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Book Cover
E-book
Author Roy, Ranjan, 1948- author.

Title Series and products in the development of mathematics / Ranjan Roy, Beloit College, Wisconsin
Edition Second edition
Published Cambridge, UK ; New York, NY : Cambridge University Press, 2021

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Description 1 online resource
Contents Cover -- Half-title -- Frontispiece -- Title page -- Copyright information -- Contents -- Contents of Volume 1 -- Preface -- 25 q-Series -- 25.1 Preliminary Remarks -- 25.2 Jakob Bernoulli's Theta Series -- 25.3 Euler's q-Series Identities -- 25.4 Euler's Pentagonal Number Theorem -- 25.5 Gauss: Triangular and Square Numbers Theorem -- 25.6 Gauss Polynomials and Gauss Sums -- 25.7 Gauss's q-Binomial Theorem and the Triple Product Identity -- 25.8 Jacobi: Triple Product Identity -- 25.9 Eisenstein: q-Binomial Theorem -- 25.10 Jacobi's q-Series Identity
25.11 Cauchy and Ramanujan: The Extension of the Triple Product -- 25.12 Rodrigues and MacMahon: Combinatorics -- 25.13 Exercises -- 25.14 Notes on the Literature -- 26 Partitions -- 26.1 Preliminary Remarks -- 26.2 Sylvester on Partitions -- 26.3 Cayley: Sylvester's Formula -- 26.4 Ramanujan: Rogers-Ramanujan Identities -- 26.5 Ramanujan's Congruence Properties of Partitions -- 26.6 Exercises -- 26.7 Notes on the Literature -- 27 q-Series and q-Orthogonal Polynomials -- 27.1 Preliminary Remarks -- 27.2 Heine's Transformation -- 27.3 Rogers: Threefold Symmetry
Summary This second edition of Sources in the Development of Mathematics, now in two volumes, traces the development of series and products from 1380-2000 through the interconnected concepts and results of unsung and celebrated mathematicians. This second volume treats more advanced topics, with extensive added context, detail, and primary source material
Notes Revised edition of: Sources in the development of mathematics : infinite series and products from the fifteenth to the twenty-first century. 2011
Bibliography Includes bibliographical references and index
"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"-Provided by publisher
Notes Print version record
Subject Mathematics -- Historiography.
Matemáticas -- Historiografía
Mathematics -- Historiography
Form Electronic book
ISBN 9781108627702
1108627706
9781108671620
1108671624
Other Titles Sources in the development of mathematics