Mathematics

**Mathematics** (din nye Dagbamba ni boondi binsheli Laasabu malibu) nyɛla baŋsim bɔhimbu yaɣi shɛli din yihiri bee n kahigira ka lahi pu n pu sɔ bɔbili shɛŋa din yina ni di ti bo ninneesim n ti tabibi baŋdiba n ti pahi laasabu malibu maŋ maŋa. Mathematics mali la yaɣa pam ka di shɛŋa nye , *number* *theory* (din bɔhimbu jandi kalinli bihi), *algebra* (din bɔhimbu jandi binyɛra biɛhigu), *geometry* (din bɔhimbu jandi binyɛra nama, poli shɛŋa di ni tooi deegi ni di lɔɣa), *analysis* (din bɔhimbu jandi taɣibu taɣibu din niŋdi saha kam), n ti pahi set thory (din bɔhimbu jandiri bin muna ka di lahi nyɛ bin shɛli din laɣimdi bin yara di ni tu ni di be luɣi shɛli, dina n nyɛ daantaligu n ti mathematics bɔhimbu dagaadam). 

Mathematics nyɛla din jandi binyɛra din ku tooi dii n nya buɣisibu n ti pahi di nahimbu biɛhigu puuni, Mathematics mali la daliri din ka daɣiri m maliwuhiri binyɛra nahingbana ni shaharanima, din dɔli zalisinima din be di puuni nam biehigu ni n yihiri laasabu bihi na, Laasabu bihi ŋɔ dina n nyɛ theorems bee axioms saha shɛŋa din gari ŋɔ nyɛla nahaingbana shɛŋa din leei pilibu shee n ti laasabu bɔhimbu ni baŋsim vihigu shee, 

Mathematics mali bukata pam n-ti *natural science*, *engineering*, *medicine*, *finance*, *computer science*, n-ti pahi *social science*. Mathematics nyɛla bɛ ni mali bin shɛli n niɣindi biɛhigu pam, mathematics daantaligi din nyɛ yɛlimaŋli kuli nyɛla di ni za di gama zuɣu ka bɛ zaŋ di maŋ n jali ''science'' tumtumsa la. Mathematics yaɣ'shɛga, kamani *statistics* mini *game theory* nyɛla din mini di *applications* kpini taba, ka bɛ pu li n niŋ *applied mathematics* bɔŋ ni. Yaɣ'shɛŋa mi biɛni ka di mini di application shɛli bɛ kpini taba ka bɛ pu dimi n niŋ *pure mathematics* bɔŋ ni, amaa nyaanga ha, di tooi mali nin nyabu *applications*.

Di yi kana taarihi polo, *mathematics* dalirinim din ne n dɔya ka ka gbaliŋ nyɛ din daa tuugi yina *Creek mathematics* puuni, din niŋ bayana *Euclid's Elements* puuni. Tum di piligu, bɛ daa pirigi la *mathematics* n-ti *geometry* mini *arithmetics* (*natural numbers* niɣimbu mini pirigibu) naɣila *16th* mini *17th* *centuries* la saha, *algebra* mini *infinitesimal calculus* ni daa yoli yina. Lala saha maa hali ni zuŋɔ, alizama di be *mathematical innovations* mini *scientific discoveries* sunsuuni chɛmi ka di zaa.zoora. 19th century bahigu ha, *mathematics* kpabu yalimuɣisira daa chɛmi ka bɛ mali ka yooi di soya, ka di chɛ ka be niŋ suhipiɛlli ni mathematics yaɣa maa kalinli pahibu ni di *applications* yaɣa. Saha ŋɔ *mathematics* din bɛ ti karim zona ni ŋɔ mali ̃Bɛ ni tooi lahi yɛli ni di nyɛla  equation shɛli din bɛ za di naba ayi zuɣu, ka nyɛ polynomial equations (din tahi algebraic geometry na).*mathematics* yaɣa din du puya n gari pihinu.

## [Areas of mathematics] mathematics yaɣa yaɣa
poi ni ninneesim mathematics daa nyala di pirgi yaɣa ayi zuɣu:: *arithmetic*, din nye kalinli yaltɔɣa, ni *geometry* din nye binyara ŋmahangbana "*shapes*" yaltɔɣa. "*pseudoscience*" yaɣ'shaŋa kaman "numerology" mini "astrology", daa nyala din ka walginsim ni mathematics.

Di ni daa ti niŋ ka nina nehi yaɣa ayi daa nyala din pahi, laasabu malibu baŋsim yaɣili zuɣu, "*Mathematical notation*"  dini n  daa zan n ti "algebra" din nye n zaŋ "*formulas*"n tumdi tuma kaman kotomsi,bi yi ti a bohigu laasabu malibu ni ni  **(x + 2 = 5)**"*algebra*" n nye din yan soŋ a  ka tooi labisi lala bohigu maa. Din pahi n nye "calculus" din nye din pirigi buyi  "differential calculus"  mini "*integral calculus*", ka di mi wuhiri ti binyara ni taɣiri sham biehigu puuni. Lala yaɣa yaɣa ŋo  arithmetic, *geometry*, *algebra*, ni *calculus*.  nyala din daa saɣi n ti ka beni  hali ni "*19th century*" (zuŋo yuun'kobshii)  naabu saha.Yaɣa kamani "*celestial mechanics*" mini "solid mechanics" daa lahi silimiinsi ni boli shaba "*mathematicians"  ni daa bohim shɛli*  amaa punpoŋo di pahila *physics* puuni.. Lala yaɣa ŋo daa kuli nyala din bohinda amaa ka daa lee bi za gama zuɣu m mali di konko yuli naɣila 17th century la saha.   

"*19th century*" (zuŋo yuun'kobshii) bahigu saha, *mathematics* kpabu yalimuɣisira daa chɛmi ka bɛ mali ka yoogi so'pala. Yuuni 200 *mathematics* din be ti karim zona ni ŋɔ mali *mathematics* yaɣa din du puya n gari pihiyobu ni ata. Lala yaɣa maa shɛga gɔhila yaɣ'kura maa, kamani di ni nyɛ yɛlimaŋli di yi kana *number theory* (dina n pa nyɛ puunpoŋo *arithmetic* di du maa) mini *geometry*. Di yaɣa din du maa shɛŋa gba mali la *geometry* di yuya puuni bee ka bɛ kuli kpuɣili kamani *geometry*  yaɣ'shɛli. *Algebra* mini *calculus* pa yaɣ'shɛli din du, amaa di pirigi mi n ti yaɣ'shɛga din dundu. Yaɣ'shɛga din pahipahi ka du daa laɣim la taba *20th century* la saha bee ka bɛ daa yi bɛ kpuɣili ka di nyɛ *mathematics* kamani *mathematical logic* mini *foundations*.

### Number Theory
*Number theory* daa pilimi ni numbanim niɣimbu, dina n nyɛ *natural numbers* (N) ka di daa ti zoogi n niŋ *integers* (Z) ni *rational numbers* (Q). *Number theory* ka bɛ daa na boondi *arithmetic*, amaa punpoŋo din ka bɛ pa mali n tiri  nambanim laasabu malibu. *Number theory* pilli yila nadaa *[[Babylon]]* mini *[[China]]* nim sani. *Number theory* diba ayi shɛga din daa kuli niŋ bayana n nyɛ *[[Euclid]]* din nyɛ daadaa la saha *[[Greece]]* nim dini nti pahi *Diophantus* din nyɛ *[[Alexandria]]* nim dini la. Saha ŋɔ *number theory* bohimbu din be suhini ka kutooi nya nyɛla din jɛndi *Pierre de Fermat* mini *Leonhard Euler*. Lala yaɣili maa daa nyɛla din nya nasara ka di nyɛla *Adrien-Marie Legendre* mini *Carl Friedrich Gauss* nuutimbu zuɣu. 

Niriba pam yalimi ni namba yɛli'muɣisira ni yan n nya faako, naɣila bɛ zaŋ la so'shɛli din du n tum tuma, din tooi yirina *mathematics* yaɣa gabbu ni na. Shɛhira din yi polo pam n nyɛ *Fermat* bahigu *theorem* maa. Lala biɛhiŋ ŋɔ maa nyɛla Pierre de Fermat ni daa sabi yuuni 1637, amaa yuuni 1994 ka Andrew Wiles daa wuhi di dihitabili, o daa zaŋla nɛma kamani *scheme theory* din be *algebraic geometry* ni la, *category theory*, n-ti pahi *homological algebra*. Di shɛhira shɛli n nyɛ Goldbach biɛhiŋ la, din yɛli ni *integer* kam din mali jaa ka gari diba ayi nyɛla *prime number* diba ayi ni laɣim taba.

*Number theory* laɣim la yaɣ'bobigu kamani *analytic number theory*, *algebraic number theory*, *geometry of numbers* (sodɔligu yaɣili), *Diophantine analysis*, nti pahi *transcendence theory* (yalli yaɣili).

### Geometry
*Geometry* nyɛla mathematics wul'kura la zaɣ'yini. Di daa pilimi ni niriba sani shɛhiranim zaŋchaŋ *shapes* kamani *lines*, *angles*, ni *circles* polo, bɛ ni daa kpaŋsi binshɛli ka di nyɛla tiŋgbana galisim zahimbu mini tiŋgbanni mɛbu zuɣu, amaa ka di daa pirigi pirigi n pili yaɣ'pala.

Nadaa la saha *Greek* n daa pili di daantali kpɛŋ din tiri dihitabili, ka di yara, ni yɛltɔɣili kam bɛ ni yɛli, ni di nyɛla yɛlimaŋli tuya kadi mali daliri. Shɛhira, ni di bɛ saɣi ni di saɣiti yalli din yɛra, ni binyɛra ayi waɣilim nyɛla dɛdɛ; di waɣilim nim maa tuya ni di mali daliri ka di yina ban namin pun niŋ li ka  mali di daliri nima (*theorem*) sani, nti pahi yɛltɔɣa din za di nyaanga. Lala yɛltɔɣa din za di nyaanga maa pala binshɛli din ni tooi lɛbi di daliri, dama di nyɛla bɛ maŋmansi dini(bɛ ni saɣi ti shɛli ka ka daliri), bɛɛ ka di pahi yɛltɔɣa shɛga din buɣisiri li (sokam ni saɣi ti shɛli ka ka bɛ daliri). Lala zalkpana ŋɔ maa nyɛla din nyɛ daantaliga n ti mathematics kam, bɛ daa yaligi lala yɛltɔɣa ŋɔ maa n ti *geometry*, ka *[[Euclid]]* daa laɣim lala yɛltɔɣa ŋɔ maa yuun kɔbisita yaanga pɔi ni anabi Isa kandina n niŋ o buku shɛli bɛ ni booni *elements* la ni.  

*Euclidean geometry* nyɛla bin shɛli din bɔhindi *shapes* mini di nɛma ni laɣimdi sham, ka di yina *lines*, *planes* ni *circles* polo. Di nyɛla din ka barilim (*two dimentional figures*) ni din mali barilim (*three-dimenrional figures*). 

*Euclidean geometry* nyɛla bɛ ni daa pili shɛli ka di ka soli taɣibu hali ni *17th century*, René Descartes ni daa pili ti ni pa booni shɛli *Cartesian coordinates* la na. Ŋɔ maa nyɛla din chɛ ka taɣibu pam kana niriba tumtumsa mini tiɛha polo: Bɛ ni daa yi buɣisi *real numbers* ni di nyɛla boobu tarisi waɣilim maa (nyam number line), punpoŋo di pa  nyɛla din mali boobu tɔbu shɛɛ ka di za nambanim zaani. *Algebra* (din daa ti pa nyɛ *calculus* la) gba zaa ni tooi n mali *geometric* yɛlimuɣisira. *Geometry* daa ti pirigi mi n niŋ yaɣ'pala diba ayi: dina n nyɛ *synthetic geometry*, bɛ ni zaŋdi *geometry* soli din nyɛ din pali ni *analytic geometry*, din mi zaŋdi *coordinates* n tumdi tuma maa. 

*Analytic geometry* nyɛla din yɛra n kpari *curves* polo, di mini *circles* mini *lines*. Lala *curves* maa nyɛla *graph of functions*, *differential geometry* ni daa yina shɛli bɔhimbu ni la. Bɛ ni tooi lahi yɛli ni di nyɛla  *equations* shɛŋa din bɛ za di naba ayi zuɣu, ka nyɛ (din tahi *algebraic geometry* na). *Analytic geometry* lahi chɛmi ka *Euclidean* luɣi shɛŋa din du n gari yaɣi shɛŋa din mali puli.  

### Etymology
### '''''mathematics''' bachi nyɛla din yina'' [[Ancient Greek]] bachi ''máthēma'' ,ka di  hurila , ka bin yihili shɛli and the derived ''mathēmatikḗ tékhnē'' (), ka di nyɛ . Di che silimiinsili saha shɛli din daa nŋɛ naabu sunsuuni siliminsili ka di yini French and Latin.

Di ŋmahanli, di nyɛla shikuru yini din yina di baa ayi puuni bin be Pythagoreanism ka boli *mathēmatikoi* (μαθηματικοί)ka lala saha maa di daa yurimi ni "bohamba" ka di so "mathematicians" in punpɔŋɔ. Ka Pythagoreans daa nyɛla ban kana piligu ni bi constrain di lihigu zan ti bachi n-ti bohambu arithmetic ni geometry. Aristotle  saha (384–322&nbsp;BC) di  hankali daa nŋɛ ya.
Latin mi ni silimiinsili ni, din pa di paala until 1700, *mathematics bachi hurimi* "astrology" ( beei saha shɛŋa "astronomy") ka di pa rather "mathematics"; ka gbunni tahira bela bela n-ti ti bin pa mili shɛli zaani gbaai 1500 to 1800. Taɣibu ŋɔ zaŋ la baŋsim taɣibu: di shahara n-nyɛ, Saint Augustine's ni a sorinima zom ka che *mathematici*, ka di wuhiri "astrologers", saha shɛŋa beni tahiri mi n-zaŋ ti bin shɛli din be niŋ zaŋ ti mathematicians.
Di zaha bobli bi ni boli silimiinsili labirimi ni ti Latin neuter zahabobli  (Cicero), zaŋ doli Greek zahabobli *ta mathēmatiká* () ka di  booni "bin sahakam mathematical", hali  din nyɛ hankali zuli ni silimiinsili daa nŋɛla be ni suhi shɛli ka di nyɛla di anfaani *mathematic(al)* ka be zaanli ni bachi namda *mathematics ni  zaha palli*,  *[[physics]]* ni *[[metaphysics]] soli ni daa naa*, be ni daa nyɛ Greek nima sani.  English ni, bachi namda *mathematics* deeri zaha yini bachi niŋdili. Ka be  maarili It is often *maths* beei,North America, *math*.
### Ancient

Din lahi pahi ti n baŋdi a ni tooi kali binyɛra shɛm ti ni nyara, pɔi ni yali kura niriba ni tooi mali gbaabu zaŋ kpa kalibu bachi ŋa ka kalinli, kamani sahadabisa, seasons, bee yuma. shahira din be tɔm din galisi polo  mathematics bi tooi yi polo naɣila zaŋ kpa 3000&nbsp;, bo saha ka Babylonians mini Egyptians piligi zaŋ tum tuma arithmetic, algebra, ni geometry zaŋ ti farigu deebu ni tuma laɣ' kalindi bo Polo , zaŋ ti mebu ni malibu, mini zaŋ ti ban mi zuɣusaa yɛltɔɣa. saha kura la saha mathematical sabbu din yina Mesopotamia mini Egypt zaa yina la 2000 ni ti  ti 1800&nbsp;BC. pam daŋ bu sabbu bolibu  Pythagorean dibaata ni so, zaŋ ti inference, the Pythagorean theorem nyami zaŋ ti pam ancient mini widespread mathematical concept zaɣ' bihi nyaaŋa arithmetic mini geometry. Di biɛla Babylonian mathematics din elementary arithmetic (laɣimbu, yihibu, multiplication, ni pirigibu) piligu yina polo din be archaeological record. The Babylonians gba kpe jishee dariza system ka tum a sexagesimal numeral system bi ni na zaŋdi shɛli n tumdi tuma zuŋɔ  n-ti zahindi angles mini saha.
system|Hindunima–larbaawa numeral system]] ni di zalisi zaŋ ti di  of its operations,di niŋ yi duniya ni zuŋɔ , ni gili chaŋ di ni taɣi di piligu  millennium AD  India puuni ni daa taɣaya ni ti Western duniya via Islamic mathematics. ni yaɣ' shɛli lɛbigimsim of Indian mathematics be lala saha maa baŋbu ni approximation of sine ni cosine, ni daŋ yibu din be kalibu ŋa ku tooi kali.]]

## Symbolic notation and terminology

Mathematical notation nyɛla din yɛligi m be  science puuni ni fitanima ni zaŋdi zaani complex concepts ni falinima m be concise, unambiguous, ni ni dede yaɣili.  notation ŋɔ laɣimla of symbols zaŋ niŋ zaŋ zali operations, di nyɛla din bi yihi kalinli shɛŋa, zo' sima ni  binshɛŋa din nyɛ mathematical binyɛra, ni n naa yi laɣimdiba ni niŋdi hankaya nima puuni ni formulas.  precisely pam, kalibunima ni  mathematical shɛŋa niŋsim deera daa zaŋ ti  by symbols bɔli yaɣa, din laɣim binshɛɣu kam  Latin bee Greek bachinima, ni din gba pahi din be sabbu yaɣ' shɛli. Operation ni zosima zaa laɣimmi zaŋ ti  symbols din gahim bee glyphs, kamani  (zaŋ laɣim),  (multiplication), \int (integral),  (zaɣ' yini), ni  (din bi paai). symbols ŋɔ maa zaa laɣimla ni zaŋ di tira zaligu din gahim ti hankaya puuni ni formulas. zaɣa maŋli ni, hankaya ni formulas bi yirina di konko, amaa di paɣala yɛltɔɣa puuni punpɔŋɔ bala, where expressions ni tum di tuma bachi namda phrases ni formulas dema
Mathematics malila yaligibu din mali yaa n taɣara  broad range yaɣa shɛŋa  din mali bohambu zaŋ kpa fali pirigibu din be yaɣa shɛŋa ni , idealized objects ni kamani bini kpɛri taba shɛm. Di biɛla rigorous baŋbu din yihi mebu din zani viɛnyɛla. An axiom bee postulate  mathematical nyɛla statement din kpuɣiri di yɛlimaŋli ka ka din bɔri proof. If a mathematical statement ni nabi yihiri (bee din bi yihira), di nin nye conjecture. Zaŋ yi di series of rigorous nangbankpeeni kpuɣibudeductive reasoning, a statement yihiri di yɛlimaŋli lɛbila a theorem. theorem shɛli din gahim nye din tum maa maŋmaŋa  prove  theorem shɛli gba booni la ''lemma''. A proven ni be yaɣ' shɛŋa ni  pam laɣimbu ni ni nyɛ ''corollary''.

Numerous technical tooi nyɛ in mathematics n nyɛ neologisms, kamani *[[polynomial|*'polynomial**]]'' ni ''[[homeomorphism|**homeomorphism*']]*. technical shɛŋa terms nyɛla bachinima bala shɛŋa din yɔli ka tum be accurate gbunni ni may differ slightly n yina bi gbunni shɛli din yɔli puuni. Ŋmahinli,  mathematics puuni, "bee" n-nyɛ "zaɣa yini, shɛli bee di zaa", ka, bal' shɛli din yɔli puuni, it is either ambiguous bee din wuhi"zaɣ' yini bee di shɛli amaa ka di zaa shɛli" (in mathematics, the latter n booni"din be kpaŋa bee"). Koobu,  mathematical pam terms nyɛla bachi shɛli din yɔli din daa zaŋ niŋ bɛ ti pali ni nyɛ gbunni shɛli din pa yim. din boŋɔ ni tooi taɣi din dɔni viɛnyɛla ni yɛlimaŋli  mathematical assertions, amaa ni yina n-nyɛ yɛltɔɣa yɔli n ti niriba ban ka bɔri din wuhi ani nyɛ so. Ŋmahinli, " module kam zaa din nyɛ alaha nyɛla zaɣ' pati" ni " field nyɛla alwa

## Kundivihira