The Mathematics of Levi ben Gershon

Simonson, Shai

doi:10.5951/mt.93.8.0659

Cited by 8 publications

(6 citation statements)

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“…Aslında bir problemi ilgi çekici yapan şey, yalnızca matematiksel içeriği değil, aynı zamanda belkide en önemlisi problemin neden dolayı ortaya çıktığıdır (Tzanakis & Thomaidis, 2000;van Maanen, 1991). Bu yüzden, öğrenciler her zaman için matematiksel gelişmeleri tetikleyen matematik tarihindeki problemleri, ders kitaplarında her bölümünün sonunda bulunan rutin alıştırma problemleri yerine yapmaktan çok daha istekli olacaklardır (Simonson, 2000;Swetz, 1989). Ayrıca, farklı zaman dilimlerinden ve kültürel kökenlerden gelen tarihi problemler, öğrencileri alternatif problem çözme stratejilerini değerlendirmeye ve karşılaştırmaya (Grugnetti, 2000), matematiksel ilişkileri kurmaya (Grugnetti & Rogers, 2000) ve daha derinlemesine araştırmalar ve incelemeler yapmaya itecektir (Reimer & Reimer, 1995;Wilson & Chauvot, 2000).…”

Section: Tutum öZ Yeterlik Motivasyon Kaygı Gibi Duyuşsal öZellikler üZerine Yapılan Vurgularunclassified

Matematik Tarihinin Matematik Öğretimine Entegrasyonu: Hârezmî’nin Tam Kareye Tamamlama Yöntemi

Genç

Karatş

2018

Kastamonu Üniversitesi Kastamonu Eğitim Dergisi

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The purpose of this study is to explore preservice elementary mathematics teachers' conceptions regarding the use of history of mathematics as a teaching tool, especially Al-Khwarizmi's method of completing the square in the learning and teaching of quadratic equations. The case study of qualitative research methods was used. The data were collected through semi-structured interviews with 10 teacher candidates. The results of the study revealed the conceptions of the influences of the use of history of mathematics, specifically Al-Khwarizmi's method of completing the square, in the teaching of quadratic equations on preservice elementary mathematics teachers' current mathematical knowledge, as well as the conceptions of the influences of the use of this method as a teaching instrument on their future teaching professions. It has been seen that using Al-Khwarizmi's method in mathematics teaching has provided prospective teachers with better understanding of the second-order equations by presenting different techniques to integrate them into teaching quadratic equations.

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Section: Tutum öZ Yeterlik Motivasyon Kaygı Gibi Duyuşsal öZellikler üZerine Yapılan Vurgularunclassified

Matematik Tarihinin Matematik Öğretimine Entegrasyonu: Hârezmî’nin Tam Kareye Tamamlama Yöntemi

Genç

Karatş

2018

Kastamonu Üniversitesi Kastamonu Eğitim Dergisi

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“…(the equation 3 r − 2 s = 1, with a musicological background, was solved by Levi ben Gershon in 1343-see Simonson 2005 for example), but for most of this section we shall consider only polynomial equations. It was Thue in 1909 who first proved that equations like x 3 − 2y 3 = 1621 in [12] have at most finitely many solutions, as a consequence of his improvement on Liouville's [7], but we have already observed the ineffectivity in that his method did not allow all the solutions to be found.…”

Section: Diophantine Equationsmentioning

confidence: 99%

Alan Baker. 19 August 1939—4 February 2018

FRS

2023

Biogr. Mems Fell. R. Soc.

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Alan Baker single-handedly transformed several areas of number theory. He achieved a major breakthrough in transcendence and applied it to obtain a new and important large class of transcendental numbers, opening the way to the subsequent discovery of several other such classes. He developed quantitative versions and applied them to the effective solutions of many classical diophantine equations as well as the first effective improvement on the 1844 result by Joseph Liouville (ForMemRS 1850) on diophantine approximation and the resolution of the celebrated Gauss Conjectures of 1801 on class numbers, not only h = 1 but also h = 2, of imaginary quadratic fields. He started the study of extensions to elliptic curves, opening the way to later generalizations to abelian varieties and commutative group varieties and in turn their applications to old and new problems in diophantine geometry. In 1970 he was awarded the Fields Medal at the International Congress in Nice on the basis of his outstanding work on linear forms in logarithms and its consequences. He received many other honours, including the prestigious University of Cambridge Adams Prize, and he was made an honorary fellow of University College London, a foreign fellow of the Indian Academy of Science, a foreign fellow of the National Academy of Sciences India, an honorary member of the Hungarian Academy of Sciences and a fellow of the American Mathematical Society.

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“…To warm up, let us show that there are at most finitely many positive integers

r, s

with

3^{r} - 2^{s} = 1621

(the equation

3^{r} - 2^{s} = 1

, with a musicological background, was already solved by Levi ben Gershon in 1343; see, for example, 〈9〉). Suppose that

H = \max {r, s}

is large, say

H ⩾ H_{0}

.…”

Section: Diophantine Equationsmentioning

confidence: 99%

Alan Baker, FRS, 1939–2018

Masser

2021

Bulletin of London Math Soc

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An excellent mathematician from whom I learnt a great deal; but I tended to follow my own lines of research.' Still, Chris Morley recalls a loud mathematical conversation between them in the Trinity Parlour, and they did write a paper together (see below). It seems that in later life he enjoyed imitating Davenport's Lancashire (Accrington) accent (and the writer has carried on this worthy tradition of imitating one's supervisor). He obtained his PhD in 1965 and MA in 1966, by which time he had already been awarded a Prize Fellowship for 1964-1968, also at Trinity. During this period, which included a year 1964-1965 at University College, he took on John Coates as a PhD student, and recalls also sharing responsibilities with Davenport in supervising T.

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The Mathematics of Levi ben Gershon

Cited by 8 publications

References 0 publications

Matematik Tarihinin Matematik Öğretimine Entegrasyonu: Hârezmî’nin Tam Kareye Tamamlama Yöntemi

Matematik Tarihinin Matematik Öğretimine Entegrasyonu: Hârezmî’nin Tam Kareye Tamamlama Yöntemi

Alan Baker. 19 August 1939—4 February 2018

Alan Baker, FRS, 1939–2018

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