Series And Products In The Development Of Mathematics
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Series And Products In The Development Of Mathematics
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Author : Ranjan Roy
language : en
Publisher: Cambridge University Press
Release Date : 2021
Series And Products In The Development Of Mathematics written by Ranjan Roy and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021 with Mathematics categories.
"Sources in the Development of Mathematics: Series and Products from the Fifteenth to the Twenty-first Century, my book of 2011, was intended for an audience of graduate students or beyond. However, since much of its mathematics lies at the foundations of the undergraduate mathematics curriculum, I decided to use portions of my book as the text for an advanced undergraduate course. I was very pleased to find that my curious and diligent students, of varied levels of mathematical talent, could understand a good bit of the material and get insight into mathematics they had already studied as well as topics with which they were unfamiliar. Of course, the students could profitably study such topics from good textbooks. But I observed that when they read original proofs, perhaps with gaps or with slightly opaque arguments, students gained very valuable insight into the process of mathematical thinking and intuition. Moreover, the study of the steps, often over long periods of time, by which earlier mathematicians refined and clarified their arguments revealed to my students the essential points at the crux of those results, points that may be more difficult to discern in later streamlined presentations. As they worked to understand the material, my students witnessed the difficulty and beauty of original mathematical work and this was a source of great enjoyment to many of them. I have now thrice taught this course, with extremely positive student response"--
Sources In The Development Of Mathematics
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Author : Ranjan Roy
language : en
Publisher: Cambridge University Press
Release Date : 2011-06-13
Sources In The Development Of Mathematics written by Ranjan Roy and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-06-13 with Mathematics categories.
The discovery of infinite products by Wallis and infinite series by Newton marked the beginning of the modern mathematical era. It allowed Newton to solve the problem of finding areas under curves defined by algebraic equations, an achievement beyond the scope of the earlier methods of Torricelli, Fermat and Pascal. While Newton and his contemporaries, including Leibniz and the Bernoullis, concentrated on mathematical analysis and physics, Euler's prodigious accomplishments demonstrated that series and products could also address problems in algebra, combinatorics and number theory. In this book, Ranjan Roy describes many facets of the discovery and use of infinite series and products as worked out by their originators, including mathematicians from Asia, Europe and America. The text provides context and motivation for these discoveries, with many detailed proofs, offering a valuable perspective on modern mathematics. Mathematicians, mathematics students, physicists and engineers will all read this book with benefit and enjoyment.
Sources In The Development Of Mathematics
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Author : Ranjan Roy
language : en
Publisher:
Release Date : 2011
Sources In The Development Of Mathematics written by Ranjan Roy and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Mathematics categories.
"The discovery of infinite products by Wallis and infinite series by Newton marked the beginning of the modern mathematical era. It allowed Newton to solve the problem of finding areas under curves defined by algebraic equations, an achievement beyond the scope of the earlier methods of Torricelli, Fermat and Pascal. While Newton and his contemporaries, including Leibniz and the Bernoullis, concentrated on mathematical analysis and physics, Euler's prodigious accomplishments demonstrated that series and products could also address problems in algebra, combinatorics and number theory. In this book, Ranjan Roy describes many facets of the discovery and use of infinite series and products as worked out by their originators, including mathematicians from Asia, Europe and America. The text provides context and motivation for these discoveries, with many detailed proofs, offering a valuable perspective on modern mathematics. Mathematicians, mathematics students, physicists and engineers will all read this book with benefit and enjoyment"--
Series And Products In The Development Of Mathematics Volume 1
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Author : Ranjan Roy
language : en
Publisher: Cambridge University Press
Release Date : 2021-03-18
Series And Products In The Development Of Mathematics Volume 1 written by Ranjan Roy and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-03-18 with Mathematics categories.
This is the first volume of a two-volume work that traces the development of series and products from 1380 to 2000 by presenting and explaining the interconnected concepts and results of hundreds of unsung as well as celebrated mathematicians. Some chapters deal with the work of primarily one mathematician on a pivotal topic, and other chapters chronicle the progress over time of a given topic. This updated second edition of Sources in the Development of Mathematics adds extensive context, detail, and primary source material, with many sections rewritten to more clearly reveal the significance of key developments and arguments. Volume 1, accessible to even advanced undergraduate students, discusses the development of the methods in series and products that do not employ complex analytic methods or sophisticated machinery. Volume 2 treats more recent work, including deBranges' solution of Bieberbach's conjecture, and requires more advanced mathematical knowledge.
The Development Of Mathematics
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Author : E. T. Bell
language : en
Publisher: Courier Corporation
Release Date : 2012-09-11
The Development Of Mathematics written by E. T. Bell and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-09-11 with Mathematics categories.
Time-honored study by a prominent scholar of mathematics traces decisive epochs from the evolution of mathematical ideas in ancient Egypt and Babylonia to major breakthroughs in the 19th and 20th centuries. 1945 edition.
Series And Products In The Development Of Mathematics Volume 2
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Author : Ranjan Roy
language : en
Publisher: Cambridge University Press
Release Date : 2021-03-18
Series And Products In The Development Of Mathematics Volume 2 written by Ranjan Roy and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-03-18 with Mathematics categories.
This is the second volume of a two-volume work that traces the development of series and products from 1380 to 2000 by presenting and explaining the interconnected concepts and results of hundreds of unsung as well as celebrated mathematicians. Some chapters deal with the work of primarily one mathematician on a pivotal topic, and other chapters chronicle the progress over time of a given topic. This updated second edition of Sources in the Development of Mathematics adds extensive context, detail, and primary source material, with many sections rewritten to more clearly reveal the significance of key developments and arguments. Volume 1, accessible even to advanced undergraduate students, discusses the development of the methods in series and products that do not employ complex analytic methods or sophisticated machinery. Volume 2 examines more recent results, including deBranges' resolution of Bieberbach's conjecture and Nevanlinna's theory of meromorphic functions.
A Generalization Of Bohr Mollerup S Theorem For Higher Order Convex Functions
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Author : Jean-Luc Marichal
language : en
Publisher: Springer Nature
Release Date : 2022-07-06
A Generalization Of Bohr Mollerup S Theorem For Higher Order Convex Functions written by Jean-Luc Marichal and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-07-06 with Mathematics categories.
In 1922, Harald Bohr and Johannes Mollerup established a remarkable characterization of the Euler gamma function using its log-convexity property. A decade later, Emil Artin investigated this result and used it to derive the basic properties of the gamma function using elementary methods of the calculus. Bohr-Mollerup's theorem was then adopted by Nicolas Bourbaki as the starting point for his exposition of the gamma function. This open access book develops a far-reaching generalization of Bohr-Mollerup's theorem to higher order convex functions, along lines initiated by Wolfgang Krull, Roger Webster, and some others but going considerably further than past work. In particular, this generalization shows using elementary techniques that a very rich spectrum of functions satisfy analogues of several classical properties of the gamma function, including Bohr-Mollerup's theorem itself, Euler's reflection formula, Gauss' multiplication theorem, Stirling's formula, and Weierstrass' canonical factorization. The scope of the theory developed in this work is illustrated through various examples, ranging from the gamma function itself and its variants and generalizations (q-gamma, polygamma, multiple gamma functions) to important special functions such as the Hurwitz zeta function and the generalized Stieltjes constants. This volume is also an opportunity to honor the 100th anniversary of Bohr-Mollerup's theorem and to spark the interest of a large number of researchers in this beautiful theory.
Mathematics Education
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Author : Khoon Yoong Wong
language : en
Publisher: World Scientific
Release Date : 2009
Mathematics Education written by Khoon Yoong Wong and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Education categories.
This title provides much food for thought and pointers to meet future challenges in mathematics education not only within Singapore, but also in other countries.
The History Of The Calculus And Its Conceptual Development
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Author : Carl B. Boyer
language : en
Publisher: Courier Corporation
Release Date : 2012-10-09
The History Of The Calculus And Its Conceptual Development written by Carl B. Boyer and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-10-09 with Mathematics categories.
Fluent description of the development of both the integral and differential calculus — its early beginnings in antiquity, medieval contributions, and a consideration of Newton and Leibniz.
The Development Of Mathematics Throughout The Centuries
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Author : Brian Evans
language : en
Publisher: John Wiley & Sons
Release Date : 2014-02-24
The Development Of Mathematics Throughout The Centuries written by Brian Evans and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-02-24 with Mathematics categories.
Throughout the book, readers take a journey throughout time and observe how people around the world have understood these patterns of quantity, structure, and dimension around them. The Development of Mathematics Throughout the Centuries: A Brief History in a Cultural Contex provides a brief overview of the history of mathematics in a very straightforward and understandable manner and also addresses major findings that influenced the development of mathematics as a coherent discipline. This book: Highlights the contributions made by various world cultures including African, Egyptian, Babylonian, Chinese, Indian, Islamic, and pre-Columbian American mathematics Features an approach that is not too rigorous and is ideal for a one-semester course of the history of mathematics. Includes a Resources and Recommended Reading section for further exploration and has been extensively classroom-tested