The development of Arabic mathematics : between arithmetic and algebra
Rushdī Rāshid (Author)
"An understanding of the developments in Arabic mathematics between the IXth and the XVth century is vital to a full appreciation of the history of classical mathematics. This book draws together more than ten studies to highlight one of the major developments in Arabic mathematical thinking, provoked by the double fecundation between arithmetic and the algebra of al-Khwarizmi, which led to the foundation of diverse chapters of mathematics: polynomial algebra, combinatorial analysis, algebraic geometry, algebraic theory of numbers, Diophantine analysis, and numerical calculus. Thanks to epistemological analysis and the discovery of hitherto unknown material, the author has brought these chapters into the light, proposes another periodization for classical mathematics, and questions current ideology in writing its history." "Since the publication of the French version of these studies and of this book, its main results have been admitted by historians of Arabic mathematics, and integrated into their recent publications. This book is already a vital reference for anyone seeking to understand history of Arabic mathematics, and its contribution to Latin as well as to later mathematics. The English translation will be of particular value to historians and philosophers of mathematics and of science."--Jacket
History
x, 372 pages : illustrations ; 23 cm.
9780792325659, 0792325656
29181926
Ch. I. The Beginnings of Algebra. 1. Al-Khwarizmi's Concept of Algebra. 2. Al-Karaji. 3. The New Beginnings of Algebra in the Eleventh and Twelfth Centuries. 4. Mathematical Induction: al-Karaji and al-Samawal
Ch. II. Numerical Analysis: The Extraction of the nth Root and the Invention of Decimal Fractions (Eleventh to Twelfth Centuries)
Ch. III. Numerical Equations: The Solution of Numerical Equations and Algebra: Sharaf al-Din al-Tusi and Viete
Ch. IV. Number Theory and Combinatorial Analysis. 1. Diophantine Analysis in the Tenth Century: al-Khazin. 2. Ibn al-Haytham and Wilson's Theorem. 3. Algebra and Linguistics: Combinatorial Analysis in Arabic Science. 4. Amicable Numbers, Aliquot Parts and Figurate Numbers in the Thirteenth and Fourteenth Centuries. 5. Ibn al-Haytham and Perfect Numbers
Appendix 1: The Notion of Western Science: "Science as a Western Phenomenon"
Appendix 2: Periodization in Classical Mathematics
Translation of: Entre arithmʹetique et algèbre : recherches sur l'histoire des mathématiques arabes