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OverviewExploring several of the evolutionary branches of the mathematical notion of genus, this book traces the idea from its prehistory in problems of integration, through algebraic curves and their associated Riemann surfaces, into algebraic surfaces, and finally into higher dimensions. Its importance in analysis, algebraic geometry, number theory and topology is emphasized through many theorems. Almost every chapter is organized around excerpts from a research paper in which a new perspective was brought on the genus or on one of the objects to which this notion applies. The author was motivated by the belief that a subject may best be understood and communicated by studying its broad lines of development, feeling the way one arrives at the definitions of its fundamental notions, and appreciating the amount of effort spent in order to explore its phenomena. Full Product DetailsAuthor: Patrick Popescu-PampuPublisher: Springer International Publishing AG Imprint: Springer International Publishing AG Edition: 1st ed. 2016 Volume: 2162 Dimensions: Width: 15.50cm , Height: 1.10cm , Length: 23.50cm Weight: 3.168kg ISBN: 9783319423111ISBN 10: 3319423118 Pages: 184 Publication Date: 02 September 2016 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: Manufactured on demand  We will order this item for you from a manufactured on demand supplier. Language: English Table of ContentsPreface.-Introduction.-Algebraic curves.-Algebraic surfaces.-Higher dimensions.-Epilogue.-Bibliography.-Index.ReviewsThis clear book thoroughly covers the metamorphosis and theoretical significance of the genus by using several historical approaches that incorporate discussions related to analysis, algebraic geometry, number theory, and topology. ... The book contains 20 figures and concludes with a list of 200 references and an index, which will help those who wish to delve into deeper studies. Summing Up: Recommended. Upper-division undergraduates and above; faculty and professionals. (D. P. Turner, Choice, Vol. 54 (9), May, 2017) This book provides a fascinating-yet technically quite demanding-tour of the ideas and generalizations that feed into our modern conception of the genus. It should therefore serve as a useful starting point for historical and even philosophical investigations into past mathematical practice of forming and shaping concepts. It may also be useful in teaching advanced mathematical content with a view to historical development ... . (Henrik Kragh Sorensen, ISIS, Vol. 109 (2), June, 2018) This book is addressed to any person with a little knowledge of mathematics (such as an undergraduate student) who wants to get an idea of some of the most important concepts that arose in geometry and topology in the last couple of centuries: the author has made a commendable effort to explain all the more advanced concepts almost from scratch (but obviously this was not possible for the last chapter). (Pietro De Poi, Mathematical Reviews, July, 2017) This clear book thoroughly covers the metamorphosis and theoretical significance of the genus by using several historical approaches that incorporate discussions related to analysis, algebraic geometry, number theory, and topology. ... The book contains 20 figures and concludes with a list of 200 references and an index, which will help those who wish to delve into deeper studies. Summing Up: Recommended. Upper-division undergraduates and above; faculty and professionals. (D. P. Turner, Choice, Vol. 54 (9), May, 2017) Author InformationTab Content 6Author Website:Countries AvailableAll regions |
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