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Mathematical Achievements Of Pre Modern Indian Mathematicians

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Mathematical Achievements of Pre modern Indian Mathematicians

Mathematical Achievements of Pre modern Indian Mathematicians Book
Author : T.K Puttaswamy
Publisher : Newnes
Release : 2012-10-22
ISBN : 0123979382
Language : En, Es, Fr & De

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Book Description :

Mathematics in India has a long and impressive history. Presented in chronological order, this book discusses mathematical contributions of Pre-Modern Indian Mathematicians from the Vedic period (800 B.C.) to the 17th Century of the Christian era. These contributions range across the fields of Algebra, Geometry and Trigonometry. The book presents the discussions in a chronological order, covering all the contributions of one Pre-Modern Indian Mathematician to the next. It begins with an overview and summary of previous work done on this subject before exploring specific contributions in exemplary technical detail. This book provides a comprehensive examination of pre-Modern Indian mathematical contributions that will be valuable to mathematicians and mathematical historians. Contains more than 160 original Sanskrit verses with English translations giving historical context to the contributions Presents the various proofs step by step to help readers understand Uses modern, current notations and symbols to develop the calculations and proofs

A Passage to Infinity

A Passage to Infinity Book
Author : George Gheverghese Joseph
Publisher : SAGE Publications India
Release : 2009-12-10
ISBN : 8132104811
Language : En, Es, Fr & De

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Book Description :

This book traces the first faltering steps taken in the mathematical theorisation of infinity which marks the emergence of modern mathematics. It analyses the part played by Indian mathematicians through the Kerala conduit, which is an important but neglected part of the history of mathematics. Passage to Infinity: Medieval Indian Mathematics from Kerala and its Impact begins with an examination of the social origins of the Kerala School and proceeds to discuss its mathematical genesis as well as its achievements. It presents the techniques employed by the School to derive the series expansions for sine, cosine, arctan, and so on. By using modern notation but remaining close to the methods in the original sources, it enables the reader with some knowledge of trigonometry and elementary algebra to follow the derivations. While delving into the nature of the socio-economic processes that led to the development of scientific knowledge in pre-modern India, the book also probes the validity or otherwise of the conjecture of the transmission of Kerala mathematics to Europe through the Jesuit channel. The book straddles two domains: science and social sciences. It will appeal to those interested in mathematics, statistics, medieval history, history of science and technology, links between mathematics and culture and the nature of movements of ideas across cultures.

Studies in Indian Mathematics and Astronomy

Studies in Indian Mathematics and Astronomy Book
Author : Aditya Kolachana,K. Mahesh,K. Ramasubramanian
Publisher : Springer
Release : 2019-05-29
ISBN : 9811373264
Language : En, Es, Fr & De

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Book Description :

This volume presents a collection of some of the seminal articles of Professor K. S. Shukla who made immense contributions to our understanding of the history and development of mathematics and astronomy in India. It consists of six parts: Part I constitutes introductory articles which give an overview of the life and work of Prof. Shukla, including details of his publications, reminiscences from his former students, and an analysis of his monumental contributions. Part II is a collection of important articles penned by Prof. Shukla related to various aspects of Indian mathematics. Part III consists of articles by Bibhutibhusan Datta and Avadhesh Narayan Singh—which together constitute the third unpublished part of their History of Hindu Mathematics—that were revised and updated by Prof. Shukla. Parts IV and V consist of a number of important articles of Prof. Shukla on different aspects of Indian astronomy. Part VI includes some important reviews authored by him and a few reviews of his work. Given the sheer range and depth of Prof. Shukla’s scholarship, this volume is essential reading for scholars seeking to deepen their understanding of the rich and varied contributions made by Indian mathematicians and astronomers.

L l vat of Bh skar c rya

L  l  vat   of Bh  skar  c  rya Book
Author : Bhāskarācārya
Publisher : Motilal Banarsidass Publ.
Release : 2001
ISBN : 9788120814202
Language : En, Es, Fr & De

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Book Description :

In 1150 AD, Bhaskaracarya (b. 1114 AD), renowned mathematician and astronomer of Vedic tradition composed Lilavati as the first part of his larger work called Siddhanta Siromani, a comprehensive exposition of arithmetic, algebra, geometry, mensuration, number theory and related topics. Lilavati has been used as a standard textbook for about 800 years. This lucid, scholarly and literary presentation has been translated into several languages of the world. Bhaskaracarya himself never gave any derivations of his formulae. N.H. Phadke (1902-1973) worked hard to construct proofs of several mathematical methods and formulae given in original Lilavati. The present work is an enlargement of his Marathi work and attempts a thorough mathematical explanation of definitions, formulae, short cuts and methodology as intended by Bhaskara. Stitches are followed by literal translations so that the reader can enjoy and appreciate the beauty of accurate and musical presentation in Lilavati. The book is useful to school going children, sophomores, teachers, scholars, historians and those working for cause of mathematics.

The Mathematics of India

The Mathematics of India Book
Author : P. P. Divakaran
Publisher : Springer
Release : 2018-09-19
ISBN : 9811317747
Language : En, Es, Fr & De

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Book Description :

This book identifies three of the exceptionally fruitful periods of the millennia-long history of the mathematical tradition of India: the very beginning of that tradition in the construction of the now-universal system of decimal numeration and of a framework for planar geometry; a classical period inaugurated by Aryabhata’s invention of trigonometry and his enunciation of the principles of discrete calculus as applied to trigonometric functions; and a final phase that produced, in the work of Madhava, a rigorous infinitesimal calculus of such functions. The main highlight of this book is a detailed examination of these critical phases and their interconnectedness, primarily in mathematical terms but also in relation to their intellectual, cultural and historical contexts. Recent decades have seen a renewal of interest in this history, as manifested in the publication of an increasing number of critical editions and translations of texts, as well as in an informed analytic interpretation of their content by the scholarly community. The result has been the emergence of a more accurate and balanced view of the subject, and the book has attempted to take an account of these nascent insights. As part of an endeavour to promote the new awareness, a special attention has been given to the presentation of proofs of all significant propositions in modern terminology and notation, either directly transcribed from the original texts or by collecting together material from several texts.

Contributions to Statistics

Contributions to Statistics Book
Author : P. C. Mahalanobis
Publisher : Elsevier
Release : 2014-05-12
ISBN : 1483282805
Language : En, Es, Fr & De

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Book Description :

Contributions to Statistics focuses on the processes, methodologies, and approaches involved in statistics. The book is presented to Professor P. C. Mahalanobis on the occasion of his 70th birthday. The selection first offers information on the recovery of ancillary information and combinatorial properties of partially balanced designs and association schemes. Discussions focus on combinatorial applications of the algebra of association matrices, sample size analogy, association matrices and the algebra of association schemes, and conceptual statistical experiments. The book then examines lattice sampling by means of Lahiri's sampling scheme; contributions of interpenetrating networks of samples; and apparently unconnected problems encountered in sampling work. The publication takes a look at screening processes, place of the design of experiments in the logic of scientific inference, and rarefaction. Topics include mathematical probability, scientific experience, combinatorial progress, gains and losses, criterion and scores, simple drug screening process, and screening of crop varieties. The manuscript then reviews the estimation and interpretation of gross differences and the simple response variance; partially balanced asymmetrical factorial designs; and approximation of distributions of sums of independent summands by infinitely divisible distributions. The selection is a dependable reference for statisticians and researchers interested in the processes, methodologies, and approaches employed in statistics.

Math Unlimited

Math Unlimited Book
Author : R. Sujatha,H. N. Ramaswamy,C. S. Yogananda
Publisher : CRC Press
Release : 2011-11-11
ISBN : 1439876339
Language : En, Es, Fr & De

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Book Description :

This collection of essays spans pure and applied mathematics. Readers interested in mathematical research and historical aspects of mathematics will appreciate the enlightening content of the material. Highlighting the pervasive nature of mathematics today in a host of different areas, the book also covers the spread of mathematical ideas and techniques in areas ranging from computer science to physics to biology.

The Cambridge History of Science Volume 1 Ancient Science

The Cambridge History of Science  Volume 1  Ancient Science Book
Author : Alexander Jones,Liba Taub
Publisher : Cambridge University Press
Release : 2018-12-13
ISBN : 1108682626
Language : En, Es, Fr & De

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Book Description :

This volume in the highly respected Cambridge History of Science series is devoted to the history of science, medicine and mathematics of the Old World in antiquity. Organized by topic and culture, its essays by distinguished scholars offer the most comprehensive and up-to-date history of ancient science currently available. Together, they reveal the diversity of goals, contexts, and accomplishments in the study of nature in Mesopotamia, Egypt, Greece, Rome, China, and India. Intended to provide a balanced and inclusive treatment of the ancient world, contributors consider scientific, medical and mathematical learning in the cultures associated with the ancient world.

Harmonic Analysis on Semisimple Lie Groups

Harmonic Analysis on Semisimple Lie Groups Book
Author : Harish-Chandra
Publisher : Unknown
Release : 1969
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download Harmonic Analysis on Semisimple Lie Groups book written by Harish-Chandra, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Tantrasa graha of N laka ha Somay j

Tantrasa   graha of N  laka      ha Somay  j   Book
Author : K. Ramasubramanian,M. S. Sriram
Publisher : Springer Science & Business Media
Release : 2011-06-16
ISBN : 0857290363
Language : En, Es, Fr & De

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Book Description :

Tantrasangraha, composed by the renowned Kerala astronomer Nīlakantha Somayājī (c.1444-1545 AD) ranks along with Āryabhatīya of Āryabhata and Siddhāntaśiromani of Bhāskarācārya as one of the major works which significantly influenced further work on astronomy in India. One of the distinguishing features is the introduction of a major revision of the traditional Indian planetary model. Nīlakantha arrived at a unified theory of planetary latitudes and a better formulation of the equation of centre for the interior planets (Mercury and Venus) than was previously available. In preparing the translation and explanatory notes, K. Ramasubramanian and M. S. Sriram have used authentic Sanskrit editions of Tantrasangraha by Surand Kunjan Pillai and K V Sarma. All verses have been translated into English, which have been supplemented with detailed explanations including all necessary mathematical relations, illustrative examples, figures and tables using modern mathematical notation.

A Modern Introduction to Ancient Indian Mathematics

A Modern Introduction to Ancient Indian Mathematics Book
Author : T. S. Bhanu Murthy
Publisher : New Age International
Release : 1993
ISBN : 9788122403718
Language : En, Es, Fr & De

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Book Description :

The Purpose Of This Book Is To Draw The Attention Of Students And Teachers Of Mathematics To The Historical Continuity Of Indian Mathematics, Starting From The Sulba Sutras Of The Vedas Up To The 17Th Century. The Book Includes Proofs, Not Presented So Far, Of The Propositions Stated In The Well-Known Treatise Vedic Mathematics By Sri Bharati Krishna Teertha. It Also Introduces To The Modern Reader The Work Of Aryabhata, Brahmagupta, Bhaskara And Madhava.

The Man of Numbers

The Man of Numbers Book
Author : Keith Devlin
Publisher : A&C Black
Release : 2012-11-01
ISBN : 1408822482
Language : En, Es, Fr & De

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Book Description :

In 1202, a 32-year old Italian finished one of the most influential books of all time, which introduced modern arithmetic to Western Europe. Devised in India in the seventh and eighth centuries and brought to North Africa by Muslim traders, the Hindu-Arabic system helped transform the West into the dominant force in science, technology, and commerce, leaving behind Muslim cultures which had long known it but had failed to see its potential.The young Italian, Leonardo of Pisa (better known today as Fibonacci), had learned the Hindu number system when he traveled to North Africa with his father, a customs agent. The book he created was Liber abbaci, the 'Book of Calculation', and the revolution that followed its publication was enormous.Arithmetic made it possible for ordinary people to buy and sell goods, convert currencies, and keep accurate records of possessions more readily than ever before. Liber abbaci's publication led directly to large-scale international commerce and the scientific revolution of the Renaissance. Yet despite the ubiquity of his discoveries, Leonardo of Pisa remains an enigma. His name is best known today in association with an exercise in Liber abbaci whose solution gives rise to a sequence of numbers - the Fibonacci sequence - used by some to predict the rise and fall of financial markets, and evident in myriad biological structures. In The Man of Numbers, Keith Devlin recreates the life and enduring legacy of an overlooked genius, and in the process makes clear how central numbers and mathematics are to our daily lives.

Ga it nanda

Ga   it  nanda Book
Author : K. Ramasubramanian
Publisher : Springer Nature
Release : 2019-11-08
ISBN : 981131229X
Language : En, Es, Fr & De

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Book Description :

This book includes 58 selected articles that highlight the major contributions of Professor Radha Charan Gupta—a doyen of history of mathematics—written on a variety of important topics pertaining to mathematics and astronomy in India. It is divided into ten parts. Part I presents three articles offering an overview of Professor Gupta’s oeuvre. The four articles in Part II convey the importance of studies in the history of mathematics. Parts III–VII constituting 33 articles, feature a number of articles on a variety of topics, such as geometry, trigonometry, algebra, combinatorics and spherical trigonometry, which not only reveal the breadth and depth of Professor Gupta’s work, but also highlight his deep commitment to the promotion of studies in the history of mathematics. The ten articles of part VIII, present interesting bibliographical sketches of a few veteran historians of mathematics and astronomy in India. Part IX examines the dissemination of mathematical knowledge across different civilisations. The last part presents an up-to-date bibliography of Gupta’s work. It also includes a tribute to him in Sanskrit composed in eight verses.

Let s Play Math

Let s Play Math Book
Author : Denise Gaskins
Publisher : Tabletop Academy Press
Release : 2012-09-04
ISBN : 1892083248
Language : En, Es, Fr & De

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Book Description :

Download Let s Play Math book written by Denise Gaskins, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

The Soviet Study of International Relations

The Soviet Study of International Relations Book
Author : Allen Lynch
Publisher : Cambridge University Press
Release : 1989-07-28
ISBN : 9780521367639
Language : En, Es, Fr & De

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Book Description :

Current divergence from traditional Leninist orthodoxy is attributed to such phenomena as nuclear warfare, continued Western prosperity and the Sino-Soviet split, according to this systematic analysis of Soviet foreign policy.

Derivative with a New Parameter

Derivative with a New Parameter Book
Author : Abdon Atangana
Publisher : Academic Press
Release : 2015-09-18
ISBN : 012803825X
Language : En, Es, Fr & De

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Book Description :

Derivative with a New Parameter: Theory, Methods and Applications discusses the first application of the local derivative that was done by Newton for general physics, and later for other areas of the sciences. The book starts off by giving a history of derivatives, from Newton to Caputo. It then goes on to introduce the new parameters for the local derivative, including its definition and properties. Additional topics define beta-Laplace transforms, beta-Sumudu transforms, and beta-Fourier transforms, including their properties, and then go on to describe the method for partial differential with the beta derivatives. Subsequent sections give examples on how local derivatives with a new parameter can be used to model different applications, such as groundwater flow and different diseases. The book gives an introduction to the newly-established local derivative with new parameters, along with their integral transforms and applications, also including great examples on how it can be used in epidemiology and groundwater studies. Introduce the new parameters for the local derivative, including its definition and properties Provides examples on how local derivatives with a new parameter can be used to model different applications, such as groundwater flow and different diseases Includes definitions of beta-Laplace transforms, beta-Sumudu transforms, and beta-Fourier transforms, their properties, and methods for partial differential using beta derivatives Explains how the new parameter can be used in multiple methods

Mathematics in India

Mathematics in India Book
Author : Kim Plofker
Publisher : Princeton University Press
Release : 2009-01-18
ISBN : 9780691120676
Language : En, Es, Fr & De

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Book Description :

Based on extensive research in Sanskrit sources, Mathematics in India chronicles the development of mathematical techniques and texts in South Asia from antiquity to the early modern period. Kim Plofker reexamines the few facts about Indian mathematics that have become common knowledge--such as the Indian origin of Arabic numerals--and she sets them in a larger textual and cultural framework. The book details aspects of the subject that have been largely passed over in the past, including the relationships between Indian mathematics and astronomy, and their cross-fertilizations with Islamic scientific traditions. Plofker shows that Indian mathematics appears not as a disconnected set of discoveries, but as a lively, diverse, yet strongly unified discipline, intimately linked to other Indian forms of learning. Far more than in other areas of the history of mathematics, the literature on Indian mathematics reveals huge discrepancies between what researchers generally agree on and what general readers pick up from popular ideas. This book explains with candor the chief controversies causing these discrepancies--both the flaws in many popular claims, and the uncertainties underlying many scholarly conclusions. Supplementing the main narrative are biographical resources for dozens of Indian mathematicians; a guide to key features of Sanskrit for the non-Indologist; and illustrations of manuscripts, inscriptions, and artifacts. Mathematics in India provides a rich and complex understanding of the Indian mathematical tradition. **Author's note: The concept of "computational positivism" in Indian mathematical science, mentioned on p. 120, is due to Prof. Roddam Narasimha and is explored in more detail in some of his works, including "The Indian half of Needham's question: some thoughts on axioms, models, algorithms, and computational positivism" (Interdisciplinary Science Reviews 28, 2003, 1-13).

The Algebra of Mohammed Ben Musa Ed and Transl by Frederic Rosen

The Algebra of Mohammed Ben Musa  Ed  and Transl  by Frederic Rosen Book
Author : 'Abu Ja'far Muhammad ibn Musa al-Hwarizmi
Publisher : Unknown
Release : 1831
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download The Algebra of Mohammed Ben Musa Ed and Transl by Frederic Rosen book written by 'Abu Ja'far Muhammad ibn Musa al-Hwarizmi, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

The Crest of the Peacock

The Crest of the Peacock Book
Author : George Gheverghese Joseph,George Joseph Ghevarghese
Publisher : Penguin Group USA
Release : 1992
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Examines the early developments and uses of mathematics in such places as Egypt, Mesopotamia, China, and India

Native American Mathematics

Native American Mathematics Book
Author : Michael P. Closs
Publisher : University of Texas Press
Release : 2010-06-28
ISBN : 0292789815
Language : En, Es, Fr & De

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Book Description :

There is no question that native cultures in the New World exhibit many forms of mathematical development. This Native American mathematics can best be described by considering the nature of the concepts found in a variety of individual New World cultures. Unlike modern mathematics in which numbers and concepts are expressed in a universal mathematical notation, the numbers and concepts found in native cultures occur and are expressed in many distinctive ways. Native American Mathematics, edited by Michael P. Closs, is the first book to focus on mathematical development indigenous to the New World. Spanning time from the prehistoric to the present, the thirteen essays in this volume attest to the variety of mathematical development present in the Americas. The data are drawn from cultures as diverse as the Ojibway, the Inuit (Eskimo), and the Nootka in the north; the Chumash of Southern California; the Aztec and the Maya in Mesoamerica; and the Inca and Jibaro of South America. Among the strengths of this collection are this diversity and the multidisciplinary approaches employed to extract different kinds of information. The distinguished contributors include mathematicians, linguists, psychologists, anthropologists, and archaeologists.