{"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}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780192863874.jpg?v=1791454085"},{"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":"intersection-homology-perverse-sheaves-with-applications-to-singularities-9783030276430","title":"Intersection Homology \u0026 Perverse Sheaves: with","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThis textbook provides a gentle introduction to intersection homology and perverse sheaves, where concrete examples and geometric applications motivate concepts throughout. By giving a taste of the main ideas in the field, the author welcomes new readers to this exciting area at the crossroads of topology, algebraic geometry, analysis, and differential equations. Those looking to delve further into the abstract theory will find ample references to facilitate navigation of both classic and recent literature. \u003c\/p\u003eBeginning with an introduction to intersection homology from a geometric and topological viewpoint, the text goes on to develop the sheaf-theoretical perspective. Then algebraic geometry comes to the fore: a brief discussion of constructibility opens onto an in-depth exploration of perverse sheaves. Highlights from the following chapters include a detailed account of the proof of the Beilinson–Bernstein–Deligne–Gabber (BBDG) decomposition theorem, applications of perverse sheaves to hypersurface singularities, and a discussion of Hodge-theoretic aspects of intersection homology via Saito’s deep theory of mixed Hodge modules. An epilogue offers a succinct summary of the literature surrounding some recent applications.\u003cbr\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003ci\u003eIntersection Homology \u0026amp; Perverse Sheaves\u003c\/i\u003e is suitable for graduate students with a basic background in topology and algebraic geometry. By building context and familiarity with examples, the text offers an ideal starting point for those entering the field. This classroom-tested approach opens the door to further study and to current research.\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\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 quite a lot for a relatively short book! … this book provides a great jumping-off point for the reader who wants to learn about these tools by a route leading to the forefront of modern research via lots of concrete geometric examples.” (Greg Friedman, Mathematical Reviews, March, 2023)\u003c\/p\u003e\u003cp\u003e“This book is a welcome addition to the family of introductions to intersection cohomology and perverse sheaves. … the author takes care to introduce and motivate the main objects of study with geometric examples. There are also regular exercises which will help readers come to grips with the material. … this book will ... be a very useful resource … .” (Jon Woolf, zbMATH 1476.55001, 2022)\u003c\/p\u003e\u003cp\u003e“This is a good textbook to prepare a student to delve into the current literature, and also a good reference for a researcher. A mathematician whose research or interest has come in contact with these topics would also find this a stimulating read on the subject.” (MAA Reviews, April 7, 2020)\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface.- 1. Topology of singular spaces: motivation, overview.- 2. Intersection Homology: definition, properties.- 3. L-classes of stratified spaces.- 4. Brief introduction to sheaf theory.- 5. Poincaré-Verdier Duality.- 6. Intersection homology after Deligne.- 7. Constructibility in algebraic geometry.- 8. Perverse sheaves.- 9. The Decomposition Package and Applications.- 10. Hypersurface singularities. Nearby and vanishing cycles.- 11. Overview of Saito's mixed Hodge modules, and immediate applications.- 12. Epilogue.- Bibliography.- Index.","brand":"Springer Nature Switzerland AG","offers":[{"title":"Default Title","offer_id":48743028654423,"sku":"9783030276430","price":999.99,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783030276430.jpg?v=1791480469"},{"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":999.99,"currency_code":"GBP","in_stock":false}],"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":999.99,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783030802417.jpg?v=1791480537"},{"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":44.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783031255694.jpg?v=1720064009"},{"product_id":"almost-automorphic-type-and-almost-periodic-type-functions-in-abstract-spaces-9783319008486","title":"Almost Automorphic Type and Almost Periodic Type","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis book presents a comprehensive introduction to the concepts of almost periodicity, asymptotic almost periodicity, almost automorphy, asymptotic almost automorphy, pseudo-almost periodicity, and pseudo-almost automorphy as well as their recent generalizations. Some of the results presented are either new or else cannot be easily found in the mathematical literature. Despite the noticeable and rapid progress made on these important topics, the only standard references that currently exist on those new classes of functions and their applications are still scattered research articles. One of the main objectives of this book is to close that gap. The prerequisites for the book is the basic introductory course in real analysis. Depending on the background of the student, the book may be suitable for a beginning graduate and\/or advanced undergraduate student. Moreover, it will be of a great interest to researchers in mathematics as well as in engineering, in physics, and related areas. Further, some parts of the book may be used for various graduate and undergraduate courses.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eFrom the book reviews:\u003c\/p\u003e\u003cp\u003e“This book is a nice text for those interested in the topics of almost automorphy and almost periodicity in abstract spaces. … It is worth mentioning that some results are new or not easily accessible in the mathematical literature, which makes the book even more interesting. In greater detail, the book is structured in twelve chapters and an appendix.” (Tomás Caraballo, Mathematical Reviews, June, 2014)\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e1. Metric, Banach, and Hilbert Spaces.- 2. Linear Operators on Banach Spaces.- 3. Almost Periodic Functions.- 4. Almost Automorphic Functions.- 5. Pseudo-Almost Periodic Functions.- 6. Pseudo-Almost Automorphic Functions.- 7. Existence Results for Some Second-Order Differential Equations.- 8. Existence Results to Some Integrodifferential Equations.- 9. Existence of C(m)-Pseudo-Almost Automorphic Solutions.- 10. Pseudo-Almost Periodic Solutions to Some Third-Order Differential Equations.- 11. Pseudo-Almost Automorphic Solutions to Some Sobolev-Type Equations.- 12. Stability Results for Some Higher-Order Difference Equations.- 13. Appendix A.- References.- Index.","brand":"Springer International Publishing AG","offers":[{"title":"Default Title","offer_id":48743091306839,"sku":"9783319008486","price":67.49,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783319008486.jpg?v=1791481703"},{"product_id":"the-real-and-the-complex-a-history-of-analysis-in-the-19th-century-9783319237145","title":"The Real and the Complex: A History of Analysis","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThis book contains a history of real and complex analysis in the nineteenth century, from the work of Lagrange and Fourier to the origins of set theory and the modern foundations of analysis. It studies the works of many contributors including Gauss, Cauchy, Riemann, and Weierstrass.\u003c\/p\u003e\u003cp\u003eThis book is unique owing to the treatment of real and complex analysis as overlapping, inter-related subjects, in keeping with how they were seen at the time. It is suitable as a course in the history of mathematics for students who have studied an introductory course in analysis, and will enrich any course in undergraduate real or complex analysis.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e“The Real and the Complex originated in a course Jeremy Gray gave to upper-level mathematics students and is part of a Springer series on undergraduate mathematics. An important aim of the book is to help the student understand how any given part of mathematics first arises and comes to fruition. … for those readers with some university-level background in mathematics who are interested in the technical contours of nineteenth-century science, Gray’s book will repay careful study and is highly recommended.” (Craig Fraser, Isis, Vol. 108 (2), June, 2017)\u003c\/p\u003e\u003cp\u003e“I view it as an extremely valuable addition to my library and a book that I am sure I will consult frequently in the future: this is a text that should serve well as a desk reference for a faculty member teaching either analysis (real or complex) or the history of mathematics. Certainly, no good university library should be without it.” (Mark Hunacek, MAA Reviews, maa.org, January, 2017)\u003c\/p\u003e“Gray’s 29 chapters take us on quite a ride through the ideas, results, and difficulties of the major figures of nineteenth-century analysis. …  Any mathematician who would like to know how analysis developed should find it interesting. Those who teach analysis can gain much insight from seeing the blind alleys as well as the great ideas … . The writing style is clear and unpretentious, as well as marked by immense learning. … I strongly recommend … .” (Judith V. Grabiner, Notices of the AMS, Vol. 64 (11), 2017)\u003cp\u003e“The Real and the Complex … develops the subject of analysis by reviewing the works of some of the prominent mathematicians of the 19th century. … Summing Up: Recommended. Upper-division undergraduates, graduate students, researchers\/faculty, professionals\/practitioners.” (M. D. Sanford, Choice, Vol. 53 (9), May, 2016)\u003c\/p\u003e\u003cp\u003e“This is a history book on the development of mathematics in the 19th century. Each chapter is built up around one or a few mathematicians. … this book is not only an interesting read for the students who (have to) study it, but equally valuable for professional mathematicians.” (Adhemar Bultheel, European Mathematical Society, euro-math-soc.eu, February, 2016)\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eLagrange and foundations for the calculus.- Joseph Fourier.- Legendre.- Cauchy and continuity.- Cauchy: differentiation and integration.- Cauchy and complex functions to 1830.- Abel.- Jacobi.- Gauss.- Cauchy and complex function theory, 1830-1857.- Complex functions and elliptic integrals.- Revision.- Gauss, Green, and potential theory.- Dirichlet, potential theory, and Fourier series.- Riemann.- Riemann and complex function theory.- Riemann's later complex function theory.- Responses to Riemann's work.- Weierstrass.- Weierstrass's foundational results.- Revision { and assessment.- Uniform Convergence.- Integration and trigonometric series.- The fundamental theorem of the calculus.- The construction of the real numbers.- Implicit functions.- Towards Lebesgue's theory of integration.- Cantor, set theory, and foundations.- Topology.- Assessment.","brand":"Springer International Publishing AG","offers":[{"title":"Default Title","offer_id":48743093109079,"sku":"9783319237145","price":29.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783319237145.jpg?v=1791481711"},{"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}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783319940625.jpg?v=1791379135"},{"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":39.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783540225164.jpg?v=1791482026"},{"product_id":"concise-complex-analysis-revised-edition-9789812706935","title":"Concise Complex Analysis (Revised Edition)","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eA concise textbook on complex analysis for undergraduate and graduate students, this book is written from the viewpoint of modern mathematics: the Bar {Partial}-equation, differential geometry, Lie groups, all the traditional material on complex analysis is included. Setting it apart from others, the book makes many statements and proofs of classical theorems in complex analysis simpler, shorter and more elegant: for example, the Mittag-Leffer theorem is proved using the Bar {Partial}-equation, and the Picard theorem is proved using the methods of differential geometry.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eCalculus; Cauchy Integral Theorem and Cauchy Integral Formula; Theory of Series of Weierstrass; Riemann Mapping Theorem; Differential Geometry and Picard Theorem; A First Taste of Function Theory of Several Complex Variables; Elliptic Functions; The Riemann Zeta Function and the Prime Number Theorem.","brand":"World Scientific Publishing Co Pte Ltd","offers":[{"title":"Default Title","offer_id":48743295877463,"sku":"9789812706935","price":77.9,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9789812706935.jpg?v=1791484046"},{"product_id":"visual-complex-analysis-9780198534464","title":"Visual Complex Analysis","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e","brand":"OUP Oxford","offers":[{"title":"Default Title","offer_id":48864215990615,"sku":"9780198534464","price":57.0,"currency_code":"GBP","in_stock":false}]},{"product_id":"applied-complex-variables-for-scientists-and-engineers-9780521701389","title":"Applied Complex Variables for Scientists and","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eAn introduction to complex variable methods for scientists and engineers, with a high proportion of the book devoted to applications to physical problems. Now containing even more exercises with solutions, it is highly suitable for those wishing to learn the elements of complex analysis in an applied context.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e'This text achieves a mixture of rigour and application that is not found in many books on complex variable theory. I think this is an advantage, allowing one to acquire the best of both mathematical precision alongside applications to physics and engineering … This must surely appeal to a wide range of learning styles and ensure a greater understanding for anyone who chooses to read this text.' W. Joyce, Contemporary Physics\u003cbr\u003e'… this book if acquired is bound to be consulted frequently on any time frame because of its breadth, versatility, completeness and mix of theory with applications.' W. Joyce, Contemporary Physics\u003cbr\u003e'… clear and comprehensible …' Bulletin of the Belgian Mathematical Society\u003cbr\u003e'The book is just right for students learning the elements of function theory in an applied context.' Zeitschrift für Angewandte Mathematik und Mechanik\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface; 1. Complex numbers; 2. Analytic functions; 3. Exponential, logarithmic and trigonometric functions; 4. Complex integration; 5. Taylor and Laurent series; 6. Singularities and calculus of residues; 7. Boundary value problems and initial-boundary value problems; 8. Conformal mappings and applications; Answers to problems; Index.","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":48864969261399,"sku":"9780521701389","price":51.21,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780521701389.jpg?v=1722273374"},{"product_id":"complex-analysis-9780691113852","title":"Complex Analysis","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eIntended for the students of mathematics, physics, engineering and other sciences, this second volume, in a three-part introduction to the subject, introduces the core areas of mathematical analysis while also illustrating the organic unity between them. It includes numerous examples and applications.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"Elias M. Stein, Winner of the 2005 Stefan Bergman Prize, American Mathematical Society\"\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eForeword vii  Introduction xv  Chapter 1. Preliminaries to Complex Analysis 1  1 Complex numbers and the complex plane 1  1.1 Basic properties 1  1.2 Convergence 5  1.3 Sets in the complex plane 5  2 Functions on the complex plane 8  2.1 Continuous functions 8  2.2 Holomorphic functions 8  2.3 Power series 14  3 Integration along curves 18  4 Exercises 24  Chapter 2. Cauchy's Theorem and Its Applications 32  1 Goursat's theorem 34  2 Local existence of primitives and Cauchy's theorem in a disc 37  3 Evaluation of some integrals 41  4 Cauchy's integral formulas 45  5 Further applications 53  5.1 Morera's theorem 53  5.2 Sequences of holomorphic functions 53  5.3 Holomorphic functions defined in terms of integrals 55  5.4 Schwarz reflection principle 57  5.5 Runge's approximation theorem 60  6 Exercises 64  7 Problems 67  Chapter 3. Meromorphic Functions and the Logarithm 71  1 Zeros and poles 72  2 The residue formula 76  2.1 Examples 77  3 Singularities and meromorphic functions 83  4 The argument principle and applications 89  5 Homotopies and simply connected domains 93  6 The complex logarithm 97  7 Fourier series and harmonic functions 101  8 Exercises 103  9 Problems 108  Chapter 4. The Fourier Transform 111  1 The class F 113  2 Action of the Fourier transform on F 114  3 Paley-Wiener theorem 121  4 Exercises 127  5 Problems 131  Chapter 5. Entire Functions 134  1 Jensen's formula 135  2 Functions of finite order 138  3 Infinite products 140  3.1 Generalities 140  3.2 Example: the product formula for the sine function 142  4 Weierstrass infinite products 145  5 Hadamard's factorization theorem 147  6 Exercises 153  7 Problems 156  Chapter 6. The Gamma and Zeta Functions 159  1 The gamma function 160  1.1 Analytic continuation 161  1.2 Further properties of T 163  2 The zeta function 168  2.1 Functional equation and analytic continuation 168  3 Exercises 174  4 Problems 179  Chapter 7. The Zeta Function and Prime Number Theorem 181  1 Zeros of the zeta function 182  1.1 Estimates for 1\/s(s) 187  2 Reduction to the functions v and v1 188  2.1 Proof of the asymptotics for v1 194  Note on interchanging double sums 197  3 Exercises 199  4 Problems 203  Chapter 8. Conformal Mappings 205  1 Conformal equivalence and examples 206  1.1 The disc and upper half-plane 208  1.2 Further examples 209  1.3 The Dirichlet problem in a strip 212  2 The Schwarz lemma; automorphisms of the disc and upper half-plane 218  2.1 Automorphisms of the disc 219  2.2 Automorphisms of the upper half-plane 221  3 The Riemann mapping theorem 224  3.1 Necessary conditions and statement of the theorem 224  3.2 Montel's theorem 225  3.3 Proof of the Riemann mapping theorem 228  4 Conformal mappings onto polygons 231  4.1 Some examples 231  4.2 The Schwarz-Christoffel integral 235  4.3 Boundary behavior 238  4.4 The mapping formula 241  4.5 Return to elliptic integrals 245  5 Exercises 248  6 Problems 254  Chapter 9. An Introduction to Elliptic Functions 261  1 Elliptic functions 262  1.1 Liouville's theorems 264  1.2 The Weierstrass p function 266  2 The modular character of elliptic functions and Eisenstein series 273  2.1 Eisenstein series 273  2.2 Eisenstein series and divisor functions 276  3 Exercises 278  4 Problems 281  Chapter 10. Applications of Theta Functions 283  1 Product formula for the Jacobi theta function 284  1.1 Further transformation laws 289  2 Generating functions 293  3 The theorems about sums of squares 296  3.1 The two-squares theorem 297  3.2 The four-squares theorem 304  4 Exercises 309  5 Problems 314  Appendix A: Asymptotics 318  1 Bessel functions 319  2 Laplace's method; Stirling's formula 323  3 The Airy function 328  4 The partition function 334  5 Problems 341  Appendix B: Simple Connectivity and Jordan Curve Theorem 344  1 Equivalent formulations of simple connectivity 345  2 The Jordan curve theorem 351  2.1 Proof of a general form of Cauchy's theorem 361  Notes and References 365  Bibliography 369  Symbol Glossary 373  Index 375","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":48865517896023,"sku":"9780691113852","price":74.8,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780691113852.jpg?v=1722274354"},{"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":73.8,"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":61.2,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780691207582.jpg?v=1722274497"},{"product_id":"a-course-in-mathematical-analysis-1-9781107614185","title":"A Course in Mathematical Analysis 1","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThe three volumes of A Course in Mathematical Analysis provide a full and detailed account of all those elements of real and complex analysis that an undergraduate mathematics student can expect to encounter in their first two or three years of study. Containing hundreds of exercises, examples and applications, these books will become an invaluable resource for both students and instructors. This first volume focuses on the analysis of real-valued functions of a real variable. Besides developing the basic theory it describes many applications, including a chapter on Fourier series. It also includes a Prologue in which the author introduces the axioms of set theory and uses them to construct the real number system. Volume 2 goes on to consider metric and topological spaces and functions of several variables. Volume 3 covers complex analysis and the theory of measure and integration.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e'Garling is a gifted expositor and the book under review really conveys the beauty of the subject, not an easy task. [It] comes with appropriate examples when needed and has plenty of well-chosen exercises as may be expected from a textbook. As the author points out in the introduction, a newcomer may be advised, on a first reading, to skip part one and take the required properties of the ordered real field as axioms; later on, as the student matures, he\/she may go back to a detailed reading of the skipped part. This is good advice.' Felipe Zaldivar, MAA Reviews\u003cbr\u003e'This work is the first in a three-volume set dedicated to real and complex analysis that 'mathematical undergraduates may expect to meet in the first two years or so … of analysis' … The exposition is superb: open and nontelegraphic. Highly recommended. Upper-division undergraduates and graduate students.' D. Robbins, Choice\u003cbr\u003e'These three volumes cover very thoroughly the whole of undergraduate analysis and much more besides.' John Baylis, The Mathematical Gazette\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eIntroduction; Part I. Prologue: The Foundations of Analysis: 1. The axioms of set theory; 2. Number systems; Part II. Functions of a Real Variable: 3. Convergent sequences; 4. Infinite series; 5. The topology of R; 6. Continuity; 7. Differentiation; 8. Integration; 9. Introduction to Fourier series; 10. Some applications; Appendix: Zorn's lemma and the well-ordering principle; Index.","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":48866342928727,"sku":"9781107614185","price":47.26,"currency_code":"GBP","in_stock":true}]},{"product_id":"course-in-complex-analysis-in-one-variable-a-9789810247805","title":"Course In Complex Analysis In One Variable, A","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eComplex analysis is a beautiful subject — perhaps the single most beautiful; and striking; in mathematics. It presents completely unforeseen results that are of a dramatic; even magical; nature. This invaluable book will convey to the student its excitement and extraordinary character. The exposition is organized in an especially efficient manner; presenting basic complex analysis in around 130 pages; with about 50 exercises. The material constantly relates to and contrasts with that of its sister subject; real analysis. An unusual feature of this book is a short final chapter containing applications of complex analysis to Lie theory.Since much of the content originated in a one-semester course given at the CUNY Graduate Center; the text will be very suitable for first year graduate students in mathematics who want to learn the basics of this important subject. For advanced undergraduates; there is enough material for a year-long course or; by concentrating on the first three chapters; for one-semester course.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eFirst Concepts; Integration Along a Contour; The Main Consequences of Cauchy's Theorem; Singularities; Conformal Mappings; Applications of Complex Analysis to Lie Theory.","brand":"World Scientific Publishing Co Pte Ltd","offers":[{"title":"Default Title","offer_id":48869594431831,"sku":"9789810247805","price":40.85,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9789810247805.jpg?v=1791483766"},{"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":"period-mappings-and-period-domains-9781108422628","title":"Period Mappings and Period Domains","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis up-to-date introduction to Griffiths' theory of period maps and period domains focusses on algebraic, group-theoretic and differential geometric aspects. The second edition has been thoroughly revised and now includes a new third section covering recent and important new developments in the field.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003eReview of previous edition: 'This book, dedicated to Philip Griffiths, provides an excellent introduction to the study of periods of algebraic integrals and their applications to complex algebraic geometry. In addition to the clarity of the presentation and the wealth of information, this book also contains numerous problems which render it ideal for use in a graduate course in Hodge theory.' Mathematical Reviews\u003cbr\u003eReview of previous edition: '… generally more informal and differential-geometric in its approach, which will appeal to many readers … the book is a useful introduction to Carlos Simpson's deep analysis of the fundamental groups of compact Kähler manifolds using harmonic maps and Higgs bundles.' Burt Totaro, University of Cambridge\u003cbr\u003e'This monograph provides an excellent introduction to Hodge theory and its applications to complex algebraic geometry.' Gregory Pearlstein, Nieuw Archief voor Weskunde\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePart I. Basic Theory: 1. Introductory examples; 2. Cohomology of compact Kähler manifolds; 3. Holomorphic invariants and cohomology; 4. Cohomology of manifolds varying in a family; 5. Period maps looked at infinitesimally; Part II. Algebraic Methods: 6. Spectral sequences; 7. Koszul complexes and some applications; 8. Torelli theorems; 9. Normal functions and their applications; 10. Applications to algebraic cycles: Nori's theorem; Part III. Differential Geometric Aspects: 11. Further differential geometric tools; 12. Structure of period domains; 13. Curvature estimates and applications; 14. Harmonic maps and Hodge theory; Part IV. Additional Topics: 15. Hodge structures and algebraic groups; 16. Mumford–Tate domains; 17. Hodge loci and special subvarieties; Appendix A. Projective varieties and complex manifolds; Appendix B. Homology and cohomology; Appendix C. Vector bundles and Chern classes; Appendix D. Lie groups and algebraic groups; References; Index.","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":48885260550487,"sku":"9781108422628","price":87.0,"currency_code":"GBP","in_stock":true}]},{"product_id":"chaotic-systems-dynamics-algorithms-synchronization-9781536110654","title":"Chaotic Systems: Dynamics, Algorithms \u0026","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis book provides new research on the dynamics, algorithms and synchronization of chaotic systems. Chapter One introduces some nonlinear techniques for the synchronization of a class of chaotic oscillator under the framework of observer design from control theory. Chapter Two discusses in detail the application of a novel multi-domain spectral collocation approach for finding solutions of ordinary differential equations that exhibit general chaotic behaviour. Chapter Three designs an adaptive state feedback controller guaranteeing the asymptotic stability followed by the synchronization of the nonlinear discrete-time error of two identical hyper chaotic systems.","brand":"Nova Science Publishers Inc","offers":[{"title":"Default Title","offer_id":48886059073879,"sku":"9781536110654","price":999.99,"currency_code":"GBP","in_stock":false}]},{"product_id":"from-chaos-to-complexity-science-20-years-of-multidisciplinary-explorations-9781536188257","title":"From Chaos to Complexity Science. 20 Years of","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis book is dedicated to the first ten years of Chaos and Complexity Letters - International Journal of Dynamical Systems Research. This journal was born to collect and disseminate complexity science related information to anybody interested in the topic; to speed up the evolutionary development of complexity science; to extend its interactions crossing over disciplines, levels of knowledge and geography; and to foster finding new pathways in research and new applications. The structure of CCL was specifically designed to add value to the trans-disciplinary approach while, at the same time, differentiating the epistemology of different contributions. In this enterprise we were sustained and inspired by two great companions that in different ways shared our project during its prehistory: Ilya Prigogine and Francisco Varela. This book collects 16 papers appeared on the first ten volumes of Chaos and Complexity Letters. They range from the life sciences, to STEM and economy, in accordance with the interdisciplinary mission of the journal. A special highlight starts with Acceleration and entropy: a macroscopic analogue of the twin paradox, possibly the last paper written by the Nobel Prize Ilya Prigogine with Gonzalo Ordonez. Important academic specialists who wrote in our scientific journal passed away. For example, Walter Freeman, Tullio Minelli, Ilya Prigogine, and Joseph P. Zbilut. This special issue is also dedicated to them. We are in opinion that their trajectories in life and research designed some contours of the shape of a new science to come.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface; Introduction; Acceleration and Entropy: A Macroscopic Analogue of the Twin Paradox; William James on Consciousness, Revisited; The Structural Equations Technique for Testing Hypotheses in Nonlinear Dynamics: Catastrophes, Chaos and Related Dynamics; Dynamical Prediction of Chaotic Time Series; Synchronization of Oscillators in Complex Networks; Contribution to the Debate on Linear and Nonlinear Analysis of the Electroencephalogram; Detection of Transient Synchronization in Multivariate Brain Signals Application to Event-Related Potentials; Brief Note on Recurrence Quantification Analysis of Bipolar Disorder Performed by Using a Van Der Pol Oscillator Model; Complex Dynamics of Visual Arts; Noninvertible Maps and Complex Basin Boundaries in Dynamic Economic Models with Coexisting Attractors; Adaptive Synchronization of Two Different Uncertain Chaotic Systems; Ex-tended Prigogine Theorem: Method for Universal Characterization of Complex System Evolution; A Beginners Guide to the Nature and Potentialities of Dynamical and Network Theory, Part I: A Very Very Brief Visual Introduction to the Theory of Dynamical Sys-tems; A Simple Model of Intermittent Chaos; Synchronization of Fractals in Logarithmic Spirals; Chaos in Returns and Volatilities of the London Gold Fix; Index.","brand":"Nova Science Publishers Inc","offers":[{"title":"Default Title","offer_id":48886188900695,"sku":"9781536188257","price":163.19,"currency_code":"GBP","in_stock":false}]},{"product_id":"lecture-notes-on-complex-analysis-9781860946424","title":"Lecture Notes On Complex Analysis","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis book is based on lectures presented over many years to second and third year mathematics students in the Mathematics Departments at Bedford College, London, and King's College, London, as part of the BSc. and MSci. program. Its aim is to provide a gentle yet rigorous first course on complex analysis.Metric space aspects of the complex plane are discussed in detail, making this text an excellent introduction to metric space theory. The complex exponential and trigonometric functions are defined from first principles and great care is taken to derive their familiar properties. In particular, the appearance of π, in this context, is carefully explained.The central results of the subject, such as Cauchy's Theorem and its immediate corollaries, as well as the theory of singularities and the Residue Theorem are carefully treated while avoiding overly complicated generality. Throughout, the theory is illustrated by examples.A number of relevant results from real analysis are collected, complete with proofs, in an appendix.The approach in this book attempts to soften the impact for the student who may feel less than completely comfortable with the logical but often overly concise presentation of mathematical analysis elsewhere.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"Good bibliography; adequate index.\"Choice\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eComplex numbers; Sequences and Series; Metric Space Properties of the Complex Plane; Analytic Functions; The Complex Exponential and Trigonometric Functions; The Complex Logarithm; Complex Integration; Cauchy's Theorem; The Laurent Expansion; Singularities and Meromorphic Functions; Theory of Residues; The Argument Principle; Maximum Modulus Principle; Mobius Transformations; Harmonic Functions; Local Properties of Analytic Functions.","brand":"Imperial College Press","offers":[{"title":"Default Title","offer_id":48888195285335,"sku":"9781860946424","price":104.5,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781860946424.jpg?v=1791479100"},{"product_id":"local-activity-principle-the-cause-of-complexity-and-symmetry-breaking-9781908977090","title":"Local Activity Principle: The Cause Of Complexity","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThe principle of local activity explains the emergence of complex patterns in a homogeneous medium. At first defined in the theory of nonlinear electronic circuits in a mathematically rigorous way, it can be generalized and proven at least for the class of nonlinear reaction-diffusion systems in physics, chemistry, biology, and brain research. Recently, it was realized by memristors for nanoelectronic device applications. In general, the emergence of complex patterns and structures is explained by symmetry breaking in homogeneous media, which is caused by local activity. This book argues that the principle of local activity is really fundamental in science, and can even be identified in quantum cosmology as symmetry breaking of local gauge symmetries generating the complexity of matter and forces in our universe. Applications are considered in economic, financial, and social systems with the emergence of equilibrium states, symmetry breaking at critical points of phase transitions and risky acting at the edge of chaos.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eThe Local Activity Principle and the Emergence of Complexity; Local Activity and Edge of Chaos in Computer Visualization; The Local Activity Principle and the Expansion of the Universe; The Local Activity Principle and the Dynamics of Matter; The Local Activity Principle and the Evolution of Life; The Local Activity Principle and the Co-evolution of Technology; The Local Activity Principle and Innovation in the Economy and Society; The Message of the Local Activity Principle.","brand":"Imperial College Press","offers":[{"title":"Default Title","offer_id":48888456610135,"sku":"9781908977090","price":137.75,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781908977090.jpg?v=1791479388"},{"product_id":"air-force-capability-development-planning-analytical-methods-to-support-investment-decisions-9781977403087","title":"Air Force Capability Development Planning:","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e","brand":"RAND","offers":[{"title":"Default Title","offer_id":48888931778903,"sku":"9781977403087","price":17.59,"currency_code":"GBP","in_stock":false}]},{"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":"moduli-spaces-and-arithmetic-geometry-9784931469389","title":"Moduli Spaces And Arithmetic Geometry","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eSince its birth algebraic geometry has been closely related to and deeply motivated by number theory. Particularly the modern study of moduli spaces and arithmetic geometry have many important techniques and ideas in common. With this close relation in mind, the RIMS conference Moduli Spaces and Arithmetic Geometry was held at Kyoto University during September 8-15, 2004 as the 13th International Research Institute of the Mathematical Society of Japan. This volume is the outcome of this conference and consists of thirteen papers by invited speakers, including C Soulé, A Beauville and C Faber, and participants. All papers, with two exceptions by C Voisin and Yoshinori Namikawa, treat moduli problem and\/or arithmetic geometry. Algebraic curves, Abelian varieties, algebraic vector bundles, connections and D-modules are the subjects of those moduli papers. Arakelov geometry and rigid geometry are studied in arithmetic papers. In the two exceptions, integral Hodge classes on Calabi-Yau threefolds and symplectic resolutions of nilpotent orbits are studied.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\u003eModuli spaces of twisted sheaves on a projective variety by K. Yoshioka Appendix. Proof of Caldararu's conjecture by D. Huybrechts and P. Stellari On integral Hodge classes on uniruled or Calabi-Yau threefolds by C. Voisin Birational geometry of symplectic resolutions of nilpotent orbits by Y. Namikawa The moduli stack of rank-two Gieseker bundles with fixed determinant on a nodal curve by T. Abe Vector bundles on curves and theta functions by A. Beauville On the finiteness of abelian varieties with bounded modular height by A. Moriwaki Moduli of regular holonomic $\\mathcal{D}_X$-modules with natural parabolic stability by N. Nitsure The cohomology groups of stable quasi-abelian schemes and degenerations associated with the $E_8$-lattice by I. Nakamura and K. Sugawara Semi-stable extensions on arithmetic surfaces by C. Soule On the cusp form motives in genus 1 and level 1 by C. Consani and C. Faber Polarized K3 surfaces of genus thirteen by S. Mukai Rigid geometry and applications by K. Fujiwara and F. Kato Moduli of stable parabolic connections, Riemann-Hilbert correspondence and geometry of Painleve equation of type VI, part II by M. Inaba, K. Iwasaki, and M. Saito.","brand":"Mathematical Society of Japan","offers":[{"title":"Default Title","offer_id":48889419989335,"sku":"9784931469389","price":80.75,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9784931469389.jpg?v=1791482575"},{"product_id":"potential-theory-in-matsue-proceedings-of-the-international-workshop-9784931469334","title":"Potential Theory In Matsue - Proceedings Of The","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis volume collects, in written form, eight plenary lectures and twenty-five selected contributions from invited and contributed lectures delivered at the International Workshop on Potential Theory 2004. The workshop was held at Shimane University, Matsue, Japan, from 23 to 28 August, 2004. The topic of the workshop was Potential Theory and its related fields. There were stimulus talks from classical potential theory to pluri-potential theory and probabilistic potential theory.Published by Mathematical Society of Japan and distributed by World Scientific Publishing Co. for all markets except North America","brand":"Mathematical Society of Japan","offers":[{"title":"Default Title","offer_id":48889420153175,"sku":"9784931469334","price":81.7,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9784931469334.jpg?v=1791482575"},{"product_id":"singularities-in-geometry-and-topology-2004-9784931469396","title":"Singularities In Geometry And Topology 2004","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis volume constitutes the proceedings of the third Franco-Japanese symposium on singularities, held in Sapporo in September 2004. It contains not only research papers on the most advanced topics in the field, but also some survey articles which give broad scopes in some areas of the subject. All the articles are carefully refereed for correctness and readability.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\u003eCobordism of fibered knots and related topics by V. Blanloeil and O. Saeki Proportionality of indices of 1-forms on singular varieties by J.-P. Brasselet, J. Seade, and T. Suwa Motivic sheaves and intersection cohomology by M. Hanamura On hyperbolic perturbations of algebraic links and small Mahler measure by E. Hironaka Stably hyperbolic polynomials by V. P. Kostov On weighted-degrees for algebraic local cohomologies associated with semiquasihomogeneous singularities by Y. Nakamura and S. Tajima The geometry of continued fractions and the topology of surface singularities by P. Popescu-Pampu Exemples de fonctions de Artin de germes d'espaces analytiques by G. Rond Perverse sheaves and Milnor fibers over singular varieties by K. Takeuchi On Horn-Kapranov uniformisation of the discriminantal loci by S. Tanabe Duality of Euler data for affine varieties by M. Tibuar Algebre graduee associee a une valuation de $K[x]$ by M. Vaquie Plane curve singularities whose Milnor and Tjurina numbers differ by three by M. Watari Characteristic classes of (pro)algebraic varieties by S. Yokura.","brand":"Mathematical Society of Japan","offers":[{"title":"Default Title","offer_id":48889420218711,"sku":"9784931469396","price":80.75,"currency_code":"GBP","in_stock":false}]},{"product_id":"zeta-regularization-techniques-with-applications-9789810214418","title":"Zeta Regularization Techniques With Applications","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis book is the result of several years of work by the authors on different aspects of zeta functions and related topics. The aim is twofold. On one hand, a considerable number of useful formulas, essential for dealing with the different aspects of zeta-function regularization (analytic continuation, asymptotic expansions), many of which appear here, in book format, for the first time are presented. On the other hand, the authors show explicitly how to make use of such formulas and techniques in practical applications to physical problems of very different nature. Virtually all types of zeta functions are dealt with in the book.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePart 1 The Riemann Zeta function: Riemann, Hurwitz, Epstein, Selberg and related zeta functions; analytic continuation - practical uses for series summation; asymptotic expansion of \"zeta\". Part 2 Zeta-function regularization of sums over known spectrum: the zeta-function regularization theorem; multiple zeta-functions with arbitrary exponents. Part 3 Zeta-function regularization when the spectrum is not known: zeta-function vs heat-kernel regularization; small-\"t\" asymptotic expansion of the heat-kernel. Part 4 The Casimir effect in flat space-time with compact spatial part: simply connected compact manifold with constant curvature; the Selberg trace formula for compact hyperbolic manifolds. Part 5 Finite temperature effects for theories defined on compact hyperbolic manifolds: basic formalism for the finite-temperature effective potential; the finite-temperature thermodynamic potential for manifolds with a compact spatial part. Part 6 Properties of the chemical potential in higher-dimensional manifolds: the flat-manifold case; the constant non-zero curvature case. Part 7 Strings at non-zero temperature and 2d gravity: free energy for the Bosonic string; vacuum energy for Torus compactified strings. Part 8 Membranes at non-zero temperatures: supermembrane free energy; free energy for the compactified supermembranes and modular invariance; and others.","brand":"World Scientific Publishing Co Pte Ltd","offers":[{"title":"Default Title","offer_id":48890166870359,"sku":"9789810214418","price":95.0,"currency_code":"GBP","in_stock":false}]},{"product_id":"semi-classical-analysis-for-nonlinear-schrodinger-equations-9789812793126","title":"Semi-classical Analysis For Nonlinear Schrodinger","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThese lecture notes review recent results on the high-frequency analysis of nonlinear Schrödinger equations in the presence of an external potential. The book consists of two relatively independent parts: WKB analysis, and caustic crossing. In the first part, the basic linear WKB theory is constructed and then extended to the nonlinear framework. The most difficult supercritical case is discussed in detail, together with some of its consequences concerning instability phenomena. Applications of WKB analysis to functional analysis, in particular to the Cauchy problem for nonlinear Schrödinger equations, are also given. In the second part, caustic crossing is described, especially when the caustic is reduced to a point, and the link with nonlinear scattering operators is investigated.These notes are self-contained and combine selected articles written by the author over the past ten years in a coherent manner, with some simplified proofs. Examples and figures are provided to support the intuition, and comparisons with other equations such as the nonlinear wave equation are provided.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eWKB Analysis: Preliminary Analysis; Weak Nonlinearity; Modulated Energy Functionals; Point-wise Description; Some Instability Phenomena; Caustic Crossing: The Case of Focal Points: Caustic Crossing: Formal Analysis; Focal Point without External Potential; Focal Point with a Potential; Some Ideas for Supercritical Cases.","brand":"World Scientific Publishing Co Pte Ltd","offers":[{"title":"Default Title","offer_id":48890213433687,"sku":"9789812793126","price":80.75,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9789812793126.jpg?v=1791484058"},{"product_id":"approximation-by-complex-bernstein-and-convolution-type-operators-9789814282420","title":"Approximation By Complex Bernstein And","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThe monograph, as its first main goal, aims to study the overconvergence phenomenon of important classes of Bernstein-type operators of one or several complex variables, that is, to extend their quantitative convergence properties to larger sets in the complex plane rather than the real intervals. The operators studied are of the following types: Bernstein, Bernstein—Faber, Bernstein-Butzer, q-Bernstein, Bernstein-Stancu, Bernstein-Kantorovich, Favard-Szász-Mirakjan, Baskakov and Balázs-Szabados.The second main objective is to provide a study of the approximation and geometric properties of several types of complex convolutions: the de la Vallée Poussin, Fejér, Riesz-Zygmund, Jackson, Rogosinski, Picard, Poisson-Cauchy, Gauss-Weierstrass, q-Picard, q-Gauss-Weierstrass, Post-Widder, rotation-invariant, Sikkema and nonlinear. Several applications to partial differential equations (PDEs) are also presented.Many of the open problems encountered in the studies are proposed at the end of each chapter. For further research, the monograph suggests and advocates similar studies for other complex Bernstein-type operators, and for other linear and nonlinear convolutions.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eBernstein-Type Operators of One Complex Variable: Auxiliary Results in Complex Analysis; Bernstein Polynomials; Iterates of Bernstein Polynomials; Generalized Voronovskaja Theorems for Bernstein Polynomials; Butzer's Linear Combination of Bernstein Polynomials; q-Bernstein Polynomials; Bernstein-Stancu Polynomials; Bernstein-Kantorovich Type Polynomials; Favard-Szasz-Mirakjan Operators; Baskakov Operators; Balazs-Szabados Operators; Bibliographical Notes and Open Problems; Bernstein-Type Operators of Several Complex Variables: Introduction; Bernstein Polynomials; Favard-Szasz-Mirakjan Operators; Baskakov Operators; Bibliographical Notes and Open Problems; Complex Convolutions: Linear Polynomial Convolutions; Linear Non-Polynomial Convolutions; Nonlinear Complex Convolutions; Bibliographical Notes and Open Problems; Appendices: Related Topics: Bernstein Polynomials of Quaternion Variable; Approximation of Vector-Valued Functions; Strong Approximation by Complex Taylor Series; Bibliographical Notes and Open Problems.","brand":"World Scientific Publishing Co Pte Ltd","offers":[{"title":"Default Title","offer_id":48890219954519,"sku":"9789814282420","price":100.7,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9789814282420.jpg?v=1791484197"},{"product_id":"mastering-frequency-domain-techniques-for-the-stability-analysis-of-lti-time-delay-systems-9781611975710","title":"Mastering Frequency Domain Techniques for the","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eIn many dynamical systems, time delays arise because of the time it takes to measure system states, perceive and evaluate events, formulate decisions, and act on those decisions. The presence of delays may lead to undesirable outcomes; without an engineered design, the dynamics may underperform, oscillate, and even become unstable. How to study the stability of dynamical systems influenced by time delays is a fundamental question. Related issues include how much time delay the system can withstand without becoming unstable and how to change system parameters to render improved dynamic characteristics, utilize or tune the delay itself to improve dynamical behavior, and assess the stability and speed of response of the dynamics. \u003cbr\u003e\u003cbr\u003e\u003ci\u003eMastering Frequency Domain Techniques for the Stability Analysis of LTI Time Delay Systems\u003c\/i\u003e addresses these questions for linear time-invariant (LTI) systems with an eigenvalue-based approach built upon frequency domain techniques. Readers will find key results from the literature, including all subtopics for those interested in deeper exploration. The book presents step-by-step demonstrations of all implementations—including those that require special care in mathematics and numerical implementation—from the simpler, more intuitive ones in the introductory chapters to the more complex ones found in the later chapters. Maple and MATLAB code is available from the author’s website.\u003cbr\u003e\u003cbr\u003eThis multipurpose book is intended for graduate students, instructors, and researchers working in control engineering, robotics, mechatronics, network control systems, human-in-the-loop systems, human-machine systems, remote control and tele-operation, transportation systems, energy systems, and process control, as well as for those working in applied mathematics, systems biology, and physics. 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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":"the-real-fatou-conjecture-9780691002583","title":"The Real Fatou Conjecture","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eIn 1920, Pierre Fatou expressed the conjecture that - except for special cases - all critical points of a rational map of the Riemann sphere tend to periodic orbits under iteration. This book provides a proof of the Real Fatou Conjecture. It includes a self-contained and complete version of the argument.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e1Review of Concepts31.1Theory of Quadratic Polynomials31.2Dense Hyperbolicity61.3Steps of the Proof of Dense Hyperbolicity122Quasiconformal Gluing252.1Extendibility and Distortion262.2Saturated Maps302.3Gluing of Saturated Maps353Polynomial-Like Property453.1Domains in the Complex Plane453.2Cutting Times474Linear Growth of Moduli674.1Box Maps and Separation Symbols674.2Conformal Roughness874.3Growth of the Separation Index1005Quasiconformal Techniques1095.1Initial Inducing1095.2Quasiconformal Pull-back1205.3Gluing Quasiconformal Maps1295.4Regularity of Saturated Maps1335.5Straightening Theorem139Bibliography143Index147","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":49403666628951,"sku":"9780691002583","price":999.99,"currency_code":"GBP","in_stock":false}]},{"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":999.99,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780691011189.jpg?v=1730484221"},{"product_id":"complex-ball-quotients-and-line-arrangements-in-the-projective-plane-9780691144771","title":"Complex Ball Quotients and Line Arrangements in","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eThis book introduces the theory of complex surfaces through a comprehensive look at finite covers of the projective plane branched along line arrangements. Paula Tretkoff emphasizes those finite covers that are free quotients of the complex two-dimensional ball. Tretkoff also includes background on the classical Gauss hypergeometric function of one\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"A very welcome addition to the literature and is recommended for anyone interested in the theory under discussion.\"--Daniel Greb, MathSciNet\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e*Frontmatter, pg. i*Contents, pg. vii*Preface, pg. ix*Introduction, pg. 1*Chapter One. Topological Invariants and Differential Geometry, pg. 6*Chapter Two. Riemann Surfaces, Coverings, and Hypergeometric Functions, pg. 23*Chapter Three. Complex Surfaces and Coverings, pg. 47*Chapter Four. Algebraic Surfaces and the Miyaoka-Yau Inequality, pg. 65*Chapter Five. Line Arrangements in P2(C) and Their Finite Covers, pg. 85*Chapter Six. Existence of Ball Quotients Covering Line Arrangements, pg. 126*Chapter Seven. Appell Hypergeometric Functions, pg. 167*Appendix A. Torsion-Free Subgroups of Finite Index by Hans-Christoph Im Hof, pg. 189*Appendix B. Kummer Coverings, pg. 197*Bibliography, pg. 205*Index, pg. 213","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":49403772698967,"sku":"9780691144771","price":60.0,"currency_code":"GBP","in_stock":false}]},{"product_id":"advances-in-analysis-9780691159416","title":"Advances in Analysis","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003ePrinceton University's Elias Stein was the first mathematician to see the profound interconnections that tie classical Fourier analysis to several complex variables and representation theory. This volume gathers papers from internationally renowned mathematicians, many of whom have been Stein's students.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface ix Chapter 1 Selected Theorems by Eli Stein 1 Charles Fefferman Chapter 2 Eli's Impact: A Case Study 35 Charles Fefferman Chapter 3 On Oscillatory Integral Operators in Higher Dimensions 47 Jean Bourgain Chapter 4 Holder Regularity for Generalized Master Equations with Rough Kernels 63 Luis Caffarelli and Luis Silvestre Chapter 5 Extremizers of a Radon Transform Inequality 84 Michael Christ Chapter 6 Should We Solve Plateau's Problem Again? 108 Guy David Chapter 7 Averages along Polynomial Sequences in Discrete Nilpotent Lie Groups: Singular Radon Transforms 146 Alexandru D. Ionescu, Akos Magyar, and Stephen Wainger Chapter 8 Internal DLA for Cylinders 189 David Jerison, Lionel Levine, and Scott Sheffield Chapter 9 The Energy Critical Wave Equation in 3D 215 Carlos Kenig Chapter 10 On the Bounded L2 Curvature Conjecture 224 Sergiu Klainerman Chapter 11 On Div-Curl for Higher Order 245 Loredana Lanzani and Andrew S. Raich Chapter 12 Square Functions and Maximal Operators Associated with Radial Fourier Multipliers 273 Sanghyuk Lee, Keith M. Rogers, and Andreas Seeger Chapter 13 Problems of Harmonic Analysis Related to Finite-Type Hypersurfaces in  3, and Newton Polyhedra 303 Detlef Muller Chapter 14 Multi-Linear Multipliers Associated to Simplexes of Arbitrary Length 346 Camil Muscalu, Terence Tao, and Christoph Thiele Chapter 15 Diagonal Estimates for Bergman Kernels in Monomial-Type Domains 402 Alexander Nagel and Malabika Pramanik Chapter 16 On the Singularities of the Pluricomplex Green's Function 419 D. H. Phong and Jacob Sturm Chapter 17 Smoothness of Spectral Multipliers and Convolution Kernels in Nilpotent Gelfand Pairs 436 Fulvio Ricci Chapter 18 On Eigenfunction Restriction Estimates and L4-Bounds for Compact Surfaces with Nonpositive Curvature 447 Christopher D. Sogge and Steve Zelditch List of Contributors 463 Index 465","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":49403801141591,"sku":"9780691159416","price":90.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780691159416.jpg?v=1791463747"},{"product_id":"topics-in-quaternion-linear-algebra-9780691161853","title":"Topics in Quaternion Linear Algebra","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eQuaternions are a number system that has become increasingly useful for representing the rotations of objects in three-dimensional space and has important applications in theoretical and applied mathematics, physics, computer science, and engineering. This is the first book to provide a systematic, accessible, and self-contained exposition of quate\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003eOne of Choice's Outstanding Academic Titles for 2015 \"Rodman fills a void in the monographic literature with this work.\"--Choice \"The book is self-contained and well organized... Full and detailed proofs are supplied. Another exciting point is the presence of many open problems throughout the book.\"--Gisele C. Ducati, MatchSciNet\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e*FrontMatter, pg. i*Contents, pg. vii*Preface, pg. xi*Chapter One. Introduction, pg. 1*Chapter Two. The algebra of quaternions, pg. 9*Chapter Three. Vector spaces and matrices: Basic theory, pg. 28*Chapter Four. Symmetric matrices and congruence, pg. 64*Chapter Five. Invariant subspaces and Jordan form, pg. 83*Chapter Six. Invariant neutral and semidefinite subspaces, pg. 131*Chapter Seven. Smith form and Kronecker canonical form, pg. 153*Chapter Eight. Pencils of hermitian matrices, pg. 172*Chapter Nine. Skewhermitian and mixed pencils, pg. 194*Chapter Ten. Indefinite inner products: Conjugation, pg. 228*Chapter Eleven. Matrix pencils with symmetries: Nonstandard involution, pg. 261*Chapter Twelve. Mixed matrix pencils: Nonstandard involutions, pg. 279*Chapter Thirteen. Indefinite inner products: Nonstandard involution, pg. 300*Chapter Fourteen. Matrix equations, pg. 328*Chapter Fifteen. Appendix: Real and complex canonical forms, pg. 339*Bibliography, pg. 353*Index, pg. 361","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":49403806122327,"sku":"9780691161853","price":73.8,"currency_code":"GBP","in_stock":true}]}],"url":"https:\/\/bookcurl.com\/collections\/complex-analysis-complex-variables.oembed?page=21","provider":"Book Curl","version":"1.0","type":"link"}