{"title":"Robert C Gunning","description":null,"products":[{"product_id":"analytic-functions-of-several-complex-variables-book-robert-c-gunning-9781470470661","title":"Analytic Functions of Several Complex Variables","description":"The theory of analytic functions of several complex variables enjoyed a period of remarkable development in the middle part of the twentieth century. After initial successes by Poincare and others in the late 19th and early 20th centuries, the theory encountered obstacles that prevented it from growing quickly into an analogue of the theory for functions of one complex variable. Beginning in the 1930s, initially through the work of Oka, then H. Cartan, and continuing with the work of Grauert, Remmert, and others, new tools were introduced into the theory of several complex variables that resolved many of the open problems and fundamentally changed the landscape of the subject. These tools included a central role for sheaf theory and increased uses of topology and algebra. The book by Gunning and Rossi was the first of the modern era of the theory of several complex variables, which is distinguished by the use of these methods.\u003cbr\u003e\u003cbr\u003eThe intention of Gunning and Rossi's book is to provide an extensive introduction to the Oka-Cartan theory and some of its applications, and to the general theory of analytic spaces.\u003cbr\u003e\u003cbr\u003eFundamental concepts and techniques are discussed as early as possible. The first chapter covers material suitable for a one-semester graduate course, presenting many of the central problems and techniques, often in special cases. The later chapters give more detailed expositions of sheaf theory for analytic functions and the theory of complex analytic spaces. Since its original publication, this book has become a classic resource for the modern approach to functions of several complex variables and the theory of analytic spaces.\u003cbr\u003e\u003cbr\u003eFurther information about this book, including updates, can be found at the following URL: www.ams.org\/publications\/authors\/books\/postpub\/chel-368.","brand":"WoB","offers":[{"title":"- \/ - \/ -","offer_id":50630781436177,"sku":"","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ GARDNERS","offer_id":50630782943505,"sku":"NGR9781470470661","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/1470470667.jpg?v=1786613843"},{"product_id":"introduction-to-analysis-book-robert-c-gunning-9780691178790","title":"An Introduction to Analysis","description":"\u003cp\u003e\u003cb\u003eAn essential undergraduate textbook on algebra, topology, and calculus\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e\u003ci\u003eAn Introduction to Analysis\u003c\/i\u003e is an essential primer on basic results in algebra, topology, and calculus for undergraduate students considering advanced degrees in mathematics. Ideal for use in a one-year course, this unique textbook also introduces students to rigorous proofs and formal mathematical writing--skills they need to excel.\u003cbr\u003e\u003cbr\u003eWith a range of problems throughout, \u003ci\u003eAn Introduction to Analysis\u003c\/i\u003e treats \u003ci\u003en\u003c\/i\u003e-dimensional calculus from the beginning—differentiation, the Riemann integral, series, and differential forms and Stokes's theorem—enabling students who are serious about mathematics to progress quickly to more challenging topics. The book discusses basic material on point set topology, such as normed and metric spaces, topological spaces, compact sets, and the Baire category theorem. It covers linear algebra as well, including vector spaces, linear mappings, Jordan normal form, bilinear mappings, and normal mappings.\u003cbr\u003e\u003cbr\u003eProven in the classroom, \u003ci\u003eAn Introduction to Analysis\u003c\/i\u003e is the first textbook to bring these topics together in one easy-to-use and comprehensive volume.\u003cbr\u003e\u003c\/p\u003e\u003cul\u003e\n\u003cli\u003eProvides a rigorous introduction to calculus in one and several variables\u003c\/li\u003e\n\u003cli\u003eIntroduces students to basic topology\u003c\/li\u003e\n\u003cli\u003eCovers topics in linear algebra, including matrices, determinants, Jordan normal form, and bilinear and normal mappings\u003c\/li\u003e\n\u003cli\u003eDiscusses differential forms and Stokes's theorem in \u003ci\u003en\u003c\/i\u003e dimensions\u003c\/li\u003e\n\u003cli\u003eAlso covers the Riemann integral, integrability, improper integrals, and series expansions\u003c\/li\u003e\n\u003c\/ul\u003e","brand":"WoB","offers":[{"title":"- \/ - \/ -","offer_id":51005725999377,"sku":"","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":51005729407249,"sku":"NIN9780691178790","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/0691178798.jpg?v=1790225585"},{"product_id":"riemann-surfaces-and-generalized-theta-functions-book-robert-c-gunning-9783642663840","title":"Riemann Surfaces and Generalized Theta Functions","description":"The investigation of the relationships between compact Riemann surfaces (al­ gebraic curves) and their associated complex tori (Jacobi varieties) has long been basic to the study both of Riemann surfaces and of complex tori. A Riemann surface is naturally imbedded as an analytic submanifold in its associated torus; and various spaces of linear equivalence elasses of divisors on the surface (or equivalently spaces of analytic equivalence elasses of complex line bundies over the surface), elassified according to the dimensions of the associated linear series (or the dimensions of the spaces of analytic cross-sections), are naturally realized as analytic subvarieties of the associated torus. One of the most fruitful of the elassical approaches to this investigation has been by way of theta functions. The space of linear equivalence elasses of positive divisors of order g -1 on a compact connected Riemann surface M of genus g is realized by an irreducible (g -1)-dimensional analytic subvariety, an irreducible hypersurface, of the associated g-dimensional complex torus J(M); this hyper­ 1 surface W- r;;;, J(M) is the image of the natural mapping Mg- -+J(M), and is g 1 1 birationally equivalent to the (g -1)-fold symmetric product Mg- jSg-l of the Riemann surface M.","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":52627161514257,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ INGRAM","offer_id":52627162169617,"sku":"NLS9783642663840","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783642663840.jpg?v=1761692773"},{"product_id":"lectures-on-modular-forms-book-robert-c-gunning-9780691079950","title":"Lectures on Modular Forms","description":"New interest in modular forms of one complex variable has been caused chiefly by the work of Selberg and of Eichler. But there has been no introductory work covering the background of these developments. H. C. Gunning's book surveys techniques and problems; only the simpler cases are treated-modular forms of even weights without multipliers, the principal congruence subgroups, and the Hecke operators for the full modular group alone.","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":53035150246161,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":53035150999825,"sku":"NIN9780691079950","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9780691079950.jpg?v=1786614055"}],"url":"https:\/\/www.worldofbooks.com\/en-gb\/collections\/author-books-by-robert-c-gunning.oembed","provider":"World of Books ","version":"1.0","type":"link"}