History of Algebra Research Papers (original) (raw)

The operation of the supply was of great importance in the armed struggle and the national liberation army could not complete its revolutionary activities if the supply stopped. Therefore, the leadership of the revolution gave great importance to the process by regulating the rules that it strictly conducts and determining the powers of the people from the sources of catering in Tebessa.
At the beginning of the revolution, the supply was imposed on the people. Their houses and farms were the centers of supply of the mujahideen, and those assigned to them did not abide by a certain method. They worked according to the available conditions. What is important is that their movement in the framework of confidentiality is quick and strategic.
Later, the supply was organized according to the provisions of the rules of the conference of the fasting, so there is a so-called supply officer, who oversees all stages of the supply of procurement, transport, distribution and storage as well as rules governing the most functions and obligations of the supply committees the establishment of the camps and the imposition of state of emergency and the bombing of villages and dwawir and the establishment of prohibited areas and the construction of an electrified dam and follow the policy of the burning land.
.Key Words: Supply, people, revolution, supply officer, electrified dam.

- by
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- History of Algebra, Algerian War (History), Contemporary Algeria, revulotion algerien

Öz: Aralarında bir bağ olması şartıyla bilinenler vasıtasıyla bilinmeyenlere ulaşmanın yöntemlerinden biri olarak bilinen cebir, III/IX. yüzyılda Harezmî'nin hakkında ilk kez sistemli bir eser telif etmesiyle ilim dalı olma yolundaki ilk adımı attı. Bundan sonraki süreçte İslam matematikçileri bir taraftan hesap ilmini cebire uygulamak suretiyle cebirin hisâbîleşmesini, neticesinde de daha kullanışlı ve özgür olmasını temin ettiler, diğer taraftan da bu kullanışlı cebiri feraiz (miras hukuku), ticaret, mesâha ve mimari gibi alanlara tatbik ederek pratik fayda sağladılar. Bir ilim dalı olarak ortaya çıkışından yaklaşık beş buçuk asır sonra cebir ilmi yukarıda sayılan faaliyetlerle zirveye ulaşmıştı. Bu zirvenin önde gelen isimlerinden İbnü'l-Hâim önce Yâsemînî şerhi sonra manzumesi el-Mukni' ve şerhi el-Mümti' ile geniş bir zaman ve mekâna yayılan bir tesir yarattı. Ancak ikincisi belki ilkinin gölgesinde kaldığından, belki de el-Mukni'nin diğer şerhleri arasında gözden kaçtığından şimdiye kadar herhangi bir çalışmaya konu olmamıştır. Hâlbuki el-Mümti' gerek mevcut cebirsel kavram ve yöntemlerin tamamını bir araya getirmesi, gerekse de İslam medeniyeti matematik tarihi boyunca cebir ilminin hisâbî mi, hendesî mi, yoksa hisâbî+hendesî mi karakterde olması gerektiği veya hangisinin cebir ilminin gelişimine daha fazla katkı sağlayacağı yönündeki soru(n)ları ve bunların felsefi boyutlarını tartışmaya açması bakımından matematik tarihi çalışmalarına yön verecek niteliktedir. İşte bu yüzden makalenin konusu, İbnü'l-Hâim'in el-Mümti' fî şerhi'l-Mukni' adlı eserinin matematik tarihindeki konumuna, öne çıkan özellikleriyle tanıtımına ve matematiksel incelemesine tahsis edilmiştir. Abstract: Algebra, defined as a method to determine the unknown by means of what is known, given the link between the two, took its initial steps toward disciplinary status during the third/ninth century when al-Khwārizmī produced the first systematic study on the subject. Later Muslim mathematicians followed his lead due to this novel discipline's propensity for improvement and beneficial application. Thus they applied arithmetic to algebra to make it more practical and open and, as a result, derived great benefits from employing it in matters of inheritance, commerce, land surveys, architecture, and other areas. Roughly 550 years after its formation as a discipline, algebra reached its peak in the aforementioned areas. One of its most famous practitioners, Ibn al-Hā'im, had a lasting and widespread influence first with his commentary on Yāsamīnī and then with his versified work al-Muqni' and its commentary al-Mumti'. However, the latter work eluded the researchers' attention – perhaps it was overshadowed by the former or lost among the other commentaries – despite its remarkable presentation of the entire conceptual and methodical repertoire of algebra as it was known at that time, not to mention its analysis of the problems and discussion of the philosophical implications in a long-lasting debate on Islamic mathematical history: Should algebra be arithmetical, geometrical, or both? Which track would be more conducive to improving the discipline so it could break new ground in the historical studies of mathematics? Thus, this article seeks to present the status of Ibn al-Hāim's al-Mumti' fī sharh al-Muqni' in the history of mathematics, along with its outstanding features and mathematical analysis. * Bu çalışmayı yapmam konusunda beni teşvik eden, yönlendiren ve müellif nüshasını temin etmemde yardımcı olan İhsan Fazlıoğlu'na, ayrıca tashih ve teklifleri için makalenin anonim hakemlerine teşekkür ederim.

- by Ian Mascorro
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- History of Algebra, Algebra Learning
- by Henrik Kragh Sørensen
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- History of Mathematics, History of Algebra
- by Fabio BERTATO
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- Mathematics, Algebra, History of Ideas, Translation Studies
- by Elif Baga
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- History of Mathematics, History of Science, History of Algebra
- by Elif Baga
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- History of Mathematics, History of Science, History of Algebra, History of Astronomy

"Michel Weber, Whitehead's Pancreativism. The Basics, Foreword by Nicholas Rescher, Frankfurt / Paris / Lancaster, ontos verlag, Process Thought VII, 2006. (278 p. ; ISBN 3-938793-15-5 ; 84 €)
There is one question that any potential reader who suspects that Alfred North Whitehead (1861–1947) might be important for past, contemporary, and future philosophy inevitably raises: how should I read Whitehead? How can I make sense of this incredibly dense tissue of imaginative systematizing, spread over decades of work in disciplines so different and specialized as algebra, geometry, logic, relativistic physics and philosophy of science? Accordingly, this monograph has two main objectives. The first one is to propose a set of efficient hermeneutical tools to get the reader started. These straightforward tools provide answers that are highly coherent and probably the most applicable to Whitehead’s entire corpus. The second objective is to illustrate how the several parts of Process and Reality are connected, something that all commentators have either failed to recognise or only incompletely acknowledged.
Table of Contents
Abbreviations
Foreword—Nicholas Rescher
Introduction
I. Historico-Conceptual Context
II. The Intertwining of Science, Philosophy and Religion
III. Process and Reality’s Goal and Method
IV. Creative Advance and Categoreal Scheme
V. Pancreativism
VI. Epochal Actuality and Types of Potentiality
VII. Conclusion
Bibliography
Analytic Table of Contents
"

- by Michel Weber
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- Evolutionary Psychology, Philosophy, Metaphysics, Ontology

En 1882, Richard Dedekind et Heinrich Weber proposent une re-définition algébraico-arithmétique de la notion de surface de Riemann utilisant les concepts et méthodes introduits par Dedekind en théorie des nombres algébriques.
Dans un effort pour regarder au-delà de l’idée d’une “approche conceptuelle”, ce travail se propose d’identifier les éléments de pratique propres à Dedekind, en partant de l’article co-écrit avec Weber. Nous mettons en avant l’idée selon laquelle, dans les travaux de Dedekind, l’arithmétique peut jouer un rôle actif et essentiel pour l’élaboration de connaissances mathématiques. Pour cela, nous proposons l’étude, dans la pratique mathématique, de la conception de l’arithmétique chez Dedekind, de la place donnée à et du rôle joué par les notions arithmétiques, et des possibles évolutions de ces idées dans les travaux de Dedekind. Cette étude est faite par l’examen serré d’une sélection de textes. Dans un premier temps, sont étudiés les premiers travaux de Dedekind, son Habilitationsvortrag en 1854 et ses premières recherches en théorie des nombres. Suite à cela, nous proposons une comparaison des deux premières versions de la théorie des nombres algébriques publiée par Dedekind en 1871 et 1877. Enfin, ayant mis en évidence le rôle central de l’arithmétique, pour les mathématiques dedekindiennes, nous nous tournons vers les travaux fondationnels de Dedekind, afin d’expliciter la spécificité de sa conception en élucidant, à travers ses travaux sur la définition des nombres, ce qui donne à l’arithmétique cette place de choix et les liens avec la définition des entiers naturels donnée dans le fameux Was sind und was sollen die Zahlen? en 1888.

Algebra, defined as a method to determine the unknown by means of what is known, given the link between the two, took its initial steps toward disciplinary status during the third/ninth century when al-Khwārizmī produced the first systematic study on the subject. Later Muslim mathematicians followed his lead due to this novel discipline’s propensity for improvement and beneficial application. Thus they applied arithmetic to algebra to make it more practical and open and, as a result, derived great benefits from employing it in matters of inheritance, commerce, land surveys, architecture, and other areas. Roughly 550 years after its formation as a discipline, algebra reached its peak in the aforementioned areas. One of its most famous practitioners, Ibn al-Hā’im, had a lasting and widespread influence first with his commentary on Yāsamīnī and then with his versified work al-Muqni‘ and its commentary al-Mumti‘. However, the latter work eluded the researchers’ attention – perhaps it was overshadowed by the former or lost among the other commentaries – despite its remarkable presentation of the entire conceptual and methodical reper-toire of algebra as it was known at that time, not to mention its analysis of the problems and discussion of the philosophical implications in a long-lasting debate on Islamic mathematical history: Should algebra be arithmetical, geometrical, or both? Which track would be more conducive to improving the discipline so it could break new ground in the historical studies of mathematics? Thus, this article seeks to present the status of Ibn al-Hāim’s al-Mumti‘ fī sharh al-Muqni‘ in the history of mathematics, along with its outstanding features and mathematical analysis.
Keywords: mathematics, algebra, Ibn Haim, al-Muqni, al-mumti.

- by Elif Baga
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- History of Mathematics, History of Science, History of Algebra

En este artículo se realiza una revisión del desarrollo histórico-epistemológico del álgebra. Indagamos acerca de su surgimiento desde la prehistoria hasta tiempos actuales; examinamos los aportes de la cultura egipcia, babilónica y china, entre otras, junto con un análisis del impacto que realizaron los árabes y los griegos en esta materia; y se muestra el tránsito hacia la consolidación del álgebra elemental, lineal, multilineal, homológica, conmutativa, no conmutativa y Booleana. Considerando estos antecedentes, presentamos una primera aproximación hacia una teoría del álgebra que considera distintas representaciones de ella, como es el significado intuitivo, clásico y matemático-axiomático.

- by Angel Alsina
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- Algebra, History of Mathematics, Mathematics Education, History of Algebra

Keywords: Geometric vs algebraic constructions Ontological and historical differences Synthesis and applications Eastern and western traditions Measurement Space Biological evolution and mathematics a b s t r a c t The human attempts to access, measure and organize physical phenomena have led to a manifold construction of mathematical and physical spaces. We will survey the evolution of geometries from Euclid to the Algebraic Geometry of the 20th century. The role of Persian/Arabic Algebra in this transition and its Western symbolic development is emphasized. In this relation, we will also discuss changes in the ontological attitudes toward mathematics and its applications. Historically, the encounter of geometric and algebraic perspectives enriched the mathematical practices and their foundations. Yet, the collapse of Euclidean certitudes, of over 2300 years, and the crisis in the mathematical analysis of the 19th century, led to the exclusion of " geometric judgments " from the foundations of Mathematics. After the success and the limits of the logico-formal analysis, it is necessary to broaden our foundational tools and reexamine the interactions with natural sciences. In particular, the way the geometric and algebraic approaches organize knowledge is analyzed as a cross-disciplinary and cross-cultural issue and will be examined in Mathematical Physics and Biology. We finally discuss how the current notions of mathematical (phase) " space " should be revisited for the purposes of life sciences.

- by Arezoo Islami and +1
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- Philosophy of Science, Philosophy Of Mathematics, History of Algebra, History and Philosophy of Physics
- by Romain Peter
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- History of Algebra, Edmund Husserl, Jean Cavaillès, Histoire Des Mathématiques

Takıyyüddin Râsıd (ö. 993/1585), Osmanlı riyâzî ilimler geleneğinin en önemli temsilcilerinden biridir. Günümüze ulaşan eserlerinden araştırmalarını astronomi, astronomi aletleri, matematik, optik, mekanik ve fizik konularında yoğunlaştırdığı anlaşılır. Osmanlı'nın tek rasathanesi olan İstanbul Rasathanesi'ni kurması ve yönetmesi, Râsıd'ı birçok yönden önemli bir figür haline getirmiştir. Ancak mezkûr öneme rağmen onun öğrendiği, öğrettiği, ürettiği ve kullandığı matematik çok az sayıda araştırmaya konu olmuştur. Halbuki yapılan bir işin veya üretilen bir eserin niteliğini ve seviyesini belirlemenin önde gelen yolu, nasıl bir "alet" ile meydana getirildiğine bakmaktır. Dolayısıyla bu makalede, riyâzî ilimlerde tebarüz etmiş bilginlerin ilmî karakteri ve kariyerini ortaya koymanın, matematik eserlerinin tahlilinden geçtiği tezinden yola çıkılarak Takıyyüddin Râsıd 'ın cebir risalesinin editio princeps, tercüme ve değerlendirmesi sunulacaktır. Cebir ilminin, herhangi bir konuda, mikdârî veya adedî fark etmeksizin karşılaşılan tüm problemlere uygulanabilme mizacı, mezkûr tezi ve dolayısıyla makalenin amacını daha anlamlı hale getirir. Klasik matematik eserlerinin sahih bir tetkiki için öncelikle orijinal metnin doğrulanması ve kolay bir okuyuş sağlayacak surete sokulması, ardından söz konusu dile kazandırılması ve son olarak matematiksel tahlil ve tarihsel değerlendirmeye tabi tutulması gerekliliği de makalenin ana yapısı ve muhtevasının gerekçesini açıklar.

- by Elif Baga
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- History of Mathematics, History of Algebra, History of Ottoman Science

Taqī al-Dīn al-Rāṣid is one of the most important representatives of the Ottoman tradition on mathematical sciences. His research focus being on astronomy, astronomical instruments, mathematics, optics, mechanics, and physics is understood from his surviving works. Taqī al-Dīn's establishment and management of the Istanbul Observatory, which was the first observatory in the Ottoman Empire, made him an important figure in many ways. However, despite the aforementioned importance, the mathematics he learned, taught, produced and used has been a subject for very few studies. The primary way of determining the quality and the level of a work is to look at the kind of tools used for its creation. Therefore, this article will present the edition princeps, the translation and the evaluation of Taqī al-Dīn al-Rāṣid's treatise on algebra, al-Nisab al-mutashākila fī ʻilm al-jabr wa-l-muqābala. It will be presented in the context of the idea that revealing a scientific character and the career of scholars who stand out in mathematical sciences can be possible by analyzing their mathematical works. The nature of the science of algebra, which can be applied to any problem encountered on any subject regardless of geometry or arithmetic, makes this idea more meaningful. For the correct examination of classical mathematical works, first the original text is verified and transformed into a format that provides an easy reading, then it is to be translated into the desired language. Finally a mathematical analysis and historical evaluation are needed to explain the main structure and justification of the content of the article.

Ce travail est une étude sur la méthode de Fermat pour le maximum et minimum. Fermat en parlait comme s' il s' agissait d'une méthode, mais il n'expliqua que quelques procédures. Nous reprenons les différentes procédures de Fermat et nous essayons de déterminer leur statut en tant que méthode. Celle-ci a, d'après Fermat, deux fondements: l'observation de Pappus à propos des extrêma et la syncrisis, ou comparaison entre équations quadratiques: la technique qui en découle fait usage de l'accroissement et de Yadaequatio (en termes modernes, f (a+ e) adégal à f (a)). Autrement dit, Fermat élabore l'expression algébrique de la comparaison de figures autour de l'extrêmum. La définition de la méthode de Fermat dépend égalememnt de sa diffusion parmi les contemporains, ainsi que de sa tradition parmi les savants. Nous parcourons donc les étapes de la transformation de la méthode, en privilégiant le Cursus mathematicus de Pierre Hérigone et la tradition de Van Schooten et Huygens, dont le rôle dans la diffusion de la méthode est mis en évidence par les nouveaux tomes de la Correspondance de Mersenne. En guise de conclusion, nous comparons la méthode de Fermat avec l'approche aux questions d'extrêma d'une théorie contemporaine, la géométrie différentielle synthétique, qui se réclame de Fermat.

The aim of this paper is to employ the newly contextualised historiographical category of ''premodern algebra'' in order to revisit the arguably most controversial topic of the last decades in the field of Greek mathematics, namely the debate on ''geometrical algebra''. Within this framework, we shift focus from the discrepancy among the views expressed in the debate to some of the historiographical assumptions and methodological approaches that the opposing sides shared. Moreover, by using a series of propositions related to Elem. II.5 as a case study, we discuss Euclid’s geometrical proofs, the so-called ''semi-algebraic'' alternative demonstrations attributed to Heron of Alexandria, as well as the solutions given by Diophantus, al-Sulamī, and al-Khwārizmī to the corresponding numerical problem. This comparative analysis offers a new reading of Heron’s practice, highlights the significance of contextualizing ''premodern algebra'', and indicates that the origins of algebraic reasoning should be sought in the problem-solving practice, rather than in the theorem-proving tradition.

- by Michalis Sialaros and +1
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- History of Mathematics, Philosophy Of Mathematics, History of Science, History of Algebra

Özet: Bu makalede, IX/XV. yüzyılda, muhtemelen Osmanlı topraklarında yaşamış meçhul bir müellifin yazdığı ve dönemin hükümdarı Sultan II. Bayezid'e sunduğu İrşâdu't-tullâb ilâ ilmi'l-hisâb adlı eserin hatimesinde yer alan, değişkenlerinin üsleri ardışık olmak şartıyla üç, dört, beş ve altıncı dereceden denklemlerin çözümünde kullandığı, tespitlerimize göre, o döneme kadar benzerine rastlanmayan bir yöntem tanıtılacaktır. Bunun için, öncelikle, konu ile ilgili kısa bir girişin ardından, üç ve daha yüksek dereceden denklemler ve çözüm yöntemlerinin tarihi hakkında özet bilgiler verilecek, daha sonra da eserin hatimesinin matematiksel tetkikine geçilecektir. Kısa bir sonuç ve değerlendirmenin sonunda yazma hâlindeki metnin tahkikli Arapça metni ve Türkçe tercümesi sunulacaktır. Anahtar Kelimeler: Yüksek Dereceden Denklemler, Osmanlılarda Cebir, Osmanlılarda Matematik, Denklem Çözme Yöntemleri, İrşadu't-tullab. Abstract: In this article, we will introduce a book, titled as Irshād al-tullāb ilā 'ilm al-hisāb, written by an anonymous author who probably lived in Ottoman lands and presented his book to Ottoman Sultan Bayezid II; and an equation solving method in the epilogue of the book, unknown up to its period according to our research, which he used to solve third, fourth, fifth and sixth degree equations whose degrees of variables are successively ordered. Following a short introduction on the subject, first we will summarize the history of solving methods for third and higher degree equations, and then we will examine the mathematical analysis of the book's epilogue. We will present, after a short conclusion, the Arabic text of the manuscript and its Turkish translation.

It's about the origins of math, and it's short.

- by Nathan Coppedge
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- History, Ancient History, Intellectual History, Cultural History
- by Valeriy Khan
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- Philosophy, Multiculturalism, Education, Persian Literature

In this essay, I will demonstrate the differences between Algeria and Tunisia that have been evident since before the end of World War II. The relationship with France proved during the 19th century quite tumultuous for the two Arab states in the conditions of the dome of colonialism under which the two countries were subjected. At the beginning of the twentieth century, the two states expressed through the formation of various political movements, the desire for liberation from French tutelage, which is very strong in the interwar period in order to suppress these movements by the power in Paris. I used four caricatures made during the period of evolution of the events to highlight, the opinion that the press had during those events and for a better understanding of the evolution of events. Tunisia and Algeria gained their independence in 1956 respectively 1962, which will lead until the time of the "Arab Spring" to a multitude of changes of power equaled by a permanent revolt by the population against the political systems of the two countries Introducere Întrebarea de la care am pornit în redactarea eseului de față: Au eșuat sau au evoluat Algeria și Tunisia ca națiuni?, este o adaptare la întrebarea: "De ce eșuează națiunile?" a lui Daron Agemoglu și James A. Robinson care pornesc în prefața cărții lor cu momentul incendierii tânărului vânzător ambulant, Mohamed Bouazizi, din decembrie 2010 care va deveni un factor din multitudine de factori ce au dus cu o lună mai târziu la renunțarea puterii de către Zine-el Abidine Ben Ali, președintele Tunisiei din 1987. 1 În ceea ce privește statul algerian, acesta este surprins de Primăvara Arabă prin izbugnirea unor proteste de stradă ale populației nemulțumite de starea deteriorată a economiei țării datorată admininstrației

- by Osvaldo Ottaviani
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- History of Mathematics, History of Algebra, Modality, Gottfried Wilhelm Leibniz
- by Giovanna Cifoletti
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- Early Modern History, History of Mathematics, History of Algebra

My core interest in the following concerns the possibility of a philosophical grammar. i call it an auxiliary structure and not an infrastructure, because referring to it or behaving in it needs thought that considers. Such a grammar allows for conception, of course, but the act of conception it structures is ampliative. i would like to consider the possibility for a philosophical grammar in which conceiving is engendering-by-inference. Ampliative inferences are inferences capable of broadening a terms extension beyond the possibilities that were contained in the premises. Such thinking- as-conceiving involves an aspect of inception, of beginnings. My interest, in short, is to regard artefacts as articulations of such a philosophical grammar, in pursuit of an architectonics that were proper to the city today.

- by Vera Bühlmann
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- Philosophy, Aesthetics, Philosophy Of Mathematics, History of Algebra
- by Fabio BERTATO
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- History of Mathematics, History of Science, History of Algebra, Girolamo Cardano

The aim of this paper is to clarify what is meant by the "invention of complex numbers'' by the Renaissance Italian algebraists Girolamo Cardano and Rafael Bombelli. The paper demonstrates that, despite the radix sophistica found in Cardano's Ars Magna that indicates the expressions apmbsqrt−1a \pm b\sqrt{-1}apmbsqrt−1, Cardano could not arithmetically operate with them, because he was not able to determine the sign of the square root of a negative number. Viceversa, Bombelli overcame this problem by inventing not "imaginary numbers'', but rather the new signs "plus of minus'' (più di meno) and "minus of minus'' (meno di meno) and their rules of composition. The radices sophisticae of Cardano and Bombelli were thus entities able to give meaning to Tartaglia's solution formula for a cubic equation in the irreducible case, just as the racines imaginaires of Albert Girard and René Descartes gave meaning to the first (weak) formulations of the Fundamental Theorem of Algebra. Ultimately, I show that in the late Renaissance the radice sophisticae or racines imaginaires were something quite different from the modern "complex numbers'', essentially because they appeared only as a useful tool to solve problems, and not yet as a true mathematical object to be studied.

In 1882, Richard Dedekind and HeinrichWeber offer an arithmetico-algebraic re-definition of the Riemann surface, using concepts and methods introduced by Dedekind in algebraic number theory. In an attempt to investigate Dedekind’s works beyond the mere idea of a “conceptual approach”, this works proposes to identify the elements of practice specific to Dedekind, starting from the paper co-written with Weber. I put forward the idea that in Dedekind’s works, arithmetic can play an essential and active role in the elaboration of mathematical knowledge. For this, I propose to study, in Dedekind’s mathematical practice, the conception of arithmetic, the place and role of arithmetical notions and the possible evolutions in Dedekind’s ideas about arithmetic. This study is based on a careful analysis of a selection of Dedekind’s texts. For this, I study Dedekind’s early works, his 1854 Habilitationsvortrag and his first works in number theory. Then, I propose a comparison between the first ...

Throughout E. T. Bell's writings on mathematics, both those aimed at other mathematicians and those for a popular audience, we find him endeavouring to promote abstract algebra generally, and the postulational method in particular. Bell evidently felt that the adoption of the latter approach to algebra (a process that he termed the `arithmetization of algebra') would lend the subject something akin to the level of rigour that analysis had achieved in the nineteenth century. However, despite promoting this point of view, it is not so much in evidence in Bell's own mathematical work. I offer an explanation for this apparent contradiction in terms of Bell's infamous penchant for mathematical `myth-making'.

- by Christopher Hollings
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- History of Mathematics, History of Algebra