{"title":"Complex analysis, complex variables Books","description":"","products":[{"product_id":"operator-theory-by-example-oxford-graduate-texts-in-mathematics-9780192863874","title":"Operator Theory by Example Oxford Graduate Texts","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eAimed at graduate students, this textbook provides an accessible and comprehensive introduction to operator theory, and covers twenty examples of operators, discussing the norm, spectrum, commutant, invariant subspaces, and interesting properties of each operator.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003eThe text is supplemented by over 600 end-of-chapter exercises, designed to help the reader master the topics covered in the chapter, as well as providing an opportunity to further explore the vast operator theory literature. Each chapter also contains well researched historical facts which place each chapter within the broader context of the development of the field as a whole. * MathSciNet *\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e1: Hilbert Spaces 2: Diagonal Operators 3: Infinite Matrices 4: Two Multiplication Operators 5: The Unilateral Shift 6: The Cesàro Operator 7: The Volterra Operator 8: Multiplication Operators 9: The Dirichlet Shift 10: The Bergman Shift 11: The Fourier Transform 12: The Hilbert Transform 13: Bishop Operators 14: Operator Matrices 15: Constructions with the Shift Operator 16: Toeplitz Operators 17: Hankel Operators 18: Composition Operators 19: Subnormal Operators 20: The Compressed Shift","brand":"Oxford University Press","offers":[{"title":"Default Title","offer_id":48732603646295,"sku":"9780192863874","price":999.99,"currency_code":"GBP","in_stock":false}]},{"product_id":"visual-complex-analysis-9780192868923","title":"Visual Complex Analysis","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eComplex Analysis is the powerful fusion of the complex numbers (involving the ''imaginary'' square root of -1) with ordinary calculus, resulting in a tool that has been of central importance to science for more than 200 years.This book brings this majestic and powerful subject to life by consistently using geometry (not calculation) as the means of explanation. The 501 diagrams of the original edition embodied geometrical arguments that (for the first time) replaced the long and often opaque computations of the standard approach, in force for the previous 200 years, providing direct, intuitive, visual access to the underlying mathematical reality.This new 25th Anniversary Edition introduces brand-new captions that fully explain the geometrical reasoning, making it possible to read the work in an entirely new wayas a highbrow comic book!\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003eVisual Complex Analysis is a delight, and a book after my own heart. By his innovative and exclusive use of the geometrical perspective, Tristan Needham uncovers many surprising and largely unappreciated aspects of the beauty of complex analysis. * Sir Roger Penrose   *\u003cbr\u003e...it is comparable with Feynman's Lectures on Physics. At every point it asks \"why\" and finds a beautiful visual answer. * Newsletter of the European Mathematical Society *\u003cbr\u003eNewton would have approved... a fascinating and refreshing look at a familiar subject... essential reading for anybody with any interest at all in this absorbing area of mathematics. * Times Higher Education Supplement *\u003cbr\u003eOne of the saddest developments in school mathematics has been the downgrading of the visual for the formal. I'm not lamenting the loss of traditional Euclidean geometry, despite its virtues, because it too emphasised stilted formalities. But to replace our rich visual tradition by silly games with 2 x 2 matrices has always seemed to me to be the height of folly. It is therefore a special pleasure to see Tristan Needham's Visual Complex Analysis with its elegantly illustrated visual approach. Yes, he has 2 x 2 matrices--but his are interesting. * Ian Stewart, New Scientist *\u003cbr\u003ean engaging, broad, thorough, and often deep, development of undergraduate complex analysis and related areas from a geometric point of view. The style is lucid, informal, reader-friendly, and rich with helpful images (e.g. the complex derivative as an \"amplitwist\"). A truly unusual and notably creative look at a classical subject. * Paul Zorn, American Mathematical Monthly   *\u003cbr\u003eIf your budget limits you to only buying one mathematics book in a year then make sure that this is the one that you buy. * Mathematical Gazette *\u003cbr\u003eI was delighted when I came across Visual Complex Analysis. As soon as I thumbed through it, I realized that this was the book I was looking for ten years ago. * Ed Catmull, former president of Pixar and Disney Animation Studios *\u003cbr\u003eThe new ideas and exercises bring together a body of information potentially invaluable to researchers in fields from topology to number theory... this is only the beginning of a long list of famous facts for which Needham offers attractive visual proofs: Cauchy's theorem is a satisfying example: you can see the contribution to the integral from each infinitesimal square vanish before your eyes. * Frank Farris, American Mathematical Monthly *\u003cbr\u003eThis informal style is excellently judged and works extremely well. Many of the arguments presented will be new even to experts, and the book will be of great interest to professionals working in either complex analysis or in any field where complex analysis is used. * David Armitage, Mathematical Reviews *\u003cbr\u003eThe arguments constructed are highly innovative; even veterans of the field will find new ideas here. This is a special book. Tristan Needham has not only completely rethought a classical field of mathematics, but has presented it in a clear and compelling way. Visual Complex Analysis is worthy of the accolades it has received * MAA Reviews *\u003cbr\u003eThis new edition of Visual Complex Analysis applies Newton's geometrical methods from the Principia and his concept of ultimate equality to Complex Analysis. * MathSciNet  *\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e1: Geometry and Complex Arithmetic 2: Complex Functions as Transformations 3: Möbius Transformations and Inversion 4: Differentiation: The Amplitwist Concept 5: Further Geometry of Differentiation 6: Non-Euclidean Geometry 7: Winding Numbers and Topology 8: Complex Integration: Cauchy's Theorem 9: Cauchy's Formula and Its Applications 10: Vector Fields: Physics and Topology 11: Vector Fields and Complex Integration 12: Flows and Harmonic Functions","brand":"Oxford University Press","offers":[{"title":"Default Title","offer_id":48732606660951,"sku":"9780192868923","price":40.84,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780192868923.jpg?v=1719997623"},{"product_id":"essential-math-for-ai-9781098107635","title":"Essential Math for AI","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis accessible guide walks you through the math necessary to thrive in the AI field such as focusing on real-world applications rather than dense academic theory. Engineers, data scientists, and students alike will examine mathematical topics critical for AI-including regression, neural networks, optimization, backpropagation, and Markov chains.","brand":"O'Reilly Media","offers":[{"title":"Default Title","offer_id":48738226733399,"sku":"9781098107635","price":47.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781098107635.jpg?v=1723811836"},{"product_id":"explorations-in-complex-functions-9783030545321","title":"Explorations in Complex Functions","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThis textbook explores a selection of topics in complex analysis. From core material in the mainstream of complex analysis itself, to tools that are widely used in other areas of mathematics, this versatile compilation offers a selection of many different paths. Readers interested in complex analysis will appreciate the unique combination of topics and connections collected in this book.\u003cbr\u003e \u003cbr\u003e Beginning with a review of the main tools of complex analysis, harmonic analysis, and functional analysis, the authors go on to present multiple different, self-contained avenues to proceed. Chapters on linear fractional transformations, harmonic functions, and elliptic functions offer pathways to hyperbolic geometry, automorphic functions, and an intuitive introduction to the Schwarzian derivative. The gamma, beta, and zeta functions lead into \u003ci\u003eL\u003c\/i\u003e-functions, while a chapter on entire functions opens pathways to the Riemann hypothesis and Nevanlinna theory. Cauchy transforms give rise to Hilbert and Fourier transforms, with an emphasis on the connection to complex analysis. Valuable additional topics include Riemann surfaces, steepest descent, tauberian theorems, and the Wiener–Hopf method.\u003c\/p\u003e  \u003cp\u003eShowcasing an array of accessible excursions, \u003ci\u003eExplorations in Complex Functions\u003c\/i\u003e is an ideal companion for graduate students and researchers in analysis and number theory. Instructors will appreciate the many options for constructing a second course in complex analysis that builds on a first course prerequisite; exercises complement the results throughout.\u003cbr\u003e\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e“This is a suitable book with a proper concept at the right time. It is suitable because it shows the beauty, power and profundity of complex analysis, enlightens how many sided it is with all its inspirations and cross-connections to other branches of mathematics.” (Heinrich Begehr, zbMATH 1460.30001, 2021)\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eBasics.- Linear Fractional Transformations.- Hyperbolic geometry.- Harmonic Functions.- Conformal maps and the Riemann mapping theorem.- The Schwarzian derivative.- Riemann surfaces and algebraic curves.- Entire functions.- Value distribution theory.- The gamma and beta functions.- The Riemann zeta function.- L-functions and primes.- The Riemann hypothesis.- Elliptic functions and theta functions.- Jacobi elliptic functions.- Weierstrass elliptic functions.- Automorphic functions and Picard's theorem.- Integral transforms.- Theorems of Phragmén–Lindelöf and Paley–Wiener.- Theorems of Wiener and Lévy; the Wiener–Hopf method.- Tauberian theorems.- Asymptotics and the method of steepest descent.- Complex interpolation and the Riesz–Thorin theorem.","brand":"Springer Nature Switzerland AG","offers":[{"title":"Default Title","offer_id":48743039893847,"sku":"9783030545321","price":52.24,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783030545321.jpg?v=1720063846"},{"product_id":"zero-product-determined-algebras-9783030802417","title":"Zero Product Determined Algebras","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThis book provides a concise survey of the theory of zero product-determined algebras, which has been developed over the last 15 years. It is divided into three parts. The first part presents the purely algebraic branch of the theory, the second part presents the functional analytic branch, and the third part discusses various applications.\u003c\/p\u003e  \u003cp\u003eThe book is intended for researchers and graduate students in ring theory, Banach algebra theory, and nonassociative algebra.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e“This book is about zero product determined algebras and is written in an attractive way. It deals with the introduction and study of this class of algebras. Most of this book is taken from research articles from the last 15 years and is suitable for researchers in this field and students with different backgrounds and can be used for self-study.” (Hoger Ghahramani, Mathematical Reviews, March, 2023)\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cb\u003e- \u003c\/b\u003e\u003cb\u003ePart I Algebraic Theory. - \u003c\/b\u003eZero Product Determined Nonassociative Algebras. - Zero Product Determined Rings and Algebras. - Zero Lie\/Jordan Product Determined Algebras. - \u003cb\u003ePart II Analytic Theory.\u003c\/b\u003e - Zero Product Determined Nonassociative Banach Algebras. - Zero Product Determined Banach Algebras. - Zero Lie\/Jordan Product Determined Banach Algebras. - \u003cb\u003ePart III Applications.\u003c\/b\u003e - Homomorphisms and Related Maps. - Derivations and Related Maps. - Miscellany.","brand":"Springer Nature Switzerland AG","offers":[{"title":"Default Title","offer_id":48743050838359,"sku":"9783030802417","price":49.99,"currency_code":"GBP","in_stock":true}]},{"product_id":"abelian-varieties-over-the-complex-numbers-a-graduate-course-9783031255694","title":"Abelian Varieties over the Complex Numbers: A","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis textbook offers an introduction to abelian varieties, a rich topic of central importance to algebraic geometry. The emphasis is on geometric constructions over the complex numbers, notably the construction of important classes of abelian varieties and their algebraic cycles.\u003cbr\u003eThe book begins with complex tori and their line bundles (theta functions), naturally leading to the definition of abelian varieties. After establishing basic properties, the moduli space of abelian varieties is introduced and studied. The next chapters are devoted to the study of the main examples of abelian varieties: Jacobian varieties, abelian surfaces, Albanese and Picard varieties, Prym varieties, and intermediate Jacobians. Subsequently, the Fourier–Mukai transform is introduced and applied to the study of sheaves, and results on Chow groups and the Hodge conjecture are obtained.\u003cbr\u003eThis book is suitable for use as the main text for a first course on abelian varieties, for instance as a second graduate course in algebraic geometry. The variety of topics and abundant exercises also make it well suited to reading courses. The book provides an accessible reference, not only for students specializing in algebraic geometry but also in related subjects such as number theory, cryptography, mathematical physics, and integrable systems.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e“The reorganization of the topics is fine surgical work. Several portions of the original monograph are sewn in a natural way in the new book, adding examples or additional text when necessary, and re-arranging the focus to make it a more friendly introduction to the subject. Careful attention to details and the required background makes the book under review accessible to an interested reader and could be a used as textbook for a course on abelian varieties.” (Felipe Zaldivar, MAA Reviews, June 18, 2023)\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e1. Line Bundles on Complex Tori.- 2 Abelian Varieties.- 3 Moduli Spaces.- 4 Jacobian Varieties.- 5 Main Examples of Abelian Varieties.- 6 The Fourier Transform for Sheaves and Cycles.- 7 Introduction to the Hodge Conjecture for Abelian Varieties.","brand":"Springer International Publishing AG","offers":[{"title":"Default Title","offer_id":48743077052759,"sku":"9783031255694","price":39.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783031255694.jpg?v=1720064009"},{"product_id":"open-conformal-systems-and-perturbations-of-transfer-operators-9783319721781","title":"Open Conformal Systems and Perturbations of","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThe focus of this book is on open conformal dynamical systems corresponding to the escape of a point through an open Euclidean ball. The ultimate goal is to understand the asymptotic behavior of the escape rate as the radius of the ball tends to zero.  In the case of hyperbolic conformal systems this has been addressed by various authors. The conformal maps considered in this book are far more general, and the analysis correspondingly more involved.\u003c\/p\u003e  \u003cp\u003eThe asymptotic existence of escape rates is proved and they are calculated in the context of (finite or infinite) countable alphabets, uniformly contracting conformal graph-directed Markov systems, and in particular, conformal countable alphabet iterated function systems. These results have direct applications to interval maps, rational functions and meromorphic maps. \u003c\/p\u003e  \u003cp\u003eTowards this goal the authors develop, on a purely symbolic level, a theory of singular perturbations of Perron--Frobenius (transfer) operators associated with countable alphabet subshifts of finite type and Hölder continuous summable potentials. This leads to a fairly full account of the structure of the corresponding open dynamical systems and their associated surviving sets.\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e1. Introduction.- 2. Singular Perturbations of Classical Original Perron–Frobenius Operators on Countable Alphabet Symbol Spaces.- 3. Symbol Escape Rates and the Survivor Set \u003ci\u003eK(U\u003c\/i\u003e\u003ci\u003e\u003csub\u003en\u003c\/sub\u003e\u003c\/i\u003e\u003ci\u003e).- 4. Escape Rates for Conformal GDMSs and IFSs.- 5. Applications: Escape Rates for Multimodal Maps\u003c\/i\u003e\u003ci\u003eand One-Dimensional Complex Dynamics.\u003c\/i\u003e","brand":"Springer International Publishing AG","offers":[{"title":"Default Title","offer_id":48743103168855,"sku":"9783319721781","price":35.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783319721781.jpg?v=1720064124"},{"product_id":"complex-analysis-with-applications-9783319940625","title":"Complex Analysis with Applications","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThis textbook is intended for a one semester course in complex analysis for upper level undergraduates in mathematics. Applications, primary motivations for this text, are presented hand-in-hand with theory enabling this text to serve well in courses for students in engineering or applied sciences. The overall aim in designing this text is to accommodate students of different mathematical backgrounds and to achieve a balance between presentations of rigorous mathematical proofs and applications.  \u003c\/p\u003eThe text is adapted to enable maximum flexibility to instructors and to students who may also choose to progress through the material outside of coursework. Detailed examples may be covered in one course, giving the instructor the option to choose those that are best suited for discussion. Examples showcase a variety of problems with completely worked out solutions, assisting students in working through the exercises. The numerous exercises vary in difficulty from simple applications of formulas to more advanced project-type problems.  Detailed hints accompany the more challenging problems.  Multi-part exercises may be assigned to individual students, to groups as projects, or serve as further illustrations for the instructor. Widely used graphics clarify both concrete and abstract concepts, helping students visualize the proofs of many results.\u003cp\u003e\u003c\/p\u003e\u003cp\u003e Freely accessible solutions to every-other-odd exercise are posted to the book’s Springer website. Additional solutions for instructors’ use may be obtained by contacting the authors directly.\u003cbr\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e“The book is a clear and rigorous introduction to complex analysis and its applications in applied mathematics, engineering and physics. … Each section of the book contains a great number of examples and exercises.” (Dorina Raducanu, zbMATH 1409.30001, 2019)\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e1. Complex Numbers and Functions.- 2. Analytic Functions.- 3. Complex Integration.- 4. Series of Analytic Functions and Singularities.- 5. Residue Theory.- 6. Harmonic Functions and Applications.- 7. Conformal Mappings.- Appendix.- Index.","brand":"Springer International Publishing AG","offers":[{"title":"Default Title","offer_id":48743110246743,"sku":"9783319940625","price":42.74,"currency_code":"GBP","in_stock":true}]},{"product_id":"a-brief-introduction-to-berezin-toeplitz-operators-on-compact-kahler-manifolds-9783319946818","title":"A Brief Introduction to Berezin–Toeplitz","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThis text provides a comprehensive introduction to Berezin–Toeplitz operators on compact Kähler manifolds. The heart of the book is devoted to a proof of the main properties of these operators which have been playing a significant role in various areas of mathematics such as complex geometry, topological quantum field theory, integrable systems, and the study of links between symplectic topology and quantum mechanics. The book is carefully designed to supply graduate students with a unique accessibility to the subject. The first part contains a review of relevant material from complex geometry. Examples are presented with explicit detail and computation; prerequisites have been kept to a minimum. Readers are encouraged to enhance their understanding of the material by working through the many straightforward exercises. \u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e“The book … represents an essential prerequisite for anyone who wants to work in the field. The author have managed to make it readable by non-specialists.” (Béchir Dali, zbMATH 1452.32002, 2021)\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface.- 1. Introduction.- 2. A short introduction to Kähler manifolds.- 3. Complex line bundles with connections.- 4. Quantization of compact Kähler manifolds.- 5. Berezin–Toeplitz operators.- 6. Schwartz kernels.- 7. Asymptotics of the projector Pi_k.- 8. Proof of product and commutator estimates.- 9. Coherent states and norm correspondence.- A. The circle bundle point of view.- Bibliography.","brand":"Springer International Publishing AG","offers":[{"title":"Default Title","offer_id":48743110639959,"sku":"9783319946818","price":49.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783319946818.jpg?v=1720064156"},{"product_id":"the-analysis-of-linear-partial-differential-operators-ii-differential-operators-with-constant-coefficients-9783540225164","title":"The Analysis of Linear Partial Differential","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eAuthor received the 1962 Fields Medal\u003c\/p\u003e \u003cp\u003eAuthor received the 1988 Wolf Prize (honoring achievemnets of a lifetime)\u003c\/p\u003e \u003cp\u003eAuthor is leading expert in partial differential equations\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eFrom the reviews: \u003c\/p\u003e\u003cp\u003e\"...these volumes are excellently written and make for greatly profitable reading. For years to come they will surely be a main reference for anyone wishing to study partial differential operators.\"-- MATHEMATICAL REVIEWS \u003c\/p\u003e\u003cp\u003e\"This volume focuses on linear partial differential operators with constant coefficients … . Each chapter ends with notes on the literature, and there is a large bibliography. … The binding of this softcover reprint seems quite good … . Overall, it is great to have this book back at an affordable price. It really does deserve to be described as a classic.\" (Fernando Q. Gouvêa, MathDL, January, 2005)\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eExistence and Approximation of Solutions of Differential Equations.- Interior Regularity of Solutions of Differential Equations.- The Cauchy and Mixed Problems.- Differential Operators of Constant Strength.- Scattering Theory.- Analytic Function Theory and Differential Equations.- Convolution Equations.","brand":"Springer-Verlag Berlin and Heidelberg GmbH \u0026 Co. KG","offers":[{"title":"Default Title","offer_id":48743129940311,"sku":"9783540225164","price":49.99,"currency_code":"GBP","in_stock":true}]},{"product_id":"dynamics-in-one-complex-variable-9780691124889","title":"Dynamics in One Complex Variable","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eHelps you study the dynamics of iterated holomorphic mappings from a Riemann surface to itself, concentrating on the classical case of rational maps of the Riemann sphere. This title introduces some key ideas in the field, and to form a basis for further study.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"John Milnor's book provides a solid foundation and the kind of bird's eye view that perhaps only a mathematician of his caliber can offer.\"--William J. Satzer, MAA Reviews\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e*FrontMatter, pg. i*Table Of Contents, pg. v*List of Figures, pg. vi*Preface to the Third Edition, pg. vii*Chronological Table, pg. viii*Riemann Surfaces, pg. 1*Iterated Holomorphic Maps, pg. 39*Local Fixed Point Theory, pg. 76*Periodic Points: Global Theory, pg. 142*Structure of the Fatou Set, pg. 161*Using the Fatou Set to Study the Julia Set, pg. 174*Appendix A. Theorems from Classical Analysis, pg. 219*Appendix B. Length-Area-Modulus Inequalities, pg. 226*Appendix C. Rotations, Continued Fractions, and Rational Approximation, pg. 234*Appendix D. Two or More Complex Variables, pg. 246*Appendix E. Branched Coverings and Orbifolds, pg. 254*Appendix F. No Wandering Fatou Components, pg. 259*Appendix G. Parameter Spaces, pg. 266*Appendix H. Computer Graphics and Effective Computation, pg. 271*References, pg. 277*Index, pg. 293","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":48865518715223,"sku":"9780691124889","price":69.7,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780691124889.jpg?v=1722274358"},{"product_id":"spin-glasses-and-complexity-9780691147338","title":"Spin Glasses and Complexity","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eSpin glasses are disordered magnetic systems that have led to the development of mathematical tools with an array of real-world applications, from airline scheduling to neural networks. This book offers an introduction to the subject, explaining what spin glasses are, and how they are opening up new ways of thinking about complexity.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"The challenge that Stein and Newman faced in creating this book ... was to write for a broad range of readers and still offer interesting depth. As they state in the preface, they are aiming for a reading level that is between Scientific American and research journals. This reviewer believes they have succeeded... Stein and Newman write well and keep the mathematics to a minimum.\"--Choice \"[A] surprisingly broad field of view is visible through the lens of the classical, equilibrium using spin glass and the authors are able to use it to explore many fascinating topics. Stein and Newman have written an excellent introduction to the field of spin glasses and the many ramifications of spin glass theory outside of condensed matter physics and statistical mechanics. Experts and novices alike will find this book interesting and useful.\"--Jonathan Machta, Journal of Statistical Physics \"Spin Glasses and Complexity is not a journalistic book that merely reports on the subject. Based on profound mathematical insights, here distilled into an incisive presentation, it represents the fruit of the lifelong commitments two experts have made to spin-glass theory within and beyond physics... Spin Glasses and Complexity is unique in successfully bringing this thrilling theme to a broader scientific audience.\"--Stefan Boettcher, Physics Today \"[T]he work is well presented and the reader will surely find it both inspiring and interesting.\"--Marco Castrillon Lopez, European Mathematical Society \"Well presented and the reader will surely find it both inspiring and interesting.\"--Marco Castrillon Lopez, European Mathematical Society\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface xi  Introduction: Why Spin Glasses? 1  *1. Order, Symmetry, and the Organization of Matter 15  *1.1 The Symmetry of Physical Laws 17  *1.2 The Hamiltonian 23  *1.3 Broken Symmetry 26  *1.4 The Order Parameter 31  *1.5 Phases of Matter 35  *1.6 Phase Transitions 39  *1.7 Summary: The Unity of Condensed Matter Physics 41  2. Glasses and Quenchied Disorder 43  *2.1 Equilibrium and Non Equilibrium 43  * 2.2 The Glass Transition 45  *2.3 Localization 49   3. Magnetic Systems 51  *3.1 Spin 51  *3.2 Magnetism in Solids 53  *3.3 The Paramagnetic Phase 55  *3.4 Magnetization 55  *3.5 The Ferromagnetic Phase and Magnetic Susceptibility 57  *3.6 The Antiferromagnetic Phase 59  *3.7 Broken Symmetry and the Heisenberg Hamiltonian 59   4. Spin Glasses: General Features 63  *4.1 Dilute Magnetic Alloys and the Kondo Effect 64  *4.2 A New State of Matter? 65  *4.3 Nonequilibrium and Dynamical Behavior 71  *4.4 Mechanisms Underlying Spin Glass Behavior 74  *4.5 The Edwards-Anderson Hamiltonian 78  *4.6 Frustration 81  *4.7 Dimensionality and Phase Transitions 83  *4.8 Broken Symmetry and the Edwards-Anderson Order Parameter 85  *4.9 Energy Landscapes and Metastability 86   5. The Infinite-Range Spin Glass 90  *5.1 Mean Field Theory 90  *5.2 The Sherrington-Kirkpatrick Hamiltonian 92  *5.3 A Problem Arises 93  *5.4 The Remedy 95  *5.5 Thermodynamic States 97  *5.6 The Meaning of Replica Symmetry Breaking 98  *5.7 The Big Picture 109   6. Applications to Other Fields 112  *6.1 Computational Time Complexity and Combinatorial Optimization 113  *6.2 Neural Networks and Neural Computation 129  *6.3 Protein Folding and Conformational Dynamics 144  *6.4 Short Takes 168   7. Short-Range Spin Glasses: Some Basic Questions 175  *7.1 Ground States 177  *7.2 Pure States 188  *7.3 Scenarios for the Spin Glass Phase of the EA Model 193  *7.4 The Replica Symmetry Breaking and Droplet\/Scaling Scenarios 194  *7.5 The Parisi Overlap Distribution 197  *7.6 Self-Averaging and Non-Self-Averaging 199  *7.7 Ruling Out the Standard RSB Scenario 201  *7.8 Chaotic Size Dependence and Metastates 203  *7.9 A New RSB Scenario 206  *7.10 Two More (Relatively) New Scenarios 211  *7.11 Why Should the SK Model Behave Differently from the EA Model? 214  *7.12 Summary: Where Do We Stand? 216   8. Are Spin Glasses Complex Systems? 218  *8.1 Three Foundational Papers 219  *8.2 Spin Glasses as a Bridge to Somewhere 227  *8.3 Modern Viewpoints on Complexity 228  *8.4 Spin Glasses: Old, New, and Quasi-Complexity 233  Notes 239  Glossary 265  Bibliography 285  Index 309","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":48865523663191,"sku":"9780691147338","price":40.5,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780691147338.jpg?v=1722274379"},{"product_id":"chaos-and-dynamical-systems-9780691161525","title":"Chaos and Dynamical Systems","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThe author presents an accessible, clear introduction to dynamical systems and chaos theory, important and exciting areas that have shaped many scientific fields. While the rules governing dynamical systems are well-specified and simple, the behavior of many dynamical systems is remarkably complex.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"Feldman succeeds in introducing the reader to the world of dynamic systems and the, almost mythical, chaos that they can produce.\"\u003cb\u003e---Adhemar Bultheel, \u003ci\u003eEuropean Mathematical Society\u003c\/i\u003e\u003c\/b\u003e\u003cbr\u003e\"[A] gentle and loving introduction to dynamical systems. . . . \u003ci\u003eChaos and Dynamical Systems\u003c\/i\u003e is a book for everyone from the layman to the expert.\"\u003cb\u003e---David S. Mazel, \u003ci\u003eMAA Reviews\u003c\/i\u003e\u003c\/b\u003e","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":48865530347863,"sku":"9780691161525","price":28.8,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780691161525.jpg?v=1722274412"},{"product_id":"dr-eulers-fabulous-formula-9780691175911","title":"Dr. Eulers Fabulous Formula","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"Nahin includes gems from all over mathematics, ranging from engineering applications to beautiful pure-mathematical identities... It would be good to have more books like this.\"--Timothy Gowers, Nature \"Nahin's tale of the formula e[pi] i+1=0, which links five of the most important numbers in mathematics, is remarkable. With a plethora of historical and anecdotal material and a knack for linking events and facts, he gives the reader a strong sense of what drove mathematicians like Euler.\"--Matthew Killeya, New Scientist \"It is very difficult to sum up the greatness of Euler... This excellent book goes a long way to explaining the kind of mathematician he really was.\"--Steve Humble, Mathematics Today \"What a treasure of a book this is! This is the fourth enthusiastic, informative, and delightful book Paul Nahin has written about the beauties of various areas of mathematics... This book is a marvelous tribute to Euler's genius and those who built upon it and would make a great present for students of mathematics, physics, and engineering and their professors.\"--Henry Ricardo, MAA Reviews \"The heart and soul of the book are the final three chapters on Fourier series, Fourier integrals, and related engineering. One can recommend them to all applied math students for their historical development and sensible content.\"--Robert E. O'Malley, Jr., SIAM Review \"This is a book for mathematicians who enjoy historically motivated mathematical explanations on a high mathematical level.\"--Eberhard Knobloch, Mathematical Reviews \"It is a 'popular' book, written for a general reader with some mathematical background equivalent to a first-year undergraduate course in the UK.\"--Robin Wilson, London Mathematical Society Newsletter\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e*FrontMatter, pg. i*Contents, pg. ix*Preface to the Paperback Edition, pg. xiii*Preface, pg. xxix*Introduction, pg. 1*Chapter 1. Complex Numbers, pg. 13*Chapter 2. Vector Trips, pg. 68*Chapter 3. The Irrationality of pi2, pg. 92*Chapter 4. Fourier Series, pg. 114*Chapter 5. Fourier Integrals, pg. 188*Chapter 6. Electronics and   -1, pg. 275*Euler: The Man and the Mathematical Physicist, pg. 324*Notes, pg. 347*Acknowledgments, pg. 375*Index, pg. 377","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":48865537360215,"sku":"9780691175911","price":18.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780691175911.jpg?v=1722274448"},{"product_id":"a-course-in-complex-analysis-9780691207582","title":"A Course in Complex Analysis","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"A no-nonsense, clearly written graduate level textbook . . . . far more approachable than many other books on complex analysis\"\u003cb\u003e---Jonathan Shock, \u003ci\u003eMathemafrica\u003c\/i\u003e\u003c\/b\u003e\u003cbr\u003e\"An excellent textbook. . . . Carefully and precisely written in a lively style.\"\u003cb\u003e---Ali Abkar, \u003ci\u003ezbMATH Open\u003c\/i\u003e\u003c\/b\u003e\u003cbr\u003e\"Beautifully produced, beautifully written, on an incomparably beautiful area of mathematics, this is an inspirational book that I shall gratefully return to again and again.\"\u003cb\u003e---Nick Lord, \u003ci\u003eMathematical Gazette\u003c\/i\u003e\u003c\/b\u003e","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":48865547059543,"sku":"9780691207582","price":57.8,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780691207582.jpg?v=1722274497"},{"product_id":"an-introduction-to-the-uncertainty-principle-hardy-s-theorem-on-lie-groups-217-progress-in-mathematics-9780817643300","title":"An Introduction to the Uncertainty Principle","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eIn particular, if f and j are x2 x 2 2 2 both O(e- \/ ), then f = j = Ae- \/ , where A is a constant;\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\"This nicely written book by Thangavelu is concerned with extensions of Hardy's theorem to settings that arise from noncommutative harmonic analysis.... Each chapter contains several applications to the heat equation in various settings and ends with an extensive presentation of related topics, current research, detailed references to the literature, and lists of open problems. This makes the book an invaluable resource for graduate students and researchers in harmonic analysis and applied mathematics.\"\u003c\/p\u003e \u003cp\u003e\u003cstrong\u003e—SIAM Review\u003c\/strong\u003e\u003c\/p\u003e \u003cp\u003e\"…Each chapter ends with useful notes and open problems. Everything is written in sufficient detail to benefit specialized interested readers…\" \u003c\/p\u003e \u003cp\u003e\u003cstrong\u003e—MATHEMATICAL REVIEWS\u003c\/strong\u003e\u003c\/p\u003e \u003cp\u003e\"The authoer discusses inthe present book the original theorem of Hardy and some of its generaliztions and its connections to noncommunitave analysis, harmonic analysis and special functions. First Hardy's theorem for the Euclidian Fourier transform is treated, and a theorem of Beurling and Hömander Subsequently Hardy's theorem is dicussed for the Fourier transfom on the Heisenberg group. finally the author discusses generaliztions of Hardy's theorem involving the Helgason Fourier transform for rank one symmetric spaces and for H-type groups. This unique book will be of great value for readers interested in this branch of analysis.\"\u003c\/p\u003e \u003cp\u003e\u003cstrong\u003e---Monatshefte für Mathematik\u003c\/strong\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e1 Euclidean Spaces.- 1.1 Fourier transform on L1(?n).- 1.2 Hermite functions and L2 theory.- 1.3 Spherical harmonics and symmetry properties.- 1.4 Hardy’s theorem on ?n.- 1.5 Beurling’s theorem and its consequences.- 1.6 Further results and open problems.- 2 Heisenberg Groups.- 2.1 Heisenberg group and its representations.- 2.2 Fourier transform on Hn.- 2.3 Special Hermite functions.- 2.4 Fourier transform of radial functions.- 2.5 Unitary group and spherical harmonics.- 2.6 Spherical harmonics and the Weyl transform.- 2.7 Weyl correspondence of polynomials.- 2.8 Heat kernel for the sublaplacian.- 2.9 Hardy’s theorem for the Heisenberg group.- 2.10 Further results and open problems.- 3 Symmetric Spaces of Rank 1.- 3.1 A Riemannian space associated to Hn.- 3.2 The algebra of radial functions on S.- 3.3 Spherical Fourier transform.- 3.4 Helgason Fourier transform.- 3.5 Hecke-Bochner formula for the Helgason Fourier transform.- 3.6 Jacobi transforms.- 3.7 Estimating the heat kernel.- 3.8 Hardy’s theorem for the Helgason Fourier transform.- 3.9 Further results and open problems.","brand":"Birkhauser Boston Inc","offers":[{"title":"Default Title","offer_id":48884696514903,"sku":"9780817643300","price":80.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780817643300.jpg?v=1722533068"},{"product_id":"singularity-theory-and-its-application-9784931469327","title":"Singularity Theory And Its Application","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis is the proceedings of the meeting entitled “The 12th MSJ International Research Institute of the Mathematical Society of Japan 2003”. The papers cover several important topics in Singularity theory. Especially some of them are survey on motivic integrations, Thom polynomials, complex analytic singularity theory, generic differential geometry etc.Published by Mathematical Society of Japan and distributed by World Scientific Publishing Co. for all markets except North America\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eInvariants of combinatorial line arrangements and Rybnikov's example by E. A. Bartolo, J. C. Ruber, J. I. Cogolludo-Agustin, and M. A. Marco-Buzunariz On time averaged optimization of dynamic inequalities on a circle by A. Davydov Thom polynomial computing strategies. A survey by L. M. Feher and R. Rimanyi The complex crystallographic groups and symmetries of $J_{10}$ by V. Goryunov and S. H. Man $tt^*$ geometry and mixed Hodge structures by C. Hertling Thom polynomials by M. Kazarian Quasi-convex decomposition in o-minimal structures. Application to the gradient conjecture by K. Kurdyka and A. Parusinski Homotopy groups of complements to ample divisors by A. Libgober Massey products of complex hypersurface complements by D. Matei On degree of mobility for complete metrics by V. S. Matveev Valuations and moduli of Goursat distributions by P. Mormul Semidifferentiabilite et version lisse de la conjecture de fibration de Whitney by C. Murolo and D. Trotman Submanifolds with a nondegenerate parallel normal vector field in euclidean spaces by J. J. Nuno-Ballesteros Weighted homogeneous polynomials and blow-analytic equivalence by O. M. Abderrahmane Characteristic classes of singular varieties by A. Parusinski On the classification of 7th degree real decomposable curves by G. M. Polotovskiy $\\mathcal A$-topological triviality of map germs and Newton filtrations by M. J. Saia and L. M. Soares On the topology of symmetry sets of smooth submanifolds in $\\mathbb{R}^k$ by V. D. Sedyh An infinitesimal criterion for topological triviality of families of sections of analytic varieties by M. A. S. Ruas and J. N. Tomazella Lines of principal curvature near singular end points of surfaces in $\\mathbb{R}^3$ by J. Sotomayor and R. Garcia $r$ does not imply $n$ or $(npf)$ for definable sets in non polynomially bounded o-minimal structures by D. Trotman and L. Wilson Valuations and local uniformization by M. Vaquie Arc spaces, motivic integration and stringy invariants by W. Veys Finite Dehn surgery along A'Campo's divide knots by Y. Yamada.","brand":"Mathematical Society of Japan","offers":[{"title":"Default Title","offer_id":48889419956567,"sku":"9784931469327","price":84.6,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9784931469327.jpg?v=1722554298"},{"product_id":"fundamentals-of-fourier-analysis-9783031564994","title":"Fundamentals of Fourier Analysis","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis self-contained text introduces Euclidean Fourier Analysis to graduate students who have completed courses in Real Analysis and Complex Variables.","brand":"Springer International Publishing","offers":[{"title":"Default Title","offer_id":49084759802199,"sku":"9783031564994","price":999.99,"currency_code":"GBP","in_stock":false}]},{"product_id":"systems-biology-9780198828372","title":"Systems Biology","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eSystems biology came about as growing numbers of engineers and scientists from other fields created algorithms which supported the analysis of biological data in incredible quantities. Whereas biologists of the past had been forced to study one item or aspect at a time, due to technical and biological limitations, it suddenly became possible to study biological phenomena within their natural contexts. This interdisciplinary field offers a holistic approach to interpreting these processes, and has been responsible for some of the most important developments in the science of human health and environmental sustainability. This Very Short Introduction outlines the exciting processes and possibilities in the new field of systems biology. Eberhard O. Voit describes how it enabled us to learn how intricately the expression of every gene is controlled, how signaling systems keep organisms running smoothly, and how complicated even the simplest cells are. He explores what this field is about, why it is needed, and how it will affect our understanding of life, particularly in the areas of personalized medicine, drug development, food and energy production, and sustainable stewardship of our environments. Throughout he considers how new tools are being provided from the fields of mathematics, computer science, engineering, physics, and chemistry to grasp the complexity of the countless interacting processes in cells which would overwhelm the cognitive and analytical capabilities of the human mind. ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eAcknowledgments 1: What is systems biology all about? 2: The exciting puzzles of computational systems biology 3: The -omics revolution 4: Computational systems biology (CSB) 5: Interdependencies of biological systems 6: Simulators 7: The lawless pursuit of biological systems References Further reading Index","brand":"Oxford University Press","offers":[{"title":"Default Title","offer_id":49369151701335,"sku":"9780198828372","price":9.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780198828372.jpg?v=1730128554"},{"product_id":"metrical-and-dynamical-aspects-in-complex-analysis-9783319658360","title":"Metrical and Dynamical Aspects in Complex","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThe central theme of this reference book is the metric geometry of complex analysis in several variables. Bridging a gap in the current literature, the text focuses on the fine behavior of the Kobayashi metric of complex manifolds and its relationships to dynamical systems, hyperbolicity in the sense of Gromov and operator theory, all very active areas of research. The modern points of view expressed in these notes, collected here for the first time, will be of interest to academics working in the fields of several complex variables and metric geometry. The different topics are treated coherently and include expository presentations of the relevant tools, techniques and objects, which will be particularly useful for graduate and PhD students specializing in the area.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e1. Invariant Distances.- 2. Dynamics in Several Complex Variables.- 3. Gromov Hyperbolic Spaces and Applications to Complex Analysis.- 4. Gromov Hyperbolicity of Bounded Convex Domains.- 5. Quasi-conformal Mappings.- 6. Carleson Measures and Toeplitz Operators. References.","brand":"Springer International Publishing AG","offers":[{"title":"Default Title","offer_id":49372699263319,"sku":"9783319658360","price":999.99,"currency_code":"GBP","in_stock":false}]},{"product_id":"what-is-a-complex-system-9780300251104","title":"What Is a Complex System","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e“A clear analysis of systems ranging from radiation to human brains”—\u003ci\u003eNature\u003c\/i\u003e\u003cbr\u003e\u003cbr\u003e“Many people might not bother to define complexity, thinking that we know it when we see it. Scientists and philosophers have no such luxury, and for them this book will be invaluable. Ladyman and Wiesner have provided a compact but comprehensive overview of the different ways that systems can be complex, ultimately arguing that complexity comes in distinct forms, but that their commonalities are nevertheless quite real.”—Sean Carroll, author of \u003ci\u003eSomething Deeply Hidden: Quantum Worlds and the Emergence of Spacetime\u003c\/i\u003e\u003cbr\u003e\u003cbr\u003e“This is an outstanding, original, and much-needed book. Ladyman and Wiesner give an accessible, engaging, and precise overview of complexity science from a panoptic perspective, spanning many different kinds of examples from a variety of disciplines”—James Owen Weatherall, coauthor of \u003ci\u003eThe Misinformation Age: How False Beliefs Spread\u003c\/i\u003e\u003cbr\u003e\u003cbr\u003e“Written in a lively and readable style, \u003ci\u003eWhat Is a Complex System?\u003c\/i\u003e provides a clear and coherent synthesis of the myriad and sometimes contradictory descriptions and definitions of complex systems.”—Colm Connaughton, Director of the Centre for Complexity Science, University of Warwick\u003cbr\u003e  \u003cbr\u003e\u003cbr\u003e“This is highly thoughtful incisive essay on the meaning and use of the concept of complex systems. I particularly like the attempt to formulate syntheses across fields, across features and across mechanisms.”—Didier Sornette, author of \u003ci\u003eWhy Stock Markets Crash: Critical Events in Complex Financial Systems\u003c\/i\u003e\u003cbr\u003e\u003cbr\u003e“This book is a superb introduction to complex systems. Ladyman and Wiesner skillfully guide the reader from examples of complex systems all-around us, to ten common features of such systems and how to mathematically measure them, to a discussion of complexity as a scientific field by itself. Anyone interested in complex systems should read this book before any other.”—Tina Eliassi-Rad, Professor of Network Science, Northeastern University\u003cbr\u003e\u003cbr\u003e","brand":"Yale University Press","offers":[{"title":"Default Title","offer_id":49401561055575,"sku":"9780300251104","price":26.12,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780300251104.jpg?v=1730477804"},{"product_id":"modern-real-and-complex-analysis-9780471107156","title":"Modern Real and Complex Analysis","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eModern Real and Complex Analysis  Thorough, well-written, and encyclopedic in its coverage, this text offers a lucid presentation of all the topics essential to graduate study in analysis. While maintaining the strictest standards of rigor, Professor Gelbaum's approach is designed to appeal to intuition whenever possible.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eREAL ANALYSIS.\u003cbr\u003e \u003cbr\u003e Fundamentals.\u003cbr\u003e \u003cbr\u003e Integration.\u003cbr\u003e \u003cbr\u003e Functional Analysis.\u003cbr\u003e \u003cbr\u003e More Measure Theory.\u003cbr\u003e \u003cbr\u003e COMPLEX ANALYSIS.\u003cbr\u003e \u003cbr\u003e Locally Holomorphic Functions.\u003cbr\u003e \u003cbr\u003e Harmonic Functions.\u003cbr\u003e \u003cbr\u003e Meromorphic and Entire Functions.\u003cbr\u003e \u003cbr\u003e Conformal Mapping.\u003cbr\u003e \u003cbr\u003e Defective Functions.\u003cbr\u003e \u003cbr\u003e Riemann Surfaces.\u003cbr\u003e \u003cbr\u003e Convexity and Complex Analysis.\u003cbr\u003e \u003cbr\u003e Several Complex Variables.\u003cbr\u003e \u003cbr\u003e Bibliography.\u003cbr\u003e \u003cbr\u003e Symbol List.\u003cbr\u003e \u003cbr\u003e Glossary\/Index.","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":49402488848727,"sku":"9780471107156","price":169.16,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780471107156.jpg?v=1730480560"},{"product_id":"spatial-tessellations-9780471986355","title":"Spatial Tessellations","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eSpatial data analysis is a fast growing area and Voronoi diagrams provide a means of naturally partitioning space into subregions to facilitate spatial data manipulation, modelling of spatial structures, pattern recognition and locational optimization.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"While this edition maintains the overall structure of the first, there are substantial changes in the content...\" (Mathematical Reviews, Issue 2001c)\u003cbr\u003e \u003cbr\u003e \"...a must...\" (Monatshefte fur Mathematik, Vol 131\/2, 2000)\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eDefinitions and Basic Properties of Voronoi Diagrams.\u003cbr\u003e \u003cbr\u003e Generalizations of the Voronoi Diagram.\u003cbr\u003e \u003cbr\u003e Algorithms for Computing Voronoi Diagrams.\u003cbr\u003e \u003cbr\u003e Poisson Voronoi Diagrams.\u003cbr\u003e \u003cbr\u003e Spatial Interpolation.\u003cbr\u003e \u003cbr\u003e Models of Spatial Processes.\u003cbr\u003e \u003cbr\u003e Point Pattern Analysis.\u003cbr\u003e \u003cbr\u003e Locational Optimization Through Voronoi Diagrams.\u003cbr\u003e \u003cbr\u003e References.\u003cbr\u003e \u003cbr\u003e Index.","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":49402709672279,"sku":"9780471986355","price":176.36,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780471986355.jpg?v=1730481301"},{"product_id":"rigid-local-systems-9780691011189","title":"Rigid Local Systems","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThe author introduced the concept of a \"local system\" on P1-{a finite set of points} nearly 140 years ago. His idea was to study nth order linear differential equations by studying the rank n local systems (of local holomorphic solutions) to which they gave rise.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"It is clear that this book presents highly important new views and results on the classical theory of complex linear differential equations.\"--Zentralblatt fur Mathematik\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e* First results on rigid local systems * The theory of middle concolution * Fourier Transform and rigidity * Middle concolution: dependence on parameters * Structure of rigid local systems * Existence algorithms for rigids * Diophantine aspects of rigidity * rigids","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":49403674722647,"sku":"9780691011189","price":74.8,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780691011189.jpg?v=1730484221"},{"product_id":"global-dynamics-9781118922286","title":"Global Dynamics","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\u003cb\u003eA world model: economies, trade, migration, security and development aid.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eThis bookprovides the analytical capability to understand and explore the dynamics of globalisation. It is anchored in economic input-output models of over 200 countries and their relationships through trade, migration, security and development aid. The tools of complexity science are brought to bear and mathematical and computer models are developed both for the elements and for an integrated whole. Models are developed at a variety of scales ranging from the global and international trade through a European model of inter-sub-regional migration to piracy in the Gulf and the London riots of 2011. The models embrace the changing technology of international shipping, the impacts of migration on economic development along with changing patterns of military expenditure and development aid. A unique contribution is the level of spatial disaggregation which presents each of 200+ countries and their mu\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003c\/p\u003e\u003cp\u003eNotes on Contributors xiii\u003c\/p\u003e \u003cp\u003eAcknowledgements xvii\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart I GLOBAL DYNAMICS AND THE TOOLS OF COMPLEXITY SCIENCE\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Global Dynamics and the Tools of Complexity Science 3\u003c\/b\u003e\u003cbr\u003e\u003ci\u003eAlan Wilson\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003eReference 7\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart II TRADE AND ECONOMIC DEVELOPMENT\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 The Global Trade System and Its Evolution 11\u003c\/b\u003e\u003cbr\u003e\u003ci\u003eSimone Caschili and Francesca Medda\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e2.1 The Evolution of the Shipping and Ports’ System 11\u003c\/p\u003e \u003cp\u003e2.2 Analyses of the Cargo Ship Network 12\u003c\/p\u003e \u003cp\u003e2.3 A Complex Adaptive Systems (CASs) Perspective 15\u003c\/p\u003e \u003cp\u003e2.4 Conclusions: The Benefits of a Systems Perspective 20\u003c\/p\u003e \u003cp\u003eReferences 21\u003c\/p\u003e \u003cp\u003eAppendix 23\u003c\/p\u003e \u003cp\u003eA.1 Complexity Science and Complex Adaptive Systems: Key Characteristics 23\u003c\/p\u003e \u003cp\u003eA.1.1 Four Properties 24\u003c\/p\u003e \u003cp\u003eA.1.2 Three Mechanisms 25\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 An Interdependent Multi-layer Model for Trade 26\u003c\/b\u003e\u003cbr\u003e\u003ci\u003eSimone Caschili, Francesca Medda, and Alan Wilson\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e3.1 Introduction 26\u003c\/p\u003e \u003cp\u003e3.2 The Interdependent Multi-layer Model: Vertical Integration 27\u003c\/p\u003e \u003cp\u003e3.3 Model Layers 30\u003c\/p\u003e \u003cp\u003e3.3.1 Economic Layer 30\u003c\/p\u003e \u003cp\u003e3.3.2 Social and Cultural Layer (Socio-cultural) 33\u003c\/p\u003e \u003cp\u003e3.3.3 Physical Layer 34\u003c\/p\u003e \u003cp\u003e3.4 The Workings of the Model 34\u003c\/p\u003e \u003cp\u003e3.5 Model Calibration 35\u003c\/p\u003e \u003cp\u003e3.6 Result 1: Steady State 39\u003c\/p\u003e \u003cp\u003e3.7 Result 2: Estimation and Propagation of Shocks in the IMM 42\u003c\/p\u003e \u003cp\u003e3.8 Discussion and Conclusions 48\u003c\/p\u003e \u003cp\u003eReferences 48\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 A Global Inter-country Economic Model Based on Linked Input–Output Models 51\u003c\/b\u003e\u003cbr\u003e\u003ci\u003eRobert G. Levy, Thomas P. Oléron Evans, and Alan Wilson\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e4.1 Introduction 51\u003c\/p\u003e \u003cp\u003e4.2 Existing Global Economic Models 52\u003c\/p\u003e \u003cp\u003e4.3 Description of the Model 53\u003c\/p\u003e \u003cp\u003e4.3.1 Outline 53\u003c\/p\u003e \u003cp\u003e4.3.2 Introduction to Input–Output Tables 53\u003c\/p\u003e \u003cp\u003e4.3.3 A Single Country Model 55\u003c\/p\u003e \u003cp\u003e4.3.4 An International Trade Model 57\u003c\/p\u003e \u003cp\u003e4.3.5 Setting Model Coefficients from Data 58\u003c\/p\u003e \u003cp\u003e4.4 Solving the Model 58\u003c\/p\u003e \u003cp\u003e4.4.1 The Leontief Equation 58\u003c\/p\u003e \u003cp\u003e4.4.2 The Drawbacks of Mathematical Elegance 59\u003c\/p\u003e \u003cp\u003e4.4.3 Algorithm for an Iterative Solution 59\u003c\/p\u003e \u003cp\u003e4.5 Analysis 61\u003c\/p\u003e \u003cp\u003e4.5.1 Introduction 61\u003c\/p\u003e \u003cp\u003e4.5.2 Simple Modelling Approaches 61\u003c\/p\u003e \u003cp\u003e4.5.3 A Unified Network Approach 64\u003c\/p\u003e \u003cp\u003e4.5.4 Comparison with a Multi-region Input–Output Model 67\u003c\/p\u003e \u003cp\u003e4.6 Conclusions 67\u003c\/p\u003e \u003cp\u003eAcknowledgements 69\u003c\/p\u003e \u003cp\u003eReferences 69\u003c\/p\u003e \u003cp\u003eAppendix 71\u003c\/p\u003e \u003cp\u003eA.1 Modelling the ‘Rest of the World’ 71\u003c\/p\u003e \u003cp\u003eA.2 Services Trade Data 71\u003c\/p\u003e \u003cp\u003eA.2.1 Importing Own Exports 72\u003c\/p\u003e \u003cp\u003eA.2.2 The Rest of the World for Sectors 72\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart III MIGRATION\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Global Migration Modelling: A Review of Key Policy Needs and Research Centres 75\u003c\/b\u003e\u003cbr\u003e\u003ci\u003eAdam Dennett and Pablo Mateos\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e5.1 Introduction 75\u003c\/p\u003e \u003cp\u003e5.2 Policy and Migration Research 76\u003c\/p\u003e \u003cp\u003e5.2.1 Key Policy Issues in Contemporary Migration Research 76\u003c\/p\u003e \u003cp\u003e5.2.2 Linking Policy Issues to Modelling Challenges 81\u003c\/p\u003e \u003cp\u003e5.2.3 Policy-related Research Questions for Modellers 82\u003c\/p\u003e \u003cp\u003e5.2.4 Other International Migration Modelling Research 83\u003c\/p\u003e \u003cp\u003e5.3 Conclusion 84\u003c\/p\u003e \u003cp\u003eReferences 84\u003c\/p\u003e \u003cp\u003eAppendix 87\u003c\/p\u003e \u003cp\u003eA.1 United Kingdom 87\u003c\/p\u003e \u003cp\u003eA.2 Rest of Europe 90\u003c\/p\u003e \u003cp\u003eA.3 Rest of the World 94\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Estimating Inter-regional Migration in Europe 97\u003c\/b\u003e\u003cbr\u003e\u003ci\u003eAdam Dennett and Alan Wilson\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e6.1 Introduction 97\u003c\/p\u003e \u003cp\u003e6.2 The Spatial System and the Modelling Challenge 98\u003c\/p\u003e \u003cp\u003e6.3 Biproportional Fitting Modelling Methodology 100\u003c\/p\u003e \u003cp\u003e6.3.1 Model (i) 104\u003c\/p\u003e \u003cp\u003e6.3.2 Model (ii) 105\u003c\/p\u003e \u003cp\u003e6.3.3 Model (iii) 105\u003c\/p\u003e \u003cp\u003e6.3.4 Model (iv) 108\u003c\/p\u003e \u003cp\u003e6.3.5 Model (v) 109\u003c\/p\u003e \u003cp\u003e6.3.6 Model (vi) 110\u003c\/p\u003e \u003cp\u003e6.4 Model Parameter Calibration 110\u003c\/p\u003e \u003cp\u003e6.5 Model Experiments 113\u003c\/p\u003e \u003cp\u003e6.6 Results 118\u003c\/p\u003e \u003cp\u003e6.7 Conclusions and Comments on the New Framework for Estimating Inter-regional, Inter-country Migration Flows in Europe 121\u003c\/p\u003e \u003cp\u003eReferences 123\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Estimating an Annual Time Series of Global Migration Flows – An Alternative Methodology for Using Migrant Stock Data 125\u003c\/b\u003e\u003cbr\u003e\u003ci\u003eAdam Dennett\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e7.1 Introduction 125\u003c\/p\u003e \u003cp\u003e7.2 Methodology 129\u003c\/p\u003e \u003cp\u003e7.2.1 Introduction 129\u003c\/p\u003e \u003cp\u003e7.2.2 Calculating Migration Probabilities 129\u003c\/p\u003e \u003cp\u003e7.2.3 Calculating Total Migrants in the Global System 130\u003c\/p\u003e \u003cp\u003e7.2.4 Generating a Consistent Time Series of Migration Probabilities 133\u003c\/p\u003e \u003cp\u003e7.2.5 Producing Annual Bilateral Estimates 135\u003c\/p\u003e \u003cp\u003e7.3 Results and Validation 135\u003c\/p\u003e \u003cp\u003e7.3.1 Introduction 135\u003c\/p\u003e \u003cp\u003e7.3.2 IMEM comparison 135\u003c\/p\u003e \u003cp\u003e7.3.3 UN Flow Data Comparison 136\u003c\/p\u003e \u003cp\u003e7.4 Discussion 138\u003c\/p\u003e \u003cp\u003e7.5 Conclusions 140\u003c\/p\u003e \u003cp\u003eReferences 140\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart IV SECURITY\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Conflict Modelling: Spatial Interaction as Threat 145\u003c\/b\u003e\u003cbr\u003e\u003ci\u003ePeter Baudains and Alan Wilson\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e8.1 Introduction 145\u003c\/p\u003e \u003cp\u003e8.2 Conflict Intensity: Space–Time Patterning of Events 146\u003c\/p\u003e \u003cp\u003e8.3 Understanding Conflict Onset: Simulation-based Models 148\u003c\/p\u003e \u003cp\u003e8.4 Forecasting Global Conflict Hotspots 150\u003c\/p\u003e \u003cp\u003e8.5 A Spatial Model of Threat 150\u003c\/p\u003e \u003cp\u003e8.6 Discussion: The Use of a Spatial Threat Measure in Models of Conflict 153\u003c\/p\u003e \u003cp\u003e8.6.1 Threat in Models for Operational Decision-Making 153\u003c\/p\u003e \u003cp\u003e8.6.2 Threat in a Model of Conflict Escalation 154\u003c\/p\u003e \u003cp\u003e8.6.3 Threat in Modelling Global Military Expenditure 156\u003c\/p\u003e \u003cp\u003e8.6.4 Summary 156\u003c\/p\u003e \u003cp\u003eReferences 157\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 Riots 159\u003c\/b\u003e\u003cbr\u003e\u003ci\u003ePeter Baudains\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e9.1 Introduction 159\u003c\/p\u003e \u003cp\u003e9.2 The 2011 Riots in London 160\u003c\/p\u003e \u003cp\u003e9.2.1 Space–Time Interaction 162\u003c\/p\u003e \u003cp\u003e9.2.2 Journey to Crime 164\u003c\/p\u003e \u003cp\u003e9.2.3 Characteristics of Rioters 165\u003c\/p\u003e \u003cp\u003e9.3 Data-Driven Modelling of Riot Diffusion 166\u003c\/p\u003e \u003cp\u003e9.4 Statistical Modelling of Target Choice 169\u003c\/p\u003e \u003cp\u003e9.5 A Generative Model of the Riots 171\u003c\/p\u003e \u003cp\u003e9.6 Discussion 172\u003c\/p\u003e \u003cp\u003eReferences 173\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 Rebellions 175\u003c\/b\u003e\u003cbr\u003e\u003ci\u003ePeter Baudains, Jyoti Belur, Alex Braithwaite, Elio Marchione and Shane D. Johnson\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e10.1 Introduction 175\u003c\/p\u003e \u003cp\u003e10.2 Data 176\u003c\/p\u003e \u003cp\u003e10.3 Hawkes model 177\u003c\/p\u003e \u003cp\u003e10.4 Results 181\u003c\/p\u003e \u003cp\u003e10.5 Discussion 183\u003c\/p\u003e \u003cp\u003eReferences 185\u003c\/p\u003e \u003cp\u003e\u003cb\u003e11 Spatial Interaction as Threat: Modelling Maritime Piracy 187\u003c\/b\u003e\u003cbr\u003e\u003ci\u003eElio Marchione and Alan Wilson\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e11.1 The Model 187\u003c\/p\u003e \u003cp\u003e11.2 The Test Case 188\u003c\/p\u003e \u003cp\u003e11.3 Uses of the Model 189\u003c\/p\u003e \u003cp\u003eReference 191\u003c\/p\u003e \u003cp\u003eAppendix 192\u003c\/p\u003e \u003cp\u003eA.1 Volume Field of Type k Ship 192\u003c\/p\u003e \u003cp\u003eA.2 Volume Field of Naval Units 193\u003c\/p\u003e \u003cp\u003eA.3 Pirates Ports and Mother Ships 193\u003c\/p\u003e \u003cp\u003e\u003cb\u003e12 Space–Time Modelling of Insurgency and Counterinsurgency in Iraq 195\u003c\/b\u003e\u003cbr\u003e\u003ci\u003eAlex Braithwaite and Shane Johnson\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e12.1 Introduction 195\u003c\/p\u003e \u003cp\u003e12.2 Counterinsurgency in Iraq 196\u003c\/p\u003e \u003cp\u003e12.3 Counterinsurgency Data 200\u003c\/p\u003e \u003cp\u003e12.4 Diagnoses of Space, Time and Space–Time Distributions 202\u003c\/p\u003e \u003cp\u003e12.4.1 Introduction 202\u003c\/p\u003e \u003cp\u003e12.4.2 Spatial Distribution 202\u003c\/p\u003e \u003cp\u003e12.4.3 Temporal Distribution 203\u003c\/p\u003e \u003cp\u003e12.4.4 Space–Time Distribution 203\u003c\/p\u003e \u003cp\u003e12.4.5 Univariate Knox Analysis 206\u003c\/p\u003e \u003cp\u003e12.4.6 Bivariate Knox Analysis 208\u003c\/p\u003e \u003cp\u003e12.5 Concluding Comments 210\u003c\/p\u003e \u003cp\u003eReferences 212\u003c\/p\u003e \u003cp\u003e\u003cb\u003e13 International Information Flows, Government Response and the Contagion of Ethnic Conflict 214\u003c\/b\u003e\u003cbr\u003e\u003ci\u003eJanina Beiser\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e13.1 Introduction 214\u003c\/p\u003e \u003cp\u003e13.2 Global Information Flows 216\u003c\/p\u003e \u003cp\u003e13.3 The Effect of Information Flows on Armed Civil Conflict 220\u003c\/p\u003e \u003cp\u003e13.4 The Effect of Information Flows on Government Repression 225\u003c\/p\u003e \u003cp\u003e13.5 Conclusion 226\u003c\/p\u003e \u003cp\u003eReferences 226\u003c\/p\u003e \u003cp\u003eAppendix 229\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart V AID AND DEVELOPMENT\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e14 International Development Aid: A Complex System 233\u003c\/b\u003e\u003cbr\u003e\u003ci\u003eBelinda Wu\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e14.1 Introduction: A Complex Systems’ Perspective 233\u003c\/p\u003e \u003cp\u003e14.2 The International Development Aid System: Definitions 234\u003c\/p\u003e \u003cp\u003e14.3 Features of International Development Aid as a Complex System 235\u003c\/p\u003e \u003cp\u003e14.3.1 Introduction 235\u003c\/p\u003e \u003cp\u003e14.3.2 Non-linearity 235\u003c\/p\u003e \u003cp\u003e14.3.3 Connectedness 237\u003c\/p\u003e \u003cp\u003e14.3.4 Self-Adapting and Self-Organising 238\u003c\/p\u003e \u003cp\u003e14.3.5 Emergence 238\u003c\/p\u003e \u003cp\u003e14.4 Complexity and Approaches to Research 238\u003c\/p\u003e \u003cp\u003e14.4.1 Organisations 238\u003c\/p\u003e \u003cp\u003e14.4.2 The Range of Issues 239\u003c\/p\u003e \u003cp\u003e14.4.3 Research Approaches 240\u003c\/p\u003e \u003cp\u003e14.4.4 The Complexity Science Approach 242\u003c\/p\u003e \u003cp\u003e14.5 The Assessment of the Effectiveness of International Development Aid 242\u003c\/p\u003e \u003cp\u003e14.5.1 Whether Aid Can Be Effective 242\u003c\/p\u003e \u003cp\u003e14.5.2 Complexity in the Measurement of Aid Effectiveness 244\u003c\/p\u003e \u003cp\u003e14.5.3 Complexity in Methods\/Standards of Measurement of Aid Effectiveness 245\u003c\/p\u003e \u003cp\u003e14.5.4 Standardising Aid Effectiveness 246\u003c\/p\u003e \u003cp\u003e14.6 Relationships and Interactions 248\u003c\/p\u003e \u003cp\u003e14.6.1 Relationships between Donor and Recipient Countries 248\u003c\/p\u003e \u003cp\u003e14.6.2 Relationships between Aid and Other Systems 249\u003c\/p\u003e \u003cp\u003e14.7 Conclusions 251\u003c\/p\u003e \u003cp\u003eReferences 252\u003c\/p\u003e \u003cp\u003e\u003cb\u003e15 Model Building for the Complex System of International Development Aid 257\u003c\/b\u003e\u003cbr\u003e\u003ci\u003eBelinda Wu, Sean Hanna and Alan Wilson\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e15.1 Introduction 257\u003c\/p\u003e \u003cp\u003e15.2 Data Collection 258\u003c\/p\u003e \u003cp\u003e15.2.1 Introduction 258\u003c\/p\u003e \u003cp\u003e15.2.2 Aid Data 258\u003c\/p\u003e \u003cp\u003e15.2.3 Trade Data 260\u003c\/p\u003e \u003cp\u003e15.2.4 Security Data 261\u003c\/p\u003e \u003cp\u003e15.2.5 Migration Data 261\u003c\/p\u003e \u003cp\u003e15.2.6 Geographical Data 261\u003c\/p\u003e \u003cp\u003e15.2.7 Data Selected 262\u003c\/p\u003e \u003cp\u003e15.3 Model Building 263\u003c\/p\u003e \u003cp\u003e15.3.1 Modelling Approach 263\u003c\/p\u003e \u003cp\u003e15.3.2 Alesina and Dollar Model 263\u003c\/p\u003e \u003cp\u003e15.3.3 Our Models 264\u003c\/p\u003e \u003cp\u003e15.3.4 Model B: Introducing Donor Interactions and Modification of the Model 267\u003c\/p\u003e \u003cp\u003e15.3.5 Findings from Model B 267\u003c\/p\u003e \u003cp\u003e15.3.6 Model C: Introducing Interactions with Trade System and Further Modification of the Model 267\u003c\/p\u003e \u003cp\u003e15.3.7 Findings from Model C 268\u003c\/p\u003e \u003cp\u003e15.4 Discussion and Future Work 268\u003c\/p\u003e \u003cp\u003eReferences 269\u003c\/p\u003e \u003cp\u003e\u003cb\u003e16 Aid Allocation: A Complex Perspective 271\u003c\/b\u003e\u003cbr\u003e\u003ci\u003eRobert J. Downes and Steven R. Bishop\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e16.1 Aid Allocation Networks 271\u003c\/p\u003e \u003cp\u003e16.1.1 Introduction 271\u003c\/p\u003e \u003cp\u003e16.1.2 Why Networks? 272\u003c\/p\u003e \u003cp\u003e16.1.3 Donor Motivation in Aid Allocation 273\u003c\/p\u003e \u003cp\u003e16.2 Quantifying Aid via a Mathematical Model 273\u003c\/p\u003e \u003cp\u003e16.2.1 Overview of Approach 273\u003c\/p\u003e \u003cp\u003e16.2.2 Basic Set-Up 274\u003c\/p\u003e \u003cp\u003e16.2.3 The Network of Nations 275\u003c\/p\u003e \u003cp\u003e16.2.4 Preference Functions 275\u003c\/p\u003e \u003cp\u003e16.2.5 Specifying the Preference Functions 275\u003c\/p\u003e \u003cp\u003e16.2.6 Recipient Selection by Donors 276\u003c\/p\u003e \u003cp\u003e16.3 Application of the Model 277\u003c\/p\u003e \u003cp\u003e16.3.1 Introduction 277\u003c\/p\u003e \u003cp\u003e16.3.2 Scenario 1. No Feedback 277\u003c\/p\u003e \u003cp\u003e16.3.3 Scenario 2. Bandwagon Feedback 281\u003c\/p\u003e \u003cp\u003e16.3.4 Scenario 3. Aid Effectiveness Feedback 283\u003c\/p\u003e \u003cp\u003e16.3.5 Aid Usage Mechanism 284\u003c\/p\u003e \u003cp\u003e16.3.6 Application 286\u003c\/p\u003e \u003cp\u003e16.3.7 Conclusions 287\u003c\/p\u003e \u003cp\u003e16.4 Remarks 287\u003c\/p\u003e \u003cp\u003eAcknowledgements 288\u003c\/p\u003e \u003cp\u003eReferences 288\u003c\/p\u003e \u003cp\u003eAppendix 290\u003c\/p\u003e \u003cp\u003eA.1 Common Functional Definitions 290\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart VI GLOBAL DYNAMICS: AN INTEGRATED MODEL AND POLICY CHALLENGES\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e17 An Integrated Model 293\u003c\/b\u003e\u003cbr\u003e\u003ci\u003eRobert G. Levy\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e17.1 Introduction 293\u003c\/p\u003e \u003cp\u003e17.2 Adding Migration 294\u003c\/p\u003e \u003cp\u003e17.2.1 Introduction 294\u003c\/p\u003e \u003cp\u003e17.2.2 The Familiarity Effect 295\u003c\/p\u003e \u003cp\u003e17.2.3 Consumption Similarity 301\u003c\/p\u003e \u003cp\u003e17.2.4 Conclusions 304\u003c\/p\u003e \u003cp\u003e17.3 Adding Aid 304\u003c\/p\u003e \u003cp\u003e17.3.1 Introduction 304\u003c\/p\u003e \u003cp\u003e17.3.2 Estimating ‘Exportness’ 305\u003c\/p\u003e \u003cp\u003e17.3.3 Modelling Approach 306\u003c\/p\u003e \u003cp\u003e17.3.4 Results 306\u003c\/p\u003e \u003cp\u003e17.3.5 Conclusions 314\u003c\/p\u003e \u003cp\u003e17.4 Adding Security 316\u003c\/p\u003e \u003cp\u003e17.4.1 Introduction 316\u003c\/p\u003e \u003cp\u003e17.4.2 Literature Review 316\u003c\/p\u003e \u003cp\u003e17.4.3 Measures of Threat and the Global Dynamics Model 317\u003c\/p\u003e \u003cp\u003e17.4.4 Trade during Changing Security Conditions 318\u003c\/p\u003e \u003cp\u003e17.4.5 An Experiment of Increased Threat in the Global Dynamics Model 318\u003c\/p\u003e \u003cp\u003e17.4.6 Conclusions 322\u003c\/p\u003e \u003cp\u003e17.5 Concluding Comments 323\u003c\/p\u003e \u003cp\u003eReferences 324\u003c\/p\u003e \u003cp\u003eIndex 327\u003c\/p\u003e","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":49406947492183,"sku":"9781118922286","price":65.5,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781118922286.jpg?v=1730497654"},{"product_id":"bureaucracy-collegiality-and-social-change-redefining-organizations-with-multilevel-relational-infrastructures-9781839102363","title":"Bureaucracy, Collegiality and Social Change:","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis insightful book theorizes the contrast between two logics of organization: bureaucracy and collegiality. Based on this theory and employing a new methodology to transform our sociological understanding, Emmanuel Lazega sheds light on complex organizational phenomena that impact markets, political economy, and social stratification.\u003cp\u003e\u003c\/p\u003e\u003cp\u003e Lazega focuses on how organizations use and combine logics of bureaucracy and collegiality, deploying and developing the analysis of multilevel networks to explore how these logics coalesce and interact in organizational settings and stratigraphies. Revisiting sociological knowledge on various phenomena, such as coopetition in science, markets and government, the creation of new institutions in political economy and elite self-segregation, this book advances our perception of the changes introduced in the contemporary 'science of organizations' by the digitalization of society.\u003c\/p\u003e\u003cp\u003e Offering new theoretical insights into organizations, this book is crucial for sociologists of organizations and management scholars, as well as postgraduate students, in search of an innovative understanding of the trajectories of contemporary organizations. The analysis of multilevel networks will also benefit practitioners and analysts working in the field.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e‘The text provides a fascinating and insightful look into the complexity of organizations.’ -- Cindy L Davis, International Social Science Review\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eContents: 1. Introduction  PART I A STRATIGRAPHIC AND MULTILEVEL NETWORK APPROACH TO ORGANIZATIONS  2. Bureaucracy and collegiality co-constituting organizations as multilevel settings  3. Combined bureaucracy and collegiality in co-constitution of organizations and their environment  PART II EXPLORATORY APPLICATIONS OF STRATIGRAPHIC AND MULTILEVEL NETWORK APPROACHES  4. Government by relationships: policy, collegial oligarchies of insiders, and institutions of the political economy  5. Revisiting the role of organizations in generating social inequalities and stratification  6. Inside-out collegiality: new bureaucratic parameterizations of commons through digitalization  7. Conclusion  References   Index","brand":"Edward Elgar Publishing Ltd","offers":[{"title":"Default Title","offer_id":49413248188759,"sku":"9781839102363","price":110.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781839102363.jpg?v=1730519518"},{"product_id":"excursions-in-harmonic-analysis-volume-6-in-honor-of-john-benedetto-s-80th-birthday-9783030696368","title":"Excursions in Harmonic Analysis, Volume 6: In","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eJohn J. Benedetto has had a profound influence not only on the direction of harmonic analysis and its applications, but also on the entire community of people involved in the field. The chapters in this volume – compiled on the occasion of his 80\u003csup\u003eth\u003c\/sup\u003e birthday – are written by leading researchers in the field and pay tribute to John’s many significant and lasting achievements. Covering a wide range of topics in harmonic analysis and related areas, these chapters are organized into four main parts: harmonic analysis, wavelets and frames, sampling and signal processing, and compressed sensing and optimization. An introductory chapter also provides a brief overview of John’s life and mathematical career. This volume will be an excellent reference for graduate students, researchers, and professionals in pure and applied mathematics, engineering, and physics.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eJohn Benedetto's mathematical work.- Absolute continuity and the Banach-Zaretsky Theorem.- Spectral Synthesis and H1(R).- Universal Upper Bound on the Blowup Rate of Nonlinear Schrodinger Equation with Rotation.- Almost Eigenvalues and Eigenvectors of Almost Mathieu Operators.- Spatio-spectral limiting on rendundant cubes: A case study.- A notion of optimal packings of subspaces with mix-rank and solutions.- Construction of Frames Using Calderon-Zygmund Operator Theory.- Equiangular frames and their duals.- Wavelet sets for crystallographic groups.- Discrete Translates in Function Spaces.- Local-to-global frames and applications to the dynamical sampling problem.- Signal analysis using Born-Jordan-type Distributions.- Sampling by averages and average splines on Dirichlet spaces and on combinatorial graphs.- Dynamical Sampling: a view from Control Theory.- Linear Multiscale Transforms Based on Even-Reversible Subdivision Operators.- Sparsity-Based MIMO Radars.- Robust width: A Characterization of uniformly stable and robust compressed sensing.- On best uniform affine approximants of convex or concave real valued functions from RK, Chebyshev equioscillation and graphics.- A Kaczmarz Algorithm for Solving Tree Based Distributed Systems of Equations.- Maximal function pooling with applications.","brand":"Springer Nature Switzerland AG","offers":[{"title":"Default Title","offer_id":49415630389591,"sku":"9783030696368","price":87.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783030696368.jpg?v=1730527579"},{"product_id":"geometric-aspects-of-harmonic-analysis-9783030720575","title":"Geometric Aspects of Harmonic Analysis","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis volume originated in talks given in Cortona at the conference \"Geometric aspects of harmonic analysis\" held in honor of the 70th birthday of Fulvio Ricci. It presents timely syntheses of several major fields of mathematics as well as original research articles contributed by some of the finest mathematicians working in these areas. The subjects dealt with are topics of current interest in closely interrelated areas of Fourier analysis, singular integral operators, oscillatory integral operators, partial differential equations, multilinear harmonic analysis, and several complex variables.\u003cbr\u003eThe work is addressed to researchers in the field.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e- An Extension Problem and Hardy Type Inequalities for the Grushin Operator. - Sharp Local Smoothing Estimates for Fourier Integral Operators. - On the Hardy–Littlewood Maximal Functions in High Dimensions: Continuous and Discrete Perspective. - Potential Spaces on Lie Groups. - On Fourier Restriction for Finite-Type Perturbations of the Hyperbolic Paraboloid. - On Young’s Convolution Inequality for Heisenberg Groups. - Young’s Inequality Sharpened. - Strongly Singular Integrals on Stratified Groups. - Singular Brascamp–Lieb: A Survey. - On the Restriction of Laplace–Beltrami Eigenfunctions and Cantor-Type Sets. - Basis Properties of the Haar System in Limiting Besov Spaces. - Obstacle Problems Generated by the Estimates of Square Function. - Of Commutators and Jacobians. - On Regularity and Irregularity of Certain Holomorphic Singular Integral Operators.","brand":"Springer Nature Switzerland AG","offers":[{"title":"Default Title","offer_id":49415631667543,"sku":"9783030720575","price":127.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783030720575.jpg?v=1730527583"},{"product_id":"birational-geometry-kahler-einstein-metrics-and-degenerations-moscow-shanghai-and-pohang-april-november-2019-9783031178580","title":"Birational Geometry, Kähler–Einstein Metrics and","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThis book collects the proceedings of a series of conferences dedicated to birational geometry of Fano varieties held in Moscow, Shanghai and Pohang\u003c\/p\u003e\u003cp\u003eThe conferences were focused on the following two related problems:\u003c\/p\u003e\u003cp\u003e•  existence of Kähler–Einstein metrics on Fano varieties\u003c\/p\u003e\u003cp\u003e•  degenerations of Fano varieties\u003c\/p\u003e\u003cp\u003eon which two famous conjectures were recently proved. The first is the famous Borisov–Alexeev–Borisov Conjecture on the boundedness of Fano varieties, proved by Caucher Birkar (for which he was awarded the Fields medal in 2018), and the second one is the (arguably even more famous) Tian–Yau–Donaldson Conjecture on the existence of Kähler–Einstein metrics on (smooth) Fano varieties and K-stability, which was proved by Xiuxiong Chen, Sir Simon Donaldson and Song Sun. The solutions for these longstanding conjectures have opened new directions in birational and Kähler geometries. These research directions generated new interesting mathematical problems, attracting the attention of mathematicians worldwide.\u003c\/p\u003e\u003cp\u003eThese conferences brought together top researchers in both fields (birational geometry and complex geometry) to solve some of these problems and understand the relations between them. The result of this activity is collected in this book, which contains contributions by sixty nine mathematicians, who contributed forty three research and survey papers to this volume. Many of them were participants of the Moscow–Shanghai–Pohang conferences, while the others helped to expand the research breadth of the volume—the diversity of their contributions reflects the vitality of modern Algebraic Geometry.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eT. Abe, Classification of exceptional complements: elliptic curve case.- E. Ballico, E. Gasparim, F. Rubilar, B. Suzuki, LAGRANGIAN SKELETA, COLLARS AND DUALITY.- G. Belousov, CYLINDERS IN DEL PEZZO SURFACES OF DEGREE TWO.- M. Benzerga, FINITENESS OF REAL STRUCTURES ON KLT CALABI-YAU REGULAR SMOOTH PAIRS OF DIMENSION 2.- C. Birkar, ANTICANONICAL VOLUME OF FANO 4-FOLDS.- C. Boyer Christina Tonnesen-Friedman, CONSTANT SCALAR CURVATURE SASAKI METRICS AND PROJECTIVE BUNDLES.- G. Brown, J. Buczynski, A. Kasprzyk, TORIC SARKISOV LINKS.- I. Burban, DU VAL SINGULARITIES.- I. Cheltsov, H. Suess, K-POLYSTABILITY OF TWO SMOOTH FANO THREEFOLDS.- G. Codogni, Z. Patakfalvi, A NOTE ON FAMILIES OF K-SEMISTABLE LOG-FANO PAIRS.- T. Delcroix, THE YAU-TIAN-DONALDSON CONJECTURE FOR COHOMOGENEITY ONE MANIFOLDS.- A. Dubouloz, FIBRATIONS BY AFFINE LINES ON RATIONAL AFFINE SURFACES WITH IRREDUCIBLE BOUNDARIES.- K. Fujita, ON FANO THREEFOLDS OF DEGREE 22 AFTER CHELTSOV AND SHRAMOV.- K. Fujita, Y. Liu, H. Suess, K. Zhang, Z. Zhuang, ON THE CHELTSOV-RUBINSTEIN CONJECTURE.- S. Grishin, Ilya Karzhemanov, Ming-Chang Kang, RATIONALITY OF QUOTIENTS BY FINITE HEISENBERG GROUPS.- Y. Hashimoto.- J. Keller, QUOT-SCHEME LIMIT OF FUBINI–STUDY METRICS AND ITS APPLICATIONS TO BALANCED METRICS.- Z. Hu, EXISTENCE OF CANONICAL MODELS FOR KAWAMATA LOG TERMINAL PAIRS.- Y. Imagi, GENERALIZED THOMAS–YAU UNIQUENESS THEOREMS.- K. Jamieson, BIRATIONALLY RIGID COMPLETE INTERSECTIONS OF CODIMENSION 3.- D. Jeong.- J. Park, SIMPLY CONNECTED SASAKI-EINSTEIN 5-MANIFOLDS: OLD AND NEW.- C. Jiang, CHARACTERIZING Q-FANO THREEFOLDS WITH THE SMALLEST ANTI-CANONICAL VOLUME.- L. Katzarkov, Kyoung-Seog Lee, J. Svoboda, A. Petkov, INTERPRETATIONS OF SPECTRA.- Young-Hoon Kiem, Kyoung-Seog Lee, FANO VISITORS, FANO DIMENSION AND FANO ORBIFOLDS.- In-kyun Kim, N. Viswanathan, J. Won, ON SINGULAR DEL PEZZO HYPERSURFACES OF INDEX 3.- S. Kudryavtsev, Blow-ups of three-dimensional toric singularities.- N. Kurnosov, E. Yasinsky, AUTOMORPHISMS OF HYPERKAHLER MANIFOLDS AND GROUPS ACTING ON CAT(0) SPACES.- A. Laface, R. Quezada, ON GENERALIZED BUCHI SURFACES.- Chi Li, K-STABILITY AND FUJITA APPROXIMATION.- Y. Li, Zhenye Li, ON A CONJECTURE OF FULTON ON ISOTROPIC GRASSMANNIANS.- Y. Maeda, Y. Odaka, FANO SHIMURA VARIETIES WITH MOSTLY BRANCHED CUSP.- L. Makar-Limanov, ON LOCALLY NILPOTENT DERIVATIONS OF DANIELEWSKI DOMAINS.- D. Markouchevitch, A. Moreau, ACTION OF THE AUTOMORPHISM GROUP ON THE JACOBIAN OF KLEIN'S QUARTIC CURVE.- J. Martinez-Garcia, C. Spotti, SOME OBSERVATIONS ON THE DIMENSION OF FANO K-MODULI.- D. Witt Nystrom, OKOUNKOV BODIES AND THE KAHLER GEOMETRY OF PROJECTIVE MANIFOLDS.- J. Park, SINGULARITIES OF PLURI-FUNDAMENTAL DIVISORS ON GORENSTEIN FANO VARIETIES OF COINDEX.-  J. Paulhus, A DATABASE OF GROUP ACTIONS ON RIEMANN SURFACES.- A. Petracci, A 1-DIMENSIONAL COMPONENT OF K-MODULI OF DEL PEZZO SURFACES.- T. De Piro, A NON-STANDARD BEZOUT THEOREM FOR CURVES.- Y. Prokhorov, EMBEDDINGS OF THE SYMMETRIC GROUPS TO THE SPACE CREMONA GROUP.- J. Ross, M. Toma, ON HODGE-RIEMANN COHOMOLOGY CLASSES.- Y. Rubinstein, ON LARGE DEVIATION PRINCIPLES AND THE MONGE–AMPERE EQUATION (FOLLOWING BERMAN, HULTGREN).- T. Sano, ON BIRATIONAL BOUNDEDNESS OF SOME CALABI-YAU HYPERSURFACES.- Y. Zarhin, ABELIAN VARIETIES, QUATERNION TRICK AND ENDOMORPHISMS.\u003cp\u003e\u003c\/p\u003e","brand":"Springer International Publishing AG","offers":[{"title":"Default Title","offer_id":49415693369687,"sku":"9783031178580","price":135.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783031178580.jpg?v=1730527811"},{"product_id":"mappings-with-direct-and-inverse-poletsky-inequalities-9783031454172","title":"Mappings with Direct and Inverse Poletsky","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThe monograph is devoted to the use of the moduli method in mapping theory, in particular, the meaning of direct and inverse modulus inequalities and their possible applications. The main goal is the development of a modulus technique in the Euclidean space and some metric spaces (manifolds, surfaces, quotient spaces, etc.). Particular attention is paid to the local and boundary behavior of mappings, as well as to obtaining modulus inequalities for some classes. The reader is invited to familiarize himself with all the main achievements of the author, synthesized in this book. The results presented here are of a high scientific level, are new and have no analogues in the world with such a degree of generality.\u003cbr\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eGeneral definitions and notation.- Boundary behavior of mappings with Poletsky inequality.- Removability of singularities of generalized quasiisometries.- Normal families of generalized quasiisometries.- On boundary behavior of mappings with Poletsky inequality in terms of prime ends.- Local and boundary behavior of mappings on Riemannian manifolds.- Local and boundary behavior of maps in metric spaces.- On Sokhotski-Casorati-Weierstrass theorem on metric spaces.- On boundary extension of mappings in metric spaces in the terms of prime ends.- On the openness and discreteness of mappings with the inverse Poletsky inequality.- Equicontinuity and isolated singularities of mappings with the inverse Poletsky inequality.- Equicontinuity of families of mappings with the inverse Poletsky inequality in terms of prime ends.- Logarithmic H¨older continuous mappings and Beltrami equation.- On logarithmic H¨older continuity of mappings on the boundary.- The Poletsky and V¨ais¨al¨a inequalities for the mappings with (p;q)-distortion.- An analog of the V¨ais¨al¨a inequality for surfaces.- Modular inequalities on Riemannian surfaces.- On the local and boundary behavior of mappings of factor spaces.- References.- Index.\u003c\/p\u003e","brand":"Springer International Publishing AG","offers":[{"title":"Default Title","offer_id":49415725056343,"sku":"9783031454172","price":999.99,"currency_code":"GBP","in_stock":false}]},{"product_id":"visual-complex-functions-an-introduction-with-phase-portraits-9783034801799","title":"Visual Complex Functions: An Introduction with","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThis book provides a systematic introduction to functions of one complex variable. Its novel feature is the consistent use of special color representations – so-called phase portraits – which visualize functions as images on their domains.\u003c\/p\u003e\u003cp\u003eReading \u003ci\u003eVisual Complex Functions\u003c\/i\u003e requires no prerequisites except some basic knowledge of real calculus and plane geometry. The text is self-contained and covers all the main topics usually treated in a first course on complex analysis. With separate chapters on various construction principles, conformal mappings and Riemann surfaces it goes somewhat beyond a standard programme and leads the reader to more advanced themes.\u003c\/p\u003e\u003cp\u003eIn a second storyline, running parallel to the course outlined above, one learns how properties of complex functions are reflected in and can be read off from phase portraits. The book contains more than 200 of these pictorial representations which endow individual faces to analytic functions. Phase portraits enhance the intuitive understanding of concepts in complex analysis and are expected to be useful tools for anybody working with special functions – even experienced researchers may be inspired by the pictures to new and challenging questions.\u003c\/p\u003e\u003cp\u003e\u003ci\u003eVisual Complex Functions\u003c\/i\u003e may also serve as a companion to other texts or as a reference work for advanced readers who wish to know more about phase portraits.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eFrom the reviews:\u003c\/p\u003e\u003cp\u003e“This textbook is an introduction to the classical theory of functions of one complex variable. Its distinctive feature are the graphical representations of functions, being the most useful tool in teaching and generally in mathematics. … The self-sufficiency of the textbook and the broad range of graphical examples makes the book useful for students as well as teachers of mathematics. … the book can be warmly recommended both to experts and to a new generation of mathematicians.” (Stanislawa Kanas, Zentralblatt MATH, Vol. 1264, 2013)\u003c\/p\u003e\u003cp\u003e“Anyone who works with complex variables should read this book. … Visual Complex Functions is a beautiful and careful presentation of an entire advanced introduction to complex analysis based on phase portraits and, where appropriate, other kinds of computer-generated pictures. … My understanding of many ideas and phenomena deepened through reading this book.” (Lloyd N. Trefethen, SIAM Review, Vol. 55 (4), 2013)\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003ePreface.- 1. Getting Acquainted.- 2. Complex Functions.- 3. Analytic Functions.- 4. Complex Calculus.- 5. Construction Principles.- 6. Conformal Mappings.- 7. Riemann Surfaces\u003c\/p\u003e","brand":"Birkhauser Verlag AG","offers":[{"title":"Default Title","offer_id":49415774077271,"sku":"9783034801799","price":999.99,"currency_code":"GBP","in_stock":false}]},{"product_id":"die-lehre-von-den-kettenbruchen-band-ii-analytisch-funktionentheoretische-kettenbruche-9783519020226","title":"Die Lehre von den Kettenbrüchen: Band II:","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eNunmehr kann ich auch den zweiten Teil meiner Lehre von den Kettenbrüchen, der den analytischen Kettenbrüchen gewidmet ist, als Band 11 in neuer Be­ arbeitung den Fachgenossen vorlegen. Ebenso wie bei dem im Jahr 1954 er­ schienenen Band I ging mein Bemühen dah~, den heutigen Stand der Wissen­ schaft in möglichst leicht verständlicher Weise darzustellen. Die leichte Ver­ ständlichkeit kann natürlich nicht bedeuten, daß der Leser das Buch wie einen Roman durcheilen kann. Wenn er aber die Technik der Differential-und Integral­ rechnung beherrscht, wenn er schon etwas von der Gammafunktion und von linearen Differentialgleichungen gehört hat und ein klein wenig Funktionen­ theorie weiß, kann er unschwer folgen; nur darf er, um in Einzelheiten ein­ zudringen, nicht die Mühe scheuen, gelegentlich Papier und Bleistift zur Hand zu nehmen und einfache Rechnungen nach gegebener Anweisung selbst durch­ zuführen. Es geht alles nach geläufigen Methoden. Der allgemeine Rahmen des Buches ist der alte geblieben; doch sind die sechs Kapitel mit weitgehend verändertem Inhalt gefüllt. Namentlich die ersten drei und auch die zweite Hälfte des vierten sind mannigfach umgestaltet und er­ weitert, während in den letzten zwei nur geringere Änderungen nötig und sogar Kürzungen möglich waren, um Raum für den neuen Stoff der früheren zu ge­ winnen. Überall in der Welt, besonders in der Neuen, ist in den letzten Dezennien ein reiches Material von neuen Kettenbruchtypen und neuen Erkenntnissen, vor allem in bezug auf Konvergenz, gewonnen worden, das gesichtet, geordnet und systematisch eingearbeitet werden mußte.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eI. Transformation von Kettenbrüchen..- § 1. Rekapitulation.- § 2. Null als Teilzähler. — Äquivalente Kettenbrüche.- § 3. Kettenbrüche mit vorgegebenen Näherungsbrüchen.- § 4. Kontraktion und Extension.- § 5. Äquivalenz von Kettenbrüchen und Reihen.- § 6. Äquivalenz von Kettenbrüchen und Produkten.- § 7. Die Transformation von Bauer und Muir.- § 8. Weitere Anwendungen. Haupformel von Ramanujan.- II. Kriterien für Konvergenz und Divergenz..- § 9. Bedingte und unbedingte Konvergenz.- § 10. Allgemeine Kriterien von Broman, Stern und Scott-Wall.- § 11. Konvergenz bei positiven Elementen.- § 12. Konvergenz bei reellen Elementen.- § 13. Irrationalität gewisser Kettenbrüche.- § 14. Die Konvergenzkriterien von Pringsheim.- § 15. Die Konvergenzkriterien von van Vleck-Jensen und Hamburger-Mall-Wall.- § 16. Anwendung: Geltungsbereich der Ramanujan-Formel.- § 17. Einige neuere Kriterien. — Das Parabeltheorem.- § 18. Periodische Kettenbrüche.- § 19. Limitärperiodische Kettenbrüche.- § 20. Die Gleichung  % MathType!MTEF!2!1!+- % feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaaca % WG4bWaaSbaaSqaaiaaicdaaeqaaaGcbaGaamiEamaaBaaaleaacaaI % XaaabeaaaaGccqGH9aqpcaWGIbWaaSbaaSqaaiaaicdaaeqaaOGaey % 4kaSYaaSaaaeaadaabcaqaaiaadggadaWgaaWcbaGaaGymaaqabaaa % kiaawIa7aaqaamaaeeaabaGaamOyamaaBaaaleaacaaIXaaabeaaaO % Gaay5bSdaaaiabgUcaRmaalaaabaWaaqGaaeaacaWGHbWaaSbaaSqa % aiaaikdaaeqaaaGccaGLiWoaaeaadaabbaqaaiaadkgadaWgaaWcba % GaaGOmaaqabaaakiaawEa7aaaacqGHRaWkcqWIVlctaaa!4F24! $$ \\frac{\u003c!-- --\u003e{\u003c!-- --\u003e{x_0}}}{\u003c!-- --\u003e{\u003c!-- --\u003e{x_1}}} = {b_0} + \\frac{\u003c!-- --\u003e{\\left. {\u003c!-- --\u003e{a_1}} \\right|}}{\u003c!-- --\u003e{\\left| {\u003c!-- --\u003e{b_1}} \\right.}} + \\frac{\u003c!-- --\u003e{\\left. {\u003c!-- --\u003e{a_2}} \\right|}}{\u003c!-- --\u003e{\\left| {\u003c!-- --\u003e{b_2}} \\right.}} +  \\cdots  $$als Folge des Rekursionssystems   % MathType!MTEF!2!1!+- % feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiEamaaBa % aaleaacaWG2baabeaakiabg2da9iaadkgadaWgaaWcbaGaamODaaqa % baGccaWG4bWaaSbaaSqaaiaadAhacqGHRaWkcaaIXaaabeaakiabgU % caRiaadggadaWgaaWcbaGaamODaiabgUcaRiaaigdaaeqaaOGaamiE % amaaBaaaleaacaWG2bGaey4kaSIaaGOmaaqabaaaaa!4763! $$ {x_v} = {b_v}{x_{v + 1}} + {a_{v + 1}}{x_{v + 2}} $$.- III. Verschiedene Zuordnungen von Potenzreihen zu Kettenbrüchen..- § 21. Allgemeine C-Kettenbrüche.- § 22. Quadratwurzeln.- § 23. Regelmäßige C-Kettenbrüche.- § 24. Die Kettenbrüche von Gauß, Heine und damit verwandte.- § 25. Der assoziierte Kettenbruch.- § 26. Zusammenhang zwischen dem korrespondierenden und assoziierten Kettenbruch. — Einige Transformationen des korrespondierenden Kettenbruches.- § 27. Konvergenz und Divergenz.- § 28. Konvergenz der Kettenbrüche von Gauß, Heine usw.- § 29. Ein bemerkenswertes Divergenzphänomen.- § 30. J-Kettenbrüche und ihre Anwendung auf Polynome, deren Wurzeln negative reelle Teile haben.- § 31. Weitere Typen von Kettenbrüchen, denen man Potenzreihen zuordnen kann.- IV. Die Kettenbrüche von Stieltjes..- § 32. Der Integralbegriff von Stieltjes.- § 33. Der korrespondierende und assoziierte Kettenbruch eines Stieltjessehen Integrals.- § 34. Der Satz von Markoff.- § 35. Die Wurzeln der Näherungsnenner von G-, H- und S-Kettenbrüchen.- § 36. Das Grommersche Auswahltheorem.- § 37. Konvergenz und analytischer Charakter der S- und H-Kettenbrüche.- § 38. Die vollständige Konvergenz der G-Kettenbrüche.- § 39. Das Momentenproblem.- V. Die P adésehe Tafel..- § 40. Begriff der Padéschen Tafel.- § 41. Normale und anormale Tafel.- § 42. Die Exponentialfunktion.- § 43. Die Laguerresche Differentialgleichung.- § 44. Die Kettenbrüche der Padéschen Tafel.- § 45. Die Konvergenzfrage.- VI. Kettenbrüche, deren Elemente a, und b, rationale Funktionen von v sind..- § 46. Die Konvergenz dieser Kettenbrüche.- § 47. Zusammenhang mit Differentialgleichungen.- § 48. Die Kettenbrüche mit dem allgemeinen Glied   % MathType!MTEF!2!1!+- % feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaada % abcaqaaiaadggadaWgaaWcbaGaamODaaqabaaakiaawIa7aaqaamaa % eeaabaGaamOyamaaBaaaleaacaWG2baabeaaaOGaay5bSdaaaiabg2 % da9maalaaabaWaaqGaaeaacaWGHbGaey4kaSIaamOyamaaBaaaleaa % caWG2baabeaaaOGaayjcSdaabaWaaqqaaeaacaWGJbGaey4kaSIaam % izamaaBaaaleaacaWG2baabeaaaOGaay5bSdaaaaaa!4961! $$ \\frac{\u003c!-- --\u003e{\\left. {\u003c!-- --\u003e{a_v}} \\right|}}{\u003c!-- --\u003e{\\left| {\u003c!-- --\u003e{b_v}} \\right.}} = \\frac{\u003c!-- --\u003e{\\left. {a + {b_v}} \\right|}}{\u003c!-- --\u003e{\\left| {c + {d_v}} \\right.}} $$.- § 49. Die Kettenbrüche mit dem allgemeinen Glied   % MathType!MTEF!2!1!+- % feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaada % abcaqaaiaadggadaWgaaWcbaGaamODaaqabaaakiaawIa7aaqaamaa % eeaabaGaamOyamaaBaaaleaacaWG2baabeaaaOGaay5bSdaaaiabg2 % da9maalaaabaWaaqGaaeaacaWGHbGaey4kaSIaamOyamaaBaaaleaa % caWG2baabeaakiabgUcaRiaadogacaWG2bWaaWbaaSqabeaacaaIYa % aaaaGccaGLiWoaaeaadaabbaqaaiaadsgacqGHRaWkcaWGLbGaamOD % aaGaay5bSdaaaaaa!4CE5! $$ \\frac{\u003c!-- --\u003e{\\left. {\u003c!-- --\u003e{a_v}} \\right|}}{\u003c!-- --\u003e{\\left| {\u003c!-- --\u003e{b_v}} \\right.}} = \\frac{\u003c!-- --\u003e{\\left. {a + {b_v} + c{v^2}} \\right|}}{\u003c!-- --\u003e{\\left| {d + ev} \\right.}} $$.- § 50. Die Methode von Cesàro.- § 51. Die Formel von Pincherle.- Literatur.- Verzeichnis der bemerkenswerten Formeln.","brand":"Springer Fachmedien Wiesbaden","offers":[{"title":"Default Title","offer_id":49419382423895,"sku":"9783519020226","price":42.74,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783519020226.jpg?v=1730538112"},{"product_id":"complex-geometry-an-introduction-9783540212904","title":"Complex Geometry: An Introduction","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eEasily accessible \u003c\/p\u003e \u003cp\u003eIncludes recent developments\u003c\/p\u003e \u003cp\u003eAssumes very little knowledge of differentiable manifolds and functional analysis\u003c\/p\u003e \u003cp\u003eParticular emphasis on topics related to mirror symmetry (SUSY, Kaehler-Einstein metrics, Tian-Todorov lemma)\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eFrom the reviews:\u003c\/p\u003e \u003cp\u003e\"The book under review provides an introduction to the contemporary theory of compact complex manifolds, with a particular emphasis on Kähler manifolds in their various aspects and applications. As the author points out in the preface, the text is based on a two-semester course taught in 2001\/2002 at the University of Cologne, Germany. Having been designed for third-year students, the aim of the course was to acquaint beginners in the field with some basic concepts, fundamental techniques, and important results in the theory of compact complex manifolds, without being neither too basic nor too sketchy. Also, as complex geometry has undergone tremendous developments during the past five decades, and become an indispensable framework in modern mathematical physics, the author has tried to teach the subject in such a way that would enable the students to understand the more recent developments in the field, too, up to some of the fascinating aspects of the stunning interplay between complex geometry and quantum field theory in theoretical physics. The present text, as an outgrowth of this special course in complex geometry, does evidently reflect these emphatic intentions of the author's in a masterly manner. Keeping the prerequisites from complex analysis and differential geometry to an absolute minimum, he provides a streamlined introduction to the theory of compact complex manifolds and Kählerian geometry, with many outlooks and applications, but without trying to be encyclopedic or panoramic. without trying to be encyclopedic or panoramic. As to the precise contents, the text consists of six chapters and two appendices. [...]\u003c\/p\u003e \u003cp\u003eThe author has added two general appendices at the end of the book. Those are\u003cbr\u003emeant to help the unexperienced reader to recall a few basic concepts and facts from differential geometry, Hodge theory on differentiable manifolds, sheaf theory, and sheaf cohomology. This very user-friendly service makes the entire introductory text more comfortable for less seasoned students, perhaps also for interested and mathematically less experienced physicists, although the author does not claim absolute self-containedness of the book. The entire text comes with a wealth of enlightening examples, historical remarks, comments and hints for further reading, outlooks to other directions of research, and numerous exercises after each section. The exercises are far from being bland and often quite demanding, but they should be mastered by ambitious and attentive readers, in the last resort after additional reading. Finally, there is a very rich bibliography of 118 references, also from the very recent research literature, which the author profusely refers to throughout the entire text. The whole exposition captivates by its clarity, profundity, versality, and didactical strategy, which lead the reader right to the more advanced literature in complex geometry as well as to the forefront of research in geometry and its applications to mathematical physics. No doubt, this book is an outstanding introduction to modern complex geometry.\"\u003c\/p\u003e \u003cp\u003e\u003cem\u003eKIeinert (Berlin), Zentralblatt für Mathematik 1055 (2005)\u003c\/em\u003e \u003c\/p\u003e \u003cp\u003e This is a very interesting and nice book. It provides a clear and deep introduction about complex geometry, namely the study of complex manifolds. These are differentiable manifolds endowed with the additional datum of a complex structure that is more rigid than the geometrical structures used in differential geometry. Complex geometry is on the crossroad of algebraic and differential geometry. Complex geometry is also becoming a stimulating and useful tool for theoretical physicists working in string theory and conformal field theory. The physicist, will be very glad to discover the interplay between complex geometry and supersymmetry and mirror symmetry.\u003c\/p\u003e \u003cp\u003eThe book begins by explaining the local theory and all you need to understand the global structure of complex manifolds. Then we get an introduction to the complex manifolds as such, where the reader can progressively perceive the difference between real manifolds and complex ones. Then he gets an account of the theory of Kälher manifolds. And the physicist will be glad to find therein a first step on the road going from complex geometry to conformal field theory and supersymmetry. One chapter is dedicated to the study of holomorphic vector bundles (connections, curvature, Chern classes). In this context, the reader will clarify the relations between Riemannian and Kälher geometries. With all this stuff it is then possible to focus on some applications of cohomology. This leads to a nice introduction to the famous Hirzebruch-Riemann-Roch theorem and to Kodaira vanishing and embedding theorems. The last chapter of the book tackles the very important topics of deformations of complex structures. \u003c\/p\u003e \u003cp\u003eThis chapter will be interesting especially for readers that are studying Calabi-Yau manifolds and mirror symmetries. The main text of the book is completed by two pedagogical appendices. One about Hodge theory and the other about sheaf cohomology.\u003c\/p\u003e \u003cp\u003eThus this beautiful textbook will be very interesting for both pure mathematicians and theoretical physicists working in recent domains of field theory. It can be used by students or scientists for a first introduction in this field. It is always very accessible and the reader will find a detailed account of the basic concepts and many well-chosen exercises that illustrate the theory. Many illuminating examples help the reader in the understanding of all fundamental notions. I could certainly recommend this textbook to my students attending my lectures on differential geometry.\u003c\/p\u003e \u003cp\u003e\u003cem\u003eProfessor Dominique LAMBERT, University of Namur; Department « sciences, philosophies et sociétés » Rue de Bruxelles 61 B-5000 Namur Belgium\u003c\/em\u003e\u003c\/p\u003e \u003cp\u003e\"As complex geometry has undergone tremendous developments … the author has tried to teach the subject in such a way that would enable the students to understand the more recent developments in the field … . This very user-friendly … more comfortable for less seasoned students … . The entire text comes with a wealth of enlightening examples, historical remarks, comments and hints … . Finally, there is a very rich bibliography … . The whole exposition captivates by its clarity, profundity, versality, and didactical strategy … . an outstanding introduction to modern complex geometry.\" (Werner Kleinert, Zentralblatt Math, Vol. 1055, 2005)\u003c\/p\u003e \u003cp\u003e\"The book contains detailed accounts of the basic concepts and the many exercises illustrate the theory. Appendices to various chapters allow an outlook to recent research directions.\" (L’Enseignment Mathematique, Vol. 50 (3-4), 2004)\u003c\/p\u003e \u003cp\u003e\"This is the book that a generation of complex geometers will wish had existed when they first learned the subject, and that the next generation of geometers will surely use. … Inserted into the standard material are some excellent appendices to stimulate interest and further reading … . the reader learning the basic material is brought quickly and often to some fascinating areas of current research. Exercises introduce many examples … . The result is an excellent course in complex geometry.\" (Richard P. Thomas, Mathematical Reviews, 2005h)\u003c\/p\u003e \u003cp\u003e\"The book is based on a year course on complex geometry and its interaction with Riemannian geometry. It prepares a basic ground for a study of complex geometry as well as for understanding ideas coming recently from string theory. … The book is a very good introduction to the subject and can be very useful both for mathematicians and mathematical physicists.\" (EMS Newsletter, June, 2005)\u003c\/p\u003e \u003cp\u003e\"The book under review is a textbook, based on a 2-semester course to third year undergraduates in the University of Cologne. … In the UK I think the book would be regarded as more suitable for a masters’ level course for students well versed in standard complex analysis and differential geometry.\" (Peter Giblin, The Mathematical Gazette, Vol. 91 (520), 2007)\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eLocal Theory.- Complex Manifolds.- Kähler Manifolds.- Vector Bundles.- Applications of Cohomology.- Deformations of Complex Structures.","brand":"Springer-Verlag Berlin and Heidelberg GmbH \u0026 Co. KG","offers":[{"title":"Default Title","offer_id":49419499405655,"sku":"9783540212904","price":61.74,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783540212904.jpg?v=1730538541"},{"product_id":"analytische-stellenalgebren-9783642650345","title":"Analytische Stellenalgebren","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eI. Konvergente Potenzreihenalgebren.- § 0. Formale Potenzreihen.- 1. Potenzreihen. Ordnung.- 2. Substitutionshomomorphismen.- 3. Partielle Ableitungen. Kettenregel.- 4. Topologie der koeffizientenweisen Konvergenz.- § 1. Analytische k-Banachalgebren.- 0. Bewertungen.- 1. Definition der Bt.- 2. Partielle Ableitungen.- 3. Topologische Eigenschaften der Bt.- § 2. Weierstraßsche Formel und Weierstraßscher Vorbereitungssatz für Bt.- 1. Weierstraßsche Formel.- 2. Weierstraßscher Vorbereitungssatz.- § 3. Konvergente Potenzreihen.- 1. Definition konvergenter Potenzreihen.- 2. Analytische Homomorphismen.- 3. Partielle Ableitungen.- 4. Schwache Topologie und analytische Konvergenz.- § 4. Weierstraßsche Formel und Weierstraßscher Vorbereitungssatz für Kn.- 1. Weierstraßsche Formel und Vorbereitungssatz.- 2. Scherungen.- 3. Analytische Karten in Kn.- Supplement zu § 4. Der Stickelberger-Siegelsche Beweis des Vorbereitungssatzes.- 1. Der Stickelbergersche Beweis.- 2. Der Siegeische Beweis.- 3. Herleitung der Weierstraßschen Formel aus dem Vorbereitungssatz.- § 5. Algebraische Struktur des Ringes Kn.- 1. Weierstraßhomomorphismen und Weierstraßpolynome.- 2. Noethereigenschaft.- 3. Unbeschränktheit der Corangfunktion.- 4. Cartanscher Abgeschlossenheitssatz.- 5. Primfaktorzerlegung.- 6. Henselsches Lemma.- Supplement zu § 5. Noethersche Banachalgebren über ? und ?.- § 6. Die Folgentopologie des Kn.- 1. Finale Topologien.- 2. Folgentopologie auf Kn.- 3. Stetigkeit analytischer Homomorphismen.- § 7. Folgentopologien bei lokal-kompaktem Grundkörper.- 1. Produkttopologie. Silvasche Topologie.- 2. Produkttopologie von Silvatopologien.- 3. Ausgezeichnete Umgebungen. Charakterisierung konvergenter Folgen.- 4. Folgentopologie auf Kn.- 5. Erstes Abzählbarkeitsaxiom und Folgenabschluß.- § 8. Silvatopologie auf Vektorräumen und Algebren.- 1. Definitionen.- 2. Restklassenräume und Restklassenalgebren.- 3. Beschränkte Mengen.- 4. Silvasche Vektorräume und Silvasche Algebren.- 5. Kompakte Mengen.- 6. Lokale Konvexität.- 7. Ausblick.- II. Analytische k-Stellenalgebren.- § 0. Analytische k-Stellenalgebren und analytische Moduln.- 1. Die Kategorie U.- 2. Die Kategorie MA.- § 1. Topologie auf analytischen Stellenalgebren und analytischen Moduln.- 1. Schwache Topologie auf analytischen Stellenalgebren.- 2. Folgentopologie auf analytischen Stellenalgebren.- 3. Schwache Topologie und Folgentopologie auf analytischen Moduln.- § 2. Quasi-endliche und endliche Homomorphismen.- 1. Quasi-endliche Moduln.- 2. Quasi-endliche und endliche analytische Homomorphismen.- 3. Analytische Epimorphismen und analytische Erzeugendensysteme.- 4. Ganze Elemente und endliche Homomorphismen.- 5. Analytische k-Unterstellenalgebren.- 6. Invarianz der Modultopologie.- 7. Relativtopologie und strikte Homomorphismen.- § 3. Einbettungsdimension. Epimorphismen. Umkehrsatz.- 1. Cotangentialraum. Einbettungsdimension. Ableitung.- 2. Epimorphiekriterium.- 3. Jacobischer Umkehrsatz.- 4. Satz über implizite Funktionen.- 5. Einbettungsdimension und Epimorphismen.- § 4. Dimensionstheorie analytischer k-Stellerialgebren. Aktives Lemma.- 1. Aktive Elemente.- 2. Artinsche Algebren.- 3. Dimension.- 4. Aktives Lemma.- 5. Konstruktion aktiver Elemente.- 6. Konstruktion von Parametersystemen.- 7. Tiefe eines Ideals.- § 5. Dimension und endliche analytische Homomorphismen.- 1. Invarianz der Dimension.- 2. Endliche Monomorphismen. Osgoodsches Beispiel.- 3. Reguläre analytische k-Stellenalgebren.- § 6. Krullsche Dimension. Rein-dimensionale analytische Stellenalgebren.- 1. Primidealketten.- 2. Krullscher Hauptidealsatz.- 3. Rein-dimensionale analytische k-Stellenalgebren.- § 7. Endliche Erweiterungen analytischer Stellenalgebren. Normalisierung.- 1. Endliche Erweiterungen.- 2. Normalisierung reduzierter analytischer Stellenalgebren.- III. Weiterführende Theorie analytischer k-Stellenalgebren und analytischer Moduln.- § 1. Homologische Codimension (Profondeur).- 1. M-Sequenzen.- 2. Homologische Codimension. Maximale M-Sequenzen.- 3. Profondeur und endliche Homomorphismen.- 4. Cohen-Macaulay-Moduln.- 5. Unvermischtheit.- 6. Freie Moduln und Macaulay-Moduln.- 7. Beispiele von Macaulay-Moduln.- 8. Beispiele von nicht-Macaulayschen Ringen.- § 2. Homologische Dimension (Syzygientheorie).- 1. Minimale Epimorphismen.- 2. Minimale-freie Auflösungen.- 3. Syzygienmoduln.- 4. Homologische Dimension.- 5. Homologische Dimension und homologische Codimension. Syzygiensatz.- 6. Konstruktion von Hilbert-Auflösungen.- 7. Koszul-Komplexe.- § 3. Invariante analytische k-Unterstellenalgebren.- 1. Invariante Algebren zu endlichen Automorphismengruppen.- 2. Linearisierung.- 3. Beispiele. Zyklische Gruppen.- § 4. Derivations- und Differentialmoduln.- 1. Derivationen.- 2. Differentialmoduln.- 3. Existenz von Differentialmoduln.- 4. Eigenschaften der Differentialmoduln.- 5. Regularitätskriterium.- 6. Äußere Differentialformen über kn. Poincaré-Sequenz.- 7. Exaktheit der Poincaré-Sequenz.- § 5. Analytische Tensorprodukte.- 1. Definition und Existenz.- 2. Endlichkeit und Freiheit.- 3. Faseralgebren und endliche Homomorphismen.- 4. Das analytische Tensorprodukt analytischer Moduln.- 5. Invarianz unter endlichen Homomorphismen.- 6. Einbettungsdimension und Dimension.- 7. Normalität und Nullteilerfreiheit.- 8. Reduziertheit.- 9. Homologische Codimension.- 10. Differentialmoduln.- Anhang. Algebraische Hilfsmittel.- § 1. Ringe und Moduln.- 1. Idealpotenzen. Nilpotente Ideale.- 2. Primideale.- 3. Radikale. Reduzierte Ringe. Multiplikative Mengen.- 4. Torsionsmoduln. Quotientenmoduln.- 5. Rang und Corang.- 6. Noethersche Moduln.- 8. Zerlegungssatz von Lasker-Noether.- § 2. Endliche Moduln über noetherschen Stellenringen.- 2. Lemma von Nakayama.- 3. Krullscher Durchschnittsatz.- 4. Corang.- 5. Jacobirang.- 6. Einbettungsdimension.- 7. Freie Moduln.- § 3. Normale noethersche Integritätsringe.- 1. Ganze Elemente. Dedekindsches Lemma.- 2. Ganzer Abschluß. Normalisierung.- 3. Charakterisierung ganz-abgeschlossener Ringe.- 4. Hauptidealsatz.- 5. Minimale Primideale.- 6. Teilbarkeitstheorie.- § 4. Reduzierte und noethersche Ringe.- 1. Direkte Summen von Ringen.- 2. Epimorphiesatz.- 3. Reduzierte noethersche Ringe.- 4. Charakterisierung von Torsionsmoduln.- Literatur.","brand":"Springer-Verlag Berlin and Heidelberg GmbH \u0026 Co. KG","offers":[{"title":"Default Title","offer_id":49420041748823,"sku":"9783642650345","price":54.99,"currency_code":"GBP","in_stock":true}]},{"product_id":"nevanlinna-theory-9789811067860","title":"Nevanlinna Theory","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis book deals with the classical theory of Nevanlinna on the value distribution of meromorphic functions of one complex variable, based on minimum prerequisites for complex manifolds. The theory was extended to several variables by S. Kobayashi, T. Ochiai, J. Carleson, and P. Griffiths in the early 1970s. K. Kodaira took up this subject in his course at The University of Tokyo in 1973 and gave an introductory account of this development in the context of his final paper, contained in this book. The first three chapters are devoted to holomorphic mappings from \u003cb\u003eC\u003c\/b\u003e to complex manifolds. In the fourth chapter, holomorphic mappings between higher dimensional manifolds are covered. The book is a valuable treatise on the Nevanlinna theory, of special interests to those who want to understand Kodaira's unique approach to basic questions on complex manifolds.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface1. Nevanlinna Theory of One Variable (1)1.1 metrics of compact Rimann surfaces1.2 integral formula1.3 holomorphic maps over compact Riemann surfaces whose genus are greater than 21.4 holomorphic maps over Riemann sphreres1.5 Defect relation\u003cbr\u003e2. Schwarz--Kobayashi's Lemma2.1 Schwarz--Kobayashi's Lemma2.2 holomorphic maps over algebraic varieties (general type)2.3 hyperbolic measures\u003cbr\u003e3. Nevanlinna Theory of One Variable (2)3.1 holomorphic maps over Riemann shpres3.2 the first main theorem3.3 the second main theorem\u003cbr\u003e4.  Nevanlinna Theory of Several Variables4.1 Biebelbach's example4.2 the first main theorem4.3 the second main theorem4.4 defect relation4.5 applications\u003cbr\u003eReferences","brand":"Springer Verlag, Singapore","offers":[{"title":"Default Title","offer_id":49427818283351,"sku":"9789811067860","price":49.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9789811067860.jpg?v=1730565781"},{"product_id":"mathematical-analysis-and-applications-maa-2020-jamshedpur-india-november-2-4-9789811681769","title":"Mathematical Analysis and Applications: MAA 2020,","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis book collects original peer-reviewed contributions presented at the \"International Conference on Mathematical Analysis and Applications (MAA 2020)\" organized by the Department of Mathematics, National Institute of Technology Jamshedpur, India, from 2–4 November 2020. This book presents peer-reviewed research and survey papers in mathematical analysis that cover a broad range of areas including approximation theory, operator theory, fixed-point theory, function spaces, complex analysis, geometric and univalent function theory, control theory, fractional calculus, special functions, operation research, theory of inequalities, equilibrium problem, Fourier and wavelet analysis, mathematical physics, graph theory, stochastic orders and numerical analysis. Some chapters of the book discuss the applications to real-life situations. This book will be of value to researchers and students associated with the field of pure and applied mathematics.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eG. K. Srinivasan, A note on isolated removable singularities of harmonic functions.- O. Chadli, Ram N. Mohapatra, B. K. Sahu, Equilibrium Problems and Variational Inequalities: a Survey of Existence Results.- O. Chadli, Ram N. Mohapatra, G. Pany, Nonlinear evolution equations by a Ky Fan minimax inequality approach.- L. A. Wani and A. Swaminathan, Sufficient Conditions Concerning the Unified Class of Starlike and Convex Functions.- S. Menchavez and I. Mae Antabo, One Dimensional Parametrized Test Functions Space of Entire Functions.- D. Raghavan and S. Nagarajan, Extremal mild solutions of Hilfer fractional Impulsive systems.- B. Roy and S. N. Bora, On existence of integral solutions for a class of mixed Volterra-Fredholm integro fractional differential equations.- P. Kumar, A. Kumar, R. Kumar Vats and A. Kumar, Trajectory Controllability of Integro-differential Systems of Fractional Order γ ∈ (1, 2] in a Banach Space with Deviated Argument.- A. S. Kelil and A. Rao Appadu, Shehu-Adomian Decomposition Method for dispersive KdV-type Equations.- A. S. Kelil, A. R. Appadu and S. Arjika, On certain properties of perturbed Freud-type  weight: a revisit.- A. K. Singh, Complex chaotic systems and its complexity.- M. Incesu, S. Y. Evren and O. Gursoy, On the bertrand pairs of open non uniform B-spline curves.- M. Verma, P. Sharma and N. Gupta, Convergence analysis of a sixth-order method under weak continuity condition with First-order Frechet derivative.- B. Kour and S. Ram, (m, n)-paranormal composition operators.- T. Yaying, On the domain of q-Euler matrix in c0 and c.- N. Sarkar and M. Sen, Study on some particular class of non linear integral equation with a hybridized approach.- D. Saha, M. Sen and S. Roy, Investigation of the existence criteria for the solution of the functional integral equation in the Lp space.- S. Das and K. Mehrez, Functional Inequalities for the Generalized Wright Functions.- S. Dutta and P. Guha, An Information Theoretic Entropy Related to Ihara $\\zeta$ Function and Billiard Dynamics.- S. Baskaran, G. Saravanan and K. Muthunagai, On a new subclass of Sakaguchi type functions using (p;q)- derivative operator.- N. K. Jangid, S. Joshi and S. D. Purohit, Some Double integral Formulae Associated with Q Function and Galue Type Struve Function.- M. Jain, M. Singh and R. K. Meena, Time-dependent analytical and computational study of an M\/M\/1 queue with disaster failure and multiple working vacations.- M. Datta and N. Gupta, Usual stochastic ordering results for series and  parallel systems with components having  Exponentiated Chen distribution.","brand":"Springer Verlag, Singapore","offers":[{"title":"Default Title","offer_id":49427835126103,"sku":"9789811681769","price":104.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9789811681769.jpg?v=1730565839"},{"product_id":"analytic-continuation-and-q-convexity-9789811912382","title":"Analytic Continuation and q-Convexity","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThe focus of this book is on the further development of the classical achievements in analysis of several complex variables, the analytic continuation and the analytic structure of sets, to settings in which the  \u003ci\u003eq-\u003c\/i\u003epseudoconvexity in the sense of Rothstein and the \u003ci\u003eq-\u003c\/i\u003econvexity in the sense of Grauert play a crucial role. After giving a brief survey of notions of generalized convexity and their most important results, the authors present recent statements on analytic continuation related to them. \u003c\/p\u003e  Rothstein (1955) first introduced \u003ci\u003eq-\u003c\/i\u003epseudoconvexity using generalized Hartogs figures. Słodkowski (1986) defined \u003ci\u003eq-\u003c\/i\u003epseudoconvex sets by means of the existence of exhaustion functions which are \u003ci\u003eq-\u003c\/i\u003eplurisubharmonic in the sense of Hunt and Murray (1978). Examples of \u003ci\u003eq-\u003c\/i\u003epseudoconvex sets appear as complements of  analytic sets. Here, the relation of the analytic structure of graphs of continuous surfaces whose complements are \u003ci\u003eq-\u003c\/i\u003epseudoconvex is investigated. As an outcome, the authors generalize results by Hartogs (1909), Shcherbina (1993), and Chirka (2001) on the existence of foliations of pseudoconcave continuous real hypersurfaces by smooth complex ones. \u003cp\u003e\u003c\/p\u003e  \u003cp\u003eA similar generalization is obtained by a completely different approach using L²-methods in the setting of \u003ci\u003eq-\u003c\/i\u003econvex spaces. The notion of \u003ci\u003eq-\u003c\/i\u003econvexity was developed by Rothstein (1955) and Grauert (1959) and extended to \u003ci\u003eq-\u003c\/i\u003econvex spaces by Andreotti and Grauert (1962). Andreotti–Grauert's finiteness theorem was applied by Andreotti and Norguet (1966–1971) to extend Grauert's solution of the Levi problem to \u003ci\u003eq-\u003c\/i\u003econvex spaces. A consequence is that the sets of (\u003ci\u003eq-\u003c\/i\u003e1)-cycles of \u003ci\u003eq-\u003c\/i\u003econvex domains with smooth boundaries in projective algebraic manifolds, which are equipped with complex structures as open subsets of Chow varieties, are in fact holomorphically convex. Complements of analytic curves are studied, and the relation of \u003ci\u003eq-\u003c\/i\u003econvexity and cycle spaces is explained. Finally, results for \u003ci\u003eq-\u003c\/i\u003econvex domains in projective spaces are shown and the \u003ci\u003eq-\u003c\/i\u003econvexity in analytic families is investigated.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e1. Analytic Continuation and Pseudoconvexity.- 2. \u003ci\u003eq\u003c\/i\u003e-Plurisubharmonicity.- 3. \u003ci\u003eq\u003c\/i\u003e-Pseudoconvexity.- 4. \u003ci\u003eq\u003c\/i\u003e-Convexity and \u003ci\u003eq\u003c\/i\u003e-Completeness.- References.- Index.","brand":"Springer Verlag, Singapore","offers":[{"title":"Default Title","offer_id":49427842892119,"sku":"9789811912382","price":38.24,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9789811912382.jpg?v=1730565863"},{"product_id":"students-solutions-manual-to-accompany-complex-variables-and-applications-9780073528991","title":"Students Solutions Manual to accompany Complex","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e","brand":"McGraw-Hill Education - Europe","offers":[{"title":"Default Title","offer_id":49524357333335,"sku":"9780073528991","price":216.24,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780073528991.jpg?v=1731856458"},{"product_id":"funktionentheorie-1-9783540317647","title":"Funktionentheorie 1","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eDie ersten vier Kapitel dieser Darstellung der klassischen Funktionentheorie vermitteln mit minimalem Begriffsaufwand und auf geringen Vorkenntnissen aufbauend zentrale Ergebnisse und Methoden der komplexen Analysis einer Veränderlichen. Sie gipfeln in einem Beweis des kleinen Riemannschen Abbildungssatzes und einer Charakterisierung einfach zusammenhängender Gebiete. Weitere Themen sind: elliptische Funktionen (Weierstraßscher, Jacobischer Ansatz), die elementare Theorie der Modulformen einer Variablen, Anwendungen der Funktionen- auf die Zahlentheorie (einschl. eines Beweises des Primzahlsatzes). Plus: über 400 Übungsaufgaben mit Lösungen. \u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"... Jeder einzelne Abschnitt enthält sorgfältig ausgewählte Übungsaufgaben.\" Monatshefte für Mathematik \"... Positiv hervorzuheben sind die optisch sehr übersichtliche Aufbereitung und der Versuch der Autoren, alle Begriffsbildungen dem Leser gegenüber soweit wie möglich zu motivieren ...\" Internationale Mathematische Nachrichten Österreich\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eDifferentialrechnung im Komplexen.- Integralrechnung im Komplexen.- Folgen und Reihen analytischer Funktionen, Residuensatz.- Konstruktion analytischer Funktionen.- Elliptische Funktionen.- Elliptische Modulformen.- Analytische Zahlentheorie.","brand":"Springer-Verlag Berlin and Heidelberg GmbH \u0026 Co. KG","offers":[{"title":"Default Title","offer_id":49537840578903,"sku":"9783540317647","price":32.99,"currency_code":"GBP","in_stock":true}]},{"product_id":"complex-analysis-cambridge-studies-in-advanced-mathematics-series-number-107-9780521809375","title":"Complex Analysis Cambridge Studies in Advanced","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eWritten by a master of the subject, this text will be appreciated by students and experts for the way it develops the classical theory of functions of a complex variable in a clear and straightforward manner. In general, the approach taken here emphasises geometrical aspects of the theory in order to avoid some of the topological pitfalls associated with this subject. Thus, Cauchy's integral formula is first proved in a topologically simple case from which the author deduces the basic properties of holomorphic functions. Starting from the basics, students are led on to the study of conformal mappings, Riemann's mapping theorem, analytic functions on a Riemann surface, and ultimately the RiemannâRoch and Abel theorems. Profusely illustrated, and with plenty of examples, and problems (solutions to many of which are included), this book should be a stimulating text for advanced courses in complex analysis.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e'While most of the material included in the first part could be used in a basic course on complex analysis, the whole book could serve as a text for an advanced course on Riemann surfaces. The book contains many pictures (helping to build geometric intuition) and problems (elementary and advanced). The book could be very helpful for students as well as for experts in the field.' European Mathematical Society Newsletter\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e1. Holomorphic functions; 2. Cauchy's theorem; 3. Conformal mappings; 4. Analytic continuation; 5. Riemann's mapping theorem; 6. Riemann surfaces; 7. The structure of Riemann surfaces; 8. Analytic functions on a closed Riemann surface.","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":49909398503767,"sku":"9780521809375","price":69.34,"currency_code":"GBP","in_stock":true}]},{"product_id":"hidden-harmonygeometric-fantasies-the-rise-of-complex-function-theory-sources-and-studies-in-the-history-of-mathematics-and-physical-sciences-9781461457244","title":"Hidden HarmonyGeometric Fantasies The Rise of","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e​This book is a history of complex function theory from its origins to 1914, when the essential features of the modern theory were in place.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e“There is much in this book that will educate, be appreciated by, and no doubt provoke mathematicians as well as historians of mathematics and of science. … It stands its ground as a scholarly treatise that fills many lacunae in the extant historical literature. It will surely provoke further debate and research. As a bonus, it comes filled with treasures for both the specialist and the novice.” (Tushar Das, MAA Reviews, July, 2015)\u003c\/p\u003e\u003cp\u003e“The book is devoted to the history of complex (analytic) function theory from its origins to 1914. … The book is highly recommended for historians of mathematics, mathematicians with historical interests, and everyone who is interested in complex function theory and its history. It offers a wealth of information that is well documented.” (Karl-Heinz Schlote, Mathematical Reviews, October, 2014)\u003c\/p\u003e\u003cp\u003e“This comprehensive, massively researched volume … is a detailed historical account of the development of analytic function theory in the 19th century, tracing its rise and ramification through that period up until about 1910. … It is a very dense and scholarly work, suitable for specialists. Summing Up: Recommended. Graduate students, researchers\/faculty, and professionals\/practitioners.” (D. Robbins, Choice, Vol. 51 (9), May, 2014)\u003c\/p\u003e“This book is the first one devoted to the history of complex function theory. The authors present the rise of analytic function theory from its origins to 1914. … This book is of great interest and help, not only for mathematicians interested in complex function theory, but also for everyone who likes the history of mathematics.” (Agnieszka Wisniowska-Wajnryb, zbMATH, Vol. 1276, 2014)\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eList of Figures.- Introduction.- 1. Elliptic Functions.- 2. From real to complex.- 3. Cauch.- 4. Elliptic integrals.- 5. Riemann.- 6. Weierstrass.- 7. Differential equations.- 8. Advanced topics.- 9. Several variables.- 10. Textbooks.","brand":"Springer New York","offers":[{"title":"Default Title","offer_id":50041282396503,"sku":"9781461457244","price":149.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781461457244.jpg?v=1740181271"},{"product_id":"analysis-and-quantum-groups-9783031072451","title":"Analysis and Quantum Groups","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThis volume presents a completely self-contained introduction to the elaborate theory of locally compact quantum groups, bringing the reader to the frontiers of present-day research. The exposition includes a substantial amount of material on functional analysis and operator algebras, subjects which in themselves have become increasingly important with the advent of quantum information theory. In particular, the rather unfamiliar modular theory of weights plays a crucial role in the theory, due to the presence of ‘Haar integrals’ on locally compact quantum groups, and is thus treated quite extensively\u003c\/p\u003e  \u003cp\u003eThe topics covered are developed independently, and each can serve either as a separate course in its own right or as part of a broader course on locally compact quantum groups. The second part of the book covers crossed products of coactions, their relation to subfactors and other types of natural products such as cocycle bicrossed products, quantum doubles and doublecrossed products. Induced corepresentations, Galois objects and deformations of coactions by cocycles are also treated. Each section is followed by a generous supply of exercises. To complete the book, an appendix is provided on topology, measure theory and complex function theory.\u003cbr\u003e\u003c\/p\u003e\u003cp\u003e\u003cbr\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface.- Set theoretic preliminaries.- Banach spaces.- Bases in Banach spaces.- Operators on Hilbert spaces.- Spectral theory.- States and  representations.- Types of von Neumann algebras.- Tensor products.- Unbounded operators.- Tomita-Takesaki theory.- Spectra and type III\u003ci\u003e \u003c\/i\u003efactors.- Quantum groups and  duality.- Special cases.- Classical crossed products.- Crossed  products for quantum groups.- Generalized and continuous crossed products.- Basic construction and quantum groups.- Galois objects and  cocycle deformations.- Doublecrossed  products of quantum groups.- Induction.-Appendix.- Bibliography.- Index.- Exercises.\u003cbr\u003e","brand":"Springer International Publishing AG","offers":[{"title":"Default Title","offer_id":50470474645847,"sku":"9783031072451","price":67.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783031072451.jpg?v=1744898434"},{"product_id":"a-software-repository-for-gaussian-quadratures-and-christoffel-functions-9781611976342","title":"A Software Repository for Gaussian Quadratures","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis companion piece to the author’s 2018 book, \u003ci\u003eA Software Repository for Orthogonal Polynomials\u003c\/i\u003e, focuses on Gaussian quadrature and the related Christoffel function. The book makes Gauss quadrature rules of any order easily accessible for a large variety of weight functions and for arbitrary precision. It also documents and illustrates known as well as original approximations for Gauss quadrature weights and Christoffel functions.\u003cbr\u003e\u003cbr\u003eThe repository contains 60  datasets, each dealing with a particular weight function. Included are classical, quasi-classical, and, most of all, nonclassical weight functions and associated orthogonal polynomials.","brand":"Society for Industrial \u0026 Applied Mathematics,U.S.","offers":[{"title":"Default Title","offer_id":50578263769431,"sku":"9781611976342","price":51.85,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781611976342.jpg?v=1746098581"},{"product_id":"the-theory-of-composites-9781611977479","title":"The Theory of Composites","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eComposites have been studied for more than 150 years, and interest in their properties has been growing. This classic volume provides the foundations for understanding a broad range of composite properties, including electrical, magnetic, electromagnetic, elastic and viscoelastic, piezoelectric, thermal, fluid flow through porous materials, thermoelectric, pyroelectric, magnetoelectric, and conduction in the presence of a magnetic field (Hall effect). Exact solutions of the PDEs in model geometries provide one avenue of understanding composites; other avenues include microstructure-independent exact relations satisfied by effective moduli, for which the general theory is reviewed; approximation formulae for effective moduli; and series expansions for the fields and effective moduli that are the basis of numerical methods for computing these fields and moduli. The range of properties that composites can exhibit can be explored either through the model geometries or through microstructure-independent bounds on the properties. These bounds are obtained through variational principles, analytic methods, and Hilbert space approaches. Most interesting is when the properties of the composite are unlike those of the constituent materials, and there has been an explosion of interest in such composites, now known as metamaterials. \u003cbr\u003e\u003cbr\u003e\u003ci\u003eThe Theory of Composites\u003c\/i\u003e surveys these aspects, among others, and complements the new body of literature that has emerged since the book was written. It remains relevant today by providing historical background, a compendium of numerous results, and through elucidating many of the tools still used today in the analysis of composite properties. \u003cbr\u003e\u003cbr\u003eThis book is intended for applied mathematicians, physicists, and electrical and mechanical engineers. It will also be of interest to graduate students.","brand":"Society for Industrial \u0026 Applied Mathematics,U.S.","offers":[{"title":"Default Title","offer_id":50578265538903,"sku":"9781611977479","price":83.3,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781611977479.jpg?v=1746098586"},{"product_id":"algebraic-curves-and-riemann-surfaces-for-undergraduates-the-theory-of-the-donut-9783031116155","title":"Algebraic Curves and Riemann Surfaces for","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThe theory relating algebraic curves and Riemann surfaces exhibits the unity of mathematics: topology, complex analysis, algebra and geometry all interact in a deep way. This textbook offers an elementary introduction to this beautiful theory for an undergraduate audience. At the heart of the subject is the theory of elliptic functions and elliptic curves. A complex torus (or “donut”) is both an abelian group and a Riemann surface. It is obtained by identifying points on the complex plane. At the same time, it can be viewed as a complex algebraic curve, with addition of points given by a geometric “chord-and-tangent” method. This book carefully develops all of the tools necessary to make sense of this isomorphism. The exposition is kept as elementary as possible and frequently draws on familiar notions in calculus and algebra to motivate new concepts. Based on a capstone course given to senior undergraduates, this book is intended as a textbook for courses at this level and includes a large number of class-tested exercises. The prerequisites for using the book are familiarity with abstract algebra, calculus and analysis, as covered in standard undergraduate courses.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e1 Introduction.- Part I Algebraic curves.- 2 Algebra.- 3 Affine space.- 4 Projective space.- 5 Tangents.- 6 Bézout’s theorem.- 7 The elliptic group.- Part II Riemann Surfaces.- 8 Quasi-Euclidean spaces.- 9 Connectedness, smooth and simple.- 10 Path integrals.- 11 Complex differentiation.- 12 Riemann surfaces.- Part III Curves and surfaces.- 13 Curves are surfaces.- 14 Elliptic functions and the isomorphism theorem.- 15 Puiseux theory.- 16 A brief history of elliptic functions.","brand":"Springer International Publishing AG","offers":[{"title":"Default Title","offer_id":50578716197207,"sku":"9783031116155","price":999.99,"currency_code":"GBP","in_stock":false}]},{"product_id":"theory-of-stein-spaces-9783540003731","title":"Theory of Stein Spaces","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eFrom the reviews: \"Theory of Stein Spaces provides a rich variety of methods, results, and motivations - a book with masterful mathematical care and judgement. It is a pleasure to have this fundamental material now readily accessible to any serious mathematician.\" --J. Eells in Bulletin of the London Mathematical Society (1980)\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\u003cbr\u003e\"Theory of Stein Spaces provides a rich variety of methods, results, and motivations - a book with masterful mathematical care and judgement. It is a pleasure to have this fundamental material now readily accessible to any serious mathematician.\"\u003cbr\u003eJ. Eells in Bulletin of the London Mathematical Society (1980)\u003c\/p\u003e \u003cp\u003e\"Written by two mathematicians who played a crucial role in the development of the modern theory of several complex variables, this is an important book.\"\u003cbr\u003eJ.B. Cooper in Internationale Mathematische Nachrichten (1979)\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eA. 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(In the absence of a Nobel prize in mathematics, they are regarded as the highest professional honour a mathematician can attain.)\u003c\/p\u003e \u003cp\u003eKodaira is an honorary member of the London Mathematical Society.\u003cbr\u003e\u003c\/p\u003e \u003cp\u003eAffordable softcover edition of 1986 classic\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eHolomorphic Functions.- Complex Manifolds.- Differential Forms, Vector Bundles, Sheaves.- Infinitesimal Deformation.- Theorem of Existence.- Theorem of Completeness.- Theorem of Stability.","brand":"Springer-Verlag Berlin and Heidelberg GmbH \u0026 Co. KG","offers":[{"title":"Default Title","offer_id":50579138937175,"sku":"9783540226147","price":49.99,"currency_code":"GBP","in_stock":true}]},{"product_id":"quasiconformal-maps-and-teichmuller-theory-9780198569268","title":"Quasiconformal Maps and Teichmüller Theory","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eBased on a series of graduate lectures given by Vladimir Markovic at the University of Warwick in spring 2003, this book is accessible to those with a grounding in complex analysis looking for an introduction to the theory of quasiconformal maps and Teichmüller theory. Assuming some familiarity with Riemann surfaces and hyperbolic geometry, topics covered include the Grötzch argument, analytical properties of quasiconformal maps, the Beltrami differential equation, holomorphic motions and Teichmüller spaces. Where proofs are omitted, references to where they may be found are always given, and the text is clearly illustrated throughout with diagrams, examples, and exercises for the reader.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface ; 1. The Grotzch argument ; 2. Geometric definition of quasiconformal maps ; 3. Analytic properties of quasiconformal maps ; 4. Quasi-isometries and quasisymmetric maps ; 5. The Beltrami differential equation ; 6. Holomorphic motions and applications ; 7. Teichmuller spaces ; 8. Extremal quasiconformal mappings ; 9. Unique extremality ; 10. Isomorphisms of Teichmuller space ; 11. Local rigidity of Teichmuller spaces ; References ; Index","brand":"Oxford University Press","offers":[{"title":"Default Title","offer_id":51017618587991,"sku":"9780198569268","price":111.62,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780198569268.jpg?v=1750774136"},{"product_id":"institutiones-calculi-differentialis-9781016366922","title":"Institutiones Calculi Differentialis...","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e","brand":"LEGARE STREET PR","offers":[{"title":"Default Title","offer_id":51018743677271,"sku":"9781016366922","price":43.6,"currency_code":"GBP","in_stock":true}]},{"product_id":"handbook-of-complex-analysis-9781032202105","title":"Handbook of Complex Analysis","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eIn spite of being nearly 500 years old, the subject of complex analysis is still today a vital and active part of mathematics. There are important applications in physics, engineering, and other aspects of technology. \u003c\/p\u003e\u003cp\u003eThis Handbook presents contributed chapters by prominent mathematicians, including the new generation of researchers. More than a compilation of recent results, this book offers students an essential stepping-stone to gain an entry into the research life of complex analysis. Classes and seminars play a role in this process. More, though, is needed for further study. This Handbook will play that role. \u003c\/p\u003e\u003cp\u003eThis book is also a reference and a source of inspiration for more seasoned mathematiciansboth specialists in complex analysis and others who want to acquaint themselves with current modes of thought.\u003c\/p\u003e\u003cp\u003eThe chapters in this volume are authored by leading experts and gifted expositors. 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