Essays In The History Of Mathematics

Author : Bruce C. Berndt
Publisher : American Mathematical Soc.
Page : 388 pages
File Size : 49,7 Mb
Release : 2001
Category : Biography & Autobiography
ISBN : 0821826247

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Ramanujan: Essays and Surveys by Bruce C. Berndt Pdf

This book contains essays on Ramanujan and his work that were written especially for this volume. It also includes important survey articles in areas influenced by Ramanujan's mathematics. Most of the articles in the book are nontechnical, but even those that are more technical contain substantial sections that will engage the general reader. The book opens with the only four existing photographs of Ramanujan, presenting historical accounts of them and information about other people in the photos. This section includes an account of a cryptic family history written by his younger brother, S. Lakshmi Narasimhan. Following are articles on Ramanujan's illness by R. A. Rankin, the British physician D. A. B. Young, and Nobel laureate S. Chandrasekhar. They present a study of his symptoms, a convincing diagnosis of the cause of his death, and a thorough exposition of Ramanujan's life as a patient in English sanitariums and nursing homes. Following this are biographies of S. Janaki (Mrs. Ramanujan) and S. Narayana Iyer, Chief Accountant of the Madras Port Trust Office, who first communicated Ramanujan's work to the Journal of the Indian Mathematical Society. The last half of the book begins with a section on ``Ramanujan's Manuscripts and Notebooks''. Included is an important article by G. E. Andrews on Ramanujan's lost notebook. The final two sections feature both nontechnical articles, such as Jonathan and Peter Borwein's ``Ramanujan and pi'', and more technical articles by Freeman Dyson, Atle Selberg, Richard Askey, and G. N. Watson. This volume complements the book Ramanujan: Letters and Commentary, Volume 9, in the AMS series, History of Mathematics. For more on Ramanujan, see these AMS publications Ramanujan: Twelve Lectures on Subjects Suggested by His Life and Work, Volume 136.H, and Collected Papers of Srinivasa Ramanujan, Volume 159.H, in the AMS Chelsea Publishing series.

Author : Armand Borel
Publisher : American Mathematical Soc.
Page : 184 pages
File Size : 54,8 Mb
Release : 2001
Category : Mathematics
ISBN : 9780821802885

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Essays in the History of Lie Groups and Algebraic Groups by Armand Borel Pdf

Algebraic groups and Lie groups are important in most major areas of mathematics, occuring in diverse roles such as the symmetries of differential equations and as central figures in the Langlands program for number theory. In this book, Professor Borel looks at the development of the theory of Lie groups and algebraic groups, highlighting the evolution from the almost purely local theory at the start to the global theory that we know today. As the starting point of this passagefrom local to global, the author takes Lie's theory of local analytic transformation groups and Lie algebras. He then follows the globalization of the process in its two most important frameworks: (transcendental) differential geometry and algebraic geometry. Chapters II to IV are devoted to the former,Chapters V to VIII, to the latter.The essays in the first part of the book survey various proofs of the full reducibility of linear representations of $SL 2M$, the contributions H. Weyl to representation and invariant theory for Lie groups, and conclude with a chapter on E. Cartan's theory of symmetric spaces and Lie groups in the large.The second part of the book starts with Chapter V describing the development of the theory of linear algebraic groups in the 19th century. Many of the main contributions here are due to E. Study, E. Cartan, and above all, to L. Maurer. After being abandoned for nearly 50 years, the theory was revived by Chevalley and Kolchin and then further developed by many others. This is the focus of Chapter VI. The book concludes with two chapters on various aspects of the works of Chevalley on Lie groupsand algebraic groups and Kolchin on algebraic groups and the Galois theory of differential fields.The author brings a unique perspective to this study. As an important developer of some of the modern elements of both the differential geometric and the algebraic geometric sides of the theory, he has a particularly deep appreciation of the underlying mathematics. His lifelong involvement and his historical research in the subject give him a special appreciation of the story of its development.

Author : Niccol- Guicciardini
Publisher : Cambridge University Press
Page : 393 pages
File Size : 46,5 Mb
Release : 2021-07-22
Category : History
ISBN : 9781108834964

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Anachronisms in the History of Mathematics by Niccol- Guicciardini Pdf

Discover essays by leading scholars on the history of mathematics from ancient to modern times in European and non-European cultures.

Author : Arthur Schlissel
Publisher : Unknown
Page : 73 pages
File Size : 51,5 Mb
Release : 1984
Category : Mathematics
ISBN : 1470407086

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Essays in the History of Mathematics by Arthur Schlissel Pdf

Author : Arthur Schlissel
Publisher : Unknown
Page : 128 pages
File Size : 49,5 Mb
Release : 1984
Category : Electronic
ISBN : OCLC:36948205

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Essays in the History of Mathematics by Arthur Schlissel Pdf

Author : J. Ferreiros,J. J. Gray
Publisher : OUP Oxford
Page : 456 pages
File Size : 40,6 Mb
Release : 2006-04-27
Category : Mathematics
ISBN : 9780191513794

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The Architecture of Modern Mathematics by J. Ferreiros,J. J. Gray Pdf

This edited volume, aimed at both students and researchers in philosophy, mathematics and history of science, highlights leading developments in the overlapping areas of philosophy and the history of modern mathematics. It is a coherent, wide ranging account of how a number of topics in the philosophy of mathematics must be reconsidered in the light of the latest historical research, and how a number of historical accounts can be deepened by embracing philosophical questions.

Author : Joseph W. Dauben
Publisher : Academic Press
Page : 288 pages
File Size : 50,7 Mb
Release : 2014-05-10
Category : Mathematics
ISBN : 9781483262574

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Mathematical Perspectives by Joseph W. Dauben Pdf

Mathematical Perspectives: Essays on Mathematics and its Historical Development is a collection of 13 biographical essays on the historical advances of science. This collection is originally meant to comprise an issue of the journal Historia Mathematica in honor of Professor Kurt R. Biermann’s 60th birthday. This 12-chapter text includes essays on studies and commentaries on the problem of “figures of equal perimeter by various authors in antiquity, including Zenodorus, Theon, and Pappus. Other essays explore the comparison of the areas of polygons with equal perimeter; the concept of function; history of mathematics; the development of mathematical physics in France; and the history of Logicism and Formalism. The remaining chapters deal with essays on an early version of Gauss’ Disquisitiones Arithmeticae, ideal numbers, a mathematical-philosophilica theory of probability, and historical examples of problem of number sequence interpolation. This book will be of value to mathematicians, historians, and researchers.

Author : Johann Pfanzagl
Publisher : Springer
Page : 316 pages
File Size : 43,5 Mb
Release : 2017-10-23
Category : Mathematics
ISBN : 9783642310843

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Mathematical Statistics by Johann Pfanzagl Pdf

This book presents a detailed description of the development of statistical theory. In the mid twentieth century, the development of mathematical statistics underwent an enduring change, due to the advent of more refined mathematical tools. New concepts like sufficiency, superefficiency, adaptivity etc. motivated scholars to reflect upon the interpretation of mathematical concepts in terms of their real-world relevance. Questions concerning the optimality of estimators, for instance, had remained unanswered for decades, because a meaningful concept of optimality (based on the regularity of the estimators, the representation of their limit distribution and assertions about their concentration by means of Anderson’s Theorem) was not yet available. The rapidly developing asymptotic theory provided approximate answers to questions for which non-asymptotic theory had found no satisfying solutions. In four engaging essays, this book presents a detailed description of how the use of mathematical methods stimulated the development of a statistical theory. Primarily focused on methodology, questionable proofs and neglected questions of priority, the book offers an intriguing resource for researchers in theoretical statistics, and can also serve as a textbook for advanced courses in statisticc.

Author : Harold M. Edwards
Publisher : Springer Nature
Page : 325 pages
File Size : 53,6 Mb
Release : 2022-09-29
Category : Mathematics
ISBN : 9783030985585

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Essays in Constructive Mathematics by Harold M. Edwards Pdf

Contents and treatment are fresh and very different from the standard treatments Presents a fully constructive version of what it means to do algebra The exposition is not only clear, it is friendly, philosophical, and considerate even to the most naive or inexperienced reader

Author : Menso Folkerts
Publisher : Taylor & Francis
Page : 384 pages
File Size : 46,6 Mb
Release : 2023-06-14
Category : History
ISBN : 9781000941364

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Essays on Early Medieval Mathematics by Menso Folkerts Pdf

This book deals with the mathematics of the medieval West between ca. 500 and 1100, the period before the translations from Arabic and Greek had their impact. Four of the studies appear for the first time in English. Among the topics treated are: the Roman surveyors (agrimensores); recreational mathematics in the period of Bede and Alcuin; geometrical texts compiled in Corbie and Lorraine from Latin sources from late antiquity; the abacus at the time of Gerbert (pope Sylvester II.); and a board-game invented in the first half of the 11th century (the 'Rithmimachia') to help people to learn mathematics. Included in the volume are critical editions of several texts, e.g. that of Franco of Liège on squaring the circle, Bede and Alcuin on recreational mathematics, and part of Pseudo-Boethius' Geometry I. The book opens with a survey of mathematics in the Middle Ages, and ends with a history of Rithmimachia up to the 17th century, when the game fell into disuse.

Author : John Stillwell
Publisher : Springer Nature
Page : 400 pages
File Size : 42,7 Mb
Release : 2020-11-07
Category : Mathematics
ISBN : 9783030551933

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Mathematics and Its History by John Stillwell Pdf

This textbook provides a unified and concise exploration of undergraduate mathematics by approaching the subject through its history. Readers will discover the rich tapestry of ideas behind familiar topics from the undergraduate curriculum, such as calculus, algebra, topology, and more. Featuring historical episodes ranging from the Ancient Greeks to Fermat and Descartes, this volume offers a glimpse into the broader context in which these ideas developed, revealing unexpected connections that make this ideal for a senior capstone course. The presentation of previous versions has been refined by omitting the less mainstream topics and inserting new connecting material, allowing instructors to cover the book in a one-semester course. This condensed edition prioritizes succinctness and cohesiveness, and there is a greater emphasis on visual clarity, featuring full color images and high quality 3D models. As in previous editions, a wide array of mathematical topics are covered, from geometry to computation; however, biographical sketches have been omitted. Mathematics and Its History: A Concise Edition is an essential resource for courses or reading programs on the history of mathematics. Knowledge of basic calculus, algebra, geometry, topology, and set theory is assumed. From reviews of previous editions: “Mathematics and Its History is a joy to read. The writing is clear, concise and inviting. The style is very different from a traditional text. I found myself picking it up to read at the expense of my usual late evening thriller or detective novel.... The author has done a wonderful job of tying together the dominant themes of undergraduate mathematics.” Richard J. Wilders, MAA, on the Third Edition "The book...is presented in a lively style without unnecessary detail. It is very stimulating and will be appreciated not only by students. Much attention is paid to problems and to the development of mathematics before the end of the nineteenth century.... This book brings to the non-specialist interested in mathematics many interesting results. It can be recommended for seminars and will be enjoyed by the broad mathematical community." European Mathematical Society, on the Second Edition

Author : Reuben Hersh
Publisher : Springer Science & Business Media
Page : 346 pages
File Size : 46,8 Mb
Release : 2006-01-16
Category : Mathematics
ISBN : 9780387298313

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18 Unconventional Essays on the Nature of Mathematics by Reuben Hersh Pdf

Collection of the most interesting recent writings on the philosophy of mathematics written by highly respected researchers from philosophy, mathematics, physics, and chemistry Interdisciplinary book that will be useful in several fields—with a cross-disciplinary subject area, and contributions from researchers of various disciplines

Author : I͡U. I. Manin,Jurij I. Manin,Yurii Ivanovich Manin,Ûrij Ivanovič Manin
Publisher : American Mathematical Soc.
Page : 258 pages
File Size : 42,7 Mb
Release : 2007
Category : Mathematics
ISBN : 9780821843314

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Mathematics as Metaphor by I͡U. I. Manin,Jurij I. Manin,Yurii Ivanovich Manin,Ûrij Ivanovič Manin Pdf

Includes essays that are grouped in three parts: Mathematics; Mathematics and Physics; and, Language, Consciousness, and Book reviews. This book is suitable for those interested in the philosophy and history of mathematics, physics, and linguistics.

Author : Thomas Hawkins
Publisher : Springer Science & Business Media
Page : 578 pages
File Size : 41,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461212027

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Emergence of the Theory of Lie Groups by Thomas Hawkins Pdf

The great Norwegian mathematician Sophus Lie developed the general theory of transformations in the 1870s, and the first part of the book properly focuses on his work. In the second part the central figure is Wilhelm Killing, who developed structure and classification of semisimple Lie algebras. The third part focuses on the developments of the representation of Lie algebras, in particular the work of Elie Cartan. The book concludes with the work of Hermann Weyl and his contemporaries on the structure and representation of Lie groups which serves to bring together much of the earlier work into a coherent theory while at the same time opening up significant avenues for further work.

Author : Charles Parsons
Publisher : Harvard University Press
Page : 365 pages
File Size : 47,8 Mb
Release : 2014-03-10
Category : Philosophy
ISBN : 9780674419490

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Philosophy of Mathematics in the Twentieth Century by Charles Parsons Pdf

In these selected essays, Charles Parsons surveys the contributions of philosophers and mathematicians who shaped the philosophy of mathematics over the past century: Brouwer, Hilbert, Bernays, Weyl, Gödel, Russell, Quine, Putnam, Wang, and Tait.