Matematika: Béda antarrépisi
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m Removing Link GA template as it is now available in wikidata |
m Ngarapihkeun éjahan, replaced: mangrupakeun → mangrupa (2), oge → ogé , nyaeta → nyaéta (3), rea → réa (4), dipake → dipaké (2), diantara → di antara, ea → éa (2), eo → éo (7), salasahiji → s using AWB |
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'''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".<ref>Peirce, p.97</ref>
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.<ref>[[Lynn Steen|Steen, L.A.]] (April 29, 1988). ''The Science of Patterns.'' [[Science (journal)|Science]], 240: 611–616. and summarized at [http://www.ascd.org/portal/site/ascd/template.chapter/menuitem.1889bf0176da7573127855b3e3108a0c/?chapterMgmtId=f97433df69abb010VgnVCM1000003d01a8c0RCRD Association for Supervision and Curriculum Development.]</ref><ref>
Ku cara [[abstraksi (matématika)|abstraksi]] jeung [[nalar]] [[logika|logis]], matématika kabangun tina prosés [[counting|ngitung]], [[measurement|ngukur]], sarta studi [[bentuk]] (en:''shape'') sacara sitematis jeung [[motion (physics)|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 [[ancient Egypt|Mesir kuna]], [[Mésopotamia]], [[History of India|India kuna]], [[ancient China|Cina kuna]], sarta [[ancient Greece|Yunani kuna]]. Argumén nu kukuh kasampak dina tulisan [[Euclid]] [[Euclid's Elements|''Elements'']]. Matématika terus mekar sanajan rada reup-reupan (en:''fitful'') nepikeun ka jaman [[Renaissance|Rénésans]] dina [[abad 16]], harita inovasi matématika pinanggih jeung [[scientific discoveries|timuan-timuan sains]], nu nyababkeun panalungtikan jadi ngagancangan, nerus nepikeun ka kiwari.<ref>Eves</ref>
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Ulikan ngeunaan struktur dimimitian ku [[wilangan]], mimiti nu geus pada mikawanoh [[wilangan natural]] jeung [[wilangan buleud]] sarta operasi [[aritmatik]]na, 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 [[ring (mathematics)|rings]] jeung [[field (mathematics)|fields]], struktur nu ngajabarkeun sifat-sifat nu dipibanda ku angka-anka anu geus umum. The physically important concept of [[vector (spatial)|vectors]], generalized to [[vector space]]s 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 kadieunakeun dijieun leuwih umum ku ulikan [[Non-euclidean geometry|non-Euclidean geometries]] nu ngabogaan pangaruh nu utama dina [[general relativity]]. Sababaraha masalah klasik ngeunaan [[ruler and compass constructions]] ahirna bisa dijawab ku [[Galois theory]]. Widang modern ngeunaan [[differential geometry]] jeung [[algebraic geometry]] ngalegakeun
Bisa ngarti jeung ngajelaskeun parobahan dina kuantitas nu ka ukur
Ku perluna ngajentrekeun jeung naliti dadasar matematik, widang [[tiori set]], [[logika matematik]] jeung [[tiori model]] dikembangkeun.
Nalika[[komputer]] mimiti katimu, sababaraha konsep 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]]
Salah sahiji widang anu penting dina [[matematika terapan]]
== Jejer-jejer na matematik ==
Di handap ieu béréndélan subwidang jeung jejer-jejer nu ngagambarkeun
=== Kuantitas ===
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=== [[Matematik Diskrit]] ===
Such topics
:[[Combinatorics]] -- [[Naive set theory]] -- [[Probability]] -- [[Computation|Theory of computation]] -- [[Finite mathematics]] -- [[Cryptography]] -- [[Graph theory]] -- [[Game theory]]
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=== Famous theorems and conjectures ===
These
:[[Fermat's last theorem]] -- [[Goldbach's conjecture]] -- [[Twin Prime Conjecture]] -- [[Gödel's incompleteness theorem]]s -- [[Poincaré conjecture]] -- [[Cantor's diagonal argument]] -- -- [[Four color theorem]] -- [[Zorn's lemma]] -- [[Euler's identity]] -- [[Scholz Conjecture]] -- [[Church-Turing thesis]]
=== Important theorems ===
These are
:[[Riemann hypothesis]] -- [[Continuum hypothesis]] -- [[Complexity classes P and NP|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]]
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=== Mathematical coincidences ===
:[[List of mathematical coincidences]]
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== Quotes ==
Referring to the axiomatic method, where certain properties of an (otherwise unknown) structure are assumed and consequences
:''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.''
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:''In mathematics you don't understand things. You just get used to them.''
About the
:''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 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
:''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.''
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