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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
The development of infinite series and products fundamentally reshaped the landscape of mathematics, enabling solutions to previously intractable problems. Ranjan Roy's work traces the origins and applications of these powerful tools, beginning with the groundbreaking discoveries of Wallis and Newton. The book details how these innovations allowed for the calculation of areas under algebraic curves, a feat beyond the capabilities of earlier methods. It further explores the expansion of their use by Euler and others into fields such as algebra, combinatorics, and number theory, demonstrating their broad applicability across diverse mathematical disciplines.
The book is presented as a valuable resource for mathematicians, students, physicists, and engineers, promising both benefit and enjoyment. The description suggests a text that provides deep context and detailed proofs, aiming to offer a unique perspective on the foundations of modern mathematics. Its focus on the original discoveries and the mathematicians behind them indicates a scholarly yet accessible approach to the subject matter.
Page Count:
994
Publication Date:
2011-01-01
ISBN-10:
0521114705
ISBN-13:
9780521114707
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