Nptel Course on Mathematics in India: from Vedic Period
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18 Medidas.Indd
Número 17 - 18. Nueva época 1.er y 2.º semestre de 2018 AWRAQRevista de análisis y pensamiento sobre el mundo árabe e islámico contemporáneo AWRAQRevista de análisis y pensamiento sobre el mundo árabe e islámico contemporáneo DIRECCIÓN Pedro Martínez-Avial, director general de Casa Árabe CONSEJO DE REDACCIÓN Karim Hauser Elena González Nuria Medina Olivia Orozco Javier Rosón SECRETARÍA DE AWRAQ [email protected] WEB Y SUSCRIPCIÓN www.awraq.es EDITORES Casa Árabe. c/ Alcalá, 62. 28009 Madrid (España) www.casaarabe.es Nota: Los artículos de la parte central de este número de Awraq son resultado del encuentro multidisciplinar que tuvo lugar en la sede de Casa Árabe en Córdoba del 20 al 22 de septiembre de 2017, en colaboración con la Fundación Ramón Areces y bajo la dirección académica de Mònica Rius Piniés (Universidad de Barcelona) y Cristina de la Puente (CSIC), bajo el título «Ciencia en al- Ándalus». El presente volumen cuenta con la coordinación académica de la profesora de la sección de Estudios Árabes del Departamento de Filología Clásica, Románica y Semítica de la Universidad de Barcelona Mònica Rius-Piniés. Copyright © Casa Árabe © de los textos: sus autores. © de los anuncios: los anunciantes. Todos los derechos reservados. Gráfica: Hurra! Estudio ISSN: 0214-834X Depósito legal: M-40073-1978 Imprenta: Imprenta Tecé Número 17-18. Nueva época 1.er y 2.º semestre de 2018 CARTA DEL DIRECTOR 3 EL TEMA: CIENCIA EN AL-ÁNDALUS Introducción. Mònica Rius 5 La ciencia en al-Ándalus y su papel como puente entre la ciencia árabe y la europea. Julio Samsó 9 Los sabios de origen andalusí y su aportación a la ciencia otomana. -
1. Essent Vol. 1
ESSENT Society for Collaborative Research and Innovation, IIT Mandi Editor: Athar Aamir Khan Editorial Support: Hemant Jalota Tejas Lunawat Advisory Committee: Dr Venkata Krishnan, Indian Institute of Technology Mandi Dr Varun Dutt, Indian Institute of Technology Mandi Dr Manu V. Devadevan, Indian Institute of Technology Mandi Dr Suman, Indian Institute of Technology Mandi AcknowledgementAcknowledgements: Prof. Arghya Taraphdar, Indian Institute of Technology Kharagpur Dr Shail Shankar, Indian Institute of Technology Mandi Dr Rajeshwari Dutt, Indian Institute of Technology Mandi SCRI Support teamteam:::: Abhishek Kumar, Nagarjun Narayan, Avinash K. Chaudhary, Ankit Verma, Sourabh Singh, Chinmay Krishna, Chandan Satyarthi, Rajat Raj, Hrudaya Rn. Sahoo, Sarvesh K. Gupta, Gautam Vij, Devang Bacharwar, Sehaj Duggal, Gaurav Panwar, Sandesh K. Singh, Himanshu Ranjan, Swarna Latha, Kajal Meena, Shreya Tangri. ©SOCIETY FOR COLLABORATIVE RESEARCH AND INNOVATION (SCRI), IIT MANDI [email protected] Published in April 2013 Disclaimer: The views expressed in ESSENT belong to the authors and not to the Editorial board or the publishers. The publication of these views does not constitute endorsement by the magazine. The editorial board of ‘ESSENT’ does not represent or warrant that the information contained herein is in every respect accurate or complete and in no case are they responsible for any errors or omissions or for the results obtained from the use of such material. Readers are strongly advised to confirm the information contained herein with other dependable sources. ESSENT|Issue1|V ol1 ESSENT Society for Collaborative Research and Innovation, IIT Mandi CONTENTS Editorial 333 Innovation for a Better India Timothy A. Gonsalves, Director, Indian Institute of Technology Mandi 555 Research, Innovation and IIT Mandi 111111 Subrata Ray, School of Engineering, Indian Institute of Technology Mandi INTERVIEW with Nobel laureate, Professor Richard R. -
BOOK REVIEW a PASSAGE to INFINITY: Medieval Indian Mathematics from Kerala and Its Impact, by George Gheverghese Joseph, Sage Pu
HARDY-RAMANUJAN JOURNAL 36 (2013), 43-46 BOOK REVIEW A PASSAGE TO INFINITY: Medieval Indian Mathematics from Kerala and its impact, by George Gheverghese Joseph, Sage Publications India Private Limited, 2009, 220p. With bibliography and index. ISBN 978-81-321-0168-0. Reviewed by M. Ram Murty, Queen's University. It is well-known that the profound concept of zero as a mathematical notion orig- inates in India. However, it is not so well-known that infinity as a mathematical concept also has its birth in India and we may largely credit the Kerala school of mathematics for its discovery. The book under review chronicles the evolution of this epoch making idea of the Kerala school in the 14th century and afterwards. Here is a short summary of the contents. After a brief introduction, chapters 2 and 3 deal with the social and mathematical origins of the Kerala school. The main mathematical contributions are discussed in the subsequent chapters with chapter 6 being devoted to Madhava's work and chapter 7 dealing with the power series for the sine and cosine function as developed by the Kerala school. The final chapters speculate on how some of these ideas may have travelled to Europe (via Jesuit mis- sionaries) well before the work of Newton and Leibniz. It is argued that just as the number system travelled from India to Arabia and then to Europe, similarly many of these concepts may have travelled as methods for computational expediency rather than the abstract concepts on which these algorithms were founded. Large numbers make their first appearance in the ancient writings like the Rig Veda and the Upanishads. -
The Kriyākramakarī's Integrative Approach to Mathematical Knowledge
History of Science in South Asia A journal for the history of all forms of scientific thought and action, ancient and modern, in all regions of South Asia The Kriyākramakarī’s Integrative Approach to Mathematical Knowledge Roy Wagner Eidgenössische Technische Hochschule Zürich MLA style citation form: Roy Wagner. “The Kriyākramakarī’s Integrative Approach to Mathematical Knowl- edge.” History of Science in South Asia, 6 (2018): 84–126. doi: 10.18732/hssa.v6i0.23. Online version available at: http://hssa-journal.org HISTORY OF SCIENCE IN SOUTH ASIA A journal for the history of all forms of scientific thought and action, ancient and modern, inall regions of South Asia, published online at http://hssa-journal.org ISSN 2369-775X Editorial Board: • Dominik Wujastyk, University of Alberta, Edmonton, Canada • Kim Plofker, Union College, Schenectady, United States • Dhruv Raina, Jawaharlal Nehru University, New Delhi, India • Sreeramula Rajeswara Sarma, formerly Aligarh Muslim University, Düsseldorf, Germany • Fabrizio Speziale, Université Sorbonne Nouvelle – CNRS, Paris, France • Michio Yano, Kyoto Sangyo University, Kyoto, Japan Publisher: History of Science in South Asia Principal Contact: Dominik Wujastyk, Editor, University of Alberta Email: ⟨[email protected]⟩ Mailing Address: History of Science in South Asia, Department of History and Classics, 2–81 HM Tory Building, University of Alberta, Edmonton, AB, T6G 2H4 Canada This journal provides immediate open access to its content on the principle that making research freely available to the public supports a greater global exchange of knowledge. Copyrights of all the articles rest with the respective authors and published under the provisions of Creative Commons Attribution-ShareAlike 4.0 License. -
October 1983 Table of Contents
Fairfield Meeting (October 28-29)- Page 614 San Luis Obispo Meeting (November 11-12)-Page 622 Evanston Meeting (November 11-12)-Page 630 Notices of the American Mathematical Society October 1983, Issue 228 Volume 30, Number 6, Pages 569- 712 Providence, Rhode Island USA ISSN 0002-9920 Calendar of AMS Meetings THIS CALENDAR lists all meetings which have been approved by the Council prior to the date this issue of the Notices was sent to press. The summer and annual meetings are joint meetings of the Mathematical Association of America and the Ameri· can Mathematical Society. The meeting dates which fall rather far in the future are subject to change; this is particularly true of meetings to which no numbers have yet been assigned. Programs of the meetings will appear in the issues indicated below. First and second announcements of the meetings will have appeared in earlier issues. ABSTRACTS OF PAPERS presented at a meeting of the Society are published in the journal Abstracts of papers presented to the American Mathematical Society in the issue corresponding to that of the Notices which contains the program of the meet· ing. Abstracts should be submitted on special forms which are available in many departments of mathematics and from the office of the Society in Providence. Abstracts of papers to be presented at the meeting must be received at the headquarters of the Society in Providence, Rhode Island, on or before the deadline given below for the meeting. Note that the deadline for ab· stracts submitted for consideration for presentation at special sessions is usually three weeks earlier than that specified below. -
An Anecdote on Mādhava School of Mathematics
Insight: An International Journal for Arts and Humanities Peer Reviewed and Refereed Vol: 1; Issue: 3 ISSN: 2582-8002 An Anecdote on Mādhava School of Mathematics Athira K Babu Research Scholar, Department of Sanskrit Sahitya, Sree Sankaracharya University of Sanskrit, Kalady, Abstract The Sanskrit term ‘Gaṇitaśāstra’, meaning literally the “science of calculation” is used for mathematics. The mathematical tradition of ancient India is an ocean of knowledge that is dealing with many topics such as the Vedic, Jain and Buddhist traditions, the mathematical astronomy, The Bhakshali manuscripts, The Kerala School of mathematics and the like. Thus India has made a valuable contribution to the world of mathematics. The origin and development of Indian mathematics are connected with Jyotiśāstra1. This paper tries to deconstructing the concept of mathematical tradition of Kerala with respect to Niḷā valley civilization especially under the background of medieval Kerala and also tries to look into the Mādhava School of mathematics through the life and works of great mathematician Mādhava of Saṅgamagrāma and his pupils who lived in and around the river Niḷā. Keywords: Niḷā, Literature review, Mathematical Tradition of medieval Kerala, Mādhava of Saṅgamagrāma, Great lineage of Mādhava. Introduction Niḷā, the Nile of Kerala is famous for the great ‘Māmāṅkam’ festival. The word ‘Niḷā’point out a culture more than just a river. It has a great role in the formation of the cultural life of south Malabar part of Kerala. It could be seen that the word ‘Peraar’ indicating the same river in ancient scripts and documents. The Niḷā is the life line of many places such as Chittur, Ottappalam, Shornur, Cheruthuruthy, Pattambi, Thrithala, Thiruvegappura, Kudallur, Pallippuram, Kumbidi, 1 The Sanskrit word used for Astronomy is Jyotiśāstra. -
Serilerin Ortaya Çikişi: Arşimet Ve Madhava Örneği
SERİLERİN ORTAYA ÇIKIŞI: ARŞİMET VE MADHAVA ÖRNEĞİ Yüksek Lisans Tezi Emre İNCEKALAN Eskişehir 2018 SERİLERİN ORTAYA ÇIKIŞI: ARŞİMET VE MADHAVA ÖRNEĞİ Emre İNCEKALAN YÜKSEK LİSANS TEZİ Matematik Anabilim Dalı Danışman: Prof. Dr. Bünyamin DEMİR Eskişehir Anadolu Üniversitesi Fen Bilimleri Enstitüsü Haziran 2018 JÜRİ VE ENSTİTÜ ONAYI Emre İNCEKALAN’ın “Serilerin Ortaya Çıkışı: Arşimet ve Madhava Örneği” başlıklı tezi 07/06/2018 tarihinde aşağıdaki jüri tarafından değerlendirilerek “Anadolu Üniversitesi Lisansüstü Eğitim-Öğretim ve Sınav Yönetmeliği”nin ilgili maddeleri uyarınca, Matematik Anabilim dalında Yüksek Lisans tezi olarak kabul edilmiştir. Jüri Üyeleri Unvanı Adı Soyadı İmza Üye (Tez Danışmanı) : Prof. Dr. Bünyamin DEMİR ……………………………… Üye : Prof. Dr. Ziya AKÇA ……………………………… Üye : Doç. Dr. Yunus ÖZDEMİR ……………………………… Prof. Dr. Ersin YÜCEL Fen Bilimleri Enstitüsü Müdürü ÖZET SERİLERİN ORTAYA ÇIKIŞI:ARŞİMET VE MADHAVA ÖRNEĞİ Emre İNCEKALAN Matematik Anabilim Dalı Anadolu Üniversitesi Fen Bilimleri Enstitüsü, Haziran 2018 Danışman: Prof. Dr. Bünyamin DEMİR Bu tezde, Arşimed’in bir parabol kesiminin alanını hesaplama yöntemi ve Madhava’nın seriler konusundaki çalışmaları, özellikle 휋 sayısını serilerle hesaplama yöntemi incelenmiştir. Bununla birlikte farklı medeniyetlerin serilerle ilgili yaklaşımlarına örnekler verilmiştir. Seriler XIX. yüzyıla gelininceye kadar farklı medeniyetlerde emekleme denilebilecek tarzda uygulama alanları bulmuştur. Örneğin Mısırlılarda ve Mezopotamyalılardaki serileri çağrıştıran örnekler incelendikten sonra, -
Craig Smoryński MVT: a Most Valuable Theorem MVT: a Most Valuable Theorem Craig Smoryński
Craig Smoryński MVT: A Most Valuable Theorem MVT: A Most Valuable Theorem Craig Smoryński MVT: A Most Valuable Theorem 123 Craig Smoryński Westmont, IL USA ISBN 978-3-319-52955-4 ISBN 978-3-319-52956-1 (eBook) DOI 10.1007/978-3-319-52956-1 Library of Congress Control Number: 2017931055 © Springer International Publishing AG 2017 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Printed -
Numbers 1 to 100
Numbers 1 to 100 PDF generated using the open source mwlib toolkit. See http://code.pediapress.com/ for more information. PDF generated at: Tue, 30 Nov 2010 02:36:24 UTC Contents Articles −1 (number) 1 0 (number) 3 1 (number) 12 2 (number) 17 3 (number) 23 4 (number) 32 5 (number) 42 6 (number) 50 7 (number) 58 8 (number) 73 9 (number) 77 10 (number) 82 11 (number) 88 12 (number) 94 13 (number) 102 14 (number) 107 15 (number) 111 16 (number) 114 17 (number) 118 18 (number) 124 19 (number) 127 20 (number) 132 21 (number) 136 22 (number) 140 23 (number) 144 24 (number) 148 25 (number) 152 26 (number) 155 27 (number) 158 28 (number) 162 29 (number) 165 30 (number) 168 31 (number) 172 32 (number) 175 33 (number) 179 34 (number) 182 35 (number) 185 36 (number) 188 37 (number) 191 38 (number) 193 39 (number) 196 40 (number) 199 41 (number) 204 42 (number) 207 43 (number) 214 44 (number) 217 45 (number) 220 46 (number) 222 47 (number) 225 48 (number) 229 49 (number) 232 50 (number) 235 51 (number) 238 52 (number) 241 53 (number) 243 54 (number) 246 55 (number) 248 56 (number) 251 57 (number) 255 58 (number) 258 59 (number) 260 60 (number) 263 61 (number) 267 62 (number) 270 63 (number) 272 64 (number) 274 66 (number) 277 67 (number) 280 68 (number) 282 69 (number) 284 70 (number) 286 71 (number) 289 72 (number) 292 73 (number) 296 74 (number) 298 75 (number) 301 77 (number) 302 78 (number) 305 79 (number) 307 80 (number) 309 81 (number) 311 82 (number) 313 83 (number) 315 84 (number) 318 85 (number) 320 86 (number) 323 87 (number) 326 88 (number) -
George Peacock's Arithmetic in the Changing Landscape of the History
George Peacock’s Arithmetic in the Changing Landscape of the History of Mathematics in India Agathe Keller To cite this version: Agathe Keller. George Peacock’s Arithmetic in the Changing Landscape of the History of Mathematics in India. Indian Journal of History of Science, 2011, 46 (2), pp.205-233. halshs-00149552v3 HAL Id: halshs-00149552 https://halshs.archives-ouvertes.fr/halshs-00149552v3 Submitted on 18 Dec 2017 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Distributed under a Creative Commons Attribution - NonCommercial - ShareAlike| 4.0 International License Indian Journal of History of Science, 46.2 (2011) 205-233 GEORGE PEACOCK’S ARITHMETIC IN THE CHANGING LANDSCAPE OF THE HISTORY OF MATHEMATICS IN INDIA AGATHE KELLER* (Received 4 May 2010; revised 11 February 2011) The changing landscape of the history of numbers and arithmetic in India at the beginning of the XXth century is examined, after a detour in mid-XIXth century France, through the debate that opposed G. R. Kaye to a group of Indian historians of mathematics and astronomy on the origins of the decimal place value position. This study highlights how Peacock’s historical analysis of algebra and arithmetic’s genesis seems to have been singular and isolated in mainstream histories of science. -
An Indian Form of Third Order Taylor Series
HISTORIA MATHEMATICA 1 /1974), 287-289 AN INDIAN FORMOF THIRD ORDERTAYLOR SERIES APPROXIMATIONOF THE SINE BY RADHA CHARAN GUPTA, BIRLA INSTITUTE OF TECHNOLOGY, RANCHI, INDIA SUMMARIES The paper describes an approximation formula for sine (x + h) that differs from the first four terms of the Taylor expansion only by having 4 in place of 6 in the denominator of the fourth term. It appears in Sanskrit stanzas quoted in a work of about the fifteenth century and given here with translation and explanation. Approximation formulas for the sine of x + h equivalent to the first two terms of the Taylor series expansion and to the first three terms were known from at least as early as the tenth century A.D. and the fourteenth century A.D. to Indian mathemati- cians [Sengupta 1932, 5; Gupta 1969, 92-941. An approximation formula equivalent to the first four terms, except that the denominator in the fourth term is 4 instead of 6, appears in a literary form in three stanzas quoted by Parameivara (circa 1360-1455) in his supercommentary, called Siddhlnta-dipikz, on Govindasvtiin's gloss (circa 800-850) on the Mahabhaskariya (about early seventh century) [Kuppanna Sastri 1957, 2051. Below we give the text in transliteration from the Siddhlnta- dipik;i and an almost literal translation of the Sanskrit stanzas. Then follows an explanation of the various steps in the rule laid down in the text. (The Indian sine, or Sine, of an angular arc $I is equal to R sin 9, where sin I+ is the modern sine of the angle 4 and R is the radius of the circle of reference). -
Indians Among the Exalted at ICM 2010 He Presence of Indian Mathematicians Number Theory, Combinatorial Number Theory, of Current Interest in Statistics
August 27, 2010 History of Mathe- On the footprints of Opinions Emmy Noether 3 5 matics in India 7 Indians Among the Exalted at ICM 2010 he presence of Indian mathematicians number theory, combinatorial number theory, of current interest in statistics. His work in Tamong the plenary and invited speakers elliptic curves and cryptography. In 1986, he multivariate analysis related to developing at ICM 2010 has been significantly more than solved the Waring problem for fourth powers geometric notions of multivariate quantiles is in the past. To be invited to deliver a plenary in collaboration with J-M. Deshouillers and F. considered a major breakthrough in the area or an invited lecture at an ICM is considered Dress. of multivariate nonparametric inference. More highly prestigious. recently, he has developed methods that en- Prof. Venkataramana has made significant able one to discover statistically significant While Prof. R. Balasubramanian of the Insti- contributions to algebraic groups and discrete features in the income distribution in different tute of Mathematical Sciences (IMSc), Chen- subgroups. He proved the positive character- populations. nai, delivered a Plenary Talk, Profs. V. istic version of the Margulis super-rigidity the- Srinivas and T. N. Venkataramana of the Tata orem and obtained important results on Prof. Arup Bose has made significant re- Institute of Fundamental Research (TIFR, cohomology of locally symmetric varieties. search contributions in resampling plans, se- Mumbai), Probal Chaudhuri and Arup Bose of quential analysis and asymptotics, statistics the Indian Statistical Institute (ISI), Kolkata, Prof. Srinivas has done significant work in as- of diffusion processes, rates of convergence, and V.