{"title":"Mathematical \/ Computational \/ Theoretical physics Books","description":"","products":[{"product_id":"general-relativity-9780141999869","title":"General Relativity","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003e\u003cp\u003e\u003cb\u003eThe latest volume in \u003ci\u003eThe New York Times \u003c\/i\u003ebestselling physics series explains Einstein''s masterpiece: the general theory of relativity\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003eHe taught us classical mechanics, quantum mechanics and special relativity. Now, physicist Leonard Susskind, assisted by a new collaborator, André Cabannes, returns to tackle Einstein''s general theory of relativity. Starting from the equivalence principle and covering the necessary mathematics of Riemannian spaces and tensor calculus, Susskind and Cabannes explain the link between gravity and geometry. They delve into black holes, establish Einstein field equations and solve them to describe gravity waves. The authors provide vivid explanations that, to borrow a phrase from Einstein himself, are as simple as possible (but no simpler).\u003cbr\u003e\u003cbr\u003eAn approachable yet rigorous introduction to one of the most important topics in physics, \u003ci\u003eGeneral Relativity\u003c\/i\u003e is a must-read for anyone who wants a deeper knowledge of the universe''s real structure.\u003c\/p\u003e","brand":"Penguin Books Ltd","offers":[{"title":"Default Title","offer_id":48732517794135,"sku":"9780141999869","price":10.44,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780141999869.jpg?v=1719997233"},{"product_id":"quantum-computing-from-alice-to-bob-9780192857989","title":"Quantum Computing From Alice to Bob","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003eQuantum Computing: From Alice to Bob provides a distinctive and accessible introduction to the rapidly growing fields of quantum information science and quantum computing. The textbook is designed for undergraduate students and upper-level secondary school students with little or no background in physics, computer science, or mathematics beyond secondary school algebra and a bit of trigonometry. Higher education faculty members and secondary school mathematics, physics, and computer science educators who want to learn about quantum computing and perhaps teach a course accessible to students with wide ranging backgrounds will also find the book useful and enjoyable. While broadly accessible, the textbook does not dodge providing a solid conceptual and formal understanding of quantum states and entanglement - the key ingredients in quantum computing. The authors dish up a hearty meal for the readers, disentangling and explaining many of the classic quantum algorithms that demonstrate how and when QC has an advantage over classical computers. The book is spiced with Try Its, brief exercises that engage the readers in problem solving (both with and without mathematics) and help them digest the many counter-intuitive quantum information science and quantum computing concepts.\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTrade Review\u003c\/h2\u003eWhile broadly accessible, the textbook does not dodge providing a solid conceptual and formal understanding of quantum states and entanglement - the key ingredients in quantum computing. The authors dish up a hearty meal for the readers, disentangling and explaining many of the classic quantum algorithms that demonstrate how and when QC has an advantage over classical computers. The book is spiced with Try Its, brief exercises that engage the readers in problem solving (both with and without mathematics) and help them digest the many counter-intuitive quantum information science and quantum computing concepts. * zb Math Open *\u003cbr\u003eThis is a refreshing, pedagogical, and timely overview of quantum computing for non-experts, by two well-qualified authors. * Shimon Kolkowitz, University of Wisconsin-Madison *\u003cbr\u003eThis is a much needed bridge between popular and technical texts that provides easy access to the topic of quantum computing for curious readers who aim to go further and deeper in their understanding. * Dieter Jaksch, University of Oxford *\u003cbr\u003eThe reader gets to avoid the complexity of technical quantum-computing books, yet gets more depth and rigor than in the popular writing on the topic...the book is written in a very conversational rather than academic tone. * Bogdan Hoanca, University of Alaska Anchorage *\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003e1: Introduction 2: Traditional Computing 3: Traditional Bits in New Clothes 4: Qubits and Quantum States 5: Quantum Measurements 6: Quantum Gates 7: Putting a Spin on Spin 8: My Basis, Your Basis 9: Multi-qubit Systems, Entanglement, and Quantum Weirdness 10: Quantum Circuits and Multi-qubit Applications 11: Quantum Computing Algorithms 12: More Quantum Algorithms 13: RSA Encryption and the Shor Factoring Algorithm 14: Fundamental Quantum Issues 15: Complexifying Quantum States 16: Present and Future QIS and QC","brand":"Oxford University Press","offers":[{"title":"Default Title","offer_id":48732600926551,"sku":"9780192857989","price":35.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780192857989.jpg?v=1719997598"},{"product_id":"quantum-computing-from-alice-to-bob-9780192857972","title":"Quantum Computing From Alice to Bob","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003eA distinctive and accessible introduction to quantum information science and quantum computing, this textbook provides a solid conceptual and formal understanding of quantum states and entanglement for undergraduate students and upper-level secondary school students with little or no background in physics, computer science, or mathematics.\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTrade Review\u003c\/h2\u003eWhile broadly accessible, the textbook does not dodge providing a solid conceptual and formal understanding of quantum states and entanglement - the key ingredients in quantum computing. The authors dish up a hearty meal for the readers, disentangling and explaining many of the classic quantum algorithms that demonstrate how and when QC has an advantage over classical computers. The book is spiced with Try Its, brief exercises that engage the readers in problem solving (both with and without mathematics) and help them digest the many counter-intuitive quantum information science and quantum computing concepts. * zb Math Open *\u003cbr\u003eThis is a refreshing, pedagogical, and timely overview of quantum computing for non-experts, by two well-qualified authors. * Shimon Kolkowitz, University of Wisconsin-Madison *\u003cbr\u003eThis is a much needed bridge between popular and technical texts that provides easy access to the topic of quantum computing for curious readers who aim to go further and deeper in their understanding. * Dieter Jaksch, University of Oxford *\u003cbr\u003eThe reader gets to avoid the complexity of technical quantum-computing books, yet gets more depth and rigor than in the popular writing on the topic...the book is written in a very conversational rather than academic tone. * Bogdan Hoanca, University of Alaska Anchorage *\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003e1: Introduction 2: Traditional Computing 3: Traditional Bits in New Clothes 4: Qubits and Quantum States 5: Quantum Measurements 6: Quantum Gates 7: Putting a Spin on Spin 8: My Basis, Your Basis 9: Multi-qubit Systems, Entanglement, and Quantum Weirdness 10: Quantum Circuits and Multi-qubit Applications 11: Quantum Computing Algorithms 12: More Quantum Algorithms 13: RSA Encryption and the Shor Factoring Algorithm 14: Fundamental Quantum Issues 15: Complexifying Quantum States 16: Present and Future QIS and QC","brand":"Oxford University Press","offers":[{"title":"Default Title","offer_id":48732601057623,"sku":"9780192857972","price":999.99,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780192857972.jpg?v=1719997597"},{"product_id":"mathematical-physics-with-differential-equations-9780192872623","title":"Mathematical Physics with Differential Equations","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003eThis textbook uses insight from differential equations to analyse fundamental subjects of modern theoretical physics, including classical and quantum mechanics, thermodynamics, electromagnetism, superconductivity, gravitational physics, and quantum field theories.\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003ePreface Notation and Convention 1: Hamiltonian Systems and Applications 2: Schrödinger Equation and Quantum Mechanics 3: Maxwell Equations, Dirac Monopole, and Gauge Fields 4: Special Relativity 5: Abelian Gauge Field Equations 6: Dirac Equations 7: GinzburgDSLandau Equations for Superconductivity 8: Magnetic Vortices in Abelian Higgs Theory 9: Non-Abelian Gauge Field Equations 10: Einstein Equations and Related Topics 11: Charged Vortices and ChernDSSimons Equations 12: Skyrme Model and Related Topics 13: Strings and Branes 14: BornDSInfeld Theory of Electromagnetism 15: Canonical Quantization of Fields Appendices Bibliography Index","brand":"Oxford University Press","offers":[{"title":"Default Title","offer_id":48732608463191,"sku":"9780192872623","price":40.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780192872623.jpg?v=1719997631"},{"product_id":"mathematical-physics-with-differential-equations-9780192872616","title":"Mathematical Physics with Differential Equations","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003eThis textbook uses insight from differential equations to analyse fundamental subjects of modern theoretical physics, including classical and quantum mechanics, thermodynamics, electromagnetism, superconductivity, gravitational physics, and quantum field theories.\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003ePreface Notation and Convention 1: Hamiltonian Systems and Applications 2: Schrödinger Equation and Quantum Mechanics 3: Maxwell Equations, Dirac Monopole, and Gauge Fields 4: Special Relativity 5: Abelian Gauge Field Equations 6: Dirac Equations 7: GinzburgDSLandau Equations for Superconductivity 8: Magnetic Vortices in Abelian Higgs Theory 9: Non-Abelian Gauge Field Equations 10: Einstein Equations and Related Topics 11: Charged Vortices and ChernDSSimons Equations 12: Skyrme Model and Related Topics 13: Strings and Branes 14: BornDSInfeld Theory of Electromagnetism 15: Canonical Quantization of Fields Appendices Bibliography Index","brand":"Oxford University Press","offers":[{"title":"Default Title","offer_id":48732608528727,"sku":"9780192872616","price":999.99,"currency_code":"GBP","in_stock":false}]},{"product_id":"lagrangian-and-hamiltonian-dynamics-9780198822387","title":"Lagrangian and Hamiltonian Dynamics","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003eThe book introduces classical mechanics. It does so in an informal style with numerous fresh, modern and inter-disciplinary applications assuming no prior knowledge of the necessary mathematics. The book provides a comprehensive and self-contained treatment of the subject matter up to the forefront of research in multiple areas.\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003ePart I: Newtonian Mechanics 1: Introduction 2: Newton's Three Laws 3: Energy and Work 4: Introductory Rotational Dynamics 5: The Harmonic Oscillator 6: Wave Mechanics \u0026amp; Elements of Mathematical Physics Part II: Langrangian Mechanics 7: Introduction 8: Coordinates \u0026amp; Constraints 9: The Stationary Action Principle 10: Constrained Langrangian Mechanics 11: Point Transformations in Langrangian Mechanics 12: The Jacobi Energy Function 13: Symmetries \u0026amp; Langrangian-Hamiltonian-Jacobi Theory 14: Near-Equilibrium Oscillations 15: Virtual Work \u0026amp; d'Alembert's Principle Part III: Canonical Mechanics 16: Introduction 17: The Hamiltonian \u0026amp; Phase Space 18: Hamiltonian's equations \u0026amp; Routhian Reduction 19: Poisson Brackets \u0026amp; Angular momentum 20: Canonical \u0026amp; Gauge Transformations 21: Hamilton-Jacobi Theory 22: Liouville's Theorem \u0026amp; Classical Statistical Mechanics 23: Constrained Hamiltonian Dynamics 24: Autonomous Geometrical Mehcanics 25: The Structure of Phase Space 26: Near-Integrable Systems Part IV: Classical Field Theory 27: Introduction 28: Langrangian Field Theory 29: Hamiltonian Field Theory 30: Clssical Electromagnetism 31: Neother's Theorem for Fields 32: Classical Path-Integrals Part V: Preliminary Mathematics 33: The (Not so?) Basics 34: Matrices 35: Partial Differentiation 36: Legendre Transformations 37: Vector Calculus 38: Differential equations 39: Calculus of Variations Part VI: Advanced Mathematics 40: Linear Algebra 41: Differential Geometry Part VII: Exam Style Questions Appendix A: Noether's Theorem Explored Appendix B: The Action Principle Explored Appendix C: Useful Relations Appendxi D: Poisson \u0026amp; Nambu Brackets Explored Appendix: Canonical Transformations Explored Appendix F: Action-Angle Variables Explored Appendix G: Statistical Mechanics Explored Appendix H: Biographies","brand":"Oxford University Press","offers":[{"title":"Default Title","offer_id":48732797108567,"sku":"9780198822387","price":999.99,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780198822387.jpg?v=1719998439"},{"product_id":"introduction-to-dynamical-wave-function-collapse-9780198901372","title":"Introduction to Dynamical Wave Function Collapse","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003eQuantum theory (QT) is the best, most useful physics theory ever invented. For example, ubiquitous are cell phones, laser scanners, medical imagers, all inventions depending on QT. However, there is something deeply wrong with QT. It describes the probabilities of what happens, but it does not give a description of what actually happens. Most (but not all) physicists are not worried about this flaw, the probabilities are good enough for them. Other physicists, the author included, believe that is not good enough. The purpose of physics is to describe reality. To not do so is to abandon ''the great enterprise'' (John Bell). This book shows one way to alter QT so that the new theory does describe what actually happens. This theory, created over three decades ago, has been called the ''Continuous Spontaneous Localization'' (CSL) theory.Many experiments over this period have tested CSL, and so far it is neither confirmed nor refuted. This book shows how CSL works, and discusses its consequ\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTrade Review\u003c\/h2\u003eA most welcome addition to the physics literature written with extreme care and covering the objective subject matter in a thorough professional and methodical manner. * Daniel Sudarsky, UNAM, Mexico City *\u003cbr\u003eA book of very high quality presenting a way of modifying quantum mechanics to remove some of its most serious problems (especially the measurement problem). * Kelvin McQueen, Chapman University, Orange, California *\u003cbr\u003ePearle is the master of this material and writes with beautiful clarity and well-judged occasional witticisms and side-remarks. His experience as teacher, as well as researcher, shows in the vivid explanations, and the careful and consistent level of detail in the exposition. * Jeremy Butterfield, University of Cambridge *\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003e1: Introduction 2: Continuous Spontaneous Localization (CSL) Theory 3: CSL Theory Refinements 4: Non-Relativistic CSL 5: Spontaneous Localization (SL) Theory 6: Some Experiments Testing CSL 7: Interpretational Remarks 8: Supplement to Chapter 1 9: Supplement to Chapter 2 10: Supplement to Chapter 3 11: Supplement to Chapter 4 12: Supplement to Chapter 5 13: Supplement to Chapter 6 14: Supplement to Chapter 7 15: A Stochastic Differential Equation Cookbook 16: CSL Expressed as a Schrodinger Stochastic DE 17: Applying the CSL Stratonovich Equation to the Free Particle Undergoing Collapse in Position 18: Applying the CSL Stratonovich Equation to the Harmonic Oscillator Undergoing Collapse in Position Appendix A: Gaussians Appendix B: Random Walk Appendix C: Brownian Motion\/Wiener Process Appendix D: White Noise Appendix E: White Noise Field Appendix F: Density Matrix Appendix G: Theoretical Constraint Calculations","brand":"Oxford University Press","offers":[{"title":"Default Title","offer_id":48732829614423,"sku":"9780198901372","price":999.99,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780198901372.jpg?v=1719998580"},{"product_id":"measurements-and-their-uncertainties-9780199566334","title":"Measurements and Their Uncertainties","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003eThis short guide to modern error analysis is primarily intended to be used in undergraduate laboratories in the physical sciences. No prior knowledge of statistics is assumed. The necessary concepts are introduced where needed and illustrated graphically. The book emphasises the use of computers for error calculations and data fitting.\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTrade Review\u003c\/h2\u003eWith the shift from analytic methods to spreadsheet-based techniques, this book will enable students simultaneously to (a) become fluent in the choice and application of appropriate methods (b) understand the underlying principles. * David Saxon, University of Glasgow *\u003cbr\u003eThis is a rather beautiful little book. * David J. Hand, International Statistical Review *\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003e1. Errors in the physical sciences ; 2. Random errors in measurement ; 3. Uncertainties as probabilities ; 4. Error propagation ; 5. Data visualisation and reduction ; 6. Least-squares fitting of complex functions ; 7. Computer minimisation and the error matrix ; 8. Hypothesis testing - how good are our models ; 9. Topics for further summary","brand":"Oxford University Press","offers":[{"title":"Default Title","offer_id":48732865921367,"sku":"9780199566334","price":26.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780199566334.jpg?v=1791378738"},{"product_id":"the-nature-of-complex-networks-9780199695119","title":"The Nature of Complex Networks","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003eThe Nature of Complex Networks provides a systematic introduction to the statistical mechanics of complex networks and the different theoretical achievements in the field that are now finding strands in common.The book presents a wide range of networks and the processes taking place on them, including recently developed directions, methods, and techniques. It assumes a statistical mechanics view of random networks based on the concept of statistical ensembles but also features the approaches and methods of modern random graph theory and their overlaps with statistical physics.This book will appeal to graduate students and researchers in the fields of statistical physics, complex systems, graph theory, applied mathematics, and theoretical epidemiology.\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTrade Review\u003c\/h2\u003eThe current volume by Dorogovtsev and Mendes takes quite a broad view of complex networks to include the analysis of finite and infinite graphs, directed and undirected graphs, multigraphs, hypergraphs, and even simplicial complexes, as networks scale according to increasing N or in some other fashion. The writing style is that of physics and especially statistical mechanics with frequent connections made to physical concepts such as Bose-Einstein condensation...The current volume can especially serve as a useful reference on complex networks from a physics perspective. * Lenwood S. Heath, MathSciNet *\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003ePreface 1: First insight 2: Graphs 3: Classical random graphs 4: Equilibrium networks 5: Evolving networks 6: Connected components 7: Epidemics and spreading phenomena 8: Networks of networks 9: Spectra and communities 10: Walks and search 11: Temporal networks 12: Cooperative systems on networks 13: Inference and reconstruction 14: What's next? Further Reading Appendices A-G References","brand":"Oxford University Press","offers":[{"title":"Default Title","offer_id":48732888170839,"sku":"9780199695119","price":89.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780199695119.jpg?v=1719998821"},{"product_id":"a-first-course-in-functional-analysis-9780367658137","title":"A First Course in Functional Analysis","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003e\u003cp\u003eWritten as a textbook, \u003cb\u003eA First Course in Functional Analysis\u003c\/b\u003e is an introduction to basic functional analysis and operator theory, with an emphasis on Hilbert space methods. The aim of this book is to introduce the basic notions of functional analysis and operator theory without requiring the student to have taken a course in measure theory as a prerequisite. It is written and structured the way a course would be designed, with an emphasis on clarity and logical development alongside real applications in analysis. The background required for a student taking this course is minimal; basic linear algebra, calculus up to Riemann integration, and some acquaintance with topological and metric spaces.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTrade Review\u003c\/h2\u003e\u003cp\u003e\u003cem\u003eA First Course in Functional Analysis\u003c\/em\u003e by Orr Moshe Shalit is an excellent introduction to linear analysis. Its straightforward approach to the key ideas of the field, with special emphasis on Hilbert spaces, will be very much appreciated both by students and instructors. The book is suitable for advanced undergraduates and beginning graduate students who have had prior exposure to advanced calculus and linear algebra. I highly recommend this book to anyone teaching a first course in abstract analysis.\u003cbr\u003e—\u003cstrong\u003eJens Harlander\u003c\/strong\u003e, Boise State University\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003e\u003cp\u003eIntroduction and the Stone-Weierstrass theorem. Hilbert spaces. Orthogonality, projections, and bases. Fourier series. Bounded linear operators on Hilbert space. Hilbert function spaces. Banach spaces. The algebra of bounded operators on a Banach space. Compact operators. Compact operators on Hilbert space. Applications of compact operators. The Fourier transform. *The Hahn-Banach Theorems. Metric and topological spaces.\u003c\/p\u003e","brand":"Taylor \u0026 Francis Ltd","offers":[{"title":"Default Title","offer_id":48733712023895,"sku":"9780367658137","price":47.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780367658137.jpg?v=1720001350"},{"product_id":"conformal-field-theory-graduate-texts-in-contemporary-physics-9780387947853","title":"Conformal Field Theory Graduate Texts in","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003eIntended primarily for graduate students and researchers in theoretical high-energy physics, mathematical physics, condensed matter theory, statistical physics, the book will also be of interest in other areas of theoretical physics and mathematics.\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003e1. Introduction; 2. Quantum Field Theory; 3. Statistical Mechanics; 4. Global Conformal Invariance; 5. Conformal Invariance in Two Dimensions; 6. The Operator Formalism I; 7. The Operator Formalism II; 8. Minimal Models; 9. The Coulomb Gas Formalism; 10. Modular Invariance; 11. Finite Size Scaling; 12. The Two-Dimensional Ising Model; 13. Simple Lie Algebras; 14. Affine Lie Algebras; 15. The WZNW Model; 16. Fusion Rules; 17. Modular Invariants; 18. The Coset Construction","brand":"Springer-Verlag New York Inc.","offers":[{"title":"Default Title","offer_id":48733726867799,"sku":"9780387947853","price":125.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780387947853.jpg?v=1720001407"},{"product_id":"mathematical-methods-of-classical-mechanics-9780387968902","title":"Mathematical Methods of Classical Mechanics","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003eI Newtonian Mechanics.- 1 Experimental facts.- 2 Investigation of the equations of motion.- II Lagrangian Mechanics.- 3 Variational principles.- 4 Lagrangian mechanics on manifolds.- 5 Oscillations.- 6 Rigid bodies.- III Hamiltonian Mechanics.- 7 Differential forms.- 8 Symplectic manifolds.- 9 Canonical formalism.- 10 Introduction to perturbation theory.- Appendix 1 Riemannian curvature.- Appendix 2 Geodesics of left-invariant metrics on Lie groups and the hydrodynamics of ideal fluids.- Appendix 3 Symplectic structures on algebraic manifolds.- Appendix 4 Contact structures.- Appendix 5 Dynamical systems with symmetries.- Appendix 6 Normal forms of quadratic hamiltonians.- Appendix 7 Normal forms of hamiltonian systems near stationary points and closed trajectories.- Appendix 8 Theory of perturbations of conditionally periodic motion, and Kolmogorov's theorem.- Appendix 9 Poincaré's geometric theorem, its generalizations and applications.- Appendix 10 Multiplicities of characteristic frequencies, and ellipsoids depending on parameters.- Appendix 11 Short wave asymptotics.- Appendix 12 Lagrangian singularities.- Appendix 13 The Korteweg-de Vries equation.- Appendix 14 Poisson structures.- Appendix 15 On elliptic coordinates.- Appendix 16 Singularities of ray systems.\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTrade Review\u003c\/h2\u003e\u003cp\u003eSecond Edition\u003c\/p\u003e \u003cp\u003eV.I. Arnol’d\u003c\/p\u003e \u003cp\u003e\u003cem\u003eMathematical Methods of Classical Mechanics\u003c\/em\u003e\u003c\/p\u003e \u003cp\u003e\u003cem\u003e\"The book's goal is to provide an overview, pointing out highlights and unsolved problems, and putting individual results into a coherent context. It is full of historical nuggets, many of them surprising . . . The examples are especially helpful; if a particular topic seems difficult, a later example frequently tames it. The writing is refreshingly direct, never degenerating into a vocabulary lesson for its own sake. The book accomplishes the goals it has set for itself. While it is not an introduction to the field, it is an excellent overview.\" \u003c\/em\u003e\u003c\/p\u003e \u003cp\u003e—AMERICAN MATHEMATICAL MONTHLY\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003eI Newtonian Mechanics.- 1 Experimental facts.- 2 Investigation of the equations of motion.- II Lagrangian Mechanics.- 3 Variational principles.- 4 Lagrangian mechanics on manifolds.- 5 Oscillations.- 6 Rigid bodies.- III Hamiltonian Mechanics.- 7 Differential forms.- 8 Symplectic manifolds.- 9 Canonical formalism.- 10 Introduction to perturbation theory.- Appendix 1 Riemannian curvature.- Appendix 2 Geodesics of left-invariant metrics on Lie groups and the hydrodynamics of ideal fluids.- Appendix 3 Symplectic structures on algebraic manifolds.- Appendix 4 Contact structures.- Appendix 5 Dynamical systems with symmetries.- Appendix 6 Normal forms of quadratic hamiltonians.- Appendix 7 Normal forms of hamiltonian systems near stationary points and closed trajectories.- Appendix 8 Theory of perturbations of conditionally periodic motion, and Kolmogorov’s theorem.- Appendix 9 Poincaré’s geometric theorem, its generalizations and applications.- Appendix 10 Multiplicities of characteristic frequencies, and ellipsoids depending on parameters.- Appendix 11 Short wave asymptotics.- Appendix 12 Lagrangian singularities.- Appendix 13 The Korteweg-de Vries equation.- Appendix 14 Poisson structures.- Appendix 15 On elliptic coordinates.- Appendix 16 Singularities of ray systems.","brand":"Springer-Verlag New York Inc.","offers":[{"title":"Default Title","offer_id":48733727752535,"sku":"9780387968902","price":45.89,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780387968902.jpg?v=1791378796"},{"product_id":"advanced-mathematical-methods-for-scientists-and-engineers-i-9780387989310","title":"Advanced Mathematical Methods for Scientists and","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003eI Fundamentals.- 1 Ordinary Differential Equations.- 2 Difference Equations.- II Local Analysis.- 3 Approximate Solution of Linear Differential Equations.- 4 Approximate Solution of Nonlinear Differential Equations.- 5 Approximate Solution of Difference Equations.- 6 Asymptotic Expansion of Integrals.- III Perturbation Methods.- 7 Perturbation Series.- 8 Summation of Series.- IV Global Analysis.- 9 Boundary Layer Theory.- 10 WKB Theory.- 11 Multiple-Scale Analysis.\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTrade Review\u003c\/h2\u003e\u003cp\u003e\"This book is a reprint of the original published by McGraw-Hill \\ref [MR0538168 (80d:00030)]. The only changes are the addition of the Roman numeral I to the title and the provision of a subtitle, \"Asymptotic methods and perturbation theory\". This latter improvement is much needed, as the original title suggested that this was a teaching book for undergraduate scientists and engineers. It is not, but is an excellent introduction to asymptotic and perturbation methods for master's degree students or beginning research students. Certain parts of it could be used for a course in asymptotics for final year undergraduates in applied mathematics or mathematical physics. \u003cbr\u003e\u003cbr\u003eThis is a book that has stood the test of time and I cannot but endorse the remarks of the original reviewer. It is written in a fresh and lively style and the many graphs and tables, comparing the results of exact and approximate methods, were in advance of its time. I have owned a copy of the original for over twenty years, using it on a regular basis, and, after the original had gone out of print, lending it to my research students. Springer-Verlag has done a great service to users of, and researchers in, asymptotics and perturbation theory by reprinting this classic.\"  (A.D. Wood, Mathematical Reviews) \u003cbr\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003eI Preface. 1 Ordinary Differential Equations. 2 Difference Equations. 3 Approximate Solution of Linear Differential Equations. 4 Approximate Solution of Nonlinear Equations. 5 Approximate Solution of Difference Equations. 6 Asymptotic Expansion of Integrals. 7 Perturbation Series. 8 Summation of Series. 9 Boundary Layer Theory. 10 WKB Theory. 11 Multiple Scales Analysis. Appendix, References, Index","brand":"Springer-Verlag New York Inc.","offers":[{"title":"Default Title","offer_id":48733728375127,"sku":"9780387989310","price":71.24,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780387989310.jpg?v=1720001411"},{"product_id":"nonlinear-dynamics-exploration-through-normal-forms-dover-books-on-physics-9780486780450","title":"Nonlinear Dynamics Exploration Through Normal","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003eGeared toward advanced undergraduates and graduate students, this exposition covers the method of normal forms and its application to ordinary differential equations through perturbation analysis. Numerous examples from engineering, physics, and other fields.1998 edition.","brand":"Dover Publications Inc.","offers":[{"title":"Default Title","offer_id":48733801185623,"sku":"9780486780450","price":18.89,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780486780450.jpg?v=1791462924"},{"product_id":"the-green-function-method-in-statistical-mechanics-dover-books-on-physics-9780486797151","title":"The Green Function Method in Statistical","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e","brand":"Dover Publications Inc.","offers":[{"title":"Default Title","offer_id":48733804200279,"sku":"9780486797151","price":15.29,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780486797151.jpg?v=1720001763"},{"product_id":"intelligent-multimedia-multiagent-systems-a-humancentered-approach-international-series-in-engineering-and-computer-science-582-the-springer-series-in-engineering-and-computer-science-9780792379799","title":"Intelligent Multimedia Multiagent Systems A","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003e\u003cbr\u003e  The authors describe an ontology of the human-centered virtual machine  which includes four components: activity-centered analysis component,  problem solving adapter component, transformation agent component, and  multimedia based interpretation component.\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTrade Review\u003c\/h2\u003e\u003cstrong\u003e`\u003c\/strong\u003eFor the research-oriented reader the book provides a  complete and interesting discussion, enriched of practical results. I  consider this book very good to have on one's shelf if one needs to  apply software agent technology for advanced multimedia.\u003cstrong\u003e'\u003c\/strong\u003e\u003cbr\u003e  \u003cstrong\u003eSoft Computing, 5 (2001)\u003c\/strong\u003e\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003ePreface. Acknowledgements. Part I: Motivation,  Technologies, Enabling Theories and Human Centered Virtual  Machine. 1. Successful Systems or Successful Technologies?  2. Technologies. 3. Pragmatic Considerations and Enabling  Theories. 4. Human-Centered System Development Framework.  5. Human-Centered Virtual Machine. Part II: HCVM Applications  in Health Informatics, Face Detection, Net Euchre and Sales  Recruitment. 6. Intelligent Multimedia Multi-Agent Clinical  Diagnosis and Treatment Support System. 7. A Multi-Agent System  for Face Detection and Annotation. 8. Modeling Human Dynamics  and Breakdowns - Intelligent Agents for Internet Games and  Recruitment. Part III: HCVM Applications in Internet and  E-Commerce. 9. Intelligent Multimedia Information Management.  10. Brokerage System for Electronic Commerce Based on HCVM.  11. User-Centered Approach to Content-Based Retrieval of medical  Images. 12. HCVM Revisited. References.","brand":"Springer","offers":[{"title":"Default Title","offer_id":48737284260183,"sku":"9780792379799","price":999.99,"currency_code":"GBP","in_stock":false}]},{"product_id":"a-new-approach-to-differential-geometry-using-cliffords-geometric-algebra-9780817682828","title":"A New Approach to Differential Geometry using","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003e\u003cp\u003eDifferential geometry is the study of the curvature and calculus of curves and surfaces. \u003ci\u003eA New Approach to Differential Geometry using Clifford''s Geometric Algebra\u003c\/i\u003e simplifies the discussion to an accessible level of differential geometry by introducing Clifford algebra. This presentation is relevant because Clifford algebra is an effective tool for dealing with the rotations intrinsic to the study of curved space.\u003c\/p\u003e\u003cp\u003e\u003ci\u003e\u003c\/i\u003e\u003c\/p\u003e\u003cp\u003eComplete with chapter-by-chapter exercises, an overview of general relativity, and brief biographies of historical figures, this comprehensive textbook presents a valuable introduction to differential geometry. It will serve as a useful resource for upper-level undergraduates, beginning-level graduate students, and researchers in the algebra and physics communities.\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003cbr\u003e\u003cbr\u003e\u003c\/p\u003e\u003ch2\u003eTrade Review\u003c\/h2\u003e\u003cp\u003eFrom the reviews:\u003c\/p\u003e\u003cp\u003e“The book is written in a very pedagogical style and seems to be the mirror of the original ideas of its author in the area of mathematical physics. … The typography is excellent and the figures are beautiful. … Graduate and advanced undergraduate students in physics and even in mathematics will find in this book an understanding of the contribution of Clifford algebras to the field of differential geometry as well as motivation to continue their study.” (Pierre Anglès, Mathematical Reviews, March, 2014)\u003c\/p\u003e\u003cp\u003e“The book under review is perfectly organized textbook for undergraduate students in mathematics and physics due to the large experience of the author. … The author provides quite interesting historical analysis … . This book is a natural continuation of the previous book of the author … .” (Milen Hristov, JGSP Journal of Geometry and Symmetry in Physics, Vol. 33, 2014)\u003c\/p\u003e\u003cp\u003e“The author develops the differential geometry of curves and surfaces by using Clifford’s geometric algebra. … The book is enriched with several very interesting and extensive historical and biographical presentations. … it can serve as an accompanying source for someone who studies differential geometry, or for someone who wants to look at known facts from a different viewpoint. Also, it is ideal for studying geometry through historical development, and thus this book could also be useful for reading courses on certain aspects of geometry.” (A. Arvanitoyeorgos, Zentralblatt MATH, Vol. 1232, 2012)\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003ePreface.- Introduction.- Clifford Algebra in Euclidean 3-Space.- Clifford Algebra in Minkowski 4-Space.- Clifford Algebra in Flat n-Space.- Curved Spaces.- The Gauss-Bonnet Formula.- Non-Euclidean (Hyperbolic) Geometry.- Some Extrinsic Geometry in E^n.- Ruled Surfaces Continued.- Lines of Curvature.- Minimal Surfaces.- Some General Relativity.- Matrix Representation of a Clifford Algebra.- Construction of Coordinate Dirac Matrices.- A Few Terms of the Taylor's Series for the Urdī-Copernican Model for the Outer Planets.- A Few Terms of the Taylor's Series for Kepler's Orbits.- References.- Index.","brand":"Birkhauser Boston Inc","offers":[{"title":"Default Title","offer_id":48737459929431,"sku":"9780817682828","price":75.99,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780817682828.jpg?v=1791467661"},{"product_id":"continuous-groups-for-physicists-9781009187053","title":"Continuous Groups for Physicists","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003eContinuous Groups for Physicists is written for graduate students as well as researchers working in the field of theoretical physics. The text has been designed uniquely and it balances coverage of advanced and non-standard topics with an equal focus on the basic concepts for a thorough understanding. The book describes the general theory of Lie groups and Lie algebras, the passage between them, and their unitary\/ Hermitian representations in the quantum mechanical setting. The four infinite classical families of compact simple Lie groups and their representations are covered in detail. Readers will benefit from the discussions on topics like spinor representations of real orthogonal groups, the Schwinger representation of a group, induced representations, systems of coherent states, real symplectic groups important in quantum mechanics, Wigner''s theorem on symmetry operations in quantum mechanics, ray representations of Lie groups, and groups associated with non-relativistic and rela\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTrade Review\u003c\/h2\u003e'… this book is a very useful and very well conceived introductory course to the theory of Lie groups, Lie algebras and their representation theory, mainly intended for theoretical physicists. The style makes the book very readable, with special focus on the physical interpretation, with problems and references that lead the reader to more specialized topics.' Rutwig Campoamor Stursberg, ZB Math\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003e1. Basic Group Theory and Representation Theory; 2. The Symmetric Group; 3. Rotations in 2 and 3 Dimensions, SU(2); 4. General Theory of Lie Groups and Lie Algebras; 5. Compact Simple Lie Algebras – Classification and Irreducible Representations; 6. Spinor Representations of the Orthogonal Groups; 7. Properties of Some Reducible Group Representations, and Systems of Generalised Coherent States; 8. Structure and some Properties and Applications of the Groups Sp(2n, R); 9. Wigner's Theorem, Ray Representations and Neutral Elements; 10. Groups Related to Space-Time.","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":48738010038615,"sku":"9781009187053","price":68.11,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781009187053.jpg?v=1791468904"},{"product_id":"quantum-mechanics-9781108423335","title":"Quantum Mechanics","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003eDesigned for a two-semester advanced undergraduate or graduate level course, this distinctive and modern textbook provides students with the physical intuition and mathematical skills to tackle even complex problems in quantum mechanics with ease and fluency. Beginning with a detailed introduction to quantum states and Dirac notation, the book then develops the overarching theoretical framework of quantum mechanics, before explaining physical quantum mechanical properties such as angular momentum and spin. Symmetries and groups in quantum mechanics, important components of current research, are covered at length. The second part of the text focuses on applications, and includes a detailed chapter on quantum entanglement, one of the most exciting modern applications of quantum mechanics, and of key importance in quantum information and computation. Numerous exercises are interspersed throughout the text, expanding upon key concepts and further developing students'' understanding. A full\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTrade Review\u003c\/h2\u003e'Berera and Del Debbio do a wonderful job of walking the reader through the mathematics of quantum theory, never shying away from the necessary complexities while keeping things as simple as they can be.' David Tong, University of Cambridge\u003cbr\u003e'Today's quantum mechanics students should learn not only the harmonic oscillator and the hydrogen atom, but also entanglement and quantum information. This book treats the old and the new with great clarity, including a first look at quantum computation through the Deutsch and Grover algorithms. Another highlight is the collection of well-crafted problems.' Matthew Reece, Harvard University\u003cbr\u003e'This text promises to be useful to a wide audience, from intermediate-level undergraduates to beginning graduate students. It is pedagogical and rather complete, and attempts to guide along readers with different backgrounds via gentle yet precise mathematical asides. The chapter on quantum entanglement is the most comprehensive and complete discussion of the topic in a broad quantum mechanics textbook and will play an important role in introducing twenty-first-century undergraduates to the contemporary and rapidly growing field of quantum computing.' André de Gouvêa, Northwestern University\u003cbr\u003e'Quantum mechanics is difficult to teach as it defies intuitions of everyday experience. The textbook by Berera and Del Debbio grounds the subject by laying its mathematical foundations first, giving students a coherent framework distilled from a century of teaching experience. Filled with helpful exercises and modern topics including quantum information theory, this book would be an excellent text for both undergraduate and graduate courses.' Maxim Lavrentovich, University of Tennessee, Knoxville\u003cbr\u003e'One of the best features of this book is the substantial chapter on quantum entanglement, quantum computing and information theory (Bell's inequality, no-cloning theorem, quantum teleportation). It is based on early introduction of the mathematical foundations and Dirac notation. Beyond the standard topics, students will appreciate the inclusion of symmetry groups, applications involving multi-electron systems, the WKB(J) method, the discussion of the Dirac equation, and an in-depth treatment of quantum scattering.' Russell Herman, University of North Carolina\u003cbr\u003e'A concise yet complete introduction to quantum mechanics at the undergraduate level. The authors do a great job of exploring the formal and qualitative aspects of the theory, as well as more modern topics of interest such as quantum computation.' Christopher Aubin, Fordham University\u003cbr\u003e'Arjun Berera and Luigi Del Debbio's Quantum Mechanics is an exceptional textbook. It, of course, offers superb coverage of the requisite material for a standard two-semester upper-level undergraduate quantum mechanics (QM) course. Nonetheless, the textbook is much richer than that. Two features make it unique: Chapter 1, 'Stories and Thoughts about Quantum Mechanics', presents a detailed and lively history of 'the tortuous path that led to the formation of the theory as we know it'. This reading both is entertaining and sets the groundwork for the chapters that follow. Also of special note is Chapter 15, 'Quantum Entanglement'. While quantum entanglement has long raised theoretical questions regarding freedom and the nature of reality, within the last two decades its applications have burst forth not just in physics, but also in engineering, computing, encryption and communications. Through very informative chapter readings and well-chosen problems, students will master associated key concepts, such as calculating and interpreting Bell's inequality; information theory and Shannon and von Neumann entropies; the no-cloning theorem, quantum teleportation and superdense coding; and quantum register and logic gates, Deutsch's algorithm and Grover's algorithm. This textbook sets the standard for quantum entanglement coverage. I ardently promote Arjun Berera and Luigi Del Debbio's Quantum Mechanics.' Gerald B. Cleaver, Baylor University\u003cbr\u003e'Lucid introduction to a complex subject accessible to advanced undergraduate and beginning graduate students in science and engineering. The authors combine physical insight and mathematical rigour in explaining abstract concepts with a variety of examples. Covers all the quintessential topics in the field, as well as a valuable modern introduction to quantum entanglement.' Kaladi Babu, Oklahoma State University\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003ePreface; Part I. Basics: 1. Stories and Thoughts about Quantum Mechanics; 2. Quantum States; 3. Observables; 4. Dynamics; 5. Potentials; 6. Harmonic Oscillator; 7. Systems in Three Spatial Dimensions; 8. Angular Momentum; 9. Spin; 10. Addition of Angular Momenta; 11. Central Potentials; 12. Hydrogen Atom; 13. Identical Particles; 14. Symmetries in Quantum Mechanics; Part II. Applications: 15. Quantum Entanglement; 16. Time-independent Perturbation Theory; 17. Calculation Methods Beyond Perturbation Theory; 18. Time-dependent Perturbation Theory; 19. Quantum Scattering Theory; Index.","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":48738287878487,"sku":"9781108423335","price":60.1,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781108423335.jpg?v=1723811892"},{"product_id":"essential-statistical-physics-9781108480789","title":"Essential Statistical Physics","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003eThis clear and pedagogical text delivers a concise overview of classical and quantum statistical physics. Essential Statistical Physics shows students how to relate the macroscopic properties of physical systems to their microscopic degrees of freedom, preparing them for graduate courses in areas such as biophysics, condensed matter physics, atomic physics and statistical mechanics. Topics covered include the microcanonical, canonical, and grand canonical ensembles, Liouville''s Theorem, Kinetic Theory, non-interacting Fermi and Bose systems and phase transitions, and the Ising model. Detailed steps are given in mathematical derivations, allowing students to quickly develop a deep understanding of statistical techniques. End-of-chapter problems reinforce key concepts and introduce more advanced applications, and appendices provide a detailed review of thermodynamics and related mathematical results. This succinct book offers a fresh and intuitive approach to one of the most challenging\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTrade Review\u003c\/h2\u003e'At last a textbook that contains all the required elements for a modern advanced undergraduate course on statistical physics: foundations, quantum statistical mechanics, phase transitions and dynamics. I particularly like the derivation of ensembles through maximization of Gibbs entropy and the Langevin description of Brownian motion. Plenty of instructive problems within ten digestible chapters make this a text I can recommend to my students.' Martin Evans, University of Edinburgh\u003cbr\u003e'Statistical mechanics is a vast and fascinating topic, sometimes intimidating beginning students. Kennett succeeds in delivering an agile, fresh and modern exposition of the essential ideas and methods, in addition to a well-thought selection of examples and applications borrowed from all branches of physics. Students and teachers alike will enjoy the carefully organized table of contents for self-study and lecture preparation.' Roberto Raimondi, Roma Tre University\u003cbr\u003e'This book incorporates, into a single course, ideas and theoretical techniques in statistical physics and quantum mechanics that are connected by the physical phenomena they are meant to describe. Yet they are rarely all found in the same text. Professor Kennett offers students of theoretical physics a rare opportunity to acquire a mature understanding of their impact and meaning.' Herbert Fertig, Indiana University, Bloomington\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003ePreface; 1. Introduction; 2. The microcanonical ensemble; 3. Liouville's theorem; 4. The canonical ensemble; 5. Kinetic theory; 6. The grand canonical ensemble; 7. Quantum statistical mechanics; 8. Fermions; 9. Bosons; 10. Phase transitions and order; Appendix A Gaussian integrals and stirling's formula; Appendix B Primer on thermal physics; Appendix C Heat capacity cusp in Bose systems; References; Index.","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":48738306654551,"sku":"9781108480789","price":32.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781108480789.jpg?v=1723811912"},{"product_id":"quantum-field-theory-9781108480901","title":"Quantum Field Theory","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003eThis modern text combines fundamental principles with advanced topics and recent techniques in a rigorous and self-contained treatment of quantum field theory.Beginning with a review of basic principles, starting with quantum mechanics and special relativity, students can refresh their knowledge of elementary aspects of quantum field theory and perturbative calculations in the Standard Model. Results and tools relevant to many applications are covered, including canonical quantization, path integrals, non-Abelian gauge theories, and the renormalization group. Advanced topics are explored, with detail given on effective field theories, quantum anomalies, stable extended field configurations, lattice field theory, and field theory at a finite temperature or in the strong field regime. Two chapters are dedicated to new methods for calculating scattering amplitudes (spinor-helicity, on-shell recursion, and generalized unitarity), equipping students with practical skills for research. Acces\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTrade Review\u003c\/h2\u003e'Quantum Field Theory: From Basics to Modern Topics, by François Gelis, is a very welcome addition to the canon of literature on quantum field theory, impressive both in its breadth and depth.  It covers, in a succinct fashion, foundational material in the subject and then treats many more modern developments: effective field theories, anomaly matching, recursion relations for gauge and gravitational amplitudes, strong fields, and more.' Laurence Yaffe, University of Washington\u003cbr\u003e'Though there are many books on quantum field theory, I have found this book valuable for its readable treatment of a diverse selection of modern topics from a uniform viewpoint. Subjects introduced well in this book that are hard to find elsewhere include Schwinger-Keldysh and finite-temperature field theory, modern tools for scattering amplitudes, worldline methods, as well as effective field theory. The discussion is illustrated with a rich set of examples, mainly from high energy physics.' John McGreevy, University of California, San Diego\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003ePreface; 1. Basics of quantum field theory; 2. Peturbation theory; 3. Quantum electrodynamics; 4. Spontaneous symmetry breaking; 5. Functional quantization; 6. Path integrals for fermions and photons; 7. Non-Abelian gauge symmetry; 8. Quantization of Yang–Mills theory; 9. Renormalization of gauge theories; 10. Renormalization group; 11. Effective field theories; 12. Quantum anomalies; 13. Localized field configurations; 14. Modern tools for tree amplitudes; 15. Wordline formalism; 16. Lattice field theory; 17. Quantum field theory at finite temperature; 18. Strong fields and semi-classical methods; 19. From trees to loops; Further reading; Index.","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":48738306752855,"sku":"9781108480901","price":58.12,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781108480901.jpg?v=1723811912"},{"product_id":"quantum-field-theory-9781108486217","title":"Quantum Field Theory","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003eQuantum field theory (QFT), the language of particle physics, is crucial to a physicist''s graduate education. Based on lecture notes for courses taught for many years at Radboud University in the Netherlands, this book presents an alternative approach to teaching QFT using Feynman diagrams. A diagrammatic approach to understanding QFT exposes young physicists to an orthogonal introduction to the theory, bringing new ways to understand challenges in the field. Diagrammatic techniques using Feynman diagrams are used didactically, starting from simple discussions in lower dimensions to more complex topics in the Standard Model. Worked examples and exercises, for which solutions are available online, help the reader develop a deep understanding and intuition that enhances their problem-solving skills and understanding of QFT. Classroom-tested, this accessible book is valuable resource for graduate students and researchers.\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTrade Review\u003c\/h2\u003e'Highly recommended.' E. Kincanon, Choice Magazine\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003ePreface. 1. QFT in zero dimensions; 2. Loop expansion and the effective action; 3. On renormalization; 4. More fields in zero dimensions; 5. QFT in Euclidean spaces; 6. QFT in Minkowski space; 7. Scattering processes; 8. Introduction to loop calculations; 9. More on renormalization; 10. Dirac particles; 11. Helicity techniques for Dirac particles; 12. Vector particles; 13. Quantum electrodynamics; 14. Higher-order effects in QED; 15. Quantum chromodynamics; 16. Higher-order effects in QCD; 17. Electroweak theory; 18. More example computations; Appendices.","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":48738309505367,"sku":"9781108486217","price":59.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781108486217.jpg?v=1791469718"},{"product_id":"introduction-to-quantum-field-theory-9781108470902","title":"Introduction to Quantum Field Theory","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003eThis textbook offers a detailed and self-contained presentation of quantum field theory, suitable for advanced undergraduate and graduate level courses. The author provides full derivations wherever possible and adopts a pedagogical tone without sacrificing rigour. A fully worked solutions manual is available online for instructors.\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTrade Review\u003c\/h2\u003e'This new and very welcome introduction to quantum field theory takes the reader from the basics of classical physics and the beauty of group theory to the intricacies and elegance of gauge field theories. Students and researchers alike will treasure this fresh approach to one of the foundation stones of modern physics.' Thomas Appelquist, Yale University\u003cbr\u003e'I wish this text had been available the last time I taught quantum field theory. The author provides clear, detailed expositions, which serve students with diverse backgrounds for multiple course syllabi.' Steve Gottlieb, Indiana University\u003cbr\u003e'The rigorous and logical approach makes this text certainly one to be seriously considered for use in a quantum field theory course. In any case, it is one which practitioners will definitely want to have within easy reach on their bookshelf.' Barry Holstein, University of Massachusetts Amherst\u003cbr\u003e'Both as an introductory text and as an excellent single-volume compendium on quantum field theory, this book is highly recommended for students as well as practitioners at all levels.' Wolfram Weise, Technical University of Munich\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003e1. Lorentz and Poincare Invariance; 2. Classical Mechanics; 3. Relativistic Classical Fields; 4. Relativistic Quantum Mechanics; 5. Introduction to Particle Physics; 6. Formulation of Quantum Field Theory; 7. Interacting Quantum Field Theories; 8. Symmetries and Renormalization; 9. Nonabelian Gauge Theories.","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":48738311504215,"sku":"9781108470902","price":66.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781108470902.jpg?v=1723811916"},{"product_id":"a-first-course-in-general-relativity-9781108492676","title":"A First Course in General Relativity","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003eUpdating one of the most widely used introductory textbooks on Einstein's general relativity, this third edition includes the latest updates on gravitational waves, black holes, and cosmology. It introduces the science of relativity to final-year undergraduates and graduate students, requiring only a minimal background in mathematics.\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTrade Review\u003c\/h2\u003ePraise for the second edition: 'Bernard Schutz's textbook A First Course in General Relativity quickly became a classic, notable for its use of the geometrical approach to the subject, combined with a refreshing succinctness. Since its first publication in 1985, the field of general relativity has exploded … Schutz has done a masterful job of incorporating these new developments into a revised edition, which is sure to become a new 'classic'.' Clifford M. Will, McDonnell Center for the Space Sciences, Washington University, St. Louis\u003cbr\u003ePraise for the second edition: 'This new edition retains all of the original's clarity and insight into the mathematical foundations of general relativity, but thoroughly updates the accounts of the application of the theory in astrophysics and cosmology. The result is an indispensable volume and this new edition will no doubt become a classic text in its own right.' Mike Hobson, Cavendish Laboratory, University of Cambridge\u003cbr\u003ePraise for the second edition: 'Schutz has updated his eminently readable and eminently teachable A First Course in General Relativity. This text will be appreciated by any upper-level undergraduate with an interest in cosmology, astrophysics, or experimentation in gravitational physics.' Richard Matzner, The Center for Relativity, University of Texas at Austin\u003cbr\u003ePraise for the second edition: ' … marvellous … very clear … I cannot recommend this book highly enough to any physicist who wants a good introduction to general relativity.' David Burton, The Observatory\u003cbr\u003ePraise for the first edition: 'Schutz has such mastery of the material that it soon becomes clear that one is in authoritative hands, and topics are selected and developed only to a point where they prove adequate for future needs.' The Times Higher Education Supplement\u003cbr\u003ePraise for the first edition: '… ought to inspire more physicists and astronomers to teach and learn the other half of the twentieth century's revolution in physics.' Foundations of Physics\u003cbr\u003ePraise for the first edition: 'The book is a goldmine of cleverly constructed problems and exercises (and solutions!).' Nature\u003cbr\u003ePraise for the first edition: '… provides the first step into general relativity for undergraduate students with a minimal background in mathematics.' Zentralblatt MATH\u003cbr\u003e'Several generations of students have benefitted from the first two editions of Professor Bernard Schutz' beautiful introductory textbook on tensor algebra, manifolds, physics in curved space times, and Einstein's field equations. Why another edition now? The answer is that, in the last years, precision measurements of stellar orbits around the central massive black hole in the Galactic Center, the detection of gravitational waves from in-spiraling binary black holes and neutron stars with LIGO, and the detection of the central 'radio wave shadow' of the supermassive black hole in the galaxy M87 have suddenly opened the magical world of strongly curved spacetime to precision experimental tests. These experiments and much more to come from ground- and space-based gravitational wave studies have started a renaissance of interest in Einstein's theory.' Reinhard Genzel, Max Planck Institute for Extraterrestrial Physics\u003cbr\u003e'Students and teachers of general relativity will welcome this new edition of Schutz' hugely popular text, significantly broadened to cover the astonishing discoveries of gravitational-wave astronomy and their implications. A pioneer of the geometrical approach to undergraduate-level teaching of GR, the book remains unmatched in its highly readable style. With vim and authority, Schutz leads his readers masterfully from mathematical foundations to the forefront of research in astronomy and cosmology, providing them with the tools to understand future discoveries. With this new edition, Schutz' classic text remains as fresh and relevant as ever.' Leor Barack, University of Southampton\u003cbr\u003e'An outstanding textbook on general relativity written with the author's customary clarity and in his engaging style. It includes not only the basics of general relativity, but also recent developments in the direct detection of gravitational waves. A clear exposition of the essential ideas and methods.' Rong-Gen Cai, Chinese Academy of Sciences\u003cbr\u003e'Professor Schutz' informal style bewitches the reader into absorbing profound and complex concepts effortlessly. Physics is explained in a lucid style with minimal mathematics, without compromising on rigour. The recent excitement in the field of gravitational waves and its implications for astronomy and cosmology is adeptly conveyed. This edition has been enriched with several more exercises which the student or the young researcher will find illuminating and instructive.' Sanjeev Dhurandhar, Inter University Centre for Astronomy and Astrophysics\u003cbr\u003e'When I first taught from this book in the 1980s, my students and I loved it for its unusual combination of clarity and brevity. This third edition is not quite as brief because so much has happened in the subject! But for an all-around text with clear writing and an engaging style, it is still top of the class.' Clifford Will, University of Florida\u003cbr\u003e'A First Course in General Relativity by Bernard Schutz is an outstanding introductory text on Einstein's theory of general relativity and offers an invaluable resource for students interested in understanding the formal and physical foundations of modern spacetime theory.' Karim Thebault, University of Bristol\u003cbr\u003e'As with its previous editions, this textbook provides a fantastically accessible introduction to the key physical concepts of general relativity and the formalism used by its practitioners. The third edition gives a much-needed update accounting for discoveries since the previous edition, with the chapters on gravitational waves in particular serving as outstanding tutorials for students who are interested in astronomical applications of this subject.' Scott Hughes, Massachusetts Institute of Technology\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003ePreface to the third edition page; Preface to the second edition; Preface to the first edition; 1. Special relativity; 2. Vector analysis in special relativity; 3. Tensor analysis in special relativity; 4. Perfect fluids in special relativity; 5. Preface to curvature; 6. Curved manifolds; 7. Physics in a curved spacetime; 8. The Einstein field equations; 9. Fundamentals of Gravitational Radiation; 10. Spherical solutions for stars; 11. Schwarzschild geometry and black holes; 12. Gravitational wave astronomy; 13. Cosmology; Appendix A. Summary of linear algebra; References; Index.","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":48738313109847,"sku":"9781108492676","price":47.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781108492676.jpg?v=1723811921"},{"product_id":"semigroups-of-linear-operators-9781108716376","title":"Semigroups of Linear Operators","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003eThe theory of semigroups of operators is one of the most important themes in modern analysis. Not only does it have great intellectual beauty, but also wide-ranging applications. In this book the author first presents the essential elements of the theory, introducing the notions of semigroup, generator and resolvent, and establishes the key theorems of HilleYosida and LumerPhillips that give conditions for a linear operator to generate a semigroup. He then presents a mixture of applications and further developments of the theory. This includes a description of how semigroups are used to solve parabolic partial differential equations, applications to Levy and FellerMarkov processes, Koopmanism in relation to dynamical systems, quantum dynamical semigroups, and applications to generalisations of the RiemannLiouville fractional integral. Along the way the reader encounters several important ideas in modern analysis including Sobolev spaces, pseudo-differential operators and the Nash inequ\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTrade Review\u003c\/h2\u003e'… Applebaum has written a book that provides substantial depth and rigor, with a plethora of references. A notable feature of the text that increases its appeal is the author's inclusion of applications of the theory of semigroups to partial differential equations, dynamical systems, physics, and probability. This book also includes several advanced topics-such as measure spaces, spectral decompositions, and fractional calculus-but Applebaum offers motivating examples for readers to consider, interesting exercises to increase their comprehension, and additional resources to help them find complete details, so that a student could successfully navigate through this material independently if need be.' M. Clay, Choice\u003cbr\u003e'Overall, this book is an interesting contribution to the semigroup literature which does not follow a standard route.' Eric Stachura, MAA Reviews\u003cbr\u003e'Experts can quickly browse through any of the chapters, and get nicely acquainted with examples they are not yet fully aware of. Students can read this book fairly casually, and gain great motivation to study functional, stochastic, and\/or harmonic analysis further. Last but not least, teachers of graduate courses can design several great courses by elaborating on one of the many threads running through the book under review and using the referred sources to turn them into self-contained stories. All will appreciate the book's excellent mix of erudition and pedagogy.' Pierre Portal, MathSciNet\u003cbr\u003e'Some readers will enjoy the topic for its inherent attraction as a means of presenting results in a simple and widely applicable way. A masters student who is interested in researching in analysis but not in technical details of PDEs may nd this text particularly useful for finding a research topic in one of the related areas. In these respects the book achieves the aims declared in its introduction, in a way which is not found in earlier texts.' Charles Batty, The Mathematical Gazette\u003cbr\u003e'This excellent book, supplementing the known texts on operator semigroups, stems from the author's lectures for students with basic knowledge of functional analysis and measure theory … the book totally meets the goals of the LMS Student Texts series and is highly recommended to the University community.' Andrey V. Bulinski, zbMATH\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003eIntroduction; 1. Semigroups and generators; 2. The generation of semigroups; 3. Convolution semigroups of measures; 4. Self adjoint semigroups and unitary groups; 5. Compact and trace class semigroups; 6. Perturbation theory; 7. Markov and Feller semigroups; 8. Semigroups and dynamics; 9. Varopoulos semigroups; Notes and further reading; Appendices: A. The space C0(Rd); B. The Fourier transform; C. Sobolev spaces; D. Probability measures and Kolmogorov's theorem on construction of stochastic processes; E. Absolute continuity, conditional expectation and martingales; F. Stochastic integration and Itô's formula; G. Measures on locally compact spaces: some brief remarks; References; Index.","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":48738323136855,"sku":"9781108716376","price":43.3,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781108716376.jpg?v=1791469729"},{"product_id":"wignertype-theorems-for-hilbert-grassmannians-9781108790918","title":"WignerType Theorems for Hilbert Grassmannians","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003eWigner''s theorem is a fundamental part of the mathematical formulation of quantum mechanics. The theorem characterizes unitary and anti-unitary operators as symmetries of quantum mechanical systems, and is a key result when relating preserver problems to quantum mechanics. At the heart of this book is a geometric approach to Wigner-type theorems, unifying both classical and more recent results. Readers are initiated in a wide range of topics from geometric transformations of Grassmannians to lattices of closed subspaces, before moving on to a discussion of applications. An introduction to all the key aspects of the basic theory is included as are plenty of examples, making this book a useful resource for beginning graduate students and non-experts, as well as a helpful reference for specialist researchers.\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003eIntroduction; 1. Two lattices; 2. Geometric transformations of Grassmannians; 3. Lattices of closed subspaces; 4. Wigner's theorem and its generalizations; 5. Compatibility relation; 6. Applications; References; Index.","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":48738330804567,"sku":"9781108790918","price":65.05,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781108790918.jpg?v=1791469739"},{"product_id":"the-general-theory-of-relativity-9781108837996","title":"The General Theory of Relativity","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003eThe book aims to expound the general theory of relativity with a mathematical point of view. Catering to the needs of postgraduate students and researchers in the field of astrophysics and mathematical physics, it offers the readers a comprehensive understanding of the advanced topics of the subject matter. It specifically discusses the mathematical foundation of tensor calculus, gives a background of geodesics, Einstein''s field equations, linearised gravity, spacetime of spherically symmetric distribution of matter and black holes, and particle and photon orbits in spacetime. Apart from the formulation of general relativity, Lie derivatives and its applications, and causality of spacetime are also discussed in detail. Certain preliminary concepts of extrinsic curvature, Lagrangian formalism of general theory of relativity and 3 + 1 decomposition of space-time are covered and are provided in the book as appendices.\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003ePreface; Acknowledgement; 1. Tensor calculus – a brief overview; 2. Geodesics; 3. Einstein field equations; 4. Linearized gravity; 5. Lie derivatives and Killing's equation; 6. Spacetimes of spherically symmetric distribution of matter and black holes; 7. Particle and photon orbits in the Schwarzschild spacetime; 8. Causal structure of spacetime; 9. Exact solutions of Einstein equations and their causal structures; 10. Rotating Black holes; 11. Elementary cosmology; 12. Elementary astrophysics; Appendix A. Extrinsic curvature; Appendix B. Lagrangian formalism of general relativity; Appendix C. 3+1 decomposition; Bibliography; Index.","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":48738341126487,"sku":"9781108837996","price":74.02,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781108837996.jpg?v=1791469748"},{"product_id":"foundations-of-modern-physics-9781108841764","title":"Foundations of Modern Physics","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003eIn addition to his ground-breaking research, Nobel Laureate Steven Weinberg is known for a series of highly praised texts on various aspects of physics, combining exceptional physical insight with his gift for clear exposition. Describing the foundations of modern physics in their historical context and with some new derivations, Weinberg introduces topics ranging from early applications of atomic theory through thermodynamics, statistical mechanics, transport theory, special relativity, quantum mechanics, nuclear physics, and quantum field theory. This volume provides the basis for advanced undergraduate and graduate physics courses as well as being a handy introduction to aspects of modern physics for working scientists.\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTrade Review\u003c\/h2\u003e'By using the notion of fundamental constituents as the guiding historical and theoretical principle, Weinberg manages to lay the foundations of diverse disciplines (hydrodynamics, statistical mechanics, kinetic theory, thermodynamics, special relativity, quantum mechanics and even field theory) in less than 300 pages.' CERN Courier, Opinion Reviews\u003cbr\u003e'Whereas many textbooks forgo historical notes, Weinberg delights the reader by adding terse yet apt context to the physical concepts he introduces … It is as if he is imagining what students might be puzzled by and then solves those problems … everyone will want to have Foundations of Modern Physics on their bookshelf. There is always something new to be found in it, and - similar to having a conversation about physics with Weinberg - there is never a dull moment when reading it.' Melissa Franklin, Physics Today\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003ePreface; 1. Early atomic theory; 2. Thermodynamics and kinetic theory; 3. Early quantum theory; 4. Relativity; 5. Quantum mechanics; 6. Nuclear physics; 7. Quantum field theory: assorted problems; Bibliography; Author index; Subject index.","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":48738343518551,"sku":"9781108841764","price":36.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781108841764.jpg?v=1723811951"},{"product_id":"constrained-willmore-surfaces-9781108794428","title":"Constrained Willmore Surfaces","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003eFrom Bäcklund to Darboux, this monograph presents a comprehensive journey through the transformation theory of constrained Willmore surfaces, a topic of great importance in modern differential geometry and, in particular, in the field of integrable systems in Riemannian geometry. The first book on this topic, it discusses in detail a spectral deformation, Bäcklund transformations and Darboux transformations, and proves that all these transformations preserve the existence of a conserved quantity, defining, in particular, transformations within the class of constant mean curvature surfaces in 3-dimensional space-forms, with, furthermore, preservation of both the space-form and the mean curvature, and bridging the gap between different approaches to the subject, classical and modern. Clearly written with extensive references, chapter introductions and self-contained accounts of the core topics, it is suitable for newcomers to the theory of constrained Wilmore surfaces. Many detailed comp\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003eIntroduction; 1. A bundle approach to conformal surfaces in space-forms; 2. The mean curvature sphere congruence; 3. Surfaces under change of flat metric connection; 4. Willmore surfaces; 5. The Euler–Lagrange constrained Willmore surface equation; 6. Transformations of generalized harmonic bundles and constrained Willmore surfaces; 7. Constrained Willmore surfaces with a conserved quantity; 8. Constrained Willmore surfaces and the isothermic surface condition; 9. The special case of surfaces in 4-space; Appendix A. Hopf differential and umbilics; Appendix B. Twisted vs. untwisted Bäcklund transformation parameters; References; Index.","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":48738537800023,"sku":"9781108794428","price":57.99,"currency_code":"GBP","in_stock":true}]},{"product_id":"hilbert-space-operators-in-quantum-physics-9781402088698","title":"Hilbert Space Operators in Quantum Physics","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003eThe new edition of this book detailing the theory of linear-Hilbert space operators and their use in quantum physics contains two new chapters devoted to properties of quantum waveguides and quantum graphs. The bibliography contains 130 new items.\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTrade Review\u003c\/h2\u003e\u003cp\u003eFrom the reviews of the second edition:\u003c\/p\u003e \u003cp\u003eSome praise for the previous edition:\u003c\/p\u003e  \u003cp\u003e“I really enjoyed reading this work. It is very well written, by three real experts in the field. It stands quite alone....” (John R. Taylor, Professor of Physics and Presidential Teaching Scholar, University of Colorado at Boulder)\u003c\/p\u003e  \u003cp\u003e\"This is an excellent textbook for graduate students and young researchers in mathematics and theoretical physics. … It is a course from the basics in functional analysis to bounded and unbounded operators, including spectral theory and operator algebras. The exposition is comprehensive, but self-contained.\" (Michael Demuth, Zentralblatt MATH, Vol. 1163, 2009)\u003c\/p\u003e  “As the title declares, the text presents a comprehensive presentation of linear spaces and their transformations. … this second edition contains two additional chapters on quantum treatments of waveguides and graphs. … The book considered is, no doubt, written for physicists and useful for them. … A valuable feature of this book is the extensive background material and discussions collected into separate sections. … The book does what it promises and does it well.” (Stig Stenholm, Contemporary Physics, January, 2010)\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003ePreface to the second edition, Preface,.  1.Some notions from functional analysis,Vector and normed spaces,1.2 Metric and topological spaces,1.3 Compactness, 1.4 Topological vector spaces, 1.5 Banach spaces and operators on them, 1.6 The principle of uniform boundedness, 1.7 Spectra of closed linear operators, Notes to Chapter 1, Problems  2. Hilbert spaces, 2.1 The geometry of Hilbert spaces, 2.2 Examples, 2.3 Direct sums of Hilbert spaces, 2.4 Tensor products, 2.4 Notes to Chapter 2, Problems  3. Bounded operators, 3.1 Basic notions, 3.2 Hermitean operators, 3.3 Unitary and isometric operators, 3.4 Spectra of bounded normal operators, 3.5 Compact operators, 3.6 Hilbert-Schmidt and trace-class operators, Notes to Chapter 3, Problems 4. Unbounded operators, 4.1 The adjoint, 4.2 Closed operators, 4.3 Normal operators. Self-adjointness, 4.4 Reducibility. Unitary equivalence, 4.5 Tensor products, 4.6 Quadratic forms, 4.7 Self-adjoint extensions, 4.8 Ordinary differential operators, 4.9 Self-adjoint extensions of differential operators, Notes to Chapter 4, Problems 5. Spectral Theory , 5.1 Projection-valued measures, 5.2 Functional calculus, 5.3 The spectral Tudorem, 5.4 Spectra of self-adjoint operators, 5.5 Functions of self-adjoint operators, 5.6 Analytic vectors, 5.7 Tensor products, 5.8 Spectral representation, 5.9 Groups of unitary operators, Notes to Chapter 5, Problems 6. Operator sets and algebra, 6.1 C^*-algebras, 6.2 GNS construction, 6.3 W^*-algebras, 6.4 Normal states on W^*-algebras, 6.5 Commutative symmetric operator sets, 6.6 Complete sets of commuting operators, 6.7 Irreducibility. Functions of non-commuting operators, 6.8 Algebras of unbounded operators, Notes to Chapter 6, Problems 7. States and observables, 7.1 Basic postulates, 7.2 Simple examples, 7.3 Mixed states, 7.4 Superselection rules, 7.5 Compatibility, 7.6 The algebraic approach, Notes to Chapter 7, Problems 8. Position and momentum, 8.1 Uncertainty relations, 8.2 The canonical commutation relations, 8.3 The classical limit and quantization, Notes to Chapter 8, Problems 9. Time evolution, 9.1 The fundamental postulate, 9.2 Pictures of motion, 9.3 Two examples, 9.4 The Feynman integral, 9.5 Nonconservative systems, 9.6 Unstable systéme, Notes to Chapter 9, Problems 10. Symmetries of quantum systéme, 10.1 Basic notions, 10.2 Some examples, 10.3 General space-time transformations, Notes to Chapter 10, Problems  11. Composite systems, 11.1 States and observables, 11.2 Reduced states, 11.3 Time evolution, 11.4 Identical particles, 11.5 Separation of variables. Symmetries, Notes to Chapter 11, Problems  12. The second quantization, 12.1 Fock spaces, 12.2 Creation and annihilation operators, 12.3 Systems of noninteracting particles, Notes to Chapter 12,  Problems 13. Axiomatization of quantum theory, 13.1 Lattices of propositions, 13.2 States on proposition systems, 13.3 Axioms for quantum field theory, Notes to Chapter 13, Problems 14. Schrödinger operators, 14.1 Self-adjointness, 14.2 The minimax principle. Analytic perturbations,  14.3 The discrete spectrum, 14.4 The essential spectrum, 14.5 Constrained motion, 14.6 Point and contact interactions, Notes to Chapter 14, Problem 15. Scattering theory, 15.1 Basic notions ,15.2 Existence of wave operators, 15.3 Potential scattering, 15.4 A model of two-channel scattering, Notes to Chapter 15, Problems  16. Quantum waveguides, 16.1 Geometric effects in Dirichlet stripes, 16.2 Point","brand":"Springer-Verlag New York Inc.","offers":[{"title":"Default Title","offer_id":48738941043031,"sku":"9781402088698","price":98.99,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781402088698.jpg?v=1791470735"},{"product_id":"introduction-to-applied-nonlinear-dynamical-systems-and-chaos-9781441918079","title":"Introduction to Applied Nonlinear Dynamical","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003e\u003cp\u003eThis introduction to applied nonlinear dynamics and chaos places emphasis on teaching the techniques and ideas that will enable students to take specific dynamical systems and obtain some quantitative                            information about their behavior. The new edition has been updated and extended throughout, and contains a detailed glossary of terms.\u003c\/p\u003e \u003cp\u003eFrom the reviews:\u003c\/p\u003e \u003cp\u003eWill serve as one of the most                            eminent introductions to the geometric theory of dynamical systems. --Monatshefte für Mathematik\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTrade Review\u003c\/h2\u003e\u003cp\u003eFrom the reviews of the second edition:\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\"This is a very substantial revision of the author’s original textbook published in 1990. It does not only contain much new material, for instance on invariant manifold theory and normal forms, it has also been restructured. … The presentation is intended for advanced undergraduates … . This second edition … will serve as one of the most eminent introductions to the geometric theory of dynamical systems.\" (R. Bürger, Monatshefte für Mathematik, Vol. 145 (4), 2005)\u003c\/p\u003e\u003cp\u003e\"This is an extensively rewritten version of the first edition which appeared in 1990, taking into account the many changes in the subject during the intervening time period. … The book is suitable for use as a textbook for graduate courses in applied mathematics or cognate fields. It is written in a readable style, with considerable motivation and many insightful examples. … Overall, the book provides a very accessible, up-to-date and comprehensive introduction to applied dynamical systems.\" (P.E. Kloeden, ZAMM-Zeitschrift für Angewandte Mathematik und Mechanik, Vol. 85 (1), 2005)\u003c\/p\u003e\u003cp\u003e\"The second edition of this popular text … is an encyclopedic introduction to dynamical systems theory and applications that includes substantial revisions and new material. It should be on the reading list of every student of the subject … . Also, the new organization makes the book more suitable as a textbook that can be used in graduate courses. This book will also be a useful reference for applied scientists … as well as a guide to the literature.\" (Carmen Chicone, Mathematical Reviews, 2004h)\u003c\/p\u003e\u003cp\u003e\"This volume includes a significant amount of new material. … Each chapter starts with a narrative … and ends with a large collection of excellent exercises. … An extensive bibliography … provide a useful guide for future study. … This is a highly recommended book for advanced undergraduate and first-year graduate students. It contains most of the necessary mathematical tools … to apply the results of the subject to problems in the physical and engineering sciences.\" (Tibor Krisztin, Acta Scientiarum Mathematicarum, Vol. 75, 2009)\u003c\/p\u003e\u003cp\u003e“It is certainly one of the most complete introductory textbooks about dynamical systems, though no single book can be really complete. … Some chapters can certainly be used as a course text for a master’s course, but the whole book is to thick for a single course. … a suitable first text for Ph.D. students who want to do research in dynamical systems, and a useful reference work for more experienced people. I definitely enjoyed reading this book and can only recommend it.” (Kurt Lust, Bulletin of the Belgian Mathematical Society, Vol. 15 (1), 2008)\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003eEquilibrium Solutions, Stability, and Linearized Stability * Liapunov Functions * Invariant Manifolds: Linear and Nonlinear Systems * Periodic Orbits * Vector Fields Possessing an Integral * Index Theory * Some General Properties of Vector Fields: Existence, Uniqueness, Differentiability, and Flows * Asymptotic Behavior * The Poincaré-Bendixson Theorem * Poincaré Maps * Conjugacies of Maps, and Varying the Cross-Section * Structural Stability, Genericity, and Transversality * Lagrange's Equations * Hamiltonian Vector Fields * Gradient Vector Fields * Reversible Dynamical Systems * Asymptotically Autonomous Vector Fields * Center Manifolds * Normal Forms * Bifurcation of Fixed Points of Vector Fields * Bifurcations of Fixed Points of Maps * On the Interpretation and Application of Bifurcation Diagrams: A Word of Caution * The Smale Horseshoe * Symbolic Dynamics * The Conley-Moser Conditions or 'How to Prove That a Dynamical System is Chaotic' * Dynamics Near Homoclinic Points of Two-Dimensional Maps * Orbits Homoclinic to Hyperbolic Fixed Points in Three-Dimensional Autonomous Vector Fields * Melnikov's Method for Homoclinic Orbits in Two-Dimensional, Time-Periodic Vector Fields * Liapunov Exponents * Chaos and Strange Attractors * Hyperbolic Invariant Sets: A Chaotic Saddle * Long Period Sinks in Dissipative Systems and Elliptic Islands in Conservative Systems * Global Bifurcations Arising from Local Codimension-Two Bifurcations * Glossary of Frequently Used Terms","brand":"Springer-Verlag New York Inc.","offers":[{"title":"Default Title","offer_id":48739209314647,"sku":"9781441918079","price":67.49,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781441918079.jpg?v=1791471197"},{"product_id":"advanced-mathematical-methods-for-scientists-and-engineers-i-9781441931870","title":"Advanced Mathematical Methods for Scientists and","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003eI Fundamentals.- 1 Ordinary Differential Equations.- 2 Difference Equations.- II Local Analysis.- 3 Approximate Solution of Linear Differential Equations.- 4 Approximate Solution of Nonlinear Differential Equations.- 5 Approximate Solution of Difference Equations.- 6 Asymptotic Expansion of Integrals.- III Perturbation Methods.- 7 Perturbation Series.- 8 Summation of Series.- IV Global Analysis.- 9 Boundary Layer Theory.- 10 WKB Theory.- 11 Multiple-Scale Analysis.\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTrade Review\u003c\/h2\u003e\u003cp\u003e\"This book is a reprint of the original published by McGraw-Hill \\ref [MR0538168 (80d:00030)]. The only changes are the addition of the Roman numeral I to the title and the provision of a subtitle, \"Asymptotic methods and perturbation theory\". This latter improvement is much needed, as the original title suggested that this was a teaching book for undergraduate scientists and engineers. It is not, but is an excellent introduction to asymptotic and perturbation methods for master's degree students or beginning research students. Certain parts of it could be used for a course in asymptotics for final year undergraduates in applied mathematics or mathematical physics. \u003cbr\u003e\u003cbr\u003eThis is a book that has stood the test of time and I cannot but endorse the remarks of the original reviewer. It is written in a fresh and lively style and the many graphs and tables, comparing the results of exact and approximate methods, were in advance of its time. I have owned a copy of the original for over twenty years, using it on a regular basis, and, after the original had gone out of print, lending it to my research students. Springer-Verlag has done a great service to users of, and researchers in, asymptotics and perturbation theory by reprinting this classic.\"  (A.D. Wood, Mathematical Reviews) \u003cbr\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003eI Preface. 1 Ordinary Differential Equations. 2 Difference Equations. 3 Approximate Solution of Linear Differential Equations. 4 Approximate Solution of Nonlinear Equations. 5 Approximate Solution of Difference Equations. 6 Asymptotic Expansion of Integrals. 7 Perturbation Series. 8 Summation of Series. 9 Boundary Layer Theory. 10 WKB Theory. 11 Multiple Scales Analysis. Appendix, References, Index","brand":"Springer-Verlag New York Inc.","offers":[{"title":"Default Title","offer_id":48739209675095,"sku":"9781441931870","price":49.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781441931870.jpg?v=1791378891"},{"product_id":"how-to-derive-a-formula-volume-1-basic-analytical-skills-and-methods-for-physical-scientists-9781786346445","title":"How To Derive A Formula - Volume 1: Basic","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003eWill artificial intelligence solve all problems, making scientific formulae redundant? The authors of this book would argue that there is still a vital role in formulating them to make sense of the laws of nature. To derive a formula one needs to follow a series of steps; last of all, check that the result is correct, primarily through the analysis of limiting cases. The book is about unravelling this machinery.Mathematics is the 'queen of all sciences', but students encounter many obstacles in learning the subject — familiarization with the proofs of hundreds of theorems, mysterious symbols, and technical routines for which the usefulness is not obvious upfront. Those interested in the physical sciences could lose motivation, not seeing the wood for the trees.How to Derive a Formula is an attempt to engage these learners, presenting mathematical methods in simple terms, with more of an emphasis on skills as opposed to technical knowledge. Based on intuition and common sense rather than mathematical rigor, it teaches students from scratch using pertinent examples, many taken across the physical sciences.This book provides an interesting new perspective of what a mathematics textbook could be, including historical facts and humour to complement the material.","brand":"World Scientific Europe Ltd","offers":[{"title":"Default Title","offer_id":48741447172439,"sku":"9781786346445","price":999.99,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781786346445.jpg?v=1720057610"},{"product_id":"mathematical-models-in-science-9781800610279","title":"Mathematical Models In Science","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003eMathematical Models in Science treats General Relativity and Quantum Mechanics in a non-commutative Algebraic Geometric framework.Based on ideas first published in Geometry of Time-Spaces: Non-commutative Algebraic Geometry Applied to Quantum Theory (World Scientific, 2011), Olav Arnfinn Laudal proposes a Toy Model as a Theory of Everything, starting with the notion of the Big Bang in Cosmology, modeled as the non-commutative deformation of a thick point. From this point, the author shows how to extract reasonable models for both General Relativity and Quantum Theory. This book concludes that the universe turns out to be the 6-dimensional Hilbert scheme of pairs of points in affine 3-space. With this in place, one may develop within the model much of the physics known to the reader. In particular, this theory is applicable to the concept of Dark Matter and its effects on our visual universe.Hence, Mathematical Models in Science proves the dependency of deformation theory in Mathematical Physics and summarizes the development of physical applications of pure mathematics developed in the twentieth century.","brand":"World Scientific Europe Ltd","offers":[{"title":"Default Title","offer_id":48741753192791,"sku":"9781800610279","price":81.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781800610279.jpg?v=1720058691"},{"product_id":"probability-in-physics-an-introductory-guide-9783030045425","title":"Probability in Physics: An Introductory Guide","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003e\u003cp\u003eThis textbook presents an introduction to the use of probability in physics, treating introductory ideas of both statistical physics and of statistical inference, as well the importance of probability in information theory, quantum mechanics, and stochastic processes, in a unified manner. The book also presents a harmonised view of frequentist and Bayesian approaches to inference, emphasising their complementary value. The aim is to steer a middle course between the \"cookbook\" style and an overly dry mathematical statistics style. The treatment is driven by real physics examples throughout, but developed with a level of mathematical clarity and rigour appropriate to mid-career physics undergraduates. Exercises and solutions are included.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003ePart I: The Basics.- Randomness and Probability.- Distributions, Moments, and Errors.- Part II: Frequency Distributions in the Physical World.- Counting the Ways: Arrangements and Subsets.- Counting Statistics: Binomial and Poisson Distributions.- Combining Many Factors: The Gaussian Distribution.- Distributions Arising from Random Processes in Time.- Part III: Probabilistic Inference: Reasoning in the Presence of Uncertainty.- Hypothesis Testing.- Parameter Estimation.- Inference With Two Variables: Correlation Testing and Line Fitting.- Model Fitting.- Part IV: Selected Topics.- Information, Uncertainty, and Surprise.- Erratic Time Series.- Probability in Quantum Physics.- Entropy, Complexity, and the Arrow of Time.- Solutions.","brand":"Springer Nature Switzerland AG","offers":[{"title":"Default Title","offer_id":48743022494039,"sku":"9783030045425","price":999.99,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783030045425.jpg?v=1791480445"},{"product_id":"classical-and-quantum-dynamics-from-classical-paths-to-path-integrals-9783030367886","title":"Classical and Quantum Dynamics: From Classical","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003e\u003cp\u003eGraduate students seeking to become familiar with advanced computational strategies in classical and quantum dynamics will find in this book both the fundamentals of a standard course and a detailed treatment of the time-dependent oscillator, Chern-Simons mechanics, the Maslov anomaly and the Berry phase, to name just a few topics. Well-chosen and detailed examples illustrate perturbation theory, canonical transformations and the action principle, and demonstrate the usage of path integrals.\u003c\/p\u003e  \u003cp\u003e \u003c\/p\u003e  \u003cp\u003eThe sixth edition has been enlarged to include the Heisenberg-Euler Lagrangian, Schwinger’s source theory treatment of the low-energy π-ρ-N physics and general relativity, where Riemann’s (Einstein’s) ideas on space and time and their philosophical implications are discussed.  \u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003eIntroduction.- The Action Principles in Mechanics.- The Action Principle in Classical Electrodynamics.- Application of the Action Principles.- Jacobi Fields, Conjugate Points.-Canonical Transformations.- The Hamilton–Jacobi Equation.- Action-Angle Variables.- The Adiabatic Invariance of the Action Variables.- Time-Independent Canonical Perturbation Theory .- Canonical Perturbation Theory with Several Degrees of Freedom.- Canonical Adiabatic Theory.- Removal of Resonances.- Superconvergent Perturbation Theory, KAM Theorem.- Poincaré Surface of Sections, Mappings.- The KAM Theorem.- Fundamental Principles of Quantum Mechanics.- Functional Derivative Approach.- Examples for Calculating Path Integrals.- Direct Evaluation of Path Integrals.- Linear Oscillator with Time-Dependent Frequency.- Propagators for Particles in an External Magnetic Field.- Simple Applications of Propagator Functions.- The WKB Approximation.- Computing the trace.- Partition Function for the Harmonic Oscillator.- Introduction to Homotopy Theory.- Classical Chern–Simons Mechanics.- Semiclassical Quantization.- The “Maslov Anomaly” for the Harmonic Oscillator.-Maslov Anomaly and the Morse Index Theorem.- Berry’s Phase.- Classical Geometric Phases: Foucault and Euler.- Berry Phase and Parametric Harmonic Oscillator.- Topological Phases in Planar Electrodynamics.- Path Integral Formulation of Quantum Electrodynamics.- Particle in Harmonic E-Field E(t) = Esin\u003ci\u003ew0\u003c\/i\u003et; Schwinger-Fock Proper-Time Method.-  The Usefulness of Lie Brackets: From Classical and Quantum Mechanics to Quantum Electrodynamics.- Green’s Function of a Spin-1\/2 Particle in a Constant External Magnetic Field.- One-Loop Effective Lagrangian in QED.- On Riemann’s Ideas on Space and Schwinger’s Treatment of Low-Energy Pion-Nucleon Physics.- The Non-Abelian Vector Gauge Particle \u003ci\u003ep\u003c\/i\u003e .- Riemann’s Result and Consequences for Physics and Philosophy.","brand":"Springer Nature Switzerland AG","offers":[{"title":"Default Title","offer_id":48743034093911,"sku":"9783030367886","price":41.24,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783030367886.jpg?v=1720063820"},{"product_id":"an-introductory-path-to-quantum-theory-using-mathematics-to-understand-the-ideas-of-physics-9783030407698","title":"An Introductory Path to Quantum Theory: Using","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003e\u003cp\u003eSince the 17th century, physical theories have been expressed in the language of mathematical equations. This introduction to quantum theory uses that language to enable the reader to comprehend the notoriously non-intuitive ideas of quantum physics. \u003c\/p\u003e\u003cp\u003eThe mathematical knowledge needed for using this book comes from standard undergraduate mathematics courses and is described in detail in the section Prerequisites. This text is especially aimed at advanced undergraduate and graduate students of mathematics, computer science, engineering and chemistry among other disciplines, provided they have the math background even though lacking preparation in physics. In fact, no previous formal study of physics is assumed.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTrade Review\u003c\/h2\u003e\u003cp\u003e“The target audience is ‘advanced undergraduate mathematics students who had no or only very little prior knowledge of physics’. It would indeed be a rare variety of mathematics advanced undergraduates who would fit this bill. … an interesting supplement for students with a mathematical bent.” (Amitava Raychaudhuri, zbMATH 1458.81002, 2021)\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003eIntroduction to this Path.- Viewpoint.- Neither Particle nor Wave.- Schrödinger's Equation.- Operators and Canonical Quantization.- The Harmonic Oscillator.- Interpreting: Mathematics.- Interpreting: Physics.- The Language of Hilbert Space.- Interpreting: Measurement.- The Hydrogen Atom.- Angular Momentum.- The Rotation Group SO(3).- Spin and SU(2).- Bosons and Fermions.- Classical and Quantum Probability.- The Heisenberg Picture.- Uncertainty (Optional).- Speaking of Quantum Theory (Optional).- Complementarity (Optional).- Axioms (Optional).- And Gravity?.- Measure Theory: A Crash Course.","brand":"Springer Nature Switzerland AG","offers":[{"title":"Default Title","offer_id":48743035306327,"sku":"9783030407698","price":999.99,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783030407698.jpg?v=1791480481"},{"product_id":"statistical-field-theory-for-neural-networks-9783030464431","title":"Statistical Field Theory for Neural Networks","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003e\u003cp\u003eThis book presents a self-contained introduction to techniques from field theory applied to stochastic and collective dynamics in neuronal networks. These powerful analytical techniques, which are well established in other fields of physics, are the basis of current developments and offer solutions to pressing open problems in theoretical neuroscience and also machine learning. They enable a systematic and quantitative understanding of the dynamics in recurrent and stochastic neuronal networks. \u003c\/p\u003e  \u003cp\u003eThis book is intended for physicists, mathematicians, and computer scientists and it is designed for self-study by researchers who want to enter the field or as the main text for a one semester course at advanced undergraduate or graduate level. The theoretical concepts presented in this book are systematically developed from the very beginning, which only requires basic knowledge of analysis and linear algebra.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003eI. Introduction\u003cbr\u003eII. Probabilities, moments, cumulantsA. Probabilities, observables, and momentsB. Transformation of random variablesC. CumulantsD. Connection between moments and cumulants\u003cbr\u003eIII. Gaussian distribution and Wick’s theoremA. Gaussian distributionB. Moment and cumulant generating function of a GaussianC. Wick’s theoremD. Graphical representation: Feynman diagramsE. Appendix: Self-adjoint operatorsF. Appendix: Normalization of a Gaussian\u003cbr\u003eIV. Perturbation expansionA. General caseB. Special case of a Gaussian solvable theoryC. Example: Example: “phi^3 + phi^4” theoryD. External sourcesE. Cancellation of vacuum diagramsF. Equivalence of graphical rules for n-point correlation and n-th momentG. Example: “phi^3 + phi^4” theoryV. Linked cluster theoremA. General proof of the linked cluster theoremB. Dependence on j - external sources - two complimentary viewsC. Example: Connected diagrams of the “phi^3 + phi^4” theory\u003cbr\u003eVI. Functional preliminariesA. Functional derivative1. Product rule2. Chain rule3. Special case of the chain rule: Fourier transformB. Functional Taylor series\u003cbr\u003eVII. Functional formulation of stochastic differential equationsA. Onsager-Machlup path integral*B. Martin-Siggia-Rose-De Dominicis-Janssen (MSRDJ) path integralC. Moment generating functionalD. Response function in the MSRDJ formalism\u003cbr\u003eVIII. Ornstein-Uhlenbeck process: The free Gaussian theoryA. DefinitionB. Propagators in time domainC. Propagators in Fourier domain\u003cbr\u003eIX. Perturbation theory for stochastic differential equationsA. Vanishing moments of response fieldsB. Vanishing response loopsC. Feynman rules for SDEs in time domain and frequency domainD. Diagrams with more than a single external legE. Appendix: Unitary Fourier transform\u003cbr\u003eX. Dynamic mean-field theory for random networksA. Definition of the model and generating functionalB. Property of self-averagingC. Average over the quenched disorderD. Stationary statistics: Self-consistent autocorrelation of as motion of a particle in a potentialE. Transition to chaosF. Assessing chaos by a pair of identical systemsG. Schrödinger equation for the maximum Lyapunov exponentH. Condition for transition to chaos\u003cbr\u003eXI. Vertex generating functionA. Motivating example for the expansion around a non-vanishing mean valueB. Legendre transform and definition of the vertex generating function GammaC. Perturbation expansion of GammaD. Generalized one-line irreducibilityE. ExampleF. Vertex functions in the Gaussian caseG. Example: Vertex functions of the “phi^3 + phi^4”-theoryH. Appendix: Explicit cancellation until second orderI. Appendix: Convexity of WJ. Appendix: Legendre transform of a Gaussian\u003cbr\u003eXII. Application: TAP approximationInverse problem\u003cbr\u003eXIII. Expansion of cumulants into tree diagrams of vertex functionsA. Self-energy or mass operator Sigma\u003cbr\u003eXIV. Loopwise expansion of the effective action - Tree levelA. Counting the number of loopsB. Loopwise expansion of the effective action - Higher numbers of loopsC. Example: phi^3 + phi^4-theoryD. Appendix: Equivalence of loopwise expansion and infinite resummationE. Appendix: Interpretation of Gamma as effective actionF. Loopwise expansion of self-consistency equation\u003cbr\u003eXV. Loopwise expansion in the MSRDJ formalismA. Intuitive approachB. Loopwise corrections to the effective equation of motionC. Corrections to the self-energy and self-consistencyD. Self-energy correction to the full propagatorE. Self-consistent one-loopF. Appendix: Solution by Fokker-Planck equation\u003cbr\u003eXVI. Nomenclature\u003cbr\u003eAcknowledgments\u003cbr\u003eReferences","brand":"Springer Nature Switzerland AG","offers":[{"title":"Default Title","offer_id":48743036682583,"sku":"9783030464431","price":56.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783030464431.jpg?v=1791480488"},{"product_id":"powers-of-two-the-information-universe-information-as-the-building-block-of-everything-9783030583477","title":"Powers of Two: The Information Universe —","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003e\u003cp\u003eIs everything Information? This is a tantalizing question which emerges in modern physics, life sciences, astronomy and in today’s information and technology-driven society. In \u003cem\u003ePowers of Two\u003c\/em\u003e expert authors undertake a unique expedition - in words and images - throughout the world (and scales) of information. The story resembles, in a way, the classic\u003cem\u003e Powers of Ten\u003c\/em\u003e\u003cem\u003e \u003c\/em\u003ejourneys through space: from us to the macro and the micro worlds . However, by following \u003cem\u003ePowers of Two\u003c\/em\u003e through the world of information, a completely different and timely paradigm unfolds. Every power of two, 1, 2, 4, 8…. tells us a different  story: starting from the creation of the very first bit at the Big Bang and the evolution of life, through 50 years of computational science, and finally into deep space, describing the information in black holes and even in the entire universe and beyond….  All this to address one question: \u003cstrong\u003eIs our universe made of information? \u003c\/strong\u003e\u003cstrong\u003e \u003c\/strong\u003eIn this book, we experience the Information Universe in nature and in our society and how information lies at the very foundation of our understanding of the Universe.\u003c\/p\u003e\u003cp\u003eFrom the Foreword by Robbert Dijkgraaf:\u003c\/p\u003e\u003cp\u003e \u003cem\u003eThis book is in many ways a vastly extended version of Shannon’s one-page blueprint. It carries us all the way to the total information content of the Universe. And it bears testimony of how widespread the use of data has become in all aspects of life. Information is the connective tissue of the modern sciences. […] Undoubtedly, future generations will look back at this time, so much enthralled by Big Data and quantum computers, as beholden to the information metaphor. But that is exactly the value of this book. \u003c\/em\u003e\u003ci\u003eWith its crisp descriptions and evocative illustrations, it brings the reader into the here and now, at the very frontier of scientific research, including the excitement and promise of all the outstanding questions and future discoveries.\u003c\/i\u003e\u003cbr\u003e\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003cb\u003eMessage for the e-reader of the book Powers of Two\u003c\/b\u003e\u003c\/p\u003e  \u003cp\u003eThe book has been designed to be read in two-page spreads in full screen mode.\u003c\/p\u003e  \u003cp\u003e  For optimal reader experience in a downloaded .pdf file we strongly recommend you use the following settings \u003cb\u003ein Adobe Acrobat Reader\u003c\/b\u003e:\u003c\/p\u003e  \u003cp\u003e      - Taskbar:  View \u0026gt; Page Display \u0026gt; two page view\u003cbr\u003e     - Taskbar:  View \u0026gt; Page Display \u0026gt; Show Cover Page in Two Page View\u003cbr\u003e     - Taskbar: ^ Preferences   \u0026gt; Full Screen \u0026gt;  deselect \" Fill screen with one page at a time\"\u003cbr\u003e     -  Taskbar: View  \u0026gt; Full screen mode or  ctrl L (cmd L on a Mac)\u003c\/p\u003e  \u003cp\u003e*****\u003c\/p\u003e  \u003cp\u003eNote: for reading the previews on \u003cb\u003eSpinger link\u003c\/b\u003e (and on-line reading in a browser), the full screen two-page view only works with these browsers:\u003c\/p\u003e  \u003cp\u003e\u003cb\u003eFirefox\u003c\/b\u003e\u003c\/p\u003e  \u003cp\u003e - Taskbar:  on top of the text, at the uppermost right you will see then \u0026gt;\u0026gt; (which is a drop-down menu)    \u0026gt;\u0026gt;\u003ci\u003e even double page\u003c\/i\u003es\u003c\/p\u003e  \u003cp\u003e - Fullscreen: F11 or Control+Cmd+F with Mac\u003c\/p\u003e  \u003cp\u003e\u003cb\u003eEdge \u003c\/b\u003e\u003c\/p\u003e  \u003cp\u003e - Taskbar middle: \u003ci\u003eTwo-page view\u003c\/i\u003e and select show cover page separately\u003c\/p\u003e\u003ci\u003e\u003c\/i\u003e\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTrade Review\u003c\/h2\u003e“The book … a very unusual collection of some facts about the relationship between the immaterial world represented by bits and the real physical world described by fundamental physical equations. This book continues the very categorical point of view of J. A. Wheeler … . The book presents short articles on various areas of modern science … in which it is shown that in these areas in some mysterious way there is a connection with the theory of information.” (Vladimir Dzhunushaliev, zbMATH 1479.83004, 2022)\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003eForeword by Robbert DijkgraafChapter 0: IntroductionJoy-riding the Universe – by the authorWorking as an astronomer, data scientist and professor of astro-informatics for nearly fifty years, Edwin Valentijn has witnessed and first-hand engineered the dawn of the era of Big Data in science and society. Throughout his career, he became increasingly aware of the role of information in our world: in computers, in our society, and even in nature and in the Universe itself.\u003cbr\u003eThe Information UniverseFollowing the increasing powers of two, the story paints a journey through the whole world of information, both in society and in nature. Each step opens a door into a new world: from the first bits with the Big Bang and the dawn of life, going through fifty years of human technology, all the way up to the information content of the whole Universe.\u003cbr\u003eWhat is Information? - Item pageThe basics of information are introduced.\u003cbr\u003eChapter 1: The beginningSpace-time foam – Ti (0 bit: 20 =1)The very first power of two: 20, corresponds to the value one. This identifies the single, eternal, indistinguishable state: the primordial sea from which our Universe emerged – sometimes called the Space-time foam. I call this Ti, the reverse of It. This is one of the miraculous new notions in the story of the Powers of Two.\u003cbr\u003eMultiverse: Anthropic principle (Item page)From Ti, the primordial space-time foam, countless universes arise with widely different characteristics: the Multiverse. The Anthropic Principle is a philosophical consideration which states that we, people, will find ourselves in a universe that is suitable for intelligent life to emerge. Therefore, this Principle demonstrates that conditions in our Universe are not “fine-tuned” to the existence of human life and a “creator” doesn’t exist.\u003cbr\u003eBig bang (1 bit: 21 =2 states)At the Big Bang the first bit is created. From the indistinguishable unity of the primordial foam Ti, “the zeros were separated from the 1’s”: the first bit corresponds to two possible states. This bit is the first step on our journey to capture the ever-increasing complexity of our expanding Universe in terms of information, through the increasing powers of two.\u003cbr\u003eWhat is a bit? (Item page)The bit is at the core of the concept of information. A bit is any system that can have two states. Humans assign meanings to these states, which are illustrated with the concept of the traffic light: red or green, stop or go. The combination of multiple bits creates an exponentially increasing number of possible states, and hence meanings.\u003cbr\u003eMulticellular life (2 bit: 22 =4 states) \/ (4 bit: 24 =16 states)?Life started with exchanging information between cells. This is fundamental for the evolution of any kind of life. It took at least two billion years for uni-cellular to evolve into multi-cellular organisms around 600 million years ago, and to start the exchange of information between their different cells. By exchanging information, cells collaborate and act as a unified whole: life.\u003cbr\u003eThe game of life (Item page)The characteristic features of life (or any complex system in the Universe) can be created from information. A simple computer game is all you need to demonstrate this concept. A famous example is Conway's Game of Life, which is full of visuals of living, growing, moving and dying objects. This game was already made on the computers of the early 70's with just a few lines of code.\u003cbr\u003eChapter 2: People's Information UniverseASCII (7 bit: 27 =128 states)There is currently no physical theory how the digital world connects to the human consciousness. In the world of Information Technology (IT) all information exchange is based on agreements between people. For instance, ASCII, a simple list relating each letter of the alphabet to a 7-bit string, connects the digital world to the human consciousness.\u003cbr\u003e Machu Picchu (8 bit: 28 =256, 1 byte)The Intiwatana stone, a giant rock carved by the Inca's of ancient Machu Picchu in Peru, can be considered as a first 8-bit hard disk. Why so? As the sunrays lit the different surfaces of this huge rock throughout the year, it triggered the Inca's activities: sowing, harvesting, celebrating and praying.This ancient stone dissolves both the boundaries between heaven and earth, and those between the digital and natural Information Universe. In fact, the stone represents an ultimate picture of the cross-over between the in vivo and the in vitro Information Universe - a main theme of the book. In vitro being the man made technology to handle information and in vivo being the information built in nature, in this case the orbit and the light rays of the sun.\u003cbr\u003eFirst computers (16 bit: 216 =65.536, 2 byte)When computers emerged in the 1970's, astronomers first adopted them to steer their telescopes. Back then, a maximal effort to understand the mathematics of the problem was needed to squeeze the solution into the small computer memory. Nowadays, with large amounts of computing power and machine learning at their disposal, scientists and computer programmers often do the reverse.\u003cbr\u003eStar Peace vs. Star Wars (Item page)King Juan Carlos adored the harmony of galaxies as a source of inspiration for people on earth, in those days when Ronald Reagan was promoting his Star-wars programme. With this adoration in mind, in 1985, he gave an inspiring speech at the Royal inauguration of the international astronomical observatory on La Palma, Canary Islands. The inauguration was attended by, for those days, an unprecedented large crowd of European royals and government officials despite the great threat of terrorist attacks by the ETA. (the next and later spreads on facts vs fakes elucidate the relevance of this spread in the story line).\u003cbr\u003ePre-internet Facts and Fakes (Item page)“Edwin Valentijn saved the life of the Dutch Queen Beatrix by catching her just before falling off a cliff at the inauguration on La Palma”, according to the headlines in Dutch newspapers. Fake news-stories are at all times alike and can only be dispelled by tracing links of information to their source, links or associations being a fundamental property of the Information Universe. Later, I discuss the less innocent case of overdrawing attention to terrorist attacks in the past decade.\u003cbr\u003eHard disk (24 bit: 224 =1.6*107, 2 Mb)Only sixty years ago, a 5 MB hard disk weighed over five tons, and had to be loaded onto an aeroplane by using a truck. Now, we carry a thousand times more information in our trouser pocket. This demonstrates the amazing advance of information technology over the past decades. (Picture: first IBM hard disk loaded onto a plane).\u003cbr\u003eThe telephone (Item page) As a precursor of the Internet, the telephone offered many of the same advantages and dangers, and was heavily discussed at its introduction. Whether telephone or the Internet, it all revolves around communication or copying of information. The telephone, as example of it, is one of the major discoveries of the 20th century. \u003cbr\u003eDNA (32 bit: 232 = 4*109, 500 Mb) – Guest author: Charley Lineweaver The information in the DNA creates life. All base pairs of the human DNA can be stored on a 500 Mb drive. How is this information communicated? How does a cell know it has to build part of a liver and not an eye, while they all have the same DNA? Apoptosis and the role of information exchange.Where does biological Information come from? (Item page) – Guest author: Charley Lineweaver Charley Lineweaver, expert on evolutionary biology, exoplanetology and astrobiology, will expand on the role of information in the evolution of life.\u003cbr\u003eLifelines (Item page) – Guest author: Morris SwertzWhat is the role of nature versus that of nurture? A key question in modern health research. In Lifesciences, this question is addressed now using Big Data, like the astronomers who acquire huge data volumes to address the same question on the nature of galaxies. In Lifelines, a cohort of 165.000 people is studied over a period of 30 years using hospital data, blood samples and DNA scans.\u003cbr\u003eDVD (33 bit: 233 =9*109, 1 Gb)It’ s amazing how fast the digital image revolution went since 1989.30 years ago, Philips lab approached me since they had made a big discovery: it was possible to store many digital images on a CD. They were chasing me for digital images. While NASA had less than a thousand, I had 32.000 galaxy images obtained by scanning photographic plates from the European Southern Observatory – the first large digital image collection.\u003cbr\u003eHuman Brain (36 bit: 236 =7*1010, 9 Gb) – Guest author: Katrin Amunts- JulichIn the large EU human brain project, the activities of the human brain are simulated in computers. This is a very difficult mission since the transistors in computers consume 100.000 billion times more energy than the synapsis of neurons. Our brains consist of 1011 neurons, corresponding to 9 Gb of data.Thinking of Karlheinz Meier, coordinator of the Human Brain Project in Heidelberg, Katrin Amunts will author two spreads on the role of information in the human brain.\u003cbr\u003eNeuromorphic computing – Guest author: Katrin AmuntsCurrently, it takes a hundred years of a supercomputer’s time to compete with the learning power of only a single day of the human brain. “Neuromorphic computing” researchers design electronic systems inspired by the human brain, in order to make computers many times faster and more energy efficient.\u003cbr\u003eCT scan (38 bit: 238 =3*1011, 34 Gb) – Guest author: Anders YnnermanNow it is possible to look inside animal and human bodies on touchscreens. Forensic investigations on, for instance, corpses of victims can be done with touch-screen tables. You can look inside, rotate, scroll and zoom animal and human bodies using tens of gigabytes of CT scan data. Prof. Anders Ynnerman explains how he does it.\u003cbr\u003eTerabytes (45 bit: 245 =4.4*1012, 1 Tb) - The largest (astronomical) datasetsDark energy and dark matter: two mysterious constituents of our Universe. How do astronomers get and handle the data from the VLT Survey Telescope on a high mountain top in Chile to shed lights on these ‘still too dark’ topics. This Telescope surveys the sky every hour at night generating Terabytes of astronomical data.\u003cbr\u003eGravity as a lens (Item page) – Guest author: Margot BrouwerWhen light rays are bent by the gravity of a heavy object, this object acts as a lens. This effect can be used to map dark matter, which is invisible but constitutes 80% of the matter in our visible Universe. In 1915, Albert Einstein posed that gravity is equivalent to the curvature of the fabric of space and time itself, leading to the lensing effect.\u003cbr\u003eWeak gravitational lensing surveys – Guest author: Margot BrouwerTerabytes of astronomical data are reduced to a few numbers, describing how dark matter behaves and what is its true nature. https:\/\/www.youtube.com\/watch?v=ZCyYGWqCmFw\u0026amp;t=23s\u003cbr\u003eEntering the Petabyte regime (53 bit: 253 =1*1015, 1 Pb)How do we technically acquire and deal with Petabytes of data?\u003cbr\u003eDark Matter maps (Item page)A first dark matter map projected on the night sky. An ultimate encounter between the digital world of modern astronomical observations, and nature: the mysterious dark matter mapped on top of the everyday “night” stellar sky. A visualization that condenses Terabytes of astronomical data to a simple map.\u003cbr\u003eMetadata for Peta-data (62 bit: 262 =6*1017, 600 Pb)With pointers, one can connect everything in the Information Universe. Pointers are often inserted in Metadata (data about data) - an ultimate tool for dealing with Big Data. It is possible to create unique pointers to hundreds of Petabytes of data, using a string of less than 64 bits. This is what makes pointers so powerful and indispensable in current and future stages of the big data era; not only for astronomical research, but also for companies like Google, Amazon and Facebook.\u003cbr\u003eDownloading the Universe (Item page)The universe can be seen as a spreadsheet, certainly in the way we map it on our computers (in vitro), but also in nature (in vivo). Perceiving the Universe as a spreadsheet links bit to It.\u003cbr\u003eMeta data (Item page)A visualisation of the enormous complexity of data models which trace all pointers between data items. (picture: thrilling still from a full dome animation of a data model)\u003cbr\u003eFuture (astronomical) datasets (item page)While current telescopes collect astronomical datasets of Terabytes, future telescopes such as the LSST and the Euclid satellite, instead, will collect Petabytes. These enormous amounts of data need a whole new approach to data management. For the Euclid satellite my “Universe as a spreadsheet” approach has been adopted.\u003cbr\u003eThe Euclid satellite (Item page) – Guest author: Margot BrouwerEuclid is ESA’s new space mission to map the Dark Universe. At a distance of 1.5 million kilometres from Earth, this telescope will observe billions of galaxies. Its goal: to shed light on the nature of Dark Matter and Dark Energy, which make up 95% of our Universe. Dr. Margot Brouwer, Dutch scientific communication officer for Euclid, will explain more.\u003cbr\u003eThe Information Universe (Item page)The resemblance of the overall structure of the real observed Universe (in vivo) with the simulated universe (in vitro), based on the concurrent cosmological model, gave a lot of credit to the latter. When we zoom out the Universe, we see billions of galaxies forming a web-like structure. Amazingly, astronomers can now compute and simulate these structures with very large supercomputers.\u003cbr\u003eThe lost boy (Item page)Information is timeless, and knows no boundaries. It crosses over the in vivo and the in vitro Information Universe. This concept is well illustrated through daily life stories involving time. At the age of five, a boy loses sight of his older brother on a train in India, and eventually gets lost on the streets of Mumbai. Twenty years later, after being adopted by a family in Australia, he is able to find his natural mother (in vivo) through only searching on Google maps (in vitro).\u003cbr\u003eQbits (50 qbit: 250 =1.1*1015 qbit, 1 Pbit) – Guest author: Lieven VandersypenUsing fundamental particles (quanta, such as electrons) to perform calculations and build computers, is one of the most exciting cross-overs between the in vivo and the in vitro Information Universe. Prof. Lieven Vandersypen, who leads a Quantum Computing group at TU Delft in the Netherlands, will explain how this technology will change the way we compute.\u003cbr\u003eQuantum entanglement (Item page) – Guest author: Lieven VandersypenThe states of two particles can be intimately linked (entangled), no matter how far they are separated. What Einstein famously dismissed as “spooky action at a distance”, can now be established on demand at TU Delft in the Netherlands. Prof. Vandersypen will explain how his research group, for the first time ever, both create and apply this entanglement in laboratory.\u003cbr\u003eEntanglement (item page) - EVThe Square Kilometre Array (64 bit: 264 =1.3*1018, 1 Eb) – Guest author: TBAThe Square Kilometre Telescope will collect data at the rate of the global internet traffic of 2013, in its endeavour to answer fundamental questions about the origin and evolution of the Universe, and its search for extra-terrestrial life.\u003cbr\u003eCryptography (128 bit: 2128 =3.4*1038) – Guest author Tanja LangeEncrypted messages should not be decoded by adversaries, be they criminals or hostile countries. Cryptography enables secure communications and is one of the few applications which require 128-bit numbers. A guest author will explain more.\u003cbr\u003eChapter 3: Deep spaceThe Desert (128-256 bit) Theoretical physics is not progressing much in the last decennia – some call it a crisis. Likely, an observational breakthrough is out of reach: the highest man-made information density on earth is produced by the high energy accelerators at CERN. But these accelerators have to be 1013 -1015 more powerful to reach the fundamental unit of information, which is probably at the same level of the Planck length. Unfortunately, there is no way to reach this unit of information with these instruments. This enormous gap in reaching all the domains in the Information Universe is illustrated in a figure and in a very sobering, but instructive table in the Appendix.\u003cbr\u003eBlack holes (128-256 bit?) – Guest author: Manus VisserCan information disappear into a black hole? The Information paradox. Stephen Hawking wondered it and started a field in which space and time are described in terms of information. Dr. Manus Visser, expert on gravity and space-time, will explain more.\u003cbr\u003eObserving a Black Hole: Event Horizon Telescope – Guest author: Heino FalckeThe first image of a black hole. Prof. Heino Falcke, chair of the Event Horizon Telescope Science Council, will explain how information from a world-wide network of telescopes was combined using atomic clocks, to create the first ever image of a black hole. (Picture: first image of a black hole)\u003cbr\u003eCogwheels: a deeper level – Guest author: Gerard 't HooftNobel laureate ‘t Hooft explains his views on cogwheels, carrying the fundamental information in the Universe.\u003cbr\u003eGravitational waves – Guest author: Chris van den Broeck\u003cbr\u003eLinks: The Universe as a spreadsheetLinks, joins, references, URLs, blockchain, associations and even entanglement in physics are all different words for the same building block, forming the connections in the Information Universe.\u003cbr\u003eCosmic Microwave Background – Guest author: Margot BrouwerParticles of light created in the hot and dense state of the Universe after the Big Bang are still flying through the Universe today. Together, these 1077 photons contain the largest amount of information known in the Universe. This information can still be accessed through telescopes, and brings us invaluable information about the dawn of our Universe.\u003cbr\u003eEmergent Gravity – Guest author: Erik VerlindeProf. Erik Verlinde, professor of theoretical physics at the University of Amsterdam, won the Spinoza prize for his new theory explaining gravity. In his theory, all matter, space and time consist of information and are all connected by entanglement. If this theory is correct, the information content of the entire Universe is 2399. This is the highest power described in this book, and actually, in physics.\u003cbr\u003eChapter 4: It from BitOne big information processing machine – Guest author: Gerard 't Hooft (TBC)t Hooftt Hooft: : ““there is something happening at a different level of nature”there is something happening at a different level of nature”..\u003cbr\u003eOn the origin of physical information. – Guest author: Stefano Gottardi\u003cbr\u003eThe ear In the ear information is copied a dozen times!\u003cbr\u003eThe eye – on the visual perception of data- climate change. Links to - facts and fakes- the system of ScienceThe System of Science\u003cbr\u003eHow does this system work? Discussing Hegel’s system of science, logic, technology, Nature, life, physics, consciousness.\u003cbr\u003eArtificial IntelligenceThe machine learning and the data-base oriented communities are still living on different planets. I discuss and revisit Tegmark’s recent book Life 3.0 by comparing 3 crosscuts through the Information Universe: i) the classical computer centric view ii) the data centric view iii) the artificial intelligence view.\u003cbr\u003eInformation densityThe average information density of the universe can be compared to that of written text.\u003cbr\u003eBlack Body radiation On the information aspects of the third big physical breakthrough of the 20th century (next to General relativity and quantum mechanics).\u003cbr\u003eEntropyDiscussing Shannon’s work and identifying that “Information only exists in relation to its environment”. Examples will be given.\u003cbr\u003eCosmic information, cosmogenesis and dark energy by PadmanabhanCosmic information connects the cosmological constant to cosmogenesis\u003cbr\u003eIt from BitIs the Universe one big information processing machine?\u003cbr\u003eConsciousnessVery little is known about the consciousness and I refrain from addressing the consciousness per se. A relevant list of about 5 facts we do know are listed. Any view on the relation between the consciousness and the Information Universe should at least deal with this list.\u003cbr\u003eSomnium – Musician Jacco Gardner performing at DOTLiveplanetarium at Eurosonic 2019 show case music festival- Inspired by Kepler’s Somnium – directed by EV \u003cbr\u003eThe Information UniverseAn overview.\u003cbr\u003eFacts and fakesHow is all this related to the current facts and fakes issues on the Internet? How do you make sure that what you are reading is accurate and comes from a reliable source?The link between Open Science, FAIR and reliability of data.","brand":"Springer Nature Switzerland AG","offers":[{"title":"Default Title","offer_id":48743041139031,"sku":"9783030583477","price":42.74,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783030583477.jpg?v=1720063853"},{"product_id":"luminescence-data-analysis-and-modeling-using-r-9783030673109","title":"Luminescence: Data Analysis and Modeling Using R","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003e​This book covers applications of R to the general discipline of radiation dosimetry and to the specific areas of luminescence dosimetry, luminescence dating, and radiation protection dosimetry. It features more than 90 detailed worked examples of R code fully integrated into the text, with extensive annotations. The book shows how researchers can use available R packages to analyze their experimental data, and how to extract the various parameters describing mathematically the luminescence signals.\u003cbr\u003e In each chapter, the theory behind the subject is summarized, and references are given from the literature, so that researchers can look up the details of the theory and the relevant experiments. Several chapters are dedicated to Monte Carlo methods, which are used to simulate the luminescence processes during the irradiation, heating, and optical stimulation of solids, for a wide variety of materials. This book will be useful to those who use the tools of luminescence dosimetry, including physicists, geologists, archaeologists, and for all researchers who use radiation in their research.\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003e1. Introduction.- 2. Analysis and Modeling of TL Data.- 3. Analysis of Experimental OSL Data.- 4. Dose Response of Dosimetric Materials.- 5. Monte Carlo Simulations With Fixed Time Interval.- 6. Luminescence as a Stochastic Life-and-Death Process.- 7. Delocalized Transitions: The R Package RLumCarlo.- 8. Localized Transitions: The R Package RLumCarlo.- 9. Quantum Tunneling and Luminescence Models.- 10. Quantum Tunneling: The R Package RLumCarlo.- 11. Comprehensive Quartz Models Using Program KMS.- 12. Quartz Models Using the R-Package RLumModel.\u003cbr\u003e","brand":"Springer Nature Switzerland AG","offers":[{"title":"Default Title","offer_id":48743044645207,"sku":"9783030673109","price":999.99,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783030673109.jpg?v=1791480516"},{"product_id":"the-structures-of-mathematical-physics-an-introduction-9783030734480","title":"The Structures of Mathematical Physics: An","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003e\u003cp\u003eThis textbook serves as an introduction to groups, rings, fields, vector and tensor spaces, algebras, topological spaces, differentiable manifolds and Lie groups --- mathematical structures which are foundational to modern theoretical physics. It is aimed primarily at undergraduate students in physics and mathematics with no previous background in these topics. Applications to physics --- such as the metric tensor of special relativity, the symplectic structures associated with Hamilton's equations and the Generalized Stokes's Theorem --- appear at appropriate places in the text. Worked examples, end-of-chapter problems (many with hints and some with answers) and guides to further reading make this an excellent book for self-study. Upon completing this book the reader will be well prepared to delve more deeply into advanced texts and specialized monographs in theoretical physics or mathematics.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTrade Review\u003c\/h2\u003e“This text approaches the reader with shocking breadth and niggardly depth. … Around each definition, there is short---and pleasant---narrative and then a number of examples are described. Chapters end with a list of straightforward exercises … . As a stand-alone mathematical dictionary, the text under review may serve a purpose … .” (Ryan Grady, MAA Reviews, January 30, 2022)\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003ePreface and Acknowledgements.- Sets and Relations.- Mappings and Functions.- Rings and Fields.- Linear Vector Spaces.- Algebras.- Basic Topology and Topological Groups.- Topological Vector Spaces.- Measure, Integration and Hilbert Space.- Operators and Spectra.- Annotated Bibliography and a Guide to Further Reading.- Index.","brand":"Springer Nature Switzerland AG","offers":[{"title":"Default Title","offer_id":48743047758167,"sku":"9783030734480","price":999.99,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783030734480.jpg?v=1791480527"},{"product_id":"making-sense-of-statistical-mechanics-9783030917937","title":"Making Sense of Statistical Mechanics","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003e\u003cp\u003eMany people, including physicists, are confused about what the Second Law of thermodynamics really means, about how it relates to the arrow of time, and about whether it can be derived from classical mechanics. They also wonder what entropy really is: Is it all about information? But, if so, then, what is its relation to fluxes of heat?\u003c\/p\u003e\u003cp\u003eOne might ask similar questions about probabilities: Do they express subjective judgments by us, humans, or do they reflect facts about the world, i.e. frequencies. And what notion of probability is used in the natural sciences, in particular statistical mechanics?\u003c\/p\u003e\u003cp\u003eThis book addresses all of these questions in the clear and pedagogical style for which the author is known. Although valuable as accompaniment to an undergraduate course on statistical mechanics or thermodynamics, it is not a standard course book. Instead it addresses both the essentials and the many subtle questions that are usually brushed under the carpet in such courses. As one of the most lucid accounts of the above questions, it provides enlightening reading for all those seeking answers, including students, lecturers, researchers and philosophers of science.\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003e\u003cp\u003eWhat We Need from Thermodynamics.- What Are Probabilities?.- Dynamical Systems.-  Statistical Mechanics 1 : The Nature of Equilibrium.- Statistical Mechanics 2: Irreversibility.- Demystifying Entropy.-  Comparison with Quantum Mechanics.\u003c\/p\u003e","brand":"Springer Nature Switzerland AG","offers":[{"title":"Default Title","offer_id":48743058473303,"sku":"9783030917937","price":999.99,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783030917937.jpg?v=1791480562"},{"product_id":"statistical-methods-for-data-analysis-with-applications-in-particle-physics-9783031199332","title":"Statistical Methods for Data Analysis: With","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003e\u003cp\u003eThis third edition expands on the original material. Large portions of the text have been reviewed and clarified. More emphasis is devoted to machine learning including more modern concepts and examples. This book provides the reader with the main concepts and tools needed to perform statistical analyses of experimental data, in particular in the field of high-energy physics (HEP).\u003c\/p\u003e\u003cp\u003eIt starts with an introduction to probability theory and basic statistics, mainly intended as a refresher from readers’ advanced undergraduate studies, but also to help them clearly distinguish between the Frequentist and Bayesian approaches and interpretations in subsequent applications. Following, the author discusses Monte Carlo methods with emphasis on techniques like Markov Chain Monte Carlo, and the combination of measurements, introducing the best linear unbiased estimator. More advanced concepts and applications are gradually presented, including unfolding and regularization procedures, culminating in the chapter devoted to discoveries and upper limits.\u003c\/p\u003e\u003cp\u003eThe reader learns through many applications in HEP where the hypothesis testing plays a major role and calculations of look-elsewhere effect are also presented. Many worked-out examples help newcomers to the field and graduate students alike understand the pitfalls involved in applying theoretical concepts to actual data.\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTrade Review\u003c\/h2\u003e“The book is important because, as AI and data science continue to shape the future, much interdisciplinary work is being done in many different domains. It is a very good example of interdisciplinary physics research using AI and data science. ... Graduate students are often expected to apply theoretical knowledge. This book will be an invaluable resource for them, to jumpstart their research by getting equipped with the right statistical and data analysis toolsets.” (Gulustan Dogan, Computing Reviews, August 8, 2023)\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003e\u003cp\u003ePreface to the third edition\u003c\/p\u003e  \u003cp\u003ePreface to previous edition\/s\u003c\/p\u003e\u003cbr\u003e\u003cp\u003e\u003c\/p\u003e  \u003cp\u003e1 Probability Theory\u003c\/p\u003e  1.1 Why Probability Matters to a Physicist\u003cp\u003e\u003c\/p\u003e  \u003cp\u003e1.2 The Concept of Probability\u003c\/p\u003e  1.3 Repeatable and Non-Repeatable Cases\u003cp\u003e\u003c\/p\u003e  \u003cp\u003e1.4 Different Approaches to Probability\u003c\/p\u003e  1.5 Classical Probability\u003cp\u003e\u003c\/p\u003e  \u003cp\u003e1.6 Generalization to the Continuum\u003c\/p\u003e  1.7 Axiomatic Probability Definition\u003cp\u003e\u003c\/p\u003e  \u003cp\u003e1.8 Probability Distributions\u003c\/p\u003e  1.9 Conditional Probability\u003cp\u003e\u003c\/p\u003e  \u003cp\u003e1.10 Independent Events\u003c\/p\u003e  1.11 Law of Total Probability\u003cp\u003e\u003c\/p\u003e  \u003cp\u003e1.12 Statistical Indicators: Average, Variance and Covariance\u003c\/p\u003e 1.13 Statistical Indicators for a Finite Sample\u003cp\u003e\u003c\/p\u003e  \u003cp\u003e1.14 Transformations of Variables\u003c\/p\u003e  1.15 The Law of Large Numbers\u003cp\u003e\u003c\/p\u003e  \u003cp\u003e1.16 Frequentist Definition of Probability\u003c\/p\u003e  References\u003cp\u003e\u003c\/p\u003e  \u003cp\u003e \u003c\/p\u003e 2 Discrete Probability Distributions\u003cp\u003e\u003c\/p\u003e  \u003cp\u003e2.1 The Bernoulli Distribution\u003c\/p\u003e  2.2 The Binomial Distribution\u003cp\u003e\u003c\/p\u003e  \u003cp\u003e2.3 The Multinomial Distribution\u003c\/p\u003e  2.4 The Poisson Distribution\u003cp\u003e\u003c\/p\u003e  \u003cp\u003eReferences\u003c\/p\u003e\u003cbr\u003e\u003cp\u003e\u003c\/p\u003e  \u003cp\u003e3 Probability Distribution Functions\u003c\/p\u003e  3.1 Introduction\u003cp\u003e\u003c\/p\u003e  \u003cp\u003e3.2 Definition of Probability Distribution Function\u003c\/p\u003e  3.3 Average and Variance in the Continuous Case\u003cp\u003e\u003c\/p\u003e  \u003cp\u003e3.4 Mode, Median, Quantiles\u003c\/p\u003e  3.5 Cumulative Distribution\u003cp\u003e\u003c\/p\u003e  \u003cp\u003e3.6 Continuous Transformations of Variables\u003c\/p\u003e  3.7 Uniform Distribution\u003cp\u003e\u003c\/p\u003e  \u003cp\u003e3.8 Gaussian Distribution\u003c\/p\u003e  3.9 X^2 Distribution\u003cp\u003e\u003c\/p\u003e  \u003cp\u003e3.10 Log Normal Distribution\u003c\/p\u003e  3.11 Exponential Distribution\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e3.12 Other Distributions Useful in Physics\u003c\/p\u003e  \u003cp\u003e3.13 Central Limit Theorem\u003c\/p\u003e  \u003cp\u003e3.14 Probability Distribution Functions in More than One Dimension\u003c\/p\u003e  \u003cp\u003e3.15 Gaussian Distributions in Two or More Dimensions\u003c\/p\u003e  \u003cp\u003eReferences\u003c\/p\u003e  \u003cp\u003e \u003c\/p\u003e  \u003cp\u003e4 Bayesian Approach to Probability\u003c\/p\u003e  4.1 Introduction\u003cp\u003e\u003c\/p\u003e  \u003cp\u003e4.2 Bayes’ Theorem\u003c\/p\u003e  4.3 Bayesian Probability Definition\u003cp\u003e\u003c\/p\u003e  \u003cp\u003e4.4 Bayesian Probability and Likelihood Functions\u003c\/p\u003e  4.5 Bayesian Inference\u003cp\u003e\u003c\/p\u003e  \u003cp\u003e4.6 Bayes Factors\u003c\/p\u003e  4.7 Subjectiveness and Prior Choice\u003cp\u003e\u003c\/p\u003e  \u003cp\u003e4.8 Jeffreys’ Prior\u003c\/p\u003e  4.9 Reference priors\u003cp\u003e\u003c\/p\u003e  \u003cp\u003e4.10 Improper Priors\u003c\/p\u003e  4.11 Transformations of Variables and Error Propagation\u003cp\u003e\u003c\/p\u003e  \u003cp\u003eReferences\u003c\/p\u003e\u003cbr\u003e\u003cp\u003e\u003c\/p\u003e  \u003cp\u003e5 Random Numbers and Monte Carlo Methods\u003c\/p\u003e  5.1 Pseudorandom Numbers\u003cp\u003e\u003c\/p\u003e  \u003cp\u003e5.2 Pseudorandom Generators Properties\u003c\/p\u003e  5.3 Uniform Random Number Generators\u003cp\u003e\u003c\/p\u003e  \u003cp\u003e5.4 Discrete Random Number Generators\u003c\/p\u003e  5.5 Nonuniform Random Number Generators\u003cp\u003e\u003c\/p\u003e  \u003cp\u003e5.6 Monte Carlo Sampling\u003c\/p\u003e  5.7 Numerical Integration with Monte Carlo Methods\u003cp\u003e\u003c\/p\u003e  \u003cp\u003e5.8 Markov Chain Monte Carlo\u003c\/p\u003e  References\u003cp\u003e\u003c\/p\u003e  \u003cp\u003e \u003c\/p\u003e  6 Parameter Estimate\u003cp\u003e\u003c\/p\u003e  \u003cp\u003e6.1 Introduction\u003c\/p\u003e  6.2 Inference\u003cp\u003e\u003c\/p\u003e  \u003cp\u003e6.3 Parameters of Interest\u003c\/p\u003e  6.4 Nuisance Parameters\u003cp\u003e\u003c\/p\u003e  \u003cp\u003e6.5 Measurements and Their Uncertainties\u003c\/p\u003e  6.6 Frequentist vs Bayesian Inference\u003cp\u003e\u003c\/p\u003e  \u003cp\u003e6.7 Estimators\u003c\/p\u003e  6.8 Properties of Estimators\u003cp\u003e\u003c\/p\u003e  \u003cp\u003e6.9 Binomial Distribution for Efficiency Estimate\u003c\/p\u003e  6.10 Maximum Likelihood Method\u003cp\u003e\u003c\/p\u003e  \u003cp\u003e6.11 Errors with the Maximum Likelihood Method\u003c\/p\u003e  6.12 Minimum X^2 and Least-Squares Methods\u003cp\u003e\u003c\/p\u003e  \u003cp\u003e6.13 Binned Data Samples\u003c\/p\u003e  6.14 Error Propagation\u003cp\u003e\u003c\/p\u003e  \u003cp\u003e6.15 Treatment of Asymmetric Errors\u003c\/p\u003e  References\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003cbr\u003e\u003c\/p\u003e7 Combining Measurements\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e7.1 Introduction\u003c\/p\u003e\u003cp\u003e7.2 Simultaneous Fits and Control Regions\u003c\/p\u003e\u003cp\u003e7.3 Weighted Average\u003c\/p\u003e\u003cp\u003e7.4 X^2 in n Dimensions\u003c\/p\u003e\u003cp\u003e7.5 The Best Linear Unbiased Estimator\u003c\/p\u003e\u003cp\u003eReferences\u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e8 Confidence Intervals\u003cp\u003e\u003c\/p\u003e\u003cp\u003e8.1 Introduction\u003c\/p\u003e8.2 Neyman Confidence Intervals\u003cp\u003e\u003c\/p\u003e\u003cp\u003e8.3 Binomial Intervals\u003c\/p\u003e8.4 The Flip-Flopping Problem\u003cp\u003e\u003c\/p\u003e\u003cp\u003e8.5 The Unified Feldman–Cousins Approach\u003c\/p\u003eReferences\u003cp\u003e\u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e9 Convolution and Unfolding\u003cp\u003e\u003c\/p\u003e\u003cp\u003e9.1 Introduction\u003c\/p\u003e9.2 Convolution\u003cp\u003e\u003c\/p\u003e\u003cp\u003e9.3 Unfolding by Inversion of the Response Matrix\u003c\/p\u003e9.4 Bin-by-Bin Correction Factors\u003cp\u003e\u003c\/p\u003e\u003cp\u003e9.5 Regularized Unfolding\u003c\/p\u003e9.6 Iterative Unfolding\u003cp\u003e\u003c\/p\u003e\u003cp\u003e9.7 Other Unfolding Methods\u003c\/p\u003e9.8 Software Implementations\u003cp\u003e\u003c\/p\u003e\u003cp\u003e9.9 Unfolding in More Dimensions\u003c\/p\u003eReferences\u003cbr\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e10 Hypothesis Tests\u003c\/p\u003e10.1 Introduction\u003cp\u003e\u003c\/p\u003e\u003cp\u003e10.2 Test Statistic\u003c\/p\u003e10.3 Type I and Type II Errors\u003cp\u003e\u003c\/p\u003e\u003cp\u003e10.4 Fisher’s Linear Discriminant\u003c\/p\u003e10.5 The Neyman–Pearson Lemma\u003cp\u003e\u003c\/p\u003e\u003cp\u003e10.6 Projective Likelihood Ratio Discriminant\u003c\/p\u003e10.7 Kolmogorov–Smirnov Test\u003cp\u003e\u003c\/p\u003e\u003cp\u003e10.8 Wilks’ Theorem\u003c\/p\u003e10.9 Likelihood Ratio in the Search for a New Signal\u003cp\u003e\u003c\/p\u003e\u003cp\u003eReferences\u003c\/p\u003e \u003cp\u003e\u003c\/p\u003e\u003cp\u003e11 Machine Learning\u003c\/p\u003e11.1 Supervised and Unsupervised Learning\u003cp\u003e\u003c\/p\u003e\u003cp\u003e11.2 Terminology\u003c\/p\u003e11.3 Machine Learning Classification from a Statistical Point of View\u003cp\u003e\u003c\/p\u003e\u003cp\u003e11.4 Bias-Variance tradeo\u003c\/p\u003e11.5 Overtraining\u003cp\u003e\u003c\/p\u003e\u003cp\u003e11.6 Artificial Neural Networks\u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e\u003cp\u003e11.7 Deep Learning\u003c\/p\u003e\u003cp\u003e11.8 Convolutional Neural Networks\u003cbr\u003e\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e11.9 Boosted Decision Trees\u003c\/p\u003e11.10 Multivariate Analysis Implementations\u003cp\u003e\u003c\/p\u003e\u003cp\u003eReferences\u003c\/p\u003e \u003cp\u003e\u003c\/p\u003e\u003cp\u003e12 Discoveries and Upper Limits\u003c\/p\u003e12.1 Searches for New Phenomena: Discovery and Upper Limits\u003cp\u003e\u003c\/p\u003e\u003cp\u003e12.2 Claiming a Discovery\u003c\/p\u003e12.3 Excluding a Signal Hypothesis\u003cp\u003e\u003c\/p\u003e\u003cp\u003e12.4 Combined Measurements and Likelihood Ratio\u003c\/p\u003e12.5 Definitions of Upper Limit\u003cp\u003e\u003c\/p\u003e\u003cp\u003e12.6 Bayesian Approach\u003c\/p\u003e12.7 Frequentist Upper Limits\u003cp\u003e\u003c\/p\u003e\u003cp\u003e12.8 Modified Frequentist Approach: the CLs Method\u003c\/p\u003e12.9 Presenting Upper Limits: the Brazil Plot\u003cp\u003e\u003c\/p\u003e\u003cp\u003e12.10 Nuisance Parameters and Systematic Uncertainties\u003c\/p\u003e12.11 Upper Limits Using the Profile Likelihood\u003cp\u003e\u003c\/p\u003e\u003cp\u003e12.12 Variations of the Profile-Likelihood Test Statistic\u003c\/p\u003e12.13 The Look Elsewhere Effect\u003cp\u003e\u003c\/p\u003e\u003cp\u003eReferences\u003c\/p\u003e \u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003cb\u003e Index\u003c\/b\u003e\u003cbr\u003e\u003c\/p\u003e","brand":"Springer International Publishing AG","offers":[{"title":"Default Title","offer_id":48743075414359,"sku":"9783031199332","price":999.99,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783031199332.jpg?v=1720064002"},{"product_id":"artificial-intelligence-for-scientific-discoveries-extracting-physical-concepts-from-experimental-data-using-deep-learning-9783031270185","title":"Artificial Intelligence for Scientific","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003e\u003cp\u003e \u003c\/p\u003eWill research soon be done by artificial intelligence, thereby making human researchers superfluous? This book explains modern approaches to discovering physical concepts with machine learning and elucidates their strengths and limitations. The automation of the creation of experimental setups and physical models, as well as model testing are discussed. The focus of the book is the automation of an important step of the model creation, namely finding a minimal number of natural parameters that contain sufficient information to make predictions about the considered system. The basic idea of this approach is to employ a deep learning architecture, SciNet, to model a simplified version of a physicist's reasoning process. SciNet finds the relevant physical parameters, like the mass of a particle, from experimental data and makes predictions based on the parameters found. The author demonstrates how to extract conceptual information from such parameters, e.g., Copernicus' conclusion that the solar system is heliocentric. \u003cp\u003e\u003c\/p\u003e  \u003cp\u003e \u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003e\u003cp\u003eIntroduction.- Machine Learning Background.- Overview of Using Machine Learning for Physical Discoveries.- Theory: Formalizing the Process of Human Model Building.- Methods: Using Neural Networks to Find Simple Representations.- Applications: Physical Toy Examples.- Open Questions and Future Prospects.\u003c\/p\u003e","brand":"Springer International Publishing AG","offers":[{"title":"Default Title","offer_id":48743078003031,"sku":"9783031270185","price":104.49,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783031270185.jpg?v=1791480657"},{"product_id":"modified-and-quantum-gravity-from-theory-to-experimental-searches-on-all-scales-9783031315190","title":"Modified and Quantum Gravity: From Theory to","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003e\u003cp\u003eThis book discusses theoretical predictions and their comparison with experiments of extended and modified classical and quantum theories of gravity. The goal is to provide a readable access and broad overview over different approaches to the topic to graduate and PhD students as well as to young researchers. The book presents both, theoretical and experimental insights and is structured in three parts. The first addresses the theoretical models beyond special and general relativity such as string theory, Poincare gauge theory and teleparallelism as well as Finsler gravity. In turn, the second part is focused on the observational effects that these models generate, accounting for tests and comparisons which can be made on all possible scales: from the universe as a whole via binary systems, stars, black holes, satellite experiments, down to laboratory experiments at micrometer and smaller scales. The last part of this book is dedicated to quantum systems and gravity, showing tests of classical gravity with quantum systems, and coupling of quantum matter and gravity.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003ePart 1: \u003cbr\u003e Theoretical Models beyond special and general relativity \u003cbr\u003e \u003cbr\u003e Section 1: Aspects of Lorentz invariance violations (Authors: Nick Mavromatos, Luci Menendez-Pidal De Cristina) \u003cbr\u003e Section 2: Deformed relativistic symmetry principles (Authors: Giulia Gubitosi, Michele Arzano, Javier Relancio) \u003cbr\u003e Section 3: Modified gravity - Poincare gauge theory and teleparallelism (Authors: Yuri Obukhov, Manuel Hohmann) \u003cbr\u003e Section 4: Aspects of Finsler gravity and modified dispersion relations in theory and observation (Authors: Volker Perlick, Jean-Francois Gliecenstein) \u003cbr\u003e \u003cbr\u003e Part 2: \u003cbr\u003e Observational effects beyond special and general relativity \u003cbr\u003e \u003cbr\u003e Section 1: Cosmic searches for Lorentz invariance violations (Authors: Tomislav Terzic, Carloes de los Heros) \u003cbr\u003e Section 2: Compact Objects (Authors: Jutta Kunz, Elisa Maggio, Yakov Shnir, Carlos Herdeiro, Aneta Wojnar) \u003cbr\u003e Section 3: Testing classical gravity (Authors: Eva Hackmann, Lijing Shao, Sven Herrmann) \u003cbr\u003e Section 4: Testing gravity and the standard model at short distance: The Casimir effect (Authors: Galina L. Klimchitskaya, Vladimir Mostepanenko)\u003cbr\u003ePart 3: \u003cbr\u003e Quantum Systems and Gravity \u003cbr\u003e \u003cbr\u003e Section 1: Testing Classical Gravity with Quantum Systems (Authors: Sven Herrmann) \u003cbr\u003e Section 2: Quantum Gravity in the Lab (Authors: Dennis Raetzel, Annupam Mazumdar, Hendrik Ulbricht) \u003cbr\u003eSection 3: Coupling Quantum Matter and Gravity (Authors: Andre Grossardt, Jan-Willem van Holten, Philip Schwartz , Domenico Giulini) ","brand":"Springer International Publishing AG","offers":[{"title":"Default Title","offer_id":48743080755543,"sku":"9783031315190","price":67.49,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783031315190.jpg?v=1791480664"},{"product_id":"the-probability-integral-its-origin-its-importance-and-its-calculation-9783031384158","title":"The Probability Integral: Its Origin, Its","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003e\u003cp\u003eThis book tells the story of the probability integral, the approaches to analyzing it throughout history, and the many areas of science where it arises. The so-called probability integral, the integral over the real line of a Gaussian function, occurs ubiquitously in mathematics, physics, engineering and probability theory. Stubbornly resistant to the undergraduate toolkit for handling integrals, calculating its value and investigating its properties occupied such mathematical luminaries as De Moivre, Laplace, Poisson, and Liouville. This book introduces the probability integral, puts it into a historical context, and describes the different approaches throughout history to evaluate and analyze it. The author also takes entertaining diversions into areas of math, science, and engineering where the probability integral arises: as well as being indispensable to probability theory and statistics, it also shows up naturally in thermodynamics and signal processing. Designed to be accessible to anyone at the undergraduate level and above, this book will appeal to anyone interested in integration techniques, as well as historians of math, science, and statistics.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003ePreface\u003cp\u003e\u003cbr\u003e\u003c\/p\u003e\u003cp\u003eChapter 1: De Moivre and the\u003c\/p\u003e\u003cp\u003eDiscovery of the Probability Integral\u003c\/p\u003e\u003cp\u003e\u003cbr\u003e\u003c\/p\u003e\u003cp\u003eEvaluating the Probability Integral\u003c\/p\u003e\u003cp\u003e— Part 1\u003c\/p\u003e\u003cp\u003e\u003cbr\u003e\u003c\/p\u003e\u003cp\u003eChapter 2: Laplace’s First\u003c\/p\u003e\u003cp\u003eDerivation\u003c\/p\u003e\u003cp\u003e\u003cbr\u003e\u003c\/p\u003e\u003cp\u003eChapter 3: How Euler Could Have Done\u003c\/p\u003e\u003cp\u003eIt Before Laplace (but did he?)\u003c\/p\u003e\u003cp\u003e\u003cbr\u003e\u003c\/p\u003e\u003cp\u003eChapter 4: Laplace’s Second\u003c\/p\u003e\u003cp\u003eDerivation\u003c\/p\u003e\u003cp\u003e\u003cbr\u003e\u003c\/p\u003e\u003cp\u003eChapter 5: Generalizing the\u003c\/p\u003e\u003cp\u003eProbability Integral\u003c\/p\u003e\u003cp\u003e\u003cbr\u003e\u003c\/p\u003e\u003cp\u003eChapter 6: Poisson’s Derivation\u003c\/p\u003e\u003cp\u003e\u003cbr\u003e\u003c\/p\u003e\u003cp\u003eInterlude\u003c\/p\u003e\u003cp\u003e\u003cbr\u003e\u003c\/p\u003e\u003cp\u003eChapter 7: Rice’s Radar Integral\u003c\/p\u003e\u003cp\u003e\u003cbr\u003e\u003c\/p\u003e\u003cp\u003eChapter 8: Liouville’s Proof That\u003c\/p\u003e\u003cp\u003e∫e−x2dx Has No Finite Form\u003c\/p\u003e\u003cp\u003e\u003cbr\u003e\u003c\/p\u003e\u003cp\u003eChapter 9: How the Error Function\u003c\/p\u003e\u003cp\u003eAppeared in the Electrical Response of the Trans-Atlantic Telegraph Cable\u003c\/p\u003e\u003cp\u003e\u003cbr\u003e\u003c\/p\u003e\u003cp\u003eEvaluating the Probability Integral\u003c\/p\u003e\u003cp\u003e— Part 2\u003c\/p\u003e\u003cp\u003e\u003cbr\u003e\u003c\/p\u003e\u003cp\u003eChapter 10: Doing the Probability\u003c\/p\u003e\u003cp\u003eIntegral with Differentiation\u003c\/p\u003e\u003cp\u003e\u003cbr\u003e\u003c\/p\u003e\u003cp\u003eChapter 11: The Probability Integral\u003c\/p\u003e\u003cp\u003eas a Volume\u003c\/p\u003e\u003cp\u003e\u003cbr\u003e\u003c\/p\u003e\u003cp\u003eChapter 12: How Cauchy Could Have\u003c\/p\u003e\u003cp\u003eDone It (but didn’t)\u003c\/p\u003e\u003cp\u003e\u003cbr\u003e\u003c\/p\u003e\u003cp\u003eChapter 13: Fourier Has the Last Word                   \u003c\/p\u003e","brand":"Springer International Publishing AG","offers":[{"title":"Default Title","offer_id":48743084228951,"sku":"9783031384158","price":49.49,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783031384158.jpg?v=1791480675"},{"product_id":"cosmic-rays-multimessenger-astrophysics-and-revolutionary-astronomy-9783031385599","title":"Cosmic Rays: Multimessenger Astrophysics and","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003e\u003cp\u003eIn recent years, cosmic rays have become the protagonists of a new scientific revolution. We are able today to film the Universe with telescopes of completely novel conception, recording information from many different messengers and accessing previously unknown cosmic regions.\u003cbr\u003eWritten by a recognized authority in physics, this book takes readers on a captivating journey through the world of cosmic rays, their role in the revolutionary field of multi-messenger astronomy, their production from powerful accelerators close to the surfaces of black holes and compact objects, reaching the highest levels of energy observed in nature, and the implications this has for our understanding of the Universe. Through the stories of pioneering scientists, explorations of cutting-edge technologies, and simple explanations related to particle physics, quantum mechanics, and astrophysics, the book provides an illuminating state-of-the-art introduction to the current state of high-energy astrophysics. The book was written in straightforward yet rigorous language, so as to be accessible to the greater public. For those curious about the cosmos and cosmic gamma rays, nuclei, neutrinos, and gravitational waves, from casual observers to professional astronomers and physicists, the book is a must-read, offering a thrilling adventure into the future of astronomy and particle physics.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003e\u003cp\u003e\u003cb\u003eIntroduction\u003c\/b\u003e\u003c\/p\u003e  \u003cp\u003e\u003cb\u003e1 The Largest Energies in the Universe\u003c\/b\u003e\u003c\/p\u003e  \u003cp\u003e1.1 The Universe around us\u003c\/p\u003e  \u003cp\u003e1.2 Particles and fields\u003c\/p\u003e  \u003cp\u003e1.3 Cosmic rays\u003c\/p\u003e  \u003cp\u003e\u003cb\u003e2 The Mystery of Cosmic Rays\u003c\/b\u003e\u003cbr\u003e\u003c\/p\u003e  \u003cp\u003e2.1 The discovery of natural radioactivity \u003c\/p\u003e  \u003cp\u003e2.2 Is natural radioactivity of extraterrestrial origin?  \u003c\/p\u003e  \u003cp\u003e2.3 Father Wulf, a true experimental physicist \u003c\/p\u003e  \u003cp\u003e2.4 Pacini’s attenuation measures in water \u003c\/p\u003e  \u003cp\u003e2.5 Hess and balloon measurements \u003c\/p\u003e  \u003cp\u003e2.6 First developments and the tragedy of the first world war \u003c\/p\u003e  \u003cp\u003e\u003cb\u003e3 Cosmic-Ray Research after the First World War\u003c\/b\u003e\u003cbr\u003e\u003c\/p\u003e  \u003cp\u003e3.1 Research in Europe and the Pacini-Hess controversy \u003c\/p\u003e  \u003cp\u003e3.2 Research in the United States \u003c\/p\u003e  \u003cp\u003e3.3 Are cosmic rays predominantly charged or neutral? \u003c\/p\u003e  \u003cp\u003e3.4 Bruno Rossi and the discoveries after 1930 \u003c\/p\u003e  \u003cp\u003e3.5 At the origins of elementary particle physics \u003c\/p\u003e  \u003cp\u003e3.6 The recognition of the scientific community \u003c\/p\u003e  3.7 Hypothesis on the origin of cosmic rays: Tesla, Zwicky, Fermi\u003cp\u003e\u003c\/p\u003e  \u003cp\u003e\u003cb\u003e4 Cosmic Rays and the Physics of Elementary Particles\u003c\/b\u003e\u003c\/p\u003e  \u003cp\u003e4.1 Leptons and mesons \u003c\/p\u003e  \u003cp\u003e4.2 The neutral pion \u003c\/p\u003e  \u003cp\u003e4.3 The discovery of strangeness \u003c\/p\u003e  \u003cp\u003e4.4 Laboratories on the mountains \u003c\/p\u003e  \u003cp\u003e4.5 Hunters become shepherds: particle accelerators\u003c\/p\u003e  \u003cp\u003e\u003cb\u003e5 Fire Under the Ashes: the Discoveries at the End of the 20th Century and at the Beginning\u003c\/b\u003e\u003cbr\u003e\u003c\/p\u003e  \u003cp\u003e\u003cb\u003eof the 21st Century\u003c\/b\u003e\u003c\/p\u003e  5.1 Cosmic rays of very-high-energy \u003cp\u003e\u003c\/p\u003e  \u003cp\u003e5.2 Anomalous events \u003c\/p\u003e  \u003cp\u003e5.3 X-rays \u003c\/p\u003e  \u003cp\u003e5.4 Neutrinos from the Sun and the cosmos\u003c\/p\u003e  \u003cp\u003e\u003cb\u003e6 Cosmic Ray Research Today: Multi-Messenger Astrophysics\u003c\/b\u003e\u003cbr\u003e\u003c\/p\u003e  \u003cp\u003eand the New Astronomy\u003c\/p\u003e  \u003cp\u003e6.1 Very-high-energy cosmic rays\u003c\/p\u003e  \u003cp\u003e6.2 Search for antimatter \u003c\/p\u003e  \u003cp\u003e6.3 Gamma rays \u003c\/p\u003e  \u003cp\u003e6.4 Cosmic neutrinos \u003c\/p\u003e  6.5 Gravitational waves \u003cp\u003e\u003c\/p\u003e  \u003cp\u003e6.6 Multi-messenger astronomy\u003c\/p\u003e  \u003cp\u003e\u003cb\u003e7 Cosmic Rays and Climate\u003c\/b\u003e\u003c\/p\u003e  \u003cp\u003e7.1 Cosmic rays and thunderstorms \u003c\/p\u003e  \u003cp\u003e7.2 Variations in the flux of cosmic rays \u003c\/p\u003e  7.3 A correlation between cosmic rays and earthquakes?\u003cp\u003e\u003c\/p\u003e  \u003cp\u003e\u003cb\u003e8 Cosmic Rays and Life\u003c\/b\u003e\u003cbr\u003e\u003c\/p\u003e  \u003cp\u003e8.1 Ionization and chemistry of the atmosphere \u003c\/p\u003e  \u003cp\u003e8.2 The Miller-Urey experiment \u003c\/p\u003e  \u003cp\u003e8.3 Biological effects of cosmic rays \u003c\/p\u003e  8.4 Implications on evolution\u003cp\u003e\u003c\/p\u003e  \u003cp\u003e\u003cb\u003e9 Cosmic Rays and the Exploration of the Universe\u003c\/b\u003e\u003c\/p\u003e  \u003cp\u003e\u003cb\u003e10 Cosmic Rays and Archaeology\u003c\/b\u003e\u003c\/p\u003e  \u003cp\u003e10.1 Dating techniques \u003c\/p\u003e  \u003cp\u003e10.2 Muon tomography\u003c\/p\u003e  \u003cb\u003e11 The Future\u003c\/b\u003e\u003cp\u003e\u003c\/p\u003e","brand":"Springer International Publishing AG","offers":[{"title":"Default Title","offer_id":48743084327255,"sku":"9783031385599","price":26.59,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783031385599.jpg?v=1720064040"},{"product_id":"special-functions-of-mathematical-geo-physics-9783034805629","title":"Special Functions of Mathematical (Geo-)Physics","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003eSpecial functions enable us to formulate a scientific problem by reduction such that a new, more concrete problem can be attacked within a well-structured framework, usually in the context of differential equations. A good understanding of special functions provides the capacity to recognize the causality between the abstractness of the mathematical concept and both the impact on and cross-sectional importance to the scientific reality.  The special functions to be discussed in this monograph vary greatly, depending on the measurement parameters examined (gravitation, electric and magnetic fields, deformation, climate observables, fluid flow, etc.) and on the respective field characteristic (potential field, diffusion field, wave field). The differential equation under consideration determines the type of special functions that are needed in the desired reduction process.  Each chapter closes with exercises that reflect significant topics, mostly in computational applications. As a result, readers are not only directly confronted with the specific contents of each chapter, but also with additional knowledge on mathematical fields of research, where special functions are essential to application. All in all, the book is an equally valuable resource for education in geomathematics and the study of applied and harmonic analysis. Students who wish to continue with further studies should consult the literature given as supplements for each topic covered in the exercises.\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTrade Review\u003c\/h2\u003e\u003cp\u003eFrom the book reviews:\u003c\/p\u003e\u003cp\u003e“This is an erudite and competent book of great value, not only to specialists in the field. It should be very useful for both advanced students and active researchers in the field of geomathematics, geophysics, and geoengineering, and also for geooriented applied mathematicians. The style is superb and clear, and the organization is very well planned. I believe this excellent book should be required reading for all earth-oriented scientists.” (Andrzej Icha, Pure and Applied Geophysics, Vol. 172, 2015)\u003c\/p\u003e\u003cp\u003e“This book provides an accessible and modern approach to special functions and applications to geomathematics, applied mathematics, environmental and engineering sciences. … this will create new interest and useful leads for those engaged in the advanced study and research in special functions and their applications. … book will continue to be very useful as a graduate level text and an interdisciplinary research reference for professionals in applied mathematics, geomathematics and harmonic analysis. … this book is a new and excellent addition to the mathematics literature.” (L. Debnath, Mathematical Reviews, October, 2013)\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003e1 Introduction: Geomathematical Motivation.- Part I: Auxiliary Functions.- 2 The Gamma Function.- 3 Orthogonal Polynomials.- Part II: Spherically Oriented Functions.- 4 Scalar Spherical Harmonics in R^3.- 5 Vectorial Spherical Harmonics in R^3.- 6 Spherical Harmonics in R^q.- 7 Classical Bessel Functions.- 8 Bessel Functions in R^q.- Part III: Periodically Oriented Functions.- 9 Lattice Functions in R.- 10 Lattice Functions in R^q.- 11 Concluding Remarks.- References.- Index.","brand":"Birkhauser Verlag AG","offers":[{"title":"Default Title","offer_id":48743086981463,"sku":"9783034805629","price":80.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783034805629.jpg?v=1791379134"},{"product_id":"computational-physics-simulation-of-classical-and-quantum-systems-9783319004006","title":"Computational Physics: Simulation of Classical","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003e\u003cp\u003eThis textbook presents basic and advanced computational physics in a very didactic style. It contains very-well-presented and simple mathematical descriptions of many of the most important algorithms used in computational physics. \u003c\/p\u003e\u003cp\u003eThe first part of the book discusses the basic numerical methods. The second part concentrates on simulation of classical and quantum systems. Several classes of integration methods are discussed including not only the standard Euler and Runge Kutta method but also multi-step methods and the class of Verlet methods, which is introduced by studying the motion in Liouville space. A general chapter on the numerical treatment of differential equations provides methods of finite differences, finite volumes, finite elements and boundary elements together with spectral methods and weighted residual based methods. \u003c\/p\u003e\u003cp\u003eThe book gives simple but non trivial examples from a broad range of physical topics trying to give the reader insight into not only the numerical treatment but also simulated problems. Different methods are compared with regard to their stability and efficiency. The exercises in the book are realised as computer experiments. \u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTrade Review\u003c\/h2\u003e\u003cp\u003eFrom the book reviews:\u003c\/p\u003e“The well-written monograph about computational physics is based on two-semester lecture courses given by the author on a period of several years for undergraduate physics and biophysics students … . convenient for students and practitioners of computer science, chemistry, and mathematics who are interested in applications of numerical methods in physics and engineering sciences. … well-organized book with a concentration to the important ideas of the methods and physical applications including software, examples, illustrations, and references to further reading.” (Georg Hebermehl, zbMATH, Vol. 1303, 2015)\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003ePart I Numerical Methods.- Error Analysis.- Interpolation.- Numerical Differentiation.- Numerical Integration.- Systems of Inhomogeneous Linear Equations.- Roots and Extremal Points.- Fourier Transformation.- Random Numbers and Monte-Carlo Methods.- Eigenvalue Problems.- Data Fitting.- Discretization of Differential Equations.- Equations of Motion.- Part II Simulation of Classical and Quantum Systems.- Rotational Motion.- Molecular Dynamics.- Thermodynamic Systems.- Random Walk and Brownian Motion.- Electrostatics.- Waves.- Diffusion.- Nonlinear Systems.- Simple Quantum Systems.","brand":"Springer International Publishing AG","offers":[{"title":"Default Title","offer_id":48743091765591,"sku":"9783319004006","price":999.99,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783319004006.jpg?v=1720064073"},{"product_id":"the-finite-volume-method-in-computational-fluid-dynamics-an-advanced-introduction-with-openfoam-r-and-matlab-9783319168739","title":"The Finite Volume Method in Computational Fluid","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003e\u003cp\u003eThis textbook explores both the theoretical foundation of the Finite Volume Method (FVM) and its applications in Computational Fluid Dynamics (CFD). Readers will discover a thorough explanation of the FVM numerics and algorithms used for the simulation of incompressible and compressible fluid flows, along with a detailed examination of the components needed for the development of a collocated unstructured pressure-based CFD solver. Two particular CFD codes are explored. The first is uFVM, a three-dimensional unstructured pressure-based finite volume academic CFD code, implemented within Matlab. The second is OpenFOAM®, an open source framework used in the development of a range of CFD programs for the simulation of industrial scale flow problems.\u003c\/p\u003e\u003cp\u003eWith over 220 figures, numerous examples and more than one hundred exercise on FVM numerics, programming, and applications, this textbook is suitable for use in an introductory course on the FVM, in an advanced course on numerics, and as a reference for CFD programmers and researchers.\u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e\u003cp\u003e\u003cb\u003e \u003c\/b\u003e\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTrade Review\u003c\/h2\u003e\u003cp\u003e“Directed towards future practitioners such as engineers the authors first provide an introduction to fluid dynamics presupposing but a modicum of mathematical and physical knowledge. … . A number of exercises plus special chapters on modelling incompressible and compressible flow make the book very useful for its purpose.” (H. Muthsam, Monatshefte für Mathematik, Vol. 187 (1), September, 2018)\u003c\/p\u003e\u003cp\u003e\u003cbr\u003e\u003c\/p\u003e\u003cp\u003e“The book is very attractive, carefully written and easy to read by those interested in learning about finite volume methods for fluid dynamics. The authors have made an important effort to bridge the gap between classroom material and actual model development questions. The text is well illustrated by means of quality figures helping to understand the described concepts. Furthermore, the book contains pieces of academic codes in MATLAB … . It is certainly a useful, practical and valuable book.” (Pilar Garcia-Navarro, Mathematical Reviews, May, 2016)\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003e\u003cp\u003e\u003cb\u003eFoundation\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e1 Introduction\u003cbr\u003e\u003cbr\u003e2 Review of Vector Calculus\u003c\/p\u003e\u003cp\u003e3 Mathematical Description of Physical Phenomena\u003cbr\u003e\u003cbr\u003e4 The Discretization Process\u003cbr\u003e\u003cbr\u003e5 The Finite Volume Method\u003cbr\u003e\u003cbr\u003e6 The Finite Volume Mesh\u003cbr\u003e\u003cbr\u003e7 The Finite Volume Mesh in OpenFOAM® and uFVM\u003cbr\u003e\u003cbr\u003e\u003cb\u003eDiscretization\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e8 Spatial Discretization: The Diffusion Term\u003c\/p\u003e\u003cp\u003e9 Gradient Computation\u003c\/p\u003e\u003cp\u003e10 Solving the System of Algebraic Equations\u003cbr\u003e\u003cbr\u003e11 Discretization of the Convection Term\u003c\/p\u003e\u003cp\u003e12 High Resolution Schemes\u003cbr\u003e\u003cbr\u003e13 Temporal Discretization: The Transient Term\u003cbr\u003e\u003cbr\u003e14 Discretization of the Source Term, Relaxation, and Other Details\u003cbr\u003e\u003cbr\u003e\u003cb\u003eAlgorithms\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e15 Fluid Flow Computation: Incompressible Flows\u003cbr\u003e\u003cbr\u003e16 Fluid Flow Computation: Compressible Flows\u003cbr\u003e\u003cbr\u003e\u003cb\u003eApplications\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e17 Turbulence Modeling\u003cbr\u003e\u003cbr\u003e18 Boundary Conditions in OpenFOAM® and uFVM\u003cbr\u003e\u003cbr\u003e19 An OpenFOAM® Turbulent Flow Application \u003c\/p\u003e\u003cp\u003e20 Closing Remarks\u003cbr\u003e\u003cbr\u003eAppendices\u003c\/p\u003e\u0026lt;\u003cp\u003e20 Closing Remarks\u003cbr\u003e\u003cbr\u003eAppendices\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e20 Closing Remarks\u003cbr\u003e\u003cbr\u003eAppendices\u003c\/p\u003e","brand":"Springer International Publishing AG","offers":[{"title":"Default Title","offer_id":48743092420951,"sku":"9783319168739","price":999.99,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783319168739.jpg?v=1720064077"}],"url":"https:\/\/bookcurl.com\/collections\/mathematical-computational-theoretical-physics.oembed?page=28","provider":"Book Curl","version":"1.0","type":"link"}