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  3. Sources in the Development of Mathematics
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    • Publisher:
      Cambridge University Press
      Publication date:
      June 2012
      June 2011
      ISBN:
      9780511844195
      DOI:
      https://doi.org/10.1017/CBO9780511844195
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      • Subjects:
      Mathematics, History of Mathematics
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    Subjects:
    Mathematics, History of Mathematics
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    Book description

    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.

    Reviews

    "This work is unbelievably thorough. Roy includes not just results but also many proofs, historic contexts, references, and exercises. Is it the sort of encyclopedic effort that one typically associates with a group of authors rather than an individual. Roy has made an important contribution with this book."
    C. Bauer, Choice Magazine

    "... will provide [Roy] unique recognition for deep scholarship and extraordinary exposition regarding the history of classical mathematical analysis and related algebraic topics. This well-written book will be a valuable source of fresh information on the wide range of topics covered. It can be expected to have great positive impact on pedagogy and understanding. It certainly seems to be the best one-volume history of mathematics I know..."
    Robert E. O'Malley, SIAM Review

    "I recommend this book to a wide audience. Undergraduates can learn of the truly vast amount of material that lies alongside some of their more standard endeavors, many of which involve only elementary matters: sums, products, limits, calculus. Graduate students and nonspecialist faculty can wonder at the ingenuity of theirpredecessors and the connections between now disparate areas that are afforded by this very classical view. They’ll also get lots of good ideas for teaching (and they may waste a good deal of time on the problems, as well). Historians, philosophers, and others should read this book, if only for the view of mathematics it propounds.And specialized researchers in the area of special functions and related fields should simply have a good time. All of these readers can benefit from the remarkable expository talents of the author and his careful choice of material. Among personalviews of mathematics that use history as a key to understanding, Roy’s book stands out as a model."
    Tom Archibald, Notices of the AMS

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