtonian dynamics, and the existence of dark matter
In addition, the cosmological predictions of the last several decades have been contradicted by recent evidence that the expansion of the universe is accelerating
Tingali Masalah nu teu bisa dipeupeuskeun pikeun "fuller treatment" tina subjek ieu
See the definition of physical
Astronomi, nu sacara "étimologis" hartina "hukum béntang" (tina Basa Yunani: αστρονομία = άστρον + νόμος) mangrupa élmu nu ngawengku panalungtikan jeung katerangan kajadian-kajadian nu tumiba di luareun Marcapada jeung atmosfirna
Astronomi ngulik sasakala, évolusi, sipat-sipat kimia jeung fisika objék-objék nu bisa kapanggih di langit (luareun Bumi), sarta prosés-prosés nu patali
Astronomi mangrupa salah sahiji ti saeutik élmu ti mana para amatir bisa boga peran nu aktif, utamana dina manggihan jeung ngawaskeun fénoména transién
Astronomi euweuh patalina jeung astrologi, pseudoscience nu nyoba-nyoba ngaramalkeun takdir jalma ku jalan nyukcruk jalur objék astronomis
Sanajan dua widang éta babagi sumber nu méh sarua, ari sabenerna mah béda pisan; astronomer maké métode ilmiah, sedengkeun astrologer mah henteu
Dina mangsa munggaranana, balik deui ka jaman Yunani kuna jeung nu séjénna, astronomi utamana ngulik astrométri, ngalelebah planét jeung bintang di langit
Kadieunakeun, pagawéan Kepler jeung Newton geus naratas jalan pikeun celestial mechanics, nu sacara matematis ngaramal ketak/pola interaksi "celestial bodies" nu kapangaruhan ku graviti, jeung objék-objék tatasurya umumna
Pagawéan-pagawéan nu dikeureuyeuh dina dua widang ieu, nu baheula lolobana dipigawé ku leungeun, ayeuna mah geus maké alat-alat otomatis, nepi ka geus dianggap lain disiplin mandiri deui
Gerakan jeung posisi objék geus gampang pisan ditéang, astronomi modérn leuwih merhatikeun jeung ngusahakeun nengetan jeung neuleuman sipat fisik sabenerna objék-objék langit—what makes them "tick"
Ti mimiti abad ka-20 widang astronomi profésional beulah jadi "observational astronomy" jeung astrofisik tioritis
Najan "astronomer" lolobana ngagabungkeun unsur-unsur ti éta dua widang dina panalungtikanana, ku sabab bédana kaahlian nu dipaké, lolobana astronomer profésional leuwih condong ka salah sahijina
"Observational astronomy" leuwih condong utamana ka ngumpulkeun data, kaasup ngawangun jeung ngaropéa instrumén sarta ngolah data nu kakumpulkeun; cabang ieu ayeuna disebut salaku "astrométri" atawa "astronomy"
Théoretical astrophysics is concerned mainly with figuring out the observational implications of different modéls, and involves working with computer or analytic modéls
Widang ulikan astronomi ogé digolongkeun dumasar dua jalan nu béda: dumasar "subjék", biasana nurutkeun wewengkon langit (misalna "Galactic astronomy") atawa "masalah nu ditujul" (saperti dibentukna béntang atawa kosmologi); atawa dumasar cara nu dipaké pikeun meunangkeun data
Dumasar subjék atawa masalah nu ditujul
Also, there are other disciplines that may be considered part of astronomy: See list of astronomical topics for a more exhaustive list of astronomy-related pages
Cara-cara ngumpulkeun informasi
Dina élmu astronomi, informasi utamana mah ditarima ku jalan ngadétéksi jeung nganalisa radiasi éléktromagnétik, photons, tapi salian ti éta informasi ogé dibawa ku sinar kosmis, neutrinos, méteors, jeung, sakedap deui, gelombang gravitasi (tingal LIGO jeung LISA)
Pangbagian tradisional élmu astronomi nu ditangtukeun ku daérah spéktrum éléctromagnétik anu ditalungtik: Astronomi optik jeung radio bisa dilaksanakeun ngagunakeun observatorium anu aya di bumi, ku lantaran Atmosfer Bumi mah transparan ka panjang gelombang éta téh
Sedengkeun cahaya Infrared kaserep kuat pisan ku uap cai, ku lantaran kitu obsérvatorium infrared biasanya ditempatkeun di lokasi anu luhur, garing,atawa di luar angkasa
Atmosfer téh opaque (teu bisa ditembus) pikeun panjang gelombang nu dipaké dina astronomi X-ray, astronomi gamma-ray, astronomi UV jeung, kacuali pikeun "jandéla" saeutik panjang gelombang, astronomi Far infrared, janten pangamatan ngan bisa dilaksanakeun ngagunakeun balon udara atawa observatorium ruang angkasa
Dina bagian awal sajarahna, astronomi ngan wungkul ngawengku observasi jeung prédiksi ketak/gerak objék-objék langit nu bisa ditempo langsung ku panon.Rigveda didumasarkeun kana 27 konstélasi nu aya patalina jeung gerakan panonpoé jeung 12 babagian zodiak langit
Yunani Kuna méré sumbangan nu kalintang lobana pikeun astronomi, di antarana definisi sistim magnitude
The Bible contains a number of statements on the position of the éarth in the universe and the nature of the stars and planets, most of which are poetic rather than literal; see Biblical cosmology
In 500 AD, Aryabhata presented a mathematical system that took the éarth to spin on its axis and considered the motions of the planets with respect to the sun
Astronomy was mostly stagnant in medieval Europe, but flourished méanwhile in the Arab world
The late 9th century Islamic astronomer al-Farghani (Abu'l-Abbas Ahmad ibn Muhammad ibn Kathir al-Farghani) wrote extensively on the motion of celestial bodies
His work was translated into Latin in the 12th century
In the late 10th century, a huge observatory was built néar Tehran, Iran, by the astronomer al-Khujandi who observed a series of meridian transits of the Sun, which allowed him to calculate the obliquity of the ecliptic
In Persia, Omar Khayyam (Ghiyath al-Din Abu'l-Fath Umar ibn Ibrahim al-Nisaburi al-Khayyami) compiled many tables and performed a reformation of the calendar that was more accurate than the Julian and came close to the Gregorian
During the Renaissance Copernicus proposed a heliocentric model of the Solar System
His work was defended, expanded upon, and corrected by Galileo Galilei and Johannes Kepler
Kepler was the first to devise a system that described correctly the details of the motion of the planets with the Sun at the center
However, Kepler did not succeed in formulating a théory behind the laws he wrote down
It was left to Newton's invention of celestial dynamics and his law of gravitation to finally explain the motions of the planets
Stars were found to be faraway objects
With the advent of spectroscopy it was proved that they were similar to our own sun, but with a wide range of temperatures, masses and sizes
The existence of our galaxy, the Milky Way, as a separate group of stars was only proven in the 20th century, along with the existence of "external" galaxies, and soon after, the expansion of the universe seen in the recession of most galaxies from us
Cosmology made huge advances during the 20th century, with the modél of the big bang héavily supported by the evidence provided by astronomy and physics, such as the cosmic microwave background radiation, Hubble's Law and cosmological abundances of elements
Matématika (dina basa Inggris disebut, mathematics atawa math) nyaéta élmu pangaweruh anu museurkeun dirina dina konsép-konsép sarupaning kuantitas, struktur, rohang, katut parobahan, sarta mangrupa widang akademik anu maluruhna
Benjamin Peirce nyebutkeun yén matématika téh "élmu nu ngahasilkeun kacindekan nu diperlukeun"
Praktisi matématika séjénna nyebutkeun yén matématika téh élmu ngeunaan pola, sarta matématikawan téh tukang néang atawa nalungtik pola-pola anu aya dina wilangan, rohang, sains, komputer, gambaran abstrak atawa di mana waé ayana
Matématikawan ngéksplorasi konsép-konsép éta pikeun ngarumuskeun konjéktur-konjéktur atawa téori-téori anyar sarta mengkuhkeun bener-henteuna ku cara déduksi nu "kukuh" tina pilihan aksioma tur définisi nu jelas tur cocog
Ku cara abstraksi jeung nalar logis, matématika kabangun tina prosés ngitung, ngukur, sarta studi bentuk (en:"shape") sacara sitematis jeung usikna banda-banda fisis
Pangaweruh tur pamakéan matématika dasar geus lila jadi hal anu inhéren sarta ngahiji dina kahirupan, boh kahirupan saurang atawa kelompok
Prosés nyampurnakeun idé-idé dasar katémbong dina téks-téks matématis nu asalna ti Mesir kuna, Mésopotamia, India kuna, Cina kuna, sarta Yunani kuna
Argumén nu kukuh kasampak dina tulisan Euclid "Elements"
Matématika terus mekar sanajan rada reup-reupan (en:"fitful") nepikeun ka jaman Rénésans dina abad 16, harita inovasi matématika pinanggih jeung timuan-timuan sains, nu nyababkeun panalungtikan jadi ngagancangan, nerus nepikeun ka kiwari
Kiwari, matématika dipaké di rupa-rupa widang sakuliah dunya, élmu alam, rékayasa, ubar, sarta élmu sosial contona ékonomi
Matématika terapan dina widang-widang kasebut, bisa ngilhamkeun timuan-timuan matématis anyar sarta sakapeung nyababkeun mekarna widang anu anyar pisan
Matématikawan ogé aya nu museurkeun usahana dina matématika murni anu awalna tanpa mikirkeun terapkeuneunana, tapi ka hareupnakeun sok aya waé anu bisa diterapkeun
Kecap 'matématika' (Yunani: μαθηματικά or "mathēmatiká") asalna téh tina basa Yunani kuna μάθημα ("máthēma"), anu hartina "diajar", "nalungtik", "sains", anu saterusna boga harti nu ngaheureutan sarta leuwih téhnis "studi matématis", saprak di jaman klasik kénéh
Kecap sipatna nyaéta μαθηματικός ("mathēmatikós"), anu hartina "hal anu pakait jeung diajar", atawa "studious", anu sigana nerus miboga harti "matématis" (en: "mathematical")
Harti husus lainna μαθηματικὴ τέχνη ("mathēmatikḗ tékhnē"), dina basa Latin "ars mathematica", nu hartina "seni matématis"
Dina basa Inggris,"mathematics" mangrupa 'noun' (kecap barang), nu mindeng disingget jadi "math" di Amérika Kalér atawa "maths"
Mun ceuk barudak sakola urang, matématika téh sok disebut ogé maté
Ihtisar jeung sajarah matematika
"Pikeun leuwih lengkep, tempo artikel sajarah matematik."
Disiplin utama dina matematik nyelengceng tina kabutuh nyieun rupa-rupa itungan dina widang bilintik/usaha, pikeun ngukur taneuh jeung pikeun ngira-ngira kajadian-kajadian astronomis
Tilu pangabutuh ieu sacara kasar bisa dipatalikeun ka rupa-rupa bagbagan matematik nu lega kana ulikan struktur, spasi (rohangan), jeung parobahan
Ulikan ngeunaan struktur dimimitian ku wilangan, mimiti nu geus pada mikawanoh wilangan natural jeung wilangan buleud sarta operasi aritmatikna, nu dicatetkeun dina aljabar dasar
Sipat wilangan nu leuwih jero diulik dina tiori wilangan
Panalungtikan ngeunaan métode-métode pikeun ngudar/meupeuskeun "persamaan" ngawujud jadi widang aljabar abstrak, nu, di antara nu séjén, ngulik rings jeung fields, struktur nu ngajabarkeun sifat-sifat nu dipibanda ku angka-anka anu geus umum
The physically important concept of vectors, generalized to vector spaces and studied in linear algebra, belongs to the two branches of structure and space
Ulikan ngeunaan rohangan dimimitian ku géometri, kahiji géométri Euclid jeung trigonométri dina rohangan tilu diménsi, tapi ka dieunakeun dijieun leuwih umum ku ulikan non-Euclidean geometries nu mibanda pangaruh nu utama dina general relativity
Sababaraha masalah klasik ngeunaan ruler and compass constructions ahirna bisa dijawab ku Galois theory
Widang modérn ngeunaan differential geometry jeung algebraic geometry ngalegakeun géometri ka arah anu rada beda: géometri differensial nekenkeun konsep fungsi, fiber bundles, derivatives, smoothness jeung arah, sedengkeun aljabar géometri naliti wangun géometri anu dijieun tina jawaban sasaruaan (persamaan) sakumpulan polynomial
Group theory naliti konsep simetri sacara abstrak jeung méré kaitan antra ulikan rohangan jeung ulikan struktur
Topology ngaitkeun ulikan rohangan jeung ulikan parobahan ku alatan nekenkeun kana konsep continuity
Bisa ngarti jeung ngajelaskeun parobahan dina kuantitas nu ka ukur mangrupa salah sahiji tema élmu alam
Kalkulus mangrupa salah sahiji alat nu utama pikeun ngajelaskeun éta perkara
Konsep nu utama pikeun nerangkeun parobahan variabel nyaéta ku konsep fungsi
Loba masalah anu bisa diterangkeun sacara alami ku kaitan antara kuantitas jeung laju parobahannana, métodeu pikeun ngajawab hal ieu di ulik dina widang differential equations
Wilangan anu dipaké pikeun nerangkeun kasinambungan kuantitas nyeta wilangan real numbers, ulikan nu taliti ngeunaan sifat wilangan réal jeung fungsi nu mibanda niléy réal disebut real analysis
Ku sababaraha alesan, wilangan réal perlu dilegakeun ka complex numbernu di ulik dina widang complex analysis
Functional analysis nekenkeun ulikanna kana(typically infinite-dimensional) rohangan fungsi, nu méré dadasar pikeun quantum mechanics di antaran nu séjénna
Loba kajadian di alam nu bisa dijelaskeun ku dynamical systems jeung chaos theory ngurus sistim anu kalakuanna méngpar tina kalakuan nu galib
Ku perluna ngajentrekeun jeung naliti dadasar matematik, widang tiori set, logika matematik jeung tiori model dikembangkeun
Nalikakomputer mimiti katimu, sababaraha konsép tioritis anu utama diwangun ku matematikawan, nu ngalahirkeun widang tiori itungan, tiori itungan komplek, tiori informasi jeung tiori informasi algoritma
Loba pamasalahan ieu nu ayeuna di taliti dina widang sain komputer tioritis
Matematik Diskrit nyaéta ngaran anu galib pikeun widang matematika anu kapaké dina élmu komputer
Salah sahiji widang anu penting dina matematika terapan nyaéta statistik, nu ngagunakeun tiori kamungkinan pikeun jadi alat nu mampuh nerangkeun, nganalisis jeung nyawang kajadian-kajadian nu bakal tumiba
Élmu ieu dipaké ampir ku sakabéh élmu alam
analisis angka nalitimétodeuanu efisien mecahkeun(meupeuskeun???)
rupa-rupa masalah matematika sacara numerik ngagunakeun komputer di mana kasalahan ngitung ogé dipertimabangkeun
Jejer-jejer na matematik
Di handap ieu béréndélan subwidang jeung jejer-jejer nu ngagambarkeun salah sahiji sawangan organisasional matematik
Sacara umum, jejer jeung pamendak némbongkeun ukuran-ukuran éksplisit ukuran wilangan atawa sét, atawa cara-cara pikeun manggihan pangukuran-pangukuran nu sarupa
Wilangan -- Wilangan natural -- Pi -- Integers -- Wilangan rasional -- Wilangan real -- Wilangan kompléks -- Wilangan hiperkompléks -- Quaternions -- Octonions -- Sedenions -- Hyperreal numbers -- Surreal numbers -- Ordinal numbers -- Cardinal numbers -- "p"-adic numbers -- Integer sequences -- Konstanta matematiks -- Number names -- Infinity -- Base Parobahan
Jejer-jejer di handap méré jalan pikeun ngukur parobahan dina rumus matematis jeung parobahan antarwilangan
Aritatik -- Kalkulus -- Kalkulus véktor -- Analisis -- Differential equations -- Sistem dinamis jeung chaos theory -- Béréndélan rumus Struktur
Rangkadak dahan matematik nu aya di handap nangtukeun ukuran jeung simétri wilangan, sarta rupa-rupa wangun
Aljabar abstrak -- Téori wilangan -- Géométri aljabar -- Group theory -- Monoids -- Analisis -- Topologi -- Aljabar liniér -- Téori grafik -- Aljabar universal -- Téori kategori -- Order theory Space
These topics tend to quantify a more visual approach to mathematics than others
Topology -- Geometry -- Trigonometry -- Algebraic geometry -- Differential geometry -- Differential topology -- Algebraic topology -- Linear algebra -- Fractal geometry Matematik Diskrit
Such topics déal with branches of mathematics with objects that can only take on specific, separated values
Combinatorics -- Naive set theory -- Probability -- Theory of computation -- Finite mathematics -- Cryptography -- Graph theory -- Game theory Matematik terapan
Widang-widang di handap nerapkeun pangaweruh matematik dina masalah-masalah kahirupan nyata
Mékanik -- Analisis numeris -- Optimization -- Probability -- Statistik -- Financial mathematics Famous theorems and conjectures
These théorems have interested mathematicians and non-mathematicians alike
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 -- Scholz Conjecture -- Church-Turing thesis Important theorems
These are théorems that have changed the face of mathematics throughout history
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 Foundations and methods
Such topics are approaches to mathematics, and influence the way mathematicians study their subject
Philosophy of mathematics -- Mathematical intuitionism -- Mathematical constructivism -- Foundations of mathematics -- Set theory -- Symbolic logic -- Model theory -- Category theory -- Theorem-proving -- Logic -- Reverse Mathematics -- Table of mathematical symbols Sajarah matematik -- Timeline of mathematics -- Matematikawan -- Fields medal -- Abel Prize -- Millennium Prize Problems (Clay Math Prize) -- International Mathematical Union -- Mathematics
-- International Mathematical Union -- Mathematics competitions -- Lateral thinking Matematik jeung arsitéktur -- Matematik jeung atikan -- Mathematics of musical scales List of mathematical coincidences Pakakas matematis
Heubeul: Anyar: Quotes
Referring to the axiomatic method, where certain properties of an (otherwise unknown) structure are assumed and consequences theréof are then logically derived, Bertrand Russell said: "Mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true."
This may explain why John Von Neumann once said: "In mathematics you don't understand things
You just get used to them."
About the béauty of Mathematics, Bertrand Russell said in "Study of Mathematics": "Mathematics, rightly viewed, possesses not only truth, but supreme beauty -- a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art
such as only the greatest art can show
The true spirit of delight, the exaltation, the sense of being more than Man, which is the touchstone of the highest excellence, is to be found in mathematics as surely as poetry."
Elucidating the symmetry between the créative and logical aspects of mathematics, W.S
Anglin observed, in "Mathematics and History": "Mathematics is not a careful march down a well-cleared highway, but a journey into a strange wilderness, where the explorers often get lost
Rigour should be a signal to the historian that the maps have been made, and the real explorers have gone elsewhere."
Elmu bumi (ing
"geoscience" atawa "the geosciences"), mangrupa salah sahiji widang élmu anu nalungtik Mayapada
Bisa dianggap kasus husus dina élmu planét, sabab mangrupa hiji-hijina planét nu dieusi ku mahluk hirup
Aya jihat réduksionis jeung holistik dina élmu Bumi
Nu geus ti baheula mula dipaké pikeun panalungtikan kuantitatif ruang Bumi di antarana fisika, matematik, kimia, jeung biologi
Dina harti umum, internét (maké aksara leutik "i", singgetan tina inter-network) mangrupa jaringan komputer nu nyambungkeun sababaraha jaringan
Salaku hiji istilah nu mandiri, Internét mangrupa sistim komputer (kaasup informasi jeung layanan nu disadiakeun pikeun nu marakéna) umum nu kasambungkeun sacara internasional ngagunakeun "suite" TCP/IP tina protokol komunikasi panyaklaran paket
Ku kituna, internet panggedéna sacara basajan disebut Internet
Seni nyambungkeun jaringan-jaringan ku cara ieu disebutna "internetworking"
Dina basa sapopoé, "Internét" kadang nujul ka layanan "World Wide Web", surat éléktronik, jeung "ngobrol online" nu aya na Internét
"Artikel utama: Sajarah Internét" Ngacambahna bibit Internét dimimitian dina taun 1969 ku ayana ARPANET nu diwangun ku "Advanced Research Projects Agency" (ARPA), Departemén Pertahanan Amérika Sarikat
Sababaraha panalungtikan munggaran nu nyumbang ka ARPANET nyéta gawé dina desentralisasi jaringan, teori antrian, jeung "packet switching"
Tanggal 1 Januari, 1983, ARPANET ngarobah inti protokol jaringanana tina NCP ka TCP/IP, nandakeun awal Internét sakumaha nu ayeuna urang apal
Léngkah penting séjén dina ngembangna Internét nyaéta ku ayana National Science Foundation's (NSF), NSFNet, taun 1986
Internét diadegkeun babarengan ku kontrak komérsil bi- atawa multilateral
Internét ogé mibanda pangaruh nu nyosok jero kana pangaweruh jeung sawangan dunya.Dibandingkeun jeung énsiklopédi sarta pabukon tradisional, Internét mintonkeun hiji desentralisasi informasi jeung data nu dadakan sakaligus ékstrim
Basa nu utama dipaké dina komunikasi di Internét umumna Inggris, dumasar ka bibit buitna, kailaharan basa program software, jeung sabab kalemahan komputer heubeul dina narima karakter-karakter lian ti alfabét kulon
Asup ka Internét
Cara akses Internét nu umum digunakeun di imah-imah nyaéta dial-up jeung broadband
Singketan hartosna Protokol Internét
Ieu mangrupikeun nomer unik anu ditugaskeun ka sadaya alat nalika dihubungkeun ka Internét - komputer desktop, laptop, tablet, smartphone, jsb
E-mail, atawa email, disundakeun jadi surélék, mangrupa landihan pikeun "surat éléktronik" nu dimaksudkeun kana nyusun/nulis, ngirim, jeung narima pesen/surat ngaliwatan sistem komunikasi éléktronik
Sistem surélék ayeuna lolobana maké Internet, malah surélék nu mangrupa pungsi Internét nu paling ilahar/popular
Béda jeung asumsi umum, surélék sabenerna geus aya méméh Internét; malah, ayana sistem surélék mangrupa alat nu penting pisan dina nyiptakeun Internét
E-mail started in 1965 as a way for multiple users of a time-sharing mainframe computer to communicate; although the exact history is murky, among the first systems to have such a facility were SDC's Q32 and MIT's CTSS
E-mail was quickly extended to become "network e-mail", allowing users to pass messages between different computers
The éarly history of network e-mail is also murky; the AUTODIN system may have been the first allowing electronic text messages to be transferred between users on different computers, in 1966, but it is possible the SAGE system had something similar some time before
The ARPANET computer network made a major contribution to the evolution of e-mail
There is one report which indicates experimental inter-system e-mail transfers on it shortly after its création, in 1969
Ray Tomlinson initiated the use of the @ sign to separate the names of the user and their machine in 1972
The common report that he "invented" e-mail is an exaggeration, although his éarly e-mail programs SNDMSG and READMAIL were very important
The ARPANet significantly incréased the popularity of e-mail, and it became the "killer app" of the ARPANET
As the utility and advantages of e-mail on the ARPANET became more widely known, the popularity of e-mail incréased, léading to demand from péople who were not allowed access to the ARPANET
A number of protocols were developed to deliver e-mail among groups of time-sharing computers over alternative transmission systems, such as UUCP and IBM's VNET e-mail system
Since not all computers or networks were directly inter-networked, e-mail addresses had to include the "route" of the message, that is, a path between the computer of the sender and the computer of the receivers
E-mail could be passed this way between a number of networks, including the ARPANET, BITNET and NSFNET, as well as to hosts connected directly to other sites via UUCP
The route was specified using so-call "bang path" addresses, specifying hops to get from some assumed-réachable location to the addressee, so called because éach hop is signified by a "bang sign", i.e
Thus, for example, the path ...!bigsite!foovax!barbox!me directs péople to route their mail to machine bigsite (presumably a well-known location accessible to everybody) and from there through the machine foovax to the account of user me on barbox
Before auto-routing mailers became commonplace, péople often published compound bang addresses using the { } convention (see glob) to give paths from several big machines, in the hopes that one's correspondent might be able to get mail to one of them reliably (example:
{seismo, ut-sally, ihnp4}!rice!beta!gamma!me)
Bang paths of 8 to 10 hops were not uncommon in 1981
Late-night dial-up UUCP links would cause week-long transmission times
Bang paths were often selected by both transmission time and reliability, as messages would often get lost
See the network and sitename
Surélék Internét Modern
Almost all e-mail is delivered directly to an Internet-connected host accepting mail for the recipient, using Simple Mail Transfer Protocol
Very few modérn servers will perform routing for messages sent by third parties due to the potential for abuse by péople sending unsolicited bulk e-mail
Those that do allow it are called open relays
A modérn Internet e-mail address is a string of the form "jsmith@domain.example"
It should be réad as "jsmith at domain dot example"
The part before the @ sign is the local part of the address, often the username of the recipient, and the part after the @ sign is a domain name which can be looked up in the Domain Name System to find the mail exchange servers accepting e-mail for that address
The format of Internet e-mail messages is defined in RFC 2822
Prior to the introduction of RFC 2822 the format was described by RFC 822
Internet e-mail messages consist of two major components: The héaders usually have at léast four fields: Note however that the "To" field does not necessarily have the e-mail address of the recipient
The information supplied in the héaders on the recipients computer is similar to that found on top of a conventional letter
The actual information such as who the message was addressed to is removed by the mail server after it assigns it to the correct user's mailbox
Also note that the from field does not have to be the réal sender of the e-mail
It is very éasy to fake the from line and let an e-mail seem to be from any mail address
It is possible to digitally sign an e-mail
This is a lot harder to fake
Other common héader fields include: Messages and mailboxes
Messages are exchanged between hosts using the Simple Mail Transfer Protocol with software like Sendmail
Users download their messages from servers usually with either the POP or IMAP protocols, yet in a large corporate environment users are likely to use some proprietary protocol such as Lotus Notes or Microsoft Exchange Server's
Mails can be stored either on the client or on the server side
Standard formats for mailboxes include Maildir and mbox
Several prominent e-mail clients use their own, proprietary format, and require conversion software to transfer e-mail between them
E-mail content encoding
E-mail is only defined to carry 7-bit ASCII messages
Although many e-mail transports are in fact "8-bit clean", this cannot be guaranteed
For this réason, e-mail has been extended by the MIME standard to allow the encoding of binary attachments including images, sounds and HTML attachments
Spamming and e-mail worms
The usefulness of e-mail is being thréatened by two phenomena, spamming and e-mail worms
Spamming is unsolicited commercial e-mail
Because of the very low cost of sending e-mail, spammers can send hundreds of millions of e-mail messages éach day over an inexpensive Internet connection
Hundreds of active spammers sending this volume of mail results in many computer users receiving tens or even hundreds of junk e-mails éach day
E-mail worms use e-mail as a way of replicating themselves into vulnerable computers
Although the first e-mail worm (the Morris worm) affected éarly UNIX computers, this problem is today almost entirely confined to the Microsoft Windows operating system
The combination of spam and worm programs results in users receiving a constant drizzle of junk e-mail, which reduces the usefulness of E-mail as a practical tool
A number of technology-based initiatives mitigate the impact of spam
Congress has also passed a law, the Can Spam Act of 2003, to regulate such e-mail
Abdullah, M. H. (1998)
"Electronic discourse: Evolving conventions in online academic environments"
Bloomington, IN: ERIC Cléaringhouse on réading, English, and Communication
[ED 422 593] Abras, C. (2002) The principle of relevance and metamessages in online discourse: Electronic exchanges in a graduate course
Language, "Literacy and Culture Review" 1(2), 39-53
Biesenbach-Lucas, S. &amp; Wiesenforth, D. (2001)
E-mail and word processing in the ESL classroom: How the medium affects the message
"Language Learning and Technology", 5 (1), 135-165
[EJ 621 506] Danet, B
Cyberplay: Communicating online
Oxford: Berg Publishing
"This article, or an earlier version, contains content derived from FOLDOC, used by permission."
Cara medar rupa-rupa widang ulikan loba ditangtukeun ku kasapukan historis ("historical convention") nepi ka jadi harti kecap nu lumaku kiwari
Gambaran tradisional pikeun élmu alam nyéta ulikan ngeunaan aspék fisik dunya "nonhuman"
Salaku kumpulan, di hiji sisi élmu alam dibédakeun ti téologi jeung "élmu sosial", di sisi séjén dibédakeun ti seni jeung kamanusaan
Matematika lain mangrupa élmu alam, tapi nyadiakeun loba bahan jeung métode dasar pikeun élmu alam
Élmu alam umumna usaha nerangkeun gawéna alam dunya leuwih ngaliwatan prosés alami batan prosés "divine"
Istilah élmu alam ogé dipaké pikeun mikawanoh "élmu" salaku hiji disiplin nu nuturkeun métode ilmiah
Di sagigireun pamakéan tradisional ieu, kiwari kecap "élmu alam" mindeng dipaké dina harti nu leuwih deukeut kana harti sapopoé
Dina jihat ieu, "élmu alam" bisa jadi frase pilihan pikeun élmu biologis (kajeujeut na prosés biologis), sarta dibédakeun ti élmu fisik (kajeujeut na hukum kimia jeung fisika nu ngadadasaran mayapada)
Dina basa sapopoé, logika mangrupa tinimbangan nu dipaké pikeun ngahontal hiji kasimpulan/kacindekan tina sakumpulan sangkaan
Nu leuwih formal, logika mangrupa ulikan ngeunaan "valid inference", nyaéta prosés ngahontal hiji kasimpulan/kacindekan tina sakumpulan sangkaan kalawan maké cara/jalan nu sistematis tur sohéh
Ceuk kasarna, kasohéhan ngandung harti nalika sakumpulan sangkaan boga ajén bener, mangka kasimpulanana ogé bener
Di sagigireun éta, logika nyadiakeun rumus/resép pikeun tinimbangan, nyéta kumaha jalma—ogé mahluk pinter séjénna, mesin, jeung sistem—sakuduna méré alesan
Ngan, rumus modél kitu lain mataholang pikeun logika sorangan, tapi leuwih mangrupa larapan
Kumaha jalma sabenerna méré alesan biasana diulik dina widang séjén, kaasup psikologi kognitif
Sacara tradisional, logika diulik minangka cabang tina filosofi
Mimiti panengah taun 1800-an logika geus umum diulik na matematik, jeung, nu leuwih mutahir, dina élmu komputer
Minangka élmu, logika nalungtik jeung ngagolongkeun struktur pernyataan jeung argumén sarta ngarancang skéma pikeun nyandikeunana
Ku sabab éta cakupan logika bisa lega pisan, kaasup tinimbangan ngeunaan probabiliti jeung kausaliti
Nu ogé diulik na logika nyéta struktur argumén salah jeung paradoks
Nuturkeun tumuwuhna, loba bébédaan geus diwanohkeun kana logika
Bébédaan ieu disadiakeun pikeun nulungan ngaresmikeun rupa-rupa bentuk logika minangka élmu
Di handap ieu sababaraha bébédaan nu penting
Tinimbangan deduktif jeung induktif
Sasakalana, logika ngan ngawengku tinimbangan deduktif ngeunaan naon-naon nu jadi akibat tina prémis nu aya
Ngan, perlu dicatet yén tinimbangan induktif—ulikan nurunkeun kacindekan umum nu bisa dipercaya tina observasi—kadang diasupkeun dina ulikan logika
Patali jeung éta, urang kudu ngabédakeun antara kasahéhan deduktif jeung induktif
Hiji inferensi sacara déduktif bakal sohéh lamun jeung ukur lamun heneuweuh situasi nu ngamungkinkeun sakabéh prémis bener sarta kasimpulannana salah
Ide kasohéhan déduktif bisa dinyatakeun sacara taliti keur sistim logika formal dina ide semantik nu gampang dipikaharti
Kasohéhan induktif dina sisi lianna nyaratkeun urang keur ngadefinisikeun "generalisasi nu handal" tina sababaraha set panalungtikan
Tugas nyayagakeun definisi ieu bisa dideukeutan dina sababaraha cara, sababaraha di antarana teu pati resmi dibandingkeun lianna; sababaraha definisi ieu bisa maké modél matematis probabilitas
Keur lolobana bagian, sawala urang ngeunaan logika ukur patali jeung logika déduktif
Logika formal jeung informal
Somewhat arbitrarily, study of logic is divided into formal and informal logic
Formal logic (sometimes called symbolic logic) approaches logic and in particular logical argument as a set of rules for manipulating symbols
There are two kinds of rules in any system of formal logic: Syntax rules and rules of inference
Syntax says how to build méaningful expressions; rules of inference say how to obtain true formulas from other true formulas
Logic also needs semantics, which says how to assign méaning to expressions
Formal logic encompasses a wide variety of logical systems
For instance, propositional logic and predicate logic are a kind of formal logic, as well as temporal logic, modal logic, Hoare logic, the calculus of constructions etc
Higher order logics refer to logical systems based on a hierarchy of types
Informal logic is the study of logic as used in natural language arguments
Informal logic is complicated by the fact that it may be very hard to téase out the formal logical structure imbedded in an argument
Informal logic is also more difficult because the semantics of natural language assertions is much more complicated than the semantics of formal logical systems
Following are more specific discussions of some systems of logic
See also: list of topics in logic
The Prior Analytics was Aristotle's pioneering work establishing a system of logic and inference based on the forms of the premises and the conclusion
These rules were codified into various forms of syllogisms which, until recently at léast, were part of the standard high school curriculum in the West, much like euclidéan plane géometry
Aristotelian logic is sometimes referred to as formal logic because it specifically déals with forms of réasoning, but is not formal in the sense we use it here or as is common in current usage
It can be considered as a precursor to formal logic
In the tradition of aristotelian logic is also term logic
Mathematical logic refers to two distinct aréas of reséarch: The first, primarily of historical interest, is the use of formal logic to study mathematical réasoning, and the second, in the other direction, the application of mathematics to the study of formal logic
At the beginning of the twentieth century, philosophical logicians including (Frege, Russell) attempted to prove that mathematics could be entirely reduced to logic
The reduction had limited success (for réasons which are well beyond the scope of this article) but in the process, logic took on much of the notation and methodology of mathematics
In the other direction, in the éarly 1930s, Kurt Gödel embarked on an ambitious program of considering logic and proof as an object of mathematical study, léading him to state far réaching results on provability and modél théory such as the incompleteness theorems of first order arithmetic
This line of reséarch has continued to the present time, léading to various stunning results such as for example, Paul Cohen's proof of the independence of the continuum hypothesis from the axioms of Zermelo-Fraenkel set théory
"Main article philosophical logic" Philosophical logic déals with formal descriptions of natural language
Most philosophers assume that the bulk of "normal" proper réasoning can be captured by logic, if one can find the right method for translating ordinary language into that logic
Philosophical logic is essentially a continuation of the traditional discipline that was called "Logic" before it was supplanted by the invention of Mathematical logic
Philosophical logic has a much gréater concern with the connection between natural language and logic
As a result, philosophical logicians have contributed a gréat déal to the development of non-standard logics (e.g., free logics, tense logics) as well as various extensions of classical logic (e.g., modal logics), and non-standard semantics for such logics (e.g., supervaluation semantics)
The logics discussed above are all "bivalent" or "two-valued"; that is, the semantics for éach of these languages will assign to every sentence either the value "True" or the value "False."
Systems which do not always maké this distinction are known as non-Aristotelian logics, or multi-valued logics
In the éarly 20th century Jan Łukasiewicz investigated the extension of the traditional true/false values to include a third value, "possible"
Logics such as fuzzy logic have since been devised with an infinite number of "degrees of truth", e.g., represented by a real number between 0 and 1
Bayesian probability can be interpreted as a system of logic where probability is the subjective truth value
Logic and computation
Logic is extensively used in the fields of artificial intelligence, and computer science
In the 1950s and 1960s, reséarchers predicted that when human knowledge could be expressed using logic with mathematical notation, it would be possible to créate a machine that réasons, or artificial intelligence
This turned out to be more difficult than expected because of the complexity of human réasoning
Logic programming is an attempt to maké computers do logical réasoning and Prolog programming language is commonly used for it
In symbolic logic and mathematical logic, proofs by humans can be computer-assisted
Using automated theorem proving the machines can find and check proofs, as well as work with proofs too lengthy to be written out by hand
In computer science, Boolean algebra is the basis of hardware design, as well as much software design
There are also various systems for réasoning about computer programs
Hoare logic is one the éarliest of such systems
Other systems are CSP, CCS, pi-calculus for réasoning about concurrent processes or mobile proceses
See also computability logic; this is a formal théory of computability in the same sense as classical logic is a formal théory of truth
Konsép logika Techniques and rules Related Topics
Budaya asalna tina basa Sansekerta nyaéta "buddhayah", nu mangrupa wangun "jamak" tina buddhi (budi atawa akal) dihartikeun minangka hal-hal nu aya pakaitna jeung budi ogé akal manusa
Dina basa Inggris, kabudayaan disebut "culture", nu asalna tina kecap Latin “Colere’, nyaéta ngolah atawa ngerjakeun
Bisa dihartikeun ogé minangka ngolah taneuh atawa tatanén
Kecap "culture" ogé bisa dihartikeun minangka “kultur” dina basa Indonesia
Ku kituna, kabudayaan mangrupa rupaning aturan, pituduh, rarancang, jeung stratégi nu ngawengku modél-modél "kognitif" nu dipiboga ku manusa jeung digunakeun sacara "selektif" dina nyanghareupan lingkunganna
Hiji kabudayaan mangrupa pangaboga babarengan dina masarakat atawa golongan sosial nu sumebar ka anggota-anggotanna
Kabudayaan diwariskeun ka generasi saterusna ngaliwatan prosés diajar jeung ngagunakeun simbol-simbol nu ngawujud boh dina wangun ucap boh henteu (kaasup ogé sarupaning pakakas nu dijieun ku manusa)
Ku kituna, sakumna warga masarakat miboga pangaweruh ngeunaan kabudayaanna nu henteu sarua jeung anggota-anggota lianna, lantaran ku pengalaman jeung prosés dihajar jeung lingkungan nu disanghareupan teu salilana sarua
Rékayasa mangrupa aplikasi élmu pikeun nedunan pangabutuh manusa
Ieu kacumponan ku ayana pangaweruh, matematik, jeung pangalaman praktis nu diterapkeun kana rancang barang atawa prosés nu mangpaat
Praktisi rékayasa nu profésional disebut insinyur
Dina sajarahna, loba ahli yakin yén kamampuhan rékayasa manusa geus ingrained "alami"
Hal ieu dicirikeun ku kamampuhan manusa mimiti nyieun parabot tina batu
Dina basa sejen, téknik asalna dumasar kana trial and error pikeun nyieun parabot pikeun nyederhanakeun kahirupan manusa
Lila-lila, élmu pangaweruh mimiti mekar, sarta mimiti ngarobah cara pandang manusa kumaha jalanna alam
Kamekaran élmu anu teras-terasan ngarobih cara rékayasa damel dugi ka ayeuna
Jalma-jalma henteu deui ngandelkeun pisan kana trial and error dina nyiptakeun atawa ngararancang pakakas, tapi leuwih ngutamakeun élmu salaku dadasar pikeun ngarancang