[過去ﾛｸﾞ] 純粋・応用数学・数学隣接分野（含むガロア理論）12 (1002ﾚｽ)

純粋・応用数学・数学隣接分野（含むガロア理論）12 http://rio2016.5ch.net/test/read.cgi/math/1671460269/

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764: 現代数学の系譜 雑談 ◆yH25M02vWFhP [] 2023/01/15(日) 14:08:22.48 ID:fdSQKtbP >>763 追加 ”CYCLOTOMIC FIELDS WITH APPLICATIONS” 188ページものPDF リンク貼る そこそこ纏まっている気がする あと、2018と新しいのが良い FFTとDFT（離散フーリエ）にも触れているが CYCLOTOMIC FIELDSが、FFTとDFTの基礎になっているみたいなニュアンスと読んだ file:///C:/Users/seta/Downloads/cyclotomic_fields2018.pdf CYCLOTOMIC FIELDS WITH APPLICATIONS 188ページもの Lecture Notes for Math 5590 Fall 2018 G. Eric Moorhouse University of Wyoming P44 The Fast Fourier Transform The Fast Fourier Transform (FFT) was known to Gauss at least as early as 1805 (predating Fourier, after whom the transform has been named). More recently, it was rediscovered by many others, notably Cooley and Tukey (1965). The point is that the Discrete Fourier Transform (DFT) over a large finite group, viewed as a square matrix, may appear quite large, requiring extensive time (presumably by a computer) in its computation. However due to the highly structured nature of this matrix, this computation can be performed in fewer steps than one might at first suppose. It is this faster approach to computing the DFT that accounts for the name FFT. The importance of this speedup is due to the vast number of problems requiring DFT for their solution, and where computational time required would otherwise be expensive or prohibitive. We begin by describing how the FFT works. We then give an application to fast multiplication for polynomials and for integer 略 P46 略 This is the idea of the FFT. Its applications are far too ubiquitous to be summarized here. We content ourselves with describing two of the many applications of FFT Fast Polynomial Multiplicatio (FFTの応用 以下P49まで) http://rio2016.5ch.net/test/read.cgi/math/1671460269/764

769: 現代数学の系譜 雑談 ◆yH25M02vWFhP [] 2023/01/15(日) 15:13:53.67 ID:fdSQKtbP >>764 追加 http://ericmoorhouse.org/handouts/cyclotomic_fields.pdf https://ericmoorhouse.org/handouts/ G. Eric Moorhouse: Handouts Number Theory 18．A first (very rough) working version of Cyclotomic Fields with Applications. Lecture notes for Fall 2018 course https://ericmoorhouse.org/ G Eric Moorhouse my email Department of Mathematics and Statistics University of Wyoming http://www.uwyo.edu/mathstats/people/faculty/moorhouse.html PROFESSOR ERIC MOORHOUSE Dr. Moorhouse Eric Moorhouse, Ph.D., University of Toronto Professor of Mathematics Ross Hall 216 Education Ph.D. Mathematics, University of Toronto, 1987 M.Sc. Mathematics, University of Toronto, 1984 B.Sc. Mathematics, University of Toronto, 1980 http://rio2016.5ch.net/test/read.cgi/math/1671460269/769

772: わかるすうがく 近谷蒙 ◆nSGM2Czuyoqf [sage] 2023/01/15(日) 15:39:39.59 ID:KCopoF1R >>763 >”n と m が互いに素な自然数の場合、 >2 つの円分体 Q(ξn) と Q(ξm) は線形に素になります。 >それらの合成 Q(ξn, ξm) は Q(ξnm) に等しく、Q(ξn) ∩ Q(ξm) = Q です” >だから、”Q(ζ55)には、虚数単位 i は含まれない”は、正しいね 三角関数の加法公式も、複素数の乗法も、全然分かってない 工業高校１年中退の君が、いくら闇雲に知識だけあさって拾い食いしても 腹壊すだけだから、高校数学から勉強しような　大学数学はその後だ >>764 まず三角関数から勉強しような　フーリエ変換はその後だ http://rio2016.5ch.net/test/read.cgi/math/1671460269/772

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