Algebraična in transcendentna števila ter njihova aproksimabilnost : magistrsko delo
Ipša, Simona
Najprej navedemo nekaj lastnosti in posebnih primerov iracionalnih števil ter definiramo algebraična in transcendentna števila. V drugem poglavju s pomočjo Hermitove metode dokažemo iracionalnost ...števil ▫$e$▫, ▫$\pi$▫ in ▫$e^r$▫, kjer je ▫$r$▫ neničelno racionalno število, ter še nekaterih drugih. V nadaljevanju povemo nekaj lastnosti algebraičnih števil ter dokažemo obstoj transcendentnih števil. V četrtem poglavju definiramo aproksimabilnost realnih števil z racionalnimi ter raziščemo red aproksimabilnosti racionalnih, iracionalnih ter še posebej algebraičnih števil. V petem poglavju dokažemo Rothov izrek, ki nam poda najvišji možni red aproksimabilnosti algebraičnih števil. Nato s pomočjo Hermitove metode dokažemo še transcedentnost števil ▫$e$▫, ▫$\pi$▫ ter ▫$e^r$▫, kjer je ▫$r$▫ neničelno racionalno število. V sedmem poglavju dokažemo, da je tudi število ▫$e^\alpha$▫, kjer je ▫$\alpha$▫ poljubno neničelno algebraično število, transcendentno.
Type of material - master's thesis
; adult, serious
Publication and manufacture - Ljubljana : [S. Ipša], 2008
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