Makemakika

Nā Helu a me ko lākou mau Waiwai ʻO nā helu helu kekahi o nā manaʻo kumu loa i ka makemakika, akā he kuleana koʻikoʻi ko lākou i ke ola o kēlā me kēia lā. Ke helu mākou i nā mea, hoʻoholo i nā mahana ma lalo o ka zero, helu i ka helu o nā papahele ma kahi hale papahele, a hoʻopaʻa paha i ka loaʻa kālā a me ka pohō ma kahi ʻoihana, ke hana nei mākou me nā helu helu. ʻO ka hoʻomaopopo ʻana i nā helu helu a me ko lākou mau waiwai e maʻalahi ai… E heluhelu hou aku

He Ala Wikiwiki e Hoʻoponopono ai i nā Pilikia Kaʻina Hana ʻO nā pilikia kaʻina hana (nā kaʻina hana helu) he ʻano pilikia maʻamau e ʻike pinepine ʻia i nā hoʻokolohua komo kula, nā hoʻokolohua koho hana, a me nā hoʻokolohua mākaukau maʻamau. He maʻalahi ka manaʻo: ua noi ʻia ʻoe e ʻimi i kahi ʻano ma kahi moʻo helu, a laila e hoʻoholo i ka helu aʻe (a i ʻole ka helu i nalowale). ʻOiai he mea paʻakikī paha lākou, hiki ke hoʻoponopono koke ʻia nā kaʻina hana inā ʻoe... E heluhelu hou aku

Nā Hana Trigonometry ma ka Astronomy ʻO Trigonometry kahi lālā o ka makemakika e aʻo ana i ka pilina ma waena o nā kihi a me nā lōʻihi o ka ʻaoʻao i loko o nā huinakolu. ʻOiai ua manaʻo pinepine ʻia he mea kula wale nō, ʻo ka trigonometry kekahi o nā "ʻōlelo nui" o ka astronomy. ʻO ka aneane o nā ana astronomy āpau—mai ka hoʻoholo ʻana i nā kūlana o nā hōkū, ka helu ʻana i nā mamao o nā mea lani, a hiki i ka wānana ʻana i nā eclipses—e pili ana i nā kihi, nā pōʻai, a me nā lakio trigonometric e like me sine, cosine, … E heluhelu hou aku

Nā Kumu o ke Kumumanaʻo Helu ʻO ke kumumanaʻo helu he lālā o ka makemakika e aʻo ana i nā waiwai o nā helu piha. ʻOiai ke ʻano maʻalahi—ʻoiai ʻo nā helu piha wale nō e komo pū me …, -2, -1, 0, 1, 2, …—loaʻa i ke kumumanaʻo helu kahi ʻano waiwai nui. Nui nā manaʻo koʻikoʻi i ka makemakika hou, ka cryptography, a me ka ʻepekema kamepiula i hoʻokumu ʻia i nā manaʻo kumu o ke kumumanaʻo helu, e like me ka divisibility, primeness, a me ka congruence. ʻO ka ʻatikala … E heluhelu hou aku

Nā Rula Permutation a me ka Hui Pū ʻana Ma ka makemakika, ʻoi aku hoʻi ma nā kahua o ka probability a me nā helu helu, hālāwai pinepine mākou i ka nīnau "ehia mau ala" e hiki ai ke hana i kahi hanana. No ka laʻana: ehia mau hoʻonohonoho noho hiki ke loaʻa no kahi hui o nā kānaka? Ehia mau ala e koho ai i nā lālā o ka hui mai kahi hui o nā haumāna? Pane ʻia nā nīnau e like me kēia me ka hoʻohana ʻana i nā lula permutation a me ka hui pū ʻana, ʻelua… E heluhelu hou aku

ʻO ke Kumumanaʻo o nā Polynomials a me ko lākou mau Waiwai ʻO nā polynomials (a i ʻole polynomials) kahi manaʻo nui i ka makemakika, i hoʻohana nui ʻia i ka algebra, calculus, statistics, a me ke kumu hoʻohālike ʻana i nā hanana honua maoli e like me ka ulu ʻana o ka heluna kanaka, nā trajectories neʻe, a me ka optimization. ʻOiai ko lākou maʻalahi, loaʻa i nā polynomials kahi ʻano i hoʻonohonoho pono ʻia a me nā waiwai koʻikoʻi e hoʻomaʻamaʻa i nā hana makemakika ʻōnaehana. Kūkākūkā kēia ʻatikala… E heluhelu hou aku

ʻO ka loiloi paʻakikī i ka makemakika ʻO ka loiloi paʻakikī kahi lālā o ka makemakika e aʻo ana i nā hana me nā helu paʻakikī a me ko lākou mau waiwai. ʻO nā helu paʻakikī, i kākau pinepine ʻia ma ke ʻano \( z = a + bi \) kahi \(a\) a me \(b\) he mau helu maoli a \(i^2 = -1\), i puka mua mai ma ke ʻano he mea hana no ka hoʻoponopono ʻana i nā kaulike quadratic ʻaʻohe aʻa maoli. … E heluhelu hou aku

Ke hoʻohana nei i nā Matrices Inverse: ʻO nā matrices inverse kahi manaʻo koʻikoʻi i ka algebra linear, i hoʻohana nui ʻia i ka makemakika i hoʻopili ʻia, ʻepekema, ʻenekinia, hoʻokele waiwai, a me ka ʻepekema ʻikepili. Hiki ke hoʻohana ʻia nā matrices inverse e hoʻoponopono i nā ʻōnaehana o nā kaulike linear, hana i nā hoʻololi inverse, a kōkua me nā helu like ʻole e pili ana i nā pilina ma waena o nā loli. Kūkākūkā kēia ʻatikala i ka wehewehe ʻana o kahi matrix inverse, nā koi no kona ola ʻana, a… E heluhelu hou aku

Kumumanaʻo Helu Kumu ʻO nā helu kumu kekahi o nā mea maʻalahi loa akā pohihihi loa i ka makemakika. He maʻalahi no ka mea he pololei ko lākou wehewehe ʻana: ʻo ka helu kumu he helu holoʻokoʻa nui aʻe ma mua o 1 nona nā mahele maikaʻi ʻelua wale nō: 1 a me ia iho. He mea pohihihi no ka mea, ʻoiai ua aʻo ʻia no nā tausani makahiki, nui nā nīnau kumu e pili ana iā lākou… E heluhelu hou aku

Nā Hoʻohana Maoli o nā Derivatives ʻO nā Derivatives kekahi o nā manaʻo koʻikoʻi loa i ka calculus, i manaʻo pinepine ʻia he abstract i ka wā i aʻo mua ʻia ai. Eia nō naʻe, aia nā derivatives i nā kūlana maoli he nui a mākou e hālāwai ai i kēlā me kēia lā—mai ka helu ʻana i ka wikiwiki o kahi kaʻa, a hiki i ka hoʻoholo ʻana i ka loaʻa kālā nui loa i kahi ʻoihana, a hiki i ke kumu hoʻohālike o ka laha ʻana o kahi maʻi. I ka ʻōlelo maʻalahi, hoʻohana ʻia nā derivatives e ana i ka wikiwiki o… Heluhelu hou aku