An Invitation to the Rogers-Ramanujan Identities

Author:   Andrew V. Sills (Georgia Southern University, Statesboro, USA)
Publisher:   Taylor & Francis Ltd
ISBN:  

9780367657611


Pages:   256
Publication Date:   30 September 2020
Format:   Paperback
Availability:   In Print   Availability explained
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An Invitation to the Rogers-Ramanujan Identities


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Overview

The Rogers--Ramanujan identities are a pair of infinite series—infinite product identities that were first discovered in 1894. Over the past several decades these identities, and identities of similar type, have found applications in number theory, combinatorics, Lie algebra and vertex operator algebra theory, physics (especially statistical mechanics), and computer science (especially algorithmic proof theory). Presented in a coherant and clear way, this will be the first book entirely devoted to the Rogers—Ramanujan identities and will include related historical material that is unavailable elsewhere.

Full Product Details

Author:   Andrew V. Sills (Georgia Southern University, Statesboro, USA)
Publisher:   Taylor & Francis Ltd
Imprint:   Chapman & Hall/CRC
Weight:   0.453kg
ISBN:  

9780367657611


ISBN 10:   0367657619
Pages:   256
Publication Date:   30 September 2020
Audience:   College/higher education ,  General/trade ,  Tertiary & Higher Education ,  General
Format:   Paperback
Publisher's Status:   Active
Availability:   In Print   Availability explained
This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us.

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Reviews

"This one-of-a-kind text, best suited for graduate level students and above, focuses exclusively on the Rogers-Ramanujan identities and their history. These two identities from number theory involve both infinite series and infinite products. The identities were independently discovered by Leonard James Rogers (1894 with proof), Srinivasa Ramanujan (before 1913 without proof), and Issai Schur (1917 with proof). The identities are relevant to the study of integer partitions, Lie algebras, statistical mechanics, computer science, and several other areas. Sills (Georgia Southern Univ.) begins with a review of partition theory and hypergeometric series. In the next two chapters, he moves on to prove the Rogers-Ramanujan identities and to explain their combinatorial aspects, as well as related identities and extensions. The final two chapters treat applications including continued fractions and knot theory. One appendix lists 236 related identities. A second appendix enhances the book's historical utility by providing transcriptions of letters between key researchers from 1943 to 1961. The book also includes more than 60 enlightening exercises. —D. P. Turner, Faulkner University, CHOICE Reviews ""In recent years ¿-series have arisen in knot theory, and Sills discusses a few ¿-series that arise in the study of certain simple fundamental knots. While there have been systematic discussions of many of the topics mentioned above in various books, monographs, and survey articles, Sills’s book is the first comprehensive discussion of R-R type identities in all their forms, describing the state of the art. Since the subject is so vast, he does not provide proofs for most of the identities discussed, but he provides an interesting and illuminating historical context for each topic, gives good motivation, and describes the key ideas underlying the proofs. He also provides a substantial number of references that will lead both the studen"


This one-of-a-kind text, best suited for graduate level students and above, focuses exclusively on the Rogers-Ramanujan identities and their history. These two identities from number theory involve both infinite series and infinite products. The identities were independently discovered by Leonard James Rogers (1894 with proof), Srinivasa Ramanujan (before 1913 without proof), and Issai Schur (1917 with proof). The identities are relevant to the study of integer partitions, Lie algebras, statistical mechanics, computer science, and several other areas. Sills (Georgia Southern Univ.) begins with a review of partition theory and hypergeometric series. In the next two chapters, he moves on to prove the Rogers-Ramanujan identities and to explain their combinatorial aspects, as well as related identities and extensions. The final two chapters treat applications including continued fractions and knot theory. One appendix lists 236 related identities. A second appendix enhances the book's historical utility by providing transcriptions of letters between key researchers from 1943 to 1961. The book also includes more than 60 enlightening exercises. -D. P. Turner, Faulkner University, CHOICE Reviews In recent years ?-series have arisen in knot theory, and Sills discusses a few ?-series that arise in the study of certain simple fundamental knots. While there have been systematic discussions of many of the topics mentioned above in various books, monographs, and survey articles, Sills's book is the first comprehensive discussion of R-R type identities in all their forms, describing the state of the art. Since the subject is so vast, he does not provide proofs for most of the identities discussed, but he provides an interesting and illuminating historical context for each topic, gives good motivation, and describes the key ideas underlying the proofs. He also provides a substantial number of references that will lead both the studen


Author Information

"Andrew Sills obtained his Ph.D. in 2002 from the University of Kentucky under. George E. Andrews, Evan Pugh Professor of Mathematics, Pennsylvania State University. He was Hill Assistant Professor of Mathematics, at Rutgers University between 2003- 2007 and a Tenure-track Assistant Professor at Georgia Southern University between 2007-2011. Since 2011 he has been Associate Professor of Mathematics at Georgia Southern, becoming a full Professor of Mathematics, effective August 1, 2015. He is a permanent Member of DIMACS (Center for Discrete Mathematics and Computer Science), since 2011. Research Grant: ""Computer Assisted Research in Additive and Combinatorial Number Theory and Allied Areas,"" National Security Agency Grant, 2014-2015."

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