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The leading text in the field, Animal Behavior shows how researchers use scientific logic to study the underlying mechanisms and evolutionary bases of behavior, now with a streamlined presentation and enhanced eBook.Be introduced to a rich array of fascinating examples of animal behavior and uses a vivid narrative voice that conveys the excitement of the subject. The upcoming 12th edition's enhanced eBook will make the subject come alive with numerous video and audio clips that will be presented in-line as students read. The enhanced eBook will also include 50 new interactive figures. Another objective instructors have is to help students master concepts and then demonstrate that mastery. To assist instructors with this goal, the 12th edition enhanced eBook will incorporate all-new inline self-assessments, as well as gradable chapter assessment quizzes.Recognise the rigorous scientific methodology involved in animal behavior research with an all-new "Behind the Scenes" feature, where each chapter will highlight a single research paper and look in-depth at how the research was conducted, taking a balanced view of the ultimate and proximate causes underlying how and why animals behave as they do. Rubenstein is renowned for its empirical presentation of the ultimate causes of animal behavior, and this edition will do an even better job of integrating concepts across levels of scale at the proximate level. This need will be addressed by including an even greater focus on Tinbergen's "Four Questions" and by including more integrative studies that cross levels of analysis. A 10% streamline across the content, a redesign of the chapter summaries and the addition of synthetic sections that link topics across the text and media resources will help you traverse Animal Behaviour with ease.NEW TO THIS EDITION:Enhanced integration of concepts across levels of scale: Greater focus on Tinbergen's "Four Questions" & Inclusion of more integrative studies that cross levels of analysis.Streamlined by approximately 10%, primarily by removal of extraneous examples.Added more proximate explanations and integrative examples.Re-designed chapter summaries.Synthetic sections that link topics across the text and media resources will help students get through the information overload.Enhanced eBook edition with numerous video and audio clips presented in-line as students read, 50 new interactive figures, inline self-assessments, lab manual, and discussion questions.This title is available as an enhanced eBook. Visit VitalSource for more information or to purchase.
(source: Nielsen Book Data)

• 1. Macroscopic connectivity as the essential characteristic of heterogeneous systems
• 2. Percolation theory: Classical and poor man's
• 3. Extensions of the classical percolation model
• 4. Characterization of porous media and materials
• 5. Connectivity of fracture and fault networks
• 6. Earthquakes, critical phenomena, and percolation
• 7. Flow and transport properties of porous materials
• 8. Mixing and dispersion in flow through porous media
• 9. Multiphase fluid flow in porous media
• 10. Percolation in evolving media
• 11. Vector percolation and rigidity of materials
• 12. Transport properties of composite materials
• 13. Rheology and elastic properties of network glasses, branched polymers, and gels
• 14. Vibrational density of states of heterogeneous materials
• 15. Hopping conductivity of heterogeneous materials
• 16. Applications of invasion percolation
• 17. Percolation in random graphs and complex networks
• 18. Percolation in biological systems
• 19. Percolation theory, ecology, hydrology, and geochemistry
• 20. Explosive percolation and its applications
• 21. Directed percolation and its applications
• 22. Percolation in large-scale systems
• References
• Index

The first edition of this book was published in 1994. Since then considerable progress has been made in both theoretical developments of percolation theory, and in its applications. The 2nd edition of this book is a response to such developments. Not only all the chapters of the 1st edition have been completely rewritten and updated all the way to 2022, but also 8 new chapters have been added that describe extensive new applications, including biological materials, networks and graphs, direcrted percolation, earthquakes, geochemical processes, and large-scale real world problems, from spread of technology to ad-hoc mobile networks--back cover

• 1. Bayesian scientific computing and inverse problems
• 2. Linear algebra
• 3. Continuous and discrete multivariate distributions
• 4. Introduction to sampling
• 5. The praise of ignorance: randomness as lack of certainty
• 6. Enter subject: construction of priors
• 7. Posterior densities, ill-conditioning, and classical regularization
• 8. Conditional Gaussian densities
• 9. Iterative linear solvers and priorconditioners
• 10. Hierarchical models and Bayesian sparsity
• 11. Sampling: the real thing
• 12. Dynamic methods and learning from the past
• 13. Bayesian filtering for Gaussian densities
• References
• Index

The once esoteric idea of embedding scientific computing into a probabilistic framework, mostly along the lines of the Bayesian paradigm, has recently enjoyed wide popularity and found its way into numerous applications. This book provides an insider's view of how to combine two mature fields, scientific computing and Bayesian inference, into a powerful language leveraging the capabilities of both components for computational efficiency, high resolution power and uncertainty quantification ability. The impact of Bayesian scientific computing has been particularly significant in the area of computational inverse problems where the data are often scarce or of low quality, but some characteristics of the unknown solution may be available a priori. The ability to combine the flexibility of the Bayesian probabilistic framework with efficient numerical methods has contributed to the popularity of Bayesian inversion, with the prior distribution being the counterpart of classical regularization. However, the interplay between Bayesian inference and numerical analysis is much richer than providing an alternative way to regularize inverse problems, as demonstrated by the discussion of time dependent problems, iterative methods, and sparsity promoting priors in this book. The quantification of uncertainty in computed solutions and model predictions is another area where Bayesian scientific computing plays a critical role. This book demonstrates that Bayesian inference and scientific computing have much more in common than what one may expect, and gradually builds a natural interface between these two areas--back cover

• The biology and genetics of cells and organisms
• The nature of cancer
• Cancer as an Infectious Disease
• Cellular oncogenes
• Growth factors, receptors, and cancer
• Cytoplasmic signaling circuitry programs many of the traits of cancer
• Tumor suppressor genes
• pRB and control of the cell cycle clock
• p53: Master Guardian and Executioner
• Eternal life : cell immortalization and tumorigenesis
• Multi-step tumorigenesis
• Shaping and Characterizing the Cancer Genome
• Dialogue replaces monologue : heterotypic interactions and the biology of angiogenesis
• Moving out : invasion and metastasis
• Crowd control : tumor immunology
• Cancer Immunotherapy
• The rational treatment of cancer

The gold standard text in cancer biology, thoroughly updated with the latest research.Incorporating the most important advances in the rapidly-evolving field of cancer biology, this book remains the defining course text on its subject. Students, instructors, researchers, and clinicians the world over admire its authoritative content, clear explanations, extensive full-color art program, and pedagogical features that promote a deep conceptual understanding of the science through the lens of fascinating tales of scientific discovery. -- Provided by publisher

• Independent random variables with independent sum and difference
• Characterization of probability distributions through the independence of linear forms
• Characterization of probability distributions through the symmetry of the conditional distribution of one linear form given another
• Characterization theorems on the field of p-adic numbers
• Miscellaneous characterization theorems

"It is well known that if two independent identically distributed random variables are Gaussian, then their sum and difference are also independent. It turns out that only Gaussian random variables have such property. This statement, known as the famous Kac-Bernstein theorem, is a typical example of a so-called characterization theorem. Characterization theorems in mathematical statistics are statements in which the description of possible distributions of random variables follows from properties of some functions of these random variables. The first results in this area are associated with famous 20th century mathematicians such as G. Pólya, M. Kac, S. N. Bernstein, and Yu. V. Linnik. By now, the corresponding theory on the real line has basically been constructed. The problem of extending the classical characterization theorems to various algebraic structures has been actively studied in recent decades. The purpose of this book is to provide a comprehensive and self-contained overview of the current state of the theory of characterization problems on locally compact Abelian groups. The book will be useful to everyone with some familiarity of abstract harmonic analysis who is interested in probability distributions and functional equations on groups" -- Provided by publisher

• Preface
• Chern-Connes-Karoubi character ismorphisms and algebras of symbols pseudodifferential operators / A. Baldare, M. Benameur, and V. Nistor
• One Perrot's index cocycles / J. Block, H. Higson, and J. Sanchez Jr.
• The Chern-Baum-Connes assembly map for Lie groupoids / P. Carrillo Rouse --Hochschild homology, trace map 9-cycles / A. Connes and C. Consani --Cyclic theory and the pericyclic category / A. Connes and C. Consani
• The image of Bott periodicity in cyclic homology / J. Cuntz
• Applications of topological cycle homology to algebraic K-theory / B. I. Dundas --Algebraic K-theory and generalized stable homotopy theory / D. Gepner --Cyclic cohomology and the extended Heisenberg calculus of Epstein and Melrose / A. Gorokhovsky and E. Van Erp
• Topological cyclic homology and the Fargues-Fontaine curve / L. Hesselholt
• Hopf cyclic cohomology and beyond / M. Khalkhali and I. Shapiro
• The Hochschild cohomology of uniform Roe algebras / M Lorentz --Quantum differentiabiltiy - the analytical perspective / E. McDonald, F. Sukochev, and X. Xiong
• Local cyclic homology for nonarchimedean Banach Algebras / R. Meyer and D. Mukherjee
• On the van Est analogy in Hopf cyclic cohomology / H. Moscovici
• Primary and secondary invariants of Dirac operators on G-proper manifolds / P. Piazza and X. Tang --Localization in Hochschild homology / M. J. Pflaum
• Cyclic homology and group actions / R. Ponge
• Cyclic cocycles and quantized pairings in materials science / E. Prodan
• Periodic cyclic homology of crossed Products / M. Puschnigg
• Trace expansions and equivariant trances on an algebra of Fourier integral operators on Rn / A. Savin and E. Schrohe
• Cartan motion group and orbital integrals / Y. Song and X. Tang
• On noncommutative crystalline cohomology / B. Tsygan --Cyclic cocycles and one-loop corrections in the spectral action / T.D. H. Nuland and and W.D. Van Suijlekom
• l1-higher index, l1-higher rho invariant and cyclic cohomology / J. Wang, Z. Xie, and G. Yu

• Preface
• Acknowledgements
• Notation and Conventions
• Chapter 1. Algebraic Preliminaries
• Chapter 2. Non-Archimedean Fields
• Chapter 3. Basic Properties of Drinfeld Modules
• Chapter 4. Drinfeld Modules over Finite Fields
• Chapter 5. Analytic Theory of Drinfeld Modules
• Chapter 6. Drinfeld Modules over Local Fields
• Chapter 7. Drinfeld Modules over Global Fields
• Appendix A. Drinfeld modules for general function rings
• Appendix B. Notes on exercises
• Bibliography
• Index.

"This textbook offers an introduction to the theory of Drinfeld modules, mathematical objects that are fundamental to modern number theory. After the first two chapters conveniently recalling prerequisites from abstract algebra and non-Archimedean analysis, Chapter 3 introduces Drinfeld modules and the key notions of isogenies and torsion points. Over the next four chapters, Drinfeld modules are studied in settings of various fields of arithmetic importance, culminating in the case of global fields. Throughout, numerous number-theoretic applications are discussed, and the analogies between classical and function field arithmetic are emphasized. Drinfeld Modules guides readers from the basics to research topics in function field arithmetic, assuming only familiarity with graduate-level abstract algebra as prerequisite. With exercises of varying difficulty included in each section, the book is designed to be used as the primary textbook for a graduate course on the topic, and may also provide a supplementary reference for courses in algebraic number theory, elliptic curves, and related fields. Furthermore, researchers in algebra and number theory will appreciate it as a self-contained reference on the topic."--Back cover.

• 1. Introduction to dynamical systems
• 2. Topological equivalence, bifurcations, and structural stability of dynamical systems
• 3. One-parameter bifurcations of equilibria in continuous-time dynamical system
• 4. One-parameter bifurcations of fixed points in discrete-time dynamical systems
• 5. Bifurcations of equilibria and periodic orbits in n-dimensional dynamical systems
• 6. Bifurcations of orbits homoclinic and heteroclinic to hyperbolic equilibria
• 7. Other one-parameter bifurcations in continuous-time dynamical systems
• 8. Two-parameter bifurcations of equilibria in continuous-time dynamical systems
• 9. Two-parameter bifurcations of fixed points in discrete-time dynamical systems
• 10. Numerical analysis of bifurcations
• Appendix A: basic notions from from algebra, analysis, and geometry
• References
• Index.

This is a book on nonlinear dynamical systems and their bifurcations under parameter variation. It provides a reader with a solid basis in dynamical systems theory, as well as explicit procedures for application of general mathematical results to particular problems. Special attention is given to efficient numerical implementations of the developed techniques. Several examples from recent research papers are used as illustrations. The book is designed for advanced undergraduate or graduate students in applied mathematics, as well as for Ph.D. students and researchers in physics, biology, engineering, and economics who use dynamical systems as model tools in their studies. A moderate mathematical background is assumed, and, whenever possible, only elementary mathematical tools are used. This new edition preserves the structure of the previous editions, while updating the context to incorporate recent theoretical and software developments and modern techniques for bifurcation analysis--back cover.

• Preface
• Acknowledgements
• Part I. Fundamentals
• 1. Introduction to behavior genetics
• 2. Mendelian genetics
• 3. Heritability
• Part II. Molecules and cells
• 4. Genes
• 5. Genetic variation
• 6. Neurogenetics
• Part III. Behaviors and behavioral disorders
• 7. Serious mental illness
• 8. Learning and memory
• 9. Emotion and depressive disorders
• 10. Fear and anxiety
• 11. Addiction
• Part IV. Health, social behavior, and implications
• 12. Eating and exercising
• 13. Social behavior
• 14. Behavior genetics in real life
• 15. Eugenics
• Glossary
• Index.
• (source: Nielsen Book Data)

Foundations of Behavior Genetics provides a forward-looking introduction to this fascinating field. Written by an experienced teacher and researcher, this text focuses on concepts, methods, and findings that inform our understanding of heredity-behavior relations. The book's neuroscience perspective asks students to think about potential neural mechanisms involved in pathways from genes to behavior. While the text is primarily focused on human behavior genetics, it also emphasizes the importance of non-human animal models in experimental studies, as well as their evolutionary connections to humans. Part I covers the history of behavior genetics and the basics of non-molecular genetics; Part II discusses molecular genetics and neurogenetics; Part III addresses various behavioral disorders; and Part IV explores health, social behavior, and ethical implications. The text includes detailed chapter summaries, several "Check-up" questions after major sections that test student understanding, and recommended readings. Instructors are provided with a test bank of multiple-choice items and hi-res JPEGs of the many illustrations created for the book.
(source: Nielsen Book Data)

Endeavors to explain Einstein's general theory of relativity, beginning with the equivalence principle and covering the necessary mathematics of Riemannian spaces and tensor calculus, offering readers a deeper understanding of the universe's real structure.

"We have expanded from seven to eight principles, which has allowed us to delve more deeply into the social and emotional components of learning. A brand new chapter (Chapter 1) explores individual differences among learners, and the intersections of identities and backgrounds that shape how students enter, respond to, and shape the learning environment. A reworked chapter (Chapter 7) investigates more fully the ways that instructors can shape the climate of their courses to make students feel included or marginalized -- and the implications for learning and performance. Across all eight principles, we updated the research previously discussed while integrating new areas of research. Wherever possible, we applied a diversity, equity, and inclusion lens, exploring issues of power, identity, and belonging as they relate to teaching and learning. We have also referenced a broader range of institution types and student populations than in the previous edition, and incorporated case studies and strategies relevant to emerging educational technologies and online and hybrid learning modalities."-- Provided by publisher

Inverse scattering theory is a major theme in applied mathematics, with applications to such diverse areas as medical imaging, geophysical exploration, and nondestructive testing. The inverse scattering problem is both nonlinear and ill-posed, thus presenting challenges in the development of efficient inversion algorithms. A further complication is that anisotropic materials cannot be uniquely determined from given scattering data. In the first edition of Inverse Scattering Theory and Transmission Eigenvalues, the authors discussed methods for determining the support of inhomogeneous media from measured far field data and the role of transmission eigenvalue problems in the mathematical development of these methods. In this second edition, three new chapters describe recent developments in inverse scattering theory. In particular, the authors explore the use of modified background media in the nondestructive testing of materials and methods for determining the modified transmission eigenvalues that arise in such applications from measured far field data. They also examine nonscattering wave numbers-a subset of transmission eigenvalues-using techniques taken from the theory of free boundary value problems for elliptic partial differential equations and discuss the dualism of scattering poles and transmission eigenvalues that has led to new methods for the numerical computation of scattering poles. This book will be of interest to research mathematicians and engineers and physicists working on problems in target identification. It will also be useful to advanced graduate students in many areas of applied mathematics.
(source: Nielsen Book Data)

• Part I. Lagerungen
• Arrangements in the plane, on the sphere, and in space : 1. Some theorems from elementary geometry
• 2. Theorems from the theory of convex bodies
• 3. Problems on packing and covering in the plane
• 4. Efficiency of packings and coverings with a sequence of convex disks
• 5. Extremal properties of regular polyhedra
• 6. Irregular packing on the sphere
• 7. Packing in space
• Part II. Notes and additional chapters to the English edition : 8. Notes / G. Fejes Tóth, L. Fejes Tóth and W. Kuperberg
• 9. Finite variations on the isoperimetric problem / G. Fejes Tóth
• 10. Higher dimensions / G. Fejes Tóth
• 11. Ball packings in hyperbolic space / G. Fejes Tóth, L. Fejes Tóth and W.. Kuperberg
• 12. Multiple arrangements / G. Fejes Tóth
• 13. Neighbors / G. Fejes Tóth, L. Fejes Tóth and W. Kuperberg
• 14. Packing and covering properties of sequences of convex bodies / G. Fejes Tóth
• 15. Four classic problems / G. Fejes Tóth and W. Kuperberg
• 16. Miscellaneous problems about packing and covering / G. Fejes Tóth, L. Fejes Tóth and W. Kuperberg
• References for Part I
• References for Part II
• Name index
• Subject index

"The publication of the first edition of 'Lagerungen in der Ebene, auf der Kugel und im Raum' in 1953 marked the birth of discrete geometry. Since then, the book has had a profound and lasting influence on the development of the field. It included many open problems and conjectures, often accompanied by suggestions for their resolution. A good number of new results were surveyed by László Fejes Tóth in his Notes to the 2nd edition. The present version of Lagerungen makes this classic monograph available in English for the first time, with updated Notes, completed by extensive surveys of the state of the art. More precisely, this book consists of: a corrected English translation of the original Lagerungen; the revised and updated Notes on the original text; eight self-contained chapters surveying additional topics in detail. The English edition provides a comprehensive update to an enduring classic. Combining the lucid exposition of the original text with extensive new material, it will be a valuable resource for researchers in discrete geometry for decades to come" -- Backside cover

• Wayfinding : composition : decomposition
• Death traps : Great Salt Lake
• Stuck : American West
• Unspiraling : North America
• The big here : Earth
• Field notes : excavations

"At Great Salt Lake, near Robert Smithson's iconic earthwork Spiral Jetty, a motley crew of scientists walks the mudflats to study fossils in the making. This reputedly dead sea is home to countless tar seeps, pools of raw oil that act as the perfect preservative, encasing organisms as they were in life. In this spare landscape, an intricate web of life unfurls. Halophiles--salt-hungry microorganisms--tint the brackish water pink and orange; crystals of gypsum stud the ground, glistening underfoot; and pelicans and other migratory birds stop for a crucial rest. Barn owls and seagulls flirt with their prey around the oozing microbial constellations, sometimes falling prey to the oil themselves. Gretchen Henderson came to the tar seeps, a kind of natural asphalt, after recovering from being hit by a car as she walked in a crosswalk--a manufactured asphalt. Like the spiraling artwork that made the Great Salt Lake's northeastern shore famous, Henderson's associations of life and death, degeneration and regeneration, and injury and healing came together as she reexamined the pressing questions this delicate area revealed about the climate crisis. How do we move beyond narrow concepts of the beautiful and the ugly to care for ecosystems that evolve over time? How do we confront our vulnerability to recognize kindred dynamics in our living planet? Through shifting lake levels, bird migrations, microbial studies, environmental arts, and cultural histories shaped by indigenous knowledge and colonial legacies, Life in the Tar Seeps contemplates the ways others have understood this overlooked region. As Henderson witnesses scientists, curators, land managers, and students working collaboratively to steward a challenging place, she grows to see the lake not as dead but as a watershed for shifting perceptions and a meditation on the environmental healing of the planet. Henderson illustrates her journey with her own vivid photographs of tar seeps and pelican death assemblages, historic maps, and contemporary art and includes a wayfinding guide for exploring places of our own"-- Provided by publisher

• 1. Shuffling cards: An introduction
• 2. Practice and history of shuffling cards
• 3. Convergence rates for riffle shuffles
• 4. Features
• 5. Eigenvectors and Hopf algebras
• 6. Shuffling and carries
• 7. Different models for riffle shuffling
• 8. Move to front shuffling and variations
• 9. Shuffling and geometry
• 10. Shuffling and algebraic topology
• 11. Type B shuffles and shelf shuffling machines
• 12. Descent algebras, 𝑃-partitions, and quasisymmetric functions
• 13. Overhand shuffling
• 14. “Smoosh” shuffle
• 15. How to shuffle perfectly (randomly)
• 16. Applications to magic tricks, traffic merging, and statistics
• 17. Shuffling and multiple zeta values.

This book gives a lively development of the mathematics needed to answer the question, “How many times should a deck of cards be shuffled to mix it up?” The shuffles studied are the usual ones that real people use: riffle, overhand, and smooshing cards around on the table.The mathematics ranges from probability (Markov chains) to combinatorics (symmetric function theory) to algebra (Hopf algebras). There are applications to magic tricks and gambling along with a careful comparison of the mathematics to the results of real people shuffling real cards. The book explores links between shuffling and higher mathematics—Lie theory, algebraic topology, the geometry of hyperplane arrangements, stochastic calculus, number theory, and more. It offers a useful springboard for seeing how probability theory is applied and leads to many corners of advanced mathematics.The book can serve as a text for an upper division course in mathematics, statistics, or computer science departments and will be appreciated by graduate students and researchers in mathematics, statistics, and computer science, as well as magicians and people with a strong background in mathematics who are interested in games that use playing cards. -- Provided by publisher.

• Rings and coefficients
• Moduli stacks of φ [phi]-modules and (φ [phi], Γ [Gamma])-modules
• Crystalline and semistable moduli stacks
• Families of extensions
• Crystalline lifts and the finer structure of Xd,red
• The rank one case
• A geometric Breuil-Mézard conjecture

"Motivated by the p-adic Langlands program, this book constructs stacks that algebraize Mazur's formal deformation rings of local Galois representations. More precisely, it constructs Noetherian formal algebraic stacks over Spf Zp that parameterize étale (φ [phi], Γ [Gamma])-modules; the formal completions of these stacks at points in their special fibres recover the universal deformation rings of local Galois representations. Matthew Emerton and Toby Gee use these stacks to show that all mod p representations of the absolute Galois group of a p-adic local field lift to characteristic zero, and indeed admit crystalline lifts. They explicitly describe the irreducible components of the underlying reduced substacks and discuss the relationship between the geometry of these stacks and the Breuil-Mézard conjecture. Along the way, they prove a number of foundational results in p-adic Hodge theory that may be of independent interest"-- Provided by publisher

• 1. Existence, Uniqueness, and Regularity of Solutions
• 2. Spatially Semidiscrete Discretization
• 3. Convolution Quadrature
• 4. Finite Difference Methods: Construction and Implementation
• 5. Finite Difference Methods on Uniform Meshes
• 6. Finite Difference Methods on Graded Meshes
• 7. Nonnegativity Preservation
• 8. Discrete Maximal Regularity
• 9. Subdiffusion with Time-Dependent Coefficients
• 10. Semilinear Subdiffusion
• 11. Time-Space Finite Element Approximation
• 12. Spectral Galerkin Approximation
• 13. Incomplete Iterative Solution at Time Levels
• 14. Optimal Control with Subdiffusion Constraint
• 15. Backward Subdiffusion
• Appendix A: Mathematical Preliminaries
• References
• Index.

This book discusses numerical methods for solving time-fractional evolution equations. The approach is based on first discretizing in the spatial variables by the Galerkin finite element method, using piecewise linear trial functions, and then applying suitable time stepping schemes, of the type either convolution quadrature or finite difference. The main concern is on stability and error analysis of approximate solutions, efficient implementation and qualitative properties, under various regularity assumptions on the problem data, using tools from semigroup theory and Laplace transform. The book provides a comprehensive survey on the present ideas and methods of analysis, and it covers most important topics in this active area of research. It is recommended for graduate students and researchers in applied and computational mathematics, particularly numerical analysis--back cover.

"A Panoply of Polygons presents and organizes hundreds of beautiful, surprising and intriguing results about polygons with more than four sides. (A Cornucopia of Quadrilaterals, a previous volume by the same authors, thoroughly explored the properties of four-sided polygons.) This panoply consists of eight chapters, one dedicated to polygonal basics, the next ones dedicated to pentagons, hexagons, heptagons, octagons and many-sided polygons. Then miscellaneous classes of polygons are explored (e.g., lattice, rectilinear, zonogons, cyclic, tangential) and the final chapter presents polygonal numbers (figurate numbers based on polygons). Applications, real-life examples, and uses in art and architecture complement the presentation where many proofs with a visual nature are included" -- back cover

"This textbook introduces the study of partial differential equations using both analytical and numerical methods. By intertwining the two complementary approaches, the authors create an ideal foundation for further study. Motivating examples from the physical sciences, engineering, and economics complete this integrated approach. A showcase of models begins the book, demonstrating how PDEs arise in practical problems that involve heat, vibration, fluid flow, and financial markets. Several important characterizing properties are used to classify mathematical similarities, then elementary methods are used to solve examples of hyperbolic, elliptic, and parabolic equations. From here, an accessible introduction to Hilbert spaces and the spectral theorem lay the foundation for advanced methods. Sobolev spaces are presented first in dimension one, before being extended to arbitrary dimension for the study of elliptic equations. An extensive chapter on numerical methods focuses on finite difference and finite element methods. Computer-aided calculation with Maple™ completes the book. Throughout, three fundamental examples are studied with different tools: Poisson's equation, the heat equation, and the wave equation on Euclidean domains. The Black-Scholes equation from mathematical finance is one of several opportunities for extension. Partial Differential Equations offers an innovative introduction for students new to the area. Analytical and numerical tools combine with modeling to form a versatile toolbox for further study in pure or applied mathematics. Illuminating illustrations and engaging exercises accompany the text throughout. Courses in real analysis and linear algebra at the upper-undergraduate level are assumed."--Provided by publisher

This book features a collection of papers by plenary, semi-plenary and invited contributors at IWOTA2021, held at Chapman University in hybrid format in August 2021. The topics span areas of current research in operator theory, mathematical physics, and complex analysis.

"This volume is one of six that together comprise the text materials for Six Ideas That Shaped Physics, a unique approach to the two- or three-semester calculusbased introductory physics course. I have designed this curriculum (for which these volumes only serve as the text component) to support an introductory course that combines three elements: Inclusion of 20th-century physics topics, A thoroughly 21st-century perspective on even classical topics, and Support for a student-centered and active-learning-based classroom"-- Provided by publisher

"This volume is one of six that together comprise the text materials for Six Ideas That Shaped Physics, a unique approach to the two- or three-semester calculusbased introductory physics course. I have designed this curriculum (for which these volumes only serve as the text component) to support an introductory course that combines three elements: Inclusion of 20th-century physics topics, A thoroughly 21st-century perspective on even classical topics, and Support for a student-centered and active-learning-based classroom"-- Provided by publisher

"This volume is one of six that together comprise the text materials for Six Ideas That Shaped Physics, a unique approach to the two- or three-semester calculusbased introductory physics course. I have designed this curriculum (for which these volumes only serve as the text component) to support an introductory course that combines three elements: Inclusion of 20th-century physics topics, A thoroughly 21st-century perspective on even classical topics, and Support for a student-centered and active-learning-based classroom"-- Provided by publisher

"This volume is one of six that together comprise the text materials for Six Ideas That Shaped Physics, a unique approach to the two- or three-semester calculusbased introductory physics course. I have designed this curriculum (for which these volumes only serve as the text component) to support an introductory course that combines three elements: Inclusion of 20th-century physics topics, A thoroughly 21st-century perspective on even classical topics, and Support for a student-centered and active-learning-based classroom"-- Provided by publisher

"This volume is one of six that together comprise the text materials for Six Ideas That Shaped Physics, a unique approach to the two- or three-semester calculusbased introductory physics course. I have designed this curriculum (for which these volumes only serve as the text component) to support an introductory course that combines three elements: Inclusion of 20th-century physics topics, A thoroughly 21st-century perspective on even classical topics, and Support for a student-centered and active-learning-based classroom"-- Provided by publisher

"This volume is one of six that together comprise the text materials for Six Ideas That Shaped Physics, a unique approach to the two- or three-semester calculusbased introductory physics course. I have designed this curriculum (for which these volumes only serve as the text component) to support an introductory course that combines three elements: Inclusion of 20th-century physics topics, A thoroughly 21st-century perspective on even classical topics, and Support for a student-centered and active-learning-based classroom"-- Provided by publisher

• Part I. Introduction
• Chapter 1. Southern Baltic Coastal Systems Analysis: Questions, Conceptions and Red Threads
• Chapter 2. Coastal Ecosystems from a Social-Ecological Perspective
• Part II. Ecological Structures and Functions of the German Baltic Sea Coast
• Chapter 3. The Abiotic Background: Climatic, Hydrological and Geological Conditions of the Southern Baltic
• Chapter 4. Geological and Sedimentary Conditions
• Chapter 5. Environmental Conditions at the Coast: The Terrestrial Ecosystems
• Chapter 6. Environmental Conditions at the Coast: Shoreline Ecosystems
• Chapter 7. Ecosystem and Landscape Functions of the Coast: Recent Research Results
• Chapter 8: Benthic Habitats and Their Inhabitants
• Part III. Ecological Structures and Functions of Coastal Water and Offshore Ecosystems
• Chapter 9. Introducing the Ecological Aspects
• Chapter 10. Baltic Sea Aquatic Ecosystems in a Gradient from Land to Open Sea
• Chapter 11. Comparison of Abiotic Parameters and Dominant Primary Producers Between the Two Main Investigation Areas
• Chapter 12. Short-Term Variability, Long-Term Trends and Seasonal Aspects in the Dar-Zingst Bodden Chain
• Chapter 13. Carbon Fluxes/Food-Webs: Effect of Macrophytes on Food Web Characteristics in Coastal Lagoons
• Chapter 14. Ecological Structure in Benthic Habitats of Offshore Waters
• Chapter 15. Patterns of Bioturbation and Associated Matter Fluxes
• Chapter 16. Seasonal Aspects and Short-Term Variability of the Pelagic Offshore Ecosystems
• Chapter 17. Long-Term Trends of the Offshore Ecosystems
• Chapter 18. Nutrient and Limitation Regimes in Coastal Water Ecosystems
• Part IV. Combining the Aspects: Ecosystem Service Assessment
• Chapter 19. The Human Factor: Coastal Social-Ecological Systems
• Chapter 20. Introduction: The Concept of Ecosystem Service Assessment Applied to Coastal Systems
• Chapter 21. The Missing Links in Ecosystem Service Research
• Chapter 22. Eudaimonic Valuation of Cultural Ecosystem Services
• Chapter 23. Economic Valuation of Cultural Ecosystem Services
• Chapter 24. Spatial Ecosystem Service Assessment Across the Land-Sea-Interface
• Chapter 25. Temporal Changes in Aquatic Ecosystem Services Provision: Approach and Examples
• Chapter 26. Assessing Temporal Changes in Ecosystem Service Provisions: Conceiving Future Pathways
• Part V. Synthesis: Assessment as a Tool for Managing Coastal Ecosystems?
• Chapter 27. Applying the Integrated Approach
• Chapter 28. Mechanisms of Ecosystem Service Production: An Outcome of Ecosystem Functions and Ecological Integrity in Coastal Lagoons
• Chapter 29. Ecosystem Service Assessment in European Coastal and Marine Policies
• Chapter 30. Ecosystem Services and Sustainable Development: The Case for Strong Sustainability
• Chapter 31. Concluding Remarks

This book gives an overall analysis of the current knowledge status about structures, functions, utilization for German Baltic coast ecosystems. The main focus of this book is on the aquatic area, but land/sea interactions as well as river outfalls are included as well. Characteristic for this book is the inclusion of social science aspects. Approximately one third of its extent will be about the ecosystem services. In this segment the results of the last 6 years are presented in which a comprehensive quantification of the social relevance of ecosystems was carried out covering the entire area of the German Baltic Sea. This part builds directly on the results of scientific investigations and are in relation to social ideals. The assessment will not only be economically and ethically but also the mechanisms that are used for the valorisation of the ecosystem services will be evaluated. Both sub-areas, the classic natural science part as well as the part of social science aspects, deal with the changes caused by increasing anthropogenic influence and social (including demographic) changes. This will be among others in the sense of an exemplary historical outline. The final chapter of the synthesis therefore not only presents a summary of the level of knowledge gained and a deduction of the research needs. It further contains a presentation of the application aspects resulting from the analysis of the social relevance gained from basic scientific research. The book is aimed at scientists (and students) of natural, life and social sciences, analysing functioning and structures of coastal ecosystems with regard to sustainable use and nature protection, including aspects of coastal protection. Besides, it is thought to become a reference for all levels of decision makers and stakeholders in coastal and marine management of the Baltic and North Sea region, providing also a blueprint for system analysis respecting for societal as well as biological aspects world-wide

• Part I. Introduction and Description of Study Area
• Chapter 1. Introduction
• Chapter 2. Climate Changes Along the German Coast
• Chapter 3. Coastal Landscapes of the North Sea and the Baltic Sea
• Chapter 4. Geography and Study Sites
• Chapter 5. Climate and Weather Conditions Along the German Shores
• Chapter 6
• Inundation Regimes of the German Coasts and the Impact of the Rising Sea Level
• Chapter 7. The Surface Salinity of the North Sea and Baltic Sea Area
• Chapter 8. Soils
• Part II. Historical and Future Changes of the Dune and Salt Marsh Fauna
• Chapter 9. General Aspects of Coastal Vegetation at the North Sea and the Baltic Sea
• Chapter 10. Predicting Plant Distribution Shifts
• Chapter 11. General Aspects of Coastal Carabid Beetle and Spider Fauna at the North Sea and the Baltic Sea
• Chapter 12. Changes of the Fauna of Digger Wasps and Bees (Hymenoptera, Aculeata) of the North Frisian Island of Sylt Effects of Climate Change?
• Chapter 13. Historical Changes in the Carabid Beetle Fauna of Mecklenburg-Western Pomerania
• Chapter 14. Distribution of Spiders and Carabid Beetles Along a Geographical Gradient
• Chapter 15. Predicting Carabid Beetle Distribution Shifts
• Part III. Experimental Assessments of the Effects of Climate Change on Habitats and Their Organisms
• Chapter 16. Field Experiment: Effects of Increased Temperature on a Tidalic Fluvisol
• Chapter 17. Field Experiment: Effects of Microclimate Modification on Soil Organisms and Aggregate Formation in Dune Sand
• Chapter 18. Expected Vegetation Dynamics in Salt Marshes at the North Sea Coast Under Changed Inundation Conditions as an Effect of Climate Change
• Chapter 19. Effects of Sedimentation and Erosion on the Development of Vegetation
• Chapter 20. Tide Simulation Experiment
• Chapter 21. Storm Surges as Natural Experiments
• Part IV. De-Embankments and Its Effects on the Vegetation and Fauna
• Chapter 22. De-embankments at the North Sea and the Baltic Sea Coasts
• Chapter 23. Salt Marsh Restoration in a Summer Polder at the Wursten Coast
• Chapter 24. Estimated Future Effects of the Sea Level Rise Exemplified by the Wursten Coast
• Chapter 25. Restoration of Salt Meadows at the Baltic Sea Coast: The De-Embankment Experiment at Karrendorf Meadows
• Part V. Synthesis and Conclusions
• Chapter 26. Expert System: Plants
• Chapter 27. Expert System: Spiders and Carabid Beetles. Chapter 28. Consequences of Climate Change for Biota of the Coastal Salt Marshes and Dunes: Synthesis, Final Conclusions, and Ideas of Compensation

Climate change is one of the most severe dangers for mankind worldwide. Beside the temperature increase, the sea level will rise and flood wide coastal areas, which is already remarkable today. The effects will be dramatic, in particular, at coasts with low elevation gradients such as at the German coasts of the North and Baltic Sea. The impact will be not only severe for coastal people, but still more for the unique coastal ecosystems, which harbors many plant and animal species that are already endangered today. This book focuses on the coastal terrestrial ecosystems of the German North and Baltic Sea. It describes the reactions of plants and animals (i.e. spiders, carabid beetles, bees and nematodes) on the future temperature and sea level increase. The combination of field and experimental studies is unique for Europe and for many parts of the world. It not only studies the actual elevation gradients and the climatic and saline gradients from West to East, but also the historical changes to document processes at coastal ecosystems that were already passed. In contrast to many books that studied the marine processes with similar backgrounds, this book concerns the terrestrial coastal ecosystems that were overall rarely studied and, in particular, never studied under this specific viewpoint

• 1. Introduction
• Part I. General Results : 2. General Intersections of Quadrics
• 3. General Operations on Intersections of Quadrics
• 4. Intersections of Coaxial Quadrics
• 5. Intersections of Coaxial Ellipsoids
• Part II. Topological Description of Transverse Intersections of Concentrie Ellipsoids : 6. Characterization of Connected Sums
• 7. Three Coaxial Ellipsoids
• 8. Three Concentric Ellipsoids
• 9. More Than Three Coaxial Ellipsoids
• 10. A Family of Surfaces That Are Intersections of Concentric, Non-Coaxial Ellipsoids
• Part III. Relations With Other Areas of Mathematics : 11. Dynamical Systems
• 12. Complex Geometry
• 13. Contact and Symplectic Geometry
• 14. Intersections with Dihedral Symmetry
• 15. Polyhedral Products
• Part IV. Appendices : A. Proof of Theorem 2.1
• B. Origins
• C. Complements of Products of Spheres in Spheres
• D. Diagonalizability of Matrices
• References
• Index

This book gives an overview of research in the topology and geometry of intersections of quadrics in Rn, with a focus on intersections of concentric ellipsoids and related spaces. Unifying and organizing material previously spread over many articles, it also contains new results. The first part provides very detailed foundations of a wide-ranging theory that could be useful for future developments. It includes chapters on general intersections of quadrics, operations on them, and intersections of concentric and coaxial quadrics. Moving from the general to the specific, the second part focuses on a topological description of transverse intersections of concentric ellipsoids, including a complete description of the case of three ellipsoids, and of some large families of more than three of them. The third part looks at relations to other areas of mathematics such as dynamical systems, complex geometry, contact and symplectic geometry, and other applications. An appendix gathers some technical items and also gives an account of the origins, motivations and progression of the subject, including historical recollections of the author, who has been central to its development--back cover

• Preface xv
• Chapter 1 Diversity, Classification, and Evolution of Vertebrates 1.1 The Vertebrate Story --Binominal nomenclature --Extant vertebrate groups 1.2 Phylogenetic Systematics 1.3 Applying Phylogenetic Criteria --Evaluating possible phylogenies --Molecules and morphology --The problem of dating --Dagger (DR) convention adopted in this book 1.4 Using Phylogenetic Trees --Extant phylogenetic brackets --Paraphyly --Crown and stem groups 1.5 Genetic Mechanisms of Evolutionary Change --Phenotypes and fitness --Developmental regulatory genes 1.6 Epigenetic Effects 1.7 Earth History and Vertebrate Evolution
• Chapter 2 What Is a Vertebrate?? 2.1 Vertebrates in Relation to Other Animals? 2.2 Characteristics of Chordates? --Chordate origins and evolution? --Extant nonvertebrate chordates? 2.3 What Distinguishes a Vertebrate?? 2.4 Vertebrate Embryonic Development? --Development of the body? --Development of the pharyngeal region? --Development of the brain? --Other neurogenic tissues of vertebrates? 2.5 Vertebrate Tissues? --Adult tissue types --Mineralized tissues 2.6 Vertebrate Organ Systems --Integumentary system --Skeletal system --Muscular system --Nervous system and sense organs --Endocrine system --Respiratory system --Circulatory system --Digestive system --Excretory and reproductive systems
• Chapter 3 Jawless Vertebrates and the Origin of Gnathostomes 3.1 Earliest Evidence of Vertebrates --Enigmas: DRConodonts and DRTullimonstrum ---Early mineralized tissues --Environment of early vertebrate evolution 3.2 Cyclostomes: Extant Jawless Vertebrate --Characters of cyclostomes --Hagfishes: Myxiniformes --Lampreys: Petromyzontiformes 3.3 Jawless Osteognathostomes 3.4 Gnathostome Body Plan --Gnathostome skeletons --What about soft anatomical features? 3.5 Origin of Jaws --Hypotheses of jaw origins --Importance of the nose --Selective value of jaws 3.6 Origin of Paired Appendages --Fin development and the lateral somitic frontier --Advantages of fins 3.7 Extinct Paleozoic Jawed Fishes
• Chapter 4 Living in Water 4.1 Aquatic Environment --Obtaining oxygen from water using gill --Obtaining oxygen from air using lungs and other respiratory structure --Adjusting buoyancy 4.2 Sensory World of Aquatic Vertebrates --Vision --Chemosensation: Olfaction and taste --Detecting water displacement --Hearing and equilibrium --Electroreception and electrogenesis 4.3 Maintaining an Internal Environment --Nitrogenous wastes and kidney --Osmoregulation --Regulation of ions and body fluids 4.4 Osmoregulation in Different Environments --Marine cartilaginous fishes and coelacanths --Marine teleosts --Freshwater teleosts and lissamphibians --Euryhaline vertebrates
• Chapter 5 Geography and Ecology of the Paleozoic 5.1 Deep Time --The Precambrian world --The Paleozoic 5.2 Continental Geography --Continental drift and plate tectonics --Shifting continents of the Paleozoic --Shifting continents and changing climates 5.3 Paleozoic Climates 5.4 Paleozoic Ecosystems --Aquatic life --Terrestrial flora --Terrestrial fauna 5.5 Extinctions
• Chapter 6 Origin and Radiation of Chondrichthyans 6.1 Acanthodii 6.2 Chondrichthyes --Habitats and diversity --Placoid scales --Cartilaginous skeleton --Teeth and tooth plates --Jaws and jaw suspension --Internal fertilization and claspers --Distinctive soft tissue and physiological features 6.3 Euchondrocephali and Chimaeriformes --Biology of extant Chimaeriformes 6.4 Elasmobranchii, Euselachii, and Neoselachii --Selachii: Sharks --Batomorphi: Skates and rays 6.5 Biology of Neoselachii --Feeding --Bioluminescence and biofluorescence ---Hypoxia and the epaulette shark --Endothermal heterothermy --Swimming --Reproduction --Elasmobranch brains --Social networks and migration in sand tiger sharks 6.6 Declining Elasmobranch Populations --Conservation and sawfishes --Threats to chondrichthyans --Vulnerabilities of chondrichthyans --Ecological impacts of shark population declines --Policies to protect sharks
• Chapter 7 Origin of Osteichthyes and Radiation of Actinopterygian 7.1 Osteichthyes, Actinopterygii, and Sarcopterygi --Osteichthyan character --Fin adaptations --Other differences between actinopterygians and sarcopterygians 7.2 Actinopterygii: Basal Group --Polypteriformes --Acipenseriformes --Neopterygii: Holostei --Neopterygii: Teleoste 7.3 Characters of Teleostei 7.4 Teleostei: Basal Groups --Elopomorpha --Osteoglossomorpha --Otocephala --Basal euteleosts 7.5 Teleostei: Acanthopterygii --Basal acanthopterygians --Percomorph 7.6 Swimming and Hydrodynamics --Generating forward thrust --Modes of locomotion --Speed and drag --Steering, stopping, and staying in place 7.7 Reproduction and Development --Oviparity --Viviparity --Sex change in teleosts 7.8 Ecology of Marine Teleosts --Black-water diving and larval teleosts --The photic zone and its subdivisions --Coral reef fishes --Pelagic and deep-sea fishes
• Chapter 8 Sarcopterygians and the Origin of Tetrapods 8.1 Phylogenetic Concepts of Tetrapoda and Characters for Sarcopterygii 8.2 The Miguasha Lagerstatte and the.
• (source: Nielsen Book Data)

Vertebrate Life distills the necessary information from vertebrate anatomy, physiology, ecology, and behavioral studies and then helps students see important connections across levels of biological scale. The result is students come to understand how organisms function effectively in their environments and how lineages of organisms change through evolutionary time. Processing complex detailed information about expansive phylogenies and diverse anatomies can be difficult for even the most motivated students, and Vertebrate Life addresses this challenge by combining appropriately-detailed, clearly-written text with outstanding phylogenies and figures, making it a thorough and engaging reference for students and instructors alike. The text's impressive illustration program helps students visualize complex concepts, allowing them to parse difficult anatomical information. The 11th edition will have an upgraded illustration program with several new and revised figures, including layered figures presented in the new enhanced eBook.
(source: Nielsen Book Data)

• The Wolf in the Human Mind Across Space and Time / Erwin van Maanen
• A History of Wolves and People in France / Jean-Marc Moriceau and P. van Maanen
• Wolves and Other Mammals Hunted in Medieval English Forests / Lee Raye
• 'Uuluesheued!' The Historical Significance of the Wolf to Early Indo-Europeans / Rob Lenders
• Wolves Behind Bars / Helen Cowie
• Nazi Werewolves from Outer Space: Posthuman-wolf-multiplicities and Their (Mis)appropriations / Jamie Mcphie
• Never Mind the Girl; What about the Wolf? / Marie Addyman
• Whose Wolf Is It Anyway? Wolves, Wilderness and Belonging / Chris Powici
• Defined 'as much by their absence as their iconography': Reimagining Wolves in Cumbria in Sarah Hall's The Wolf Border / Penny Bradshaw
• A 'Wasteland' Infested by Wolves: The Fallacy of 'Dark Age' England / Elizabeth Marshall
• The Wolf Pack / Peter Davis
• The Wolf in the Pastoral System of Southern France / Jean-Marc Landry and Jean-Luc Borelli
• Contemporary Public Images of the Wolf / Helene Figari and Ketil Skogen
• The Sweetness of Freedom: Reflections on the Occasion of the Japanese Wolf / Holger Funk
• Reimagining the Dingo: The 'Australian Wolf' or Just a Feral Dog? / Bradley P. Smith, Robert G. Appleby and Kylie M. Cairns
• Pushing the Ecological Niche: A Sea Wolf Called Takaya / Cheryl Alexander and Karen Lloyd
• 'Hunger-Greedy Appetite': The Wolf in Early-Modern English Natural History / Marie Addyman
• What About the Coywolf? / Javier D. Monzón
• Is that a Wolf? Politics, Science and Red Wolf Identity / Peter Brewitt and Lawson Giles
• The Thylacine: A Wolf in Name Only / Stephen R. Sleightholme and Cameron R. Campbell
• Landscapes of Coexistence: Livestock and Wolves in the Mountains of North Spain / Nigel Dykes
• The Wolves of Yellowstone: Saviours of the Songbird or Pieces of the Puzzle? / Rene Beyers, T.J. Clark-Wolf, Peter Brewitt, Owen Nevin and Ian Convery
• Wolf-Beaver Dynamics in the Greater Voyageurs Ecosystem, Minnesota / Thomas D. Gable, Sean Johnson-Bice, Austin T. Homkes, Steve K. Windels, John G. Bruggink and Joseph K. Bump
• The Return of the Wolf in Germany: A Success Story of Rewilding with a Future? / James Brückner and Erwin van Maanen
• Finding Common Ground with Wolves: Interspecies Communication is a Shared Landscape / Martin Drenthen
• The Case for Wolves in the UK / Ian Convery, Owen Nevin, Elsie Blackshaw-Crosby, Deborah Brady and Mark Fisher
• Tracking Wolves in Western Europe: A Photo-Essay / Photography by Marielle van Uitert and text by Karen Lloyd
• Speaking Out for Wolves: A Personal Reflection / Tracy Hayes
• To Receive the Wolf / Karen Lloyd
• Úlfr and Gris: Spectral Animal Companions of the Atomic Priest / Robert Williams
• The Three-Legged Stool: Wolves, Shepherds and Sheep / Lee Schofield
• The Helsfell Wolf / Karen Lloyd
• Afterword: The Ecological Disadvantage of Living on an Island / Mark Fisher

This abstract algebra textbook takes an integrated approach that highlights the similarities of fundamental algebraic structures among a number of topics. The book begins by introducing groups, rings, vector spaces, and fields, emphasizing examples, definitions, homomorphisms, and proofs. The goal is to explain how all of the constructions fit into an axiomatic framework and to emphasize the importance of studying those maps that preserve the underlying algebraic structure. This fast-paced introduction is followed by chapters in which each of the four main topics is revisited and deeper results are proven. The second half of the book contains material of a more advanced nature. It includes a thorough development of Galois theory, a chapter on modules, and short surveys of additional algebraic topics designed to whet the reader's appetite for further study. This book is intended for a first introduction to abstract algebra and requires only a course in linear algebra as a prerequisite. The more advanced material could be used in an introductory graduate-level course.
(source: Nielsen Book Data)

• The first germs of amenability: paradoxical decompositions
• Elementary amenable groups
• The topological full group of a Cantor minimal system
• Lamplighter actions and extensive amenability
• Amenability of topological full groups
• Subgroups of topological full groups of intermediate growth
• An amenability criterion via actions
• Groups acting on Bratteli diagrams
• Groups acting on rooted trees
• Definitions of amenability and basic facts

The main topic of the book is amenable groups, i.e., groups on which there exist invariant finitely additive measures. It was discovered that the existence or non-existence of amenability is responsible for many interesting phenomena such as, e.g., the Banach-Tarski Paradox about breaking a sphere into two spheres of the same radius. Since then, amenability has been actively studied and a number of different approaches resulted in many examples of amenable and non-amenable groups. In the book, the author puts together main approaches to study amenability. A novel feature of the book is that the exposition of the material starts with examples which introduce a method rather than illustrating it. This allows the reader to quickly move on to meaningful material without learning and remembering a lot of additional definitions and preparatory results; those are presented after analyzing the main examples. The techniques that are used for proving amenability in this book are mainly a combination of analytic and probabilistic tools with geometric group theory.
(source: Nielsen Book Data)