Sources in the Development of Mathematics

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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 Review
There are books on history of math, but they lack in detail! and there are books that treat math in detail, but they lack historical perspective and concepts spring up out of thin air, as if without roots or parentage!
Roy's book fills this void; it provides us the details as well as their historical development!
A word about the subtitle of the book concerning series and products: As many of us know, the finite and infinite series and products have played an indispensable role in the understanding and development of mathematical ideas; without them, it is impossible to understand even the simplest of mathematical numbers or functions, like pi, or sin(x).
Why and how did these mathematical series arose and were manipulated by the original mathematicians of the bygone era? How their mind worked? and how they surmounted problems without adequate tools at their disposal? how their insight led to great mathematical ideas for successive mathematicians to develop the subject further? and finally how and why we have reached where we are today?
If you are interested in or curious to know all these in sufficient (and not just superficial or anecdotal) detail, I strongly recommend that you must read and digest this book; you would enjoy it thoroughly, it would brighten you, it would make the famous mathematicians of yore more near and real to you - almost like they are your friends -; and you may not need to go anywhere else!
Roy's book spares no details! We all know about the most famous mathematicians - Archimedes, Newton, Cauchy, Euler ....et. al. , but how many of us know that it was an Italian mathematician named MAUROLICO, who in 1575 first gave us the Principle of mathematical Induction!
Roy's " Sources in the development of mathematics" is truly a detailed study and development of modern mathematical ideas through the march of history in their full glory. Roy deals with each subject in a manner, so that a modern student or teacher today can experience the pleasure of working out the details of the original formalisms without any difficulty like having to read the original papers in Latin or Greek or Arabic or Sanskrit and understanding them in a modern context). And there are plenty of exercises to play around with in each chapter.
Could there be a better way to truly understand the mathematical concepts and, kind of, "own" them as your own?
Undoubtedly the book will serve as a great reference book for a long long time - probably the ultimate one in our era.
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