{"title":"Irena Swanson","description":null,"products":[{"product_id":"introduction-to-analysis-with-complex-numbers-book-irena-swanson-9789811227691","title":"Introduction To Analysis With Complex Numbers","description":"This is a self-contained book that covers the standard topics in introductory analysis and that in addition constructs the natural, rational, real and complex numbers, and also handles complex-valued functions, sequences, and series.  The book teaches how to write proofs. Fundamental proof-writing logic is covered in Chapter 1 and is repeated and enhanced in two appendices. Many examples of proofs appear with words in a different font for what should be going on in the proof writer's head.  The book contains many examples and exercises to solidify the understanding. The material is presented rigorously with proofs and with many worked-out examples. Exercises are varied, many involve proofs, and some provide additional learning materials.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ GARDNERS","offer_id":49741898678545,"sku":"NGR9789811227691","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ VERY_GOOD \/ SBYB","offer_id":50253788643601,"sku":"CIN9811227691VG","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"US \/ GOOD \/ SBYB","offer_id":50492131246353,"sku":"CIN9811227691G","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ NEW \/ INGRAM","offer_id":52435637502225,"sku":"NLS9789811227691","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9811227691.jpg?v=1751419587"},{"product_id":"integral-closure-of-ideals-rings-and-modules-book-irena-swanson-9780521688604","title":"Integral Closure of Ideals, Rings, and Modules","description":"Integral closure has played a role in number theory and algebraic geometry since the nineteenth century, but a modern formulation of the concept for ideals perhaps began with the work of Krull and Zariski in the 1930s. It has developed into a tool for the analysis of many algebraic and geometric problems. This book collects together the central notions of integral closure and presents a unified treatment. Techniques and topics covered include: behavior of the Noetherian property under integral closure, analytically unramified rings, the conductor, field separability, valuations, Rees algebras, Rees valuations, reductions, multiplicity, mixed multiplicity, joint reductions, the Brian on-Skoda theorem, Zariski's theory of integrally closed ideals in two-dimensional regular local rings, computational aspects, adjoints of ideals and normal homomorphisms. With many worked examples and exercises, this book will provide graduate students and researchers in commutative algebra or ring theory with an approachable introduction leading into the current literature.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52129970651409,"sku":"NLS9780521688604","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9780521688604.jpg?v=1757500658"},{"product_id":"introduction-to-analysis-with-complex-numbers-book-irena-swanson-9789811225857","title":"Introduction To Analysis With Complex Numbers","description":"This is a self-contained book that covers the standard topics in introductory analysis and that in addition constructs the natural, rational, real and complex numbers, and also handles complex-valued functions, sequences, and series.  The book teaches how to write proofs. Fundamental proof-writing logic is covered in Chapter 1 and is repeated and enhanced in two appendices. Many examples of proofs appear with words in a different font for what should be going on in the proof writer's head.  The book contains many examples and exercises to solidify the understanding. The material is presented rigorously with proofs and with many worked-out examples. Exercises are varied, many involve proofs, and some provide additional learning materials.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52435666764049,"sku":"NLS9789811225857","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9789811225857.jpg?v=1759184689"},{"product_id":"lectures-on-tight-closure-and-its-applications-book-irena-swanson-9781470478384","title":"Lectures on Tight Closure and Its Applications","description":"This volume consists of edited lecture notes from two events at the International Centre for Theoretical Physics (ICTP) in Trieste, Italy, organized in honor of Melvin Hochster and Craig Huneke. The two events were the online International Graduate course on Tight Closure and Its Applications, spread over summer 2022 and the May 2023 School on Commutative Algebra and Algebraic Geometry in Prime Characteristics. The unifying basis of these events was the theory of tight closure, the brainchild of Melvin Hochster and Craig Huneke in the late 1980s, which has had a dramatic effect on the field of commutative algebra, giving unified proofs and strong generalizations of many major theorems in commutative algebra, and stimulating much research, including recent proofs of longstanding conjectures. The aim of the two events as well as of this volume is to provide training in the foundations of commutative algebra and algebraic geometry in prime characteristic and to present some of the exciting recent developments in and beyond tight closure. The lecture notes for the online school also come with exercises and solutions.  The topics in the volume include characteristic p methods, test ideals, direct summands, singularities, Hilbert-Kunz multiplicity, Briancon-Skoda theorems, big Cohen-Macaulay algebras, the localization problem, uniform Artin-Rees results, vector bundles and tight closure, singularity invariants. The intended audience is graduate students learning the material as well as researchers wanting the latest advances in one reference.","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":53080323227921,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ GARDNERS","offer_id":53080323326225,"sku":"NGR9781470478384","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9781470478384.jpg?v=1769891075"}],"url":"https:\/\/www.worldofbooks.com\/collections\/author-books-by-irena-swanson.oembed","provider":"World of Books ","version":"1.0","type":"link"}