DOCSLIB.ORG

A Tribute to C. S. Seshadri

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
A Tribute to C. S. Seshadri A Tribute to C. S. Seshadri Perspectives in Geometry and Representation Theory Volumes containing conference proceedings, lecture series, and collection of invited articles in any area of mathematics are published. The aim is to provide an overview of the development through surveys, recent trends, problems and their current status as well as historical background. All contributions for publication should be thoroughly reviewed before submitting to us. We need manuscripts ready for direct reproduction. All articles must be prepared in a uniform format. Necessary instructions for format etc., are available from the publisher. Already Published Volumes Algebra-Some Recent Advances Edited by I. B. S. Passi Number Theory Edited by R. P. Bambah, V. C. Dumir, R. J. Hans-Gill Number Theory and Discrete Mathematics Edited by A. K. Agarwal, Bruce C. Berndt, Christian F. Krattenthaler, Gray L. Mullen, K. Ramachandra and Michel Waldschmidt Current Trends in Number Theory Edited by S.D. Adhikari, S.A. Katre, B. Ramakrishnan Advances in Algebra and Geometry Edited by C. Musili A Tribute to C. S. Seshadri Perspectives in Geometry and Representation Theory Edited by V. Lakshmibai V. Balaji V. B. Mehta K. R. Nagarajan K. Pranjape P. Sankaran R. Sridharan ~HINDUSTAN U LQj UBOOKAGENCY Published by Hindustan Book Agency (India) Visit our home page at: http://www.hindbook.com VOLUME SPONSORED BY Chennai Mathematical Institute 92, G. N. Chetty Road, Chennai Copyright © 2003 by Hindustan Book Agency (India) No part of the material protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording or by any information storage and retrieval system, without written permission from the copyright owner, who has also the sole right to grant licences for translation into other languages and publication thereof. All export rights for this edition vest exclusively with Hindustan Book Agency (India). Unauthorized export is a violation of Copyright Law and is subject to legal action. ISBN 978-81-85931-39-5 ISBN 978-93-86279-11-8 (eBook) DOI 10.1007/978-93-86279-11-8 Contents Preface ................................................................ ix C.S. Seshadri - A Biographical Sketch ................................. xi List of Publications of C.S. Seshadri .................................. xiii List of Participants at the Symposium ................................ xvi Excerpts from Birthday Messages .. .. ...... .. ..................... xviii Part I Mathematical Contributions of C.S. Seshadri Talks given at the Symposium The Early Work of C.S. Seshadri S. Ramanan .. .. ................. .. .... ..... ..... ...................... 1 Geometry of Moduli Spaces (The Work of C.S. Seshadri) V. Balaji ............................ .................................. 6 Seshadri's Contributions to Moduli and Geometric Invariant Theory V.B. Mehta ........................................................... 16 Seshadri's Work on Moduli Spaces - The Case of Singular Curves D.S. Nagaraj ........ ... ......... .. ... ......... ............. ....... ... 20 Parabolic Bundles N. Nitsure ............................................................ 28 Seshadri's Work on Flag and Schubert Varieties V. Lakshmibai and C. Musili .......................................... 34 Seshadri and the Chennai Mathematical Institute K.R. Nagarajan ....................................................... 42 vi C.S. Seshadri's Impact on Education: A Computer Scientist's· Perspective M. Mukund ........................................................... 47 CMI's Undergraduate Programme and NBHM M.S. Raghunathan .................................................... 49 Part II - Invited Articles Translates of Polynomials S.S. Abhyankar, w.J. Heinzer, A. Sathaye ............................ 51 Orbits of Certain Endomorphisms of Nilmanifolds and Haus­ dorff Dimension C.S. Amvinda and P. Sankamn ...................................... 125 A Family of Quantum Stabilizer Codes Based on the Weyl Commutation Relations over a Finite Field V. Arvind and K.R. Parthasamthy ................................... 133 Principal Bundles, Parabolic Bundles, and Holomorphic Con­ nection 1. Biswas ............................................................ 154 The Cone of Effective One-Cycles of Certain G-Varieties M. Brion ............................................................ 180 Representations of Double Affine Lie Algebras V. Chari and Thang Le .............................................. 199 Poincare Series of Line Bundles on Varieties S.D. Cutkosky ........................................ ............... 220 Triple Canonical Covers of Varieties of Minimal Degree F.J. Gallego and B.P. Purnapmjna .................................. 241 Semistability and Semi simplicity in Representations of Low Height in Positive Characteristic S. Ilangovan, V.B. Mehta and A.J. Pammeswamn ................... 271 The Development of Standard Monomial Theory-II V. Lakshmibai ........................................................ 283 vii Maximal Subbundles and Gromov-Witten Invariants H. Lange and P. Newstead ........................................... 310 Bases for Representations, LS-Paths and Verma Flags P. Littelmann ........................................................ 323 Invariant Tensor Fields and Orbit Varieties for Finite Algebraic Transformation Groups M. Losik, P. W. Michor, and V.L. Popov ............................. 346 Generators of a General Ideal M.P. Murthy ......................................................... 379 The Development of Standard Monomial Theory-I C. Musili ............................................................ 385 Measures on the Circle Invariant Under z -+ Z2 and z -+ z3 M.G. Nadkarni ....................................................... 421 Affine Hecke Algebras, Cyclotomic Hecke Algebras, and Clif­ ford Theory A. Ram and J. Rammage ............................................ 428 The Helgason Fourier Transform for Symmetric Spaces R.P. Sarkar and A. Sitaram .......................................... 467 On Representations of Special Orthogonal Groups over Fields of Positive Characteristics S. Senthamaraikannan and K. V. Subrahmanyam ..................... 474 Equivariant Analogue of Grothendieck's Theorem for Vector Bundles on pI S. Kumar ............................................................ 500 Vector Bundles and Connections in Physics and Mathematics: Some Historical Remarks V.S. Varadarajan .................................................... 502 C.S. Seshadri Preface Seshadri turned seventy on March 1st, 2002. Some of his colleagues, friends and students in India and abroad decided to celebrate this occasion by holding a symposium to highlight Seshadri's contributions to mathe­ matics and to felicitate him. A one-day symposium was organised by The Chennai Mathematical Institute and the Institute of Mathematical Sciences, Chennai on March 1st, 2002, and held at The Hotel Residency. Invitations were sent to a large number of friends and admirers of Se­ shadri. Many of them attended the function and those who could not, sent in their greetings. The proceedings began with an inauguration by Prof. R. Balasubrama­ niam, the director of the Institute of Mathematical Sciences, Chennai. The academic session started with some of Seshadri's colleagues and students giving talks on various aspects of his mathematical contributions spread over nearly five decades. The speakers were: S. Ramanan, V. Balaji, V. Mehta, N. Nitsure, D.S. Nagaraj, C. Musili and V. Lakshmibai. This was followed by talks by K.R. Nagarajan and M. Mukund on the educational programme at CMI, initiated by Seshadri. The session concluded with a talk by M.S. Raghunathan on the National Board for Higher Mathematics and the role of CMI in mathematics education. Late in the afternoon, the invitees gathered to felicitate Seshadri, his mother Chudamani and his wife Sundari. Messages of greetings from many of his friends were read out. Several distinguished guests also spoke bringing out the multi-faceted personality of Seshadri. Seshadri, in his reply, recalled among other things the genesis of CMI and the key role played by the late Dr. S. Parthasarathy and Shri A.C. Muthiah in its development. The day, which was marked by warmth and goodwill, ended with a banquet in honour of Seshadri. The help and cooperation extended by several individuals made the function a memorable one. Sripathy and his colleagues at the offfice of the CMI deserve special mention for their unstinted and enthusiastic support. About this volume: We thought that it would be appropriate to publish a volume in honour of Seshadri, containing the texts of the talks at the symposium as well as invited research and expository articles from some of his colleagues. The response to our invitation was spontaneous, and I want to thank all the authors who have contributed to this volume. The articles published here were refereed, and I am indebted to the referees for their gracious cooperation. I thank the Hindustan Book Agency, New Delhi for their immense help in bringing out this volume. Finally, I am x much obliged to my colleagues in the editorial board for their efforts which made this volume possible. v. Lakshmibai Chief Editor C.S. Seshadri A Biographical Sketch Conjeevaram Srirangachari SESHADRI was born on February 29th, 1932, in Kanchipuram (the "Golden City" turned into "Conjeevaram" dur­ ing the British Raj). He was the eldest among eleven children of his
Load more

Recommended publications
  • Notices of the American Mathematical Society June/July 2006
    of the American Mathematical Society ... (I) , Ate._~ f.!.o~~Gffi·u.­ .4-e.e..~ ~~~- •i :/?I:(; $~/9/3, Honoring J ~ rt)d ~cLra-4/,:e~ o-n. /'~7 ~ ~<A at a Gift from fL ~ /i: $~ "'7/<J/3. .} -<.<>-a.-<> ~e.Lz?-1~ CL n.y.L;; ro'T>< 0 -<>-<~:4z_ I Kumbakonam li .d. ~ ~~d a. v#a.d--??">ovt<.·c.-6 ~~/f. t:JU- Lo,.,do-,......) ~a page 640 ~!! ?7?.-L ..(; ~7 Ca.-uM /3~~-d~ .Y~~:Li: ~·e.-l a:.--nd '?1.-d- p ~ .di.,r--·c/~ C(c£~r~~u . J~~~aq_ f< -e-.-.ol ~ ~ ~/IX~ ~ /~~ 4)r!'a.. /:~~c~ •.7~ The Millennium Grand Challenge .(/.) a..Lu.O<"'? ...0..0~ e--ne_.o.AA/T..C<.r~- /;;; '7?'E.G .£.rA-CLL~ ~ ·d ~ in Mathematics C>n.A..U-a.A-d ~~. J /"-L .h. ?n.~ ~?(!.,£ ~ ~ &..ct~ /U~ page 652 -~~r a-u..~~r/a.......<>l/.k> 0?-t- ~at o ~~ &~ -~·e.JL d ~~ o(!'/UJD/ J;I'J~~Lcr~~ 0 ??u£~ ifJ>JC.Qol J ~ ~ ~ -0-H·d~-<.() d Ld.orn.J,k, -F-'1-. ~- a-o a.rd· J-c~.<-r:~ rn-u-{-r·~ ~'rrx ~~/ ~-?naae ~~ a...-'XS.otA----o-n.<l C</.J.d:i. ~~~ ~cL.va- 7 ??.L<A) ~ - Ja/d ~~ ./1---J- d-.. ~if~ ~0:- ~oj'~ t1fd~u: - l + ~ _,. :~ _,. .~., -~- .. =- ~ ~ d.u. 7 ~'d . H J&."dIJ';;;::. cL. r ~·.d a..L- 0.-n(U. jz-o-cn-...l- o~- 4; ~ .«:... ~....£.~.:: a/.l~!T cLc.·£o.-4- ~ d.v. /-)-c~ a;- ~'>'T/JH'..,...~ ~ d~~ ~u ~­ ~ a..t-4. l& foLk~ '{j ~~- e4 -7'~ -£T JZ~~c~ d.,_ .&~ o-n ~ -d YjtA:o ·C.LU~ ~or /)-<..,.,r &-.
    [Show full text]
  • Indian Mathematics
    Indian Mathemtics V. S. Varadarajan University of California, Los Angeles, CA, USA UCLA, March 3-5, 2008 Abstract In these two lectures I shall talk about some Indian mathe- maticians and their work. I have chosen two examples: one from the 7th century, Brahmagupta, and the other, Ra- manujan, from the 20th century. Both of these are very fascinating figures, and their histories illustrate various as- pects of mathematics in ancient and modern times. In a very real sense their works are still relevant to the mathe- matics of today. Some great ancient Indian figures of Science Varahamihira (505–587) Brahmagupta (598-670) Bhaskara II (1114–1185) The modern era Ramanujan, S (1887–1920) Raman, C. V (1888–1970) Mahalanobis, P. C (1893–1972) Harish-Chandra (1923–1983) Bhaskara represents the peak of mathematical and astro- nomical knowledge in the 12th century. He reached an un- derstanding of calculus, astronomy, the number systems, and solving equations, which were not to be achieved any- where else in the world for several centuries...(Wikipedia). Indian science languished after that, the British colonial occupation did not help, but in the 19th century there was a renaissance of arts and sciences, and Indian Science even- tually reached a level comparable to western science. BRAHMAGUPTA (598–670c) Some quotations of Brahmagupta As the sun eclipses the stars by its brilliancy, so the man of knowledge will eclipse the fame of others in assemblies of the people if he proposes algebraic problems, and still more, if he solves them. Quoted in F Cajori, A History of Mathematics A person who can, within a year, solve x2 92y2 =1, is a mathematician.
    [Show full text]
  • After Ramanujan Left Us– a Stock-Taking Exercise S
    Ref: after-ramanujanls.tex Ver. Ref.: : 20200426a After Ramanujan left us– a stock-taking exercise S. Parthasarathy [email protected] 1 Remembering a giant This article is a sequel to my article on Ramanujan [14]. April 2020 will mark the death centenary of the legendary Indian mathe- matician – Srinivasa Ramanujan (22 December 1887 – 26 April 1920). There will be celebrations of course, but one way to honour Ramanujan would be to do some introspection and stock-taking. This is a short survey of notable achievements and contributions to mathematics by Indian institutions and by Indian mathematicians (born in India) and in the last hundred years since Ramanujan left us. It would be highly unfair to compare the achievements of an individual, Ramanujan, during his short life span (32 years), with the achievements of an entire nation over a century. We should also consider the context in which Ramanujan lived, and the most unfavourable and discouraging situation in which he grew up. We will still attempt a stock-taking, to record how far we have moved after Ramanujan left us. Note : The table below should not be used to compare the relative impor- tance or significance of the contributions listed there. It is impossible to list out the entire galaxy of mathematicians for a whole century. The table below may seem incomplete and may contain some inad- vertant errors. If you notice any major lacunae or omissions, or if you have any suggestions, please let me know at [email protected]. 1 April 1920 – April 2020 Year Name/instit. Topic Recognition 1 1949 Dattatreya Kaprekar constant, Ramchandra Kaprekar number Kaprekar [1] [2] 2 1968 P.C.
    [Show full text]
  • Debashish Goswami Jyotishman Bhowmick Quantum Isometry Groups Infosys Science Foundation Series
    Infosys Science Foundation Series in Mathematical Sciences Debashish Goswami Jyotishman Bhowmick Quantum Isometry Groups Infosys Science Foundation Series Infosys Science Foundation Series in Mathematical Sciences Series editors Gopal Prasad, University of Michigan, USA Irene Fonseca, Mellon College of Science, USA Editorial Board Chandrasekhar Khare, University of California, USA Mahan Mj, Tata Institute of Fundamental Research, Mumbai, India Manindra Agrawal, Indian Institute of Technology Kanpur, India S.R.S. Varadhan, Courant Institute of Mathematical Sciences, USA Weinan E, Princeton University, USA The Infosys Science Foundation Series in Mathematical Sciences is a sub-series of The Infosys Science Foundation Series. This sub-series focuses on high quality content in the domain of mathematical sciences and various disciplines of mathematics, statistics, bio-mathematics, financial mathematics, applied mathematics, operations research, applies statistics and computer science. All content published in the sub-series are written, edited, or vetted by the laureates or jury members of the Infosys Prize. With the Series, Springer and the Infosys Science Foundation hope to provide readers with monographs, handbooks, professional books and textbooks of the highest academic quality on current topics in relevant disciplines. Literature in this sub-series will appeal to a wide audience of researchers, students, educators, and professionals across mathematics, applied mathematics, statistics and computer science disciplines. More information
    [Show full text]
  • Srinivasa Ramanujan Iyengar
    Srinivasa Ramanujan Iyengar Srinivasa Ramanujan Iyengar (Srinivāsa Rāmānujan Iyengār)() (December 22, 1887 – April 26, 1920) was an Indian mathematician widely regarded as one of the greatest mathematical minds in recent history. With almost no formal training in mathematics, he made profound contributions in the areas of analysis and number theory. A child prodigy, Ramanujan was largely self-taught and compiled nearly 3,884 theorems during his short lifetime. Although a small number of these theorems were actually false, most of his statements have now been proven to be correct. His deep intuition and uncanny algebraic manipulative ability enabled him to state highly original and unconventional results that have inspired a vast amount of research; however, some of his discoveries have been slow to enter the mathematical mainstream. Recently his formulae have begun to be applied in the field of crystallography and physics. The Ramanujan Journal was launched specifically to publish work "in areas of mathematics influenced by Ramanujan". With the encouragement of friends, he wrote to mathematicians in Cambridge seeking validation of his work. Twice he wrote with no response; on the third try, he found the English Mathematician G. H. Hardy. Ramanujan's arrival at Cambridge (March 1914) was the beginning of a very successful five-year collaboration with Hardy. One remarkable result of the Hardy-Ramanujan collaboration was a formula for the number p(n) exp(π 2n /3) of partitions of a number n: pn()∼ asn→∞.A partition of a positive integer n is just an expression for n as a sum of 43n positive integers, regardless of order.
    [Show full text]
  • A NEW APPROACH to UNRAMIFIED DESCENT in BRUHAT-TITS THEORY by Gopal Prasad
    A NEW APPROACH TO UNRAMIFIED DESCENT IN BRUHAT-TITS THEORY By Gopal Prasad Dedicated to my wife Indu Prasad with gratitude Abstract. We present a new approach to unramified descent (\descente ´etale") in Bruhat-Tits theory of reductive groups over a discretely valued field k with Henselian valuation ring which appears to be conceptually simpler, and more geometric, than the original approach of Bruhat and Tits. We are able to derive the main results of the theory over k from the theory over the maximal unramified extension K of k. Even in the most interesting case for number theory and representation theory, where k is a locally compact nonarchimedean field, the geometric approach described in this paper appears to be considerably simpler than the original approach. Introduction. Let k be a field given with a nontrivial R-valued nonarchimedean valuation !. We will assume throughout this paper that the valuation ring × o := fx 2 k j !(x) > 0g [ f0g of this valuation is Henselian. Let K be the maximal unramified extension of k (the term “unramified extension" includes the condition that the residue field extension is separable, so the residue field of K is the separable closure κs of the residue field κ of k). While discussing Bruhat-Tits theory in this introduction, and beginning with 1.6 everywhere in the paper, we will assume that ! is a discrete valuation. Bruhat- Tits theory of connected reductive k-groups G that are quasi-split over K (i.e., GK contains a Borel subgroup, or, equivalently, the centralizer of a maximal K-split torus of GK is a torus) has two parts.
    [Show full text]
  • Secondary Indian Culture and Heritage
    Culture: An Introduction MODULE - I Understanding Culture Notes 1 CULTURE: AN INTRODUCTION he English word ‘Culture’ is derived from the Latin term ‘cult or cultus’ meaning tilling, or cultivating or refining and worship. In sum it means cultivating and refining Ta thing to such an extent that its end product evokes our admiration and respect. This is practically the same as ‘Sanskriti’ of the Sanskrit language. The term ‘Sanskriti’ has been derived from the root ‘Kri (to do) of Sanskrit language. Three words came from this root ‘Kri; prakriti’ (basic matter or condition), ‘Sanskriti’ (refined matter or condition) and ‘vikriti’ (modified or decayed matter or condition) when ‘prakriti’ or a raw material is refined it becomes ‘Sanskriti’ and when broken or damaged it becomes ‘vikriti’. OBJECTIVES After studying this lesson you will be able to: understand the concept and meaning of culture; establish the relationship between culture and civilization; Establish the link between culture and heritage; discuss the role and impact of culture in human life. 1.1 CONCEPT OF CULTURE Culture is a way of life. The food you eat, the clothes you wear, the language you speak in and the God you worship all are aspects of culture. In very simple terms, we can say that culture is the embodiment of the way in which we think and do things. It is also the things Indian Culture and Heritage Secondary Course 1 MODULE - I Culture: An Introduction Understanding Culture that we have inherited as members of society. All the achievements of human beings as members of social groups can be called culture.
    [Show full text]
  • Tata Institute of Fundamental Research Prof
    Annual Report 1988-89 Tata Institute of Fundamental Research Prof. M. G. K. Menon inaugurating the Pelletron Accelerator Facility at TIFR on December 30, 1988. Dr. S. S. Kapoor, Project Director, Pelletron Accelerator Facility, explaining salient features of \ Ion source to Prof. M. G. K. Menon, Dr. M. R. Srinivasan, and others. Annual Report 1988-89 Contents Council of Management 3 School of Physics 19 Homi Bhabha Centre for Science Education 80 Theoretical Physics l'j Honorary Fellows 3 Theoretical A strophysics 24 Astronomy 2') Basic Dental Research Unit 83 Gravitation 37 A wards and Distinctions 4 Cosmic Ray and Space Physics 38 Experimental High Energy Physics 41 Publications, Colloquia, Lectures, Seminars etc. 85 Introduction 5 Nuclear and Atomic Physics 43 Condensed Matter Physics 52 Chemical Physics 58 Obituaries 118 Faculty 9 Hydrology M Physics of Semi-Conductors and Solid State Electronics 64 Group Committees 10 Molecular Biology o5 Computer Science 71 Administration. Engineering Energy Research 7b and Auxiliary Services 12 Facilities 77 School of Mathematics 13 Library 79 Tata Institute of Fundamental Research Homi Bhabha Road. Colaba. Bombav 400005. India. Edited by J.D. hloor Published by Registrar. Tata Institute of Fundamental Research Homi Bhabha Road, Colaba. Bombay 400 005 Printed bv S.C. Nad'kar at TATA PRESS Limited. Bombay 400 025 Photo Credits Front Cover: Bharat Upadhyay Inside: Bharat Upadhyay & R.A. A chary a Design and Layout by M.M. Vajifdar and J.D. hloor Council of Management Honorary Fellows Shri J.R.D. Tata (Chairman) Prof. H. Alfven Chairman. Tata Sons Limited Prof. S. Chandrasekhar Prof.
    [Show full text]
  • Sir Michael Atiyah the ASIAN JOURNAL of MATHEMATICS
    .'•V'pXi'iMfA Sir Michael Atiyah THE ASIAN JOURNAL OF MATHEMATICS Editors-in-Chief Shing-Tung Yau, Harvard University Raymond H. Chan, Chinese University of Hong Kong Editorial Board Richard Brent, Oxford University Ching-Li Chai, University of Pennsylvania Tony F. Chan, University of California, Los Angeles Shiu-Yuen Cheng, Hong Kong University of Science and Technology John Coates, Cambridge University Ding-Zhu Du, University of Minnesota Kenji Fulcaya, Kyoto University Hillel Furstenberg, Hebrew University of Jerusalem Jia-Xing Hong, Fudan University Thomas Kailath, Stanford University Masaki Kashiwara, Kyoto University Ka-Sing Lau, Chinese University of Hong Kong Jun Li, Stanford University Chang-Shou Lin, National Chung Cheng University Xiao-Song Lin, University of California, Riverside Raman Parimala, Tata Institute of Fundamental Research Duong H. Phong, Columbia University Gopal Prasad, Michigan University Hyam Rubinstein, University of Melbourne Kyoji Saito, Kyoto University Jalal Shatah, Courant Institute of Mathematical Sciences Saharon Shelah, Hebrew University of Jerusalem Leon Simon, Stanford University Vasudevan Srinivas, Tata Institue of Fundamental Research Srinivasa Varadhan, Courant Institute of Mathematical Sciences Vladimir Voevodsky, Northwestern University Jeff Xia, Northwestern University Zhou-Ping Xin, Courant Institute of Mathematical Sciences Horng-Tzer Yau, Courant Institute of Mathematical Sciences Mathematics in the Asian region has grown tremendously in recent years. The Asian Journal of Mathematics (ISSN 1093-6106), from International Press, provides a forum for these developments, and aims to stimulate mathematical research in the Asian region. It publishes original research papers and survey articles in all areas of pure mathematics, and theoretical applied mathematics. High standards will be applied in evaluating submitted manuscripts, and the entire editorial board must approve the acceptance of any paper.
    [Show full text]
  • Muramatsu's Method Aryabhata (499 AD) Brahmagupta (640 AD
    π in Other Eastern Countries Japan India In the Edo Period of Japan (1603 to 1868), 3.16 was used for π. But Aryabhata (499 AD) as people recognized that this value was not accurate, different values for π were calculated. Wasan scholars such as Muramatsu Shigekiyo, Seki Takakazu, Kamata Toshikiyo, Takebe Katahiro, and Matsunaga Aryabhata usedp the perimeter of a 384-sided poly- Yoshisuke all made calculations of π, and accomplished results gon to find π ≈ 9:8684. Later Aryabhata would comparable to their European mathematician counterparts. publish an “approximation” for his square root value, 3.1416. Note that his approximation is Muramatsu’s Method more accurate than his official value! Shigekiyo Muramatsu published Sanso in 1663. Muramatsu served the Asano family and possibly had a math insti- Brahmagupta (640 AD) tute in Edo (present day Tokyo). In his Brahmagupta used a pattern of inscribed polygons that work, Sanso, Muramatsu arranged prob- increased in the number of sides to calculate the perime- lems published earlier in Japanese math- ter of a circle.p Using these data points, he came to believe ematics texts without answers. Mura- that π = 10: matsu classified these problems into dif- ferent levels according to how difficult he thought they’d be to learn. Asano Crest It is in this book that he also showed the calculation of π from the regular inscribed polygon of 32,768 sides. He correctly obtained the Ramanujan (1887-1920) value 3.1415926. Thus, this book was the first to contain a mathematical calculation of π in Japan. 1 Srinivasa Ramanujan found several formulas for π.
    [Show full text]
  • Ancient India and Mathematics Sundar Sarukkai
    11 Ancient India and Mathematics Sundar Sarukkai ne way to approach this very broad topic is to list There are some things in all that the ancient Indian mathematicians did – common between Indian and Oand they did do an enormous amount of Greek Mathematics but there Mathematics: arithmetic (including the creation of decimal are also significant differences – place notation, the invention of zero), trigonometry (the not just in style but also in the detailed tables of sines), algebra (binomial theorem, larger world view (which influences, for solving quadratic equations), astronomy and astrology example, the completely different ways of understanding (detailed numerical calculations). Later Indian the nature of numbers in the Greek and the Indian Mathematics, the Kerala school, discovered the notions of traditions). This difference has led many writers to claim infinite series, limits and analysis which are the precursors that Indians (and Chinese among others) did not possess to calculus. the notions of Science and Mathematics. The first, and enduring response, to the question of Science and Since these details are easily available I am not going to list Mathematics in ancient non-Western civilizations is one of them here. What is of interest to me is to understand in skepticism. Did the Indians and Chinese really have Science what sense these activities were 'mathematical'. By doing and Mathematics as we call it now? This skepticism has so, I am also responding to the charge that these people been held over centuries and by the most prominent were not doing Mathematics but something else. This is a thinkers of the west (and is in fact so widespread as to charge similar to that addressed to Science in ancient India include claims that Indians did not 'have' philosophy, logic – the claim here is that what was being done in metallurgy, and even religion).
    [Show full text]
  • Editors Seek the Blessings of Mahasaraswathi
    OM GAM GANAPATHAYE NAMAH I MAHASARASWATHYAI NAMAH Editors seek the blessings of MahaSaraswathi Kamala Shankar (Editor-in-Chief) Laxmikant Joshi Chitra Padmanabhan Madhu Ramesh Padma Chari Arjun I Shankar Srikali Varanasi Haranath Gnana Varsha Narasimhan II Thanks to the Authors Adarsh Ravikumar Omsri Bharat Akshay Ravikumar Prerana Gundu Ashwin Mohan Priyanka Saha Anand Kanakam Pranav Raja Arvind Chari Pratap Prasad Aravind Rajagopalan Pavan Kumar Jonnalagadda Ashneel K Reddy Rohit Ramachandran Chandrashekhar Suresh Rohan Jonnalagadda Divya Lambah Samika S Kikkeri Divya Santhanam Shreesha Suresha Dr. Dharwar Achar Srinivasan Venkatachari Girish Kowligi Srinivas Pyda Gokul Kowligi Sahana Kribakaran Gopi Krishna Sruti Bharat Guruganesh Kotta Sumedh Goutam Vedanthi Harsha Koneru Srinath Nandakumar Hamsa Ramesha Sanjana Srinivas HCCC Y&E Balajyothi class S Srinivasan Kapil Gururangan Saurabh Karmarkar Karthik Gururangan Sneha Koneru Komal Sharma Sadhika Malladi Katyayini Satya Srivishnu Goutam Vedanthi Kaushik Amancherla Saransh Gupta Medha Raman Varsha Narasimhan Mahadeva Iyer Vaishnavi Jonnalagadda M L Swamy Vyleen Maheshwari Reddy Mahith Amancherla Varun Mahadevan Nikky Cherukuthota Vaishnavi Kashyap Narasimham Garudadri III Contents Forword VI Preface VIII Chairman’s Message X President’s Message XI Significance of Maha Kumbhabhishekam XII Acharya Bharadwaja 1 Acharya Kapil 3 Adi Shankara 6 Aryabhatta 9 Bhadrachala Ramadas 11 Bhaskaracharya 13 Bheeshma 15 Brahmagupta Bhillamalacarya 17 Chanakya 19 Charaka 21 Dhruva 25 Draupadi 27 Gargi
    [Show full text]