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• 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

This book provides an introduction to the study of the stochastic properties of probability preserving dynamical systems. Only the usual knowledge of the first year of a Master's degree is required. Many reminders are given. The definitions and results are illustrated by examples and corrected exercises. The book presents the notions of Poincaré's recurrence, of ergodicity, of mixing. It enlights also existing links between dynamical systems and Markov chains. The final objective of this book is to present three methods for establishing central limit theorems in the context of chaotic dynamical systems: a first method based on martingale approximations, a second method based on perturbation of quasi-compact linear operators and a third method based on decorrelation estimates

• Getting started
• A diversity of birds
• How to identify birds
• Understanding birds
• Field craft
• Birding at home
• Go farther

"Targeted to beginners and beyond, National Geographic's fun, inspiring guide to the art, craft, and science of bird-watching combines practical know-how and expert knowledge. Browsable and bursting with helpful illustrations and photographs, Birding Basics offers new ideas for when, where, and how to get to know the birds in your world. Not a field guide but a primer in best practices, authored by birding expert Noah Strycker, this breezy book features easy-to-follow advice on what to look and listen for, how to use field guides and birding apps, the best equipment to start with, and ways to engage with other birders around the world. Filled with fun facts and seasoned advice, this useful book will help you attract birds to your backyard, master bird identification, name a bird by its song, and witness the magic of migration. Sidebars feature fun facts, identification tips, and easy projects for exploring the world on the wing. For everyone who loves watching the birds, whether out the window or on the trail, this colorful, easy-to-use guide to better birding has everything you need"-- Provided by publisher

• I. Foundations. Evolution, science, and molecular biology ; DNA : the repository of biological information ; Chemical basis of information molecules ; Protein structure ; Protein function
• II. Nucleic acid structure and methods. DNA and RNA structure ; Studying genes ; Genomes, transcriptomes, and proteomes ; Topology : functional deformations of DNA ; Nucleosomes, chromatin, and chromosome structure
• III. Information transfer. DNA replication ; DNA mutation and repair ; Recombinational DNA repair and homologous recombination ; Site-specific recombination and transposition ; Transcription : DNA-dependent synthesis of RNA ; RNA processing ; The genetic code ; Protein synthesis
• IV. Regulation. Regulating the flow of information ; The regulation of gene expression in bacteria ; The transcriptional regulation of gene expression in eukaryotes ; The posttranscriptional regulation of gene expression in eukaryotes
• Model organisms appendix
• Glossary
• Solution to problems

Written and illustrated with unsurpassed clarity, "Molecular Biology: Principles and Practice" introduces fundamental concepts while exposing students to how science is done. The authors convey the sense of joy and excitement that comes from scientific discovery, highlighting the work of researchers who have shaped and who continue to shape the field today.See what's in the LaunchPad"

• Precambrian. Hadean; Archaean; Proterozoic; Ediacaran
• Palaeozoic. Cambrian; Ordovician; Silurian; Devonian; Carboniferous; Permian
• Mesozoic. Triassic; Jurassic; Cretaceous
• Cenozoic. Palaeogene; Neogene; Quaternary

"It is difficult to conceive of the vast scale of the history of life on Earth, from the very first living organisms sparking into life in hydrothermal deep-sea vents to the dizzying diversity of life today. The evolution of life is a sweeping epic of a tale, with twists and turns, surprising heroes and unlikely survivors. The Earth beautifully distils this complex story into a meaningful scale. In taking a closer look at 47 carefully selected organisms over fifteen periods in our planetary history, this book tells the whole story of life on Earth, and the interconnectedness that unites us through our ecosystems and planetary history. Prepare to be confounded by the ingenuity of evolutionary biologies, humbled by our own brief part in this epic history, and disquieted by our disproportionate impact on the world we call home"--Amazon

"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

• 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

• 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. Multivariant linear regression
• 2. Reduced-rank regression model
• 3. Reduced-rank regression modes with two sets of regressors
• 4. Reduced-rank regression model with autoregressive errors
• 5. Multiple time series modeling with reduced ranks
• 6. The growth curve model and reduced-rank regression methods
• 7. Seemingly unrelated regressions models with reduced ranks
• 8. Applications of reduced-rank regression in financial economics
• 9. Partially reduced-rank regression with grouped responses
• 10. High-dimensional reduced-rank regression
• 11. Unbiased risk estimation in reduced-rank regression
• 12. Generalized reduced-rank regression
• 13. Sparse reduced-rank regression
• Appendix

This book provides an account of multivariate reduced-rank regression, a tool of multivariate analysis that enjoys a broad array of applications. In addition to a historical review of the topic, its connection to other widely used statistical methods, such as multivariate analysis of variance (MANOVA), discriminant analysis, principal components, canonical correlation analysis, and errors-in-variables models, is also discussed. This new edition incorporates Big Data methodology and its applications, as well as high-dimensional reduced-rank regression, generalized reduced-rank regression with complex data, and sparse and low-rank regression methods. Each chapter contains developments of basic theoretical results, as well as details on computational procedures, illustrated with numerical examples drawn from disciplines such as biochemistry, genetics, marketing, and finance. This book is designed for advanced students, practitioners, and researchers, who may deal with moderate and high-dimensional multivariate data. Because regression is one of the most popular statistical methods, the multivariate regression analysis tools described should provide a natural way of looking at large (both cross-sectional and chronological) data sets. This book can be assigned in seminar-type courses taken by advanced graduate students in statistics, machine learning, econometrics, business, and engineering

"This textbook explores two distinct stochastic processes that evolve at random: weakly stationary processes and discrete parameter Markov processes. Building from simple examples, the authors focus on developing context and intuition before formalizing the theory of each topic. This inviting approach illuminates the key ideas and computations in the proofs, forming an ideal basis for further study. After recapping the essentials from Fourier analysis, the book begins with an introduction to the spectral representation of a stationary process. Topics in ergodic theory follow, including Birkhoff's Ergodic Theorem and an introduction to dynamical systems. From here, the Markov property is assumed and the theory of discrete parameter Markov processes is explored on a general state space. Chapters cover a variety of topics, including birth-death chains, hitting probabilities and absorption, the representation of Markov processes as iterates of random maps, and large deviation theory for Markov processes. A chapter on geometric rates of convergence to equilibrium includes a splitting condition that captures the recurrence structure of certain iterated maps in a novel way. A selection of special topics concludes the book, including applications of large deviation theory, the FKG inequalities, coupling methods, and the Kalman filter. Featuring many short chapters and a modular design, this textbook offers an in-depth study of stationary and discrete-time Markov processes. Students and instructors alike will appreciate the accessible, example-driven approach and engaging exercises throughout. A single, graduate-level course in probability is assumed."--Provided by publisher

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.

• Endless possibilities
• Life, the universe and everything
• The perfect circle
• Rock of ages
• A brief history of time
• Live free
• The magic orchid
• Does my dog love me?
• The universe through a keyhole

"The complete story of the universe and absolutely everything in it (minus the boring parts). Despite our clever linguistic abilities, humans are spectacularly ill-equipped to comprehend what's happening in the universe. Our senses and intuition routinely mislead us. "The Complete Guide to Absolutely Everything (Abridged)" tells the story of how we came to suppress our monkey minds and perceive the true nature of reality. Written with wit and humor, this brief book tells the story of science -- tales of fumbles and missteps, errors and egos, hard work, accidents, and some really bad decisions -- all of which have created the sum total of human knowledge. Geneticist Adam Rutherford and mathematician Hannah Fry guide readers through time and space, through our bodies and brains, showing how emotions shape our view of reality, how our minds tell us lies, and why a mostly bald and curious ape decided to begin poking at the fabric of the universe. Rutherford and Fry shine as science sleuths, wrestling with some truly head-scratching questions: Where did time come from? Do we have free will? Does my dog love me? Hilarious sidebars present memorable scientific oddities: for example, hypnotized snails, human-sized ants, and the average time it takes most animals to evacuate their bladders. (A surprisingly consistent twenty-one seconds, if you must know.) Both rigorous and playful, this book is a celebration of the weirdness of the cosmos, the strangeness of humans, and the joys and follies of scientific discovery"-- Provided by publisher

• Part I. Introduction to the Cell
• Chapter 1. Cells, genomes, and the diversity of life
• Chapter 2. Cell chemistry and bioenergetics
• Chapter 3. Proteins
• Part II. Basic Genetic Mechanisms
• Chapter 4. DNA, chromosomes, and genomes
• Chapter 5. DNA replication, repair, and recombination
• Chapter 6. How cells read the genome : From DNA to protein
• Chapter 7. Control of gene expression
• Part III. Ways of Working with Cells
• Chapter 8. Analyzing cells, molecules, and systems
• Chapter 9. Visualizing cells and their molecules
• Part IV. Internal Organization of the Cell
• Chapter 10. Membrane structure
• Chapter 11. Small-molecule transport and electrical properties of membranes
• Chapter 12. Intracellular organization and protein sorting
• Chapter 13. Intracellular membrane traffic
• Chapter 14. Energy conversion and metabolic compartmentation : Mitochondria and chloroplasts
• Chapter 15. Cell signaling
• Chapter 16. The cytoskeleton
• Chapter 17. The cell cycle
• Chapter 18. Cell death
• Part V. Cells in Their Social Context
• Chapter 19. Cell junctions and the extracellular matrix
• Chapter 20. Cancer
• Chapter 21. Development of multicellular organisms
• Chapter 22. Stem cells in tissue homeostasis and regeneration
• Chapter 23. Pathogens and infection
• Chapter 24. The innate and adaptive immune systems
• Glossary
• Index

For more than four decades, Molecular Biology of the Cell has distilled the vast amount of scientific knowledge to illuminate basic principles, enduring concepts, and cutting-edge research. The Seventh Edition has been extensively revised and updated with the latest research, and has been thoroughly vetted by experts and instructors. The classic companion text, The Problems Book, has been reimagined as the Digital Problems Book in Smartwork, an interactive digital assessment course with a wide selection of questions and automatic-grading functionality. The digital format with embedded animations and dynamic question types makes the Digital Problems Book in Smartwork easier to assign than ever before-for both in-person and online classes. .
(source: Nielsen Book Data)

• 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. The Study of Behavioral Endocrinology
• 2. The Endocrine System
• 3. Sex Differences in Behavior: Sex Determination and Differentiation
• 4. Sex Differences in Behavior: Animal Models and Humans
• 5. Male Reproductive Behavior
• 6. Female Reproductive Behavior
• 7. Parental Behavior
• 8. Hormones and Social Behavior
• 9. Homeostasis and Behavior
• 10. Biological Rhythms
• 11. Stress
• 12. Learning and Memory
• 13. Hormones and Affective Disorders Glossary Illustration Credits References Index.
• (source: Nielsen Book Data)

The market-leading text, An Introduction to Behavioral Endocrinology, Sixth Edition provides an updated, integrated presentation of the study of hormone-behavior-brain interactions. Maintaining a comparative approach, the text explores the endocrine mechanisms that have evolved in both human and nonhuman animals to solve common problems in survival and reproduction. The text describes interactions among hormones, brain, and behavior from a historical perspective, emphasizing connections among key theories and tracing the emergence of important hypotheses. The book is organized around the conceptual theme that hormones affect behavior by influencing one or more of three "components" of behaving animals-input mechanisms (such as sensory or perceptual processes), the central processing mechanisms of the nervous system (either directly, or by affecting its development or structure), and output mechanisms (such as effectors or peripheral structures). Despite increased coverage of molecular and cellular approaches, the book strives for accessibility for non-biological science students. An Introduction to Behavioral Endocrinology, Sixth Edition, is appropriate for upper-level undergraduate and graduate courses in psychology, biology, anthropology, or zoology. It contains several important pedagogical features: *Learning objectives are set out at the beginning of each chapter and now include 3 multiple choice questions per objective in the enhanced ebook. *Learning Activity in each chapter (new to this edition) *Key terms are defined in the margins throughout the text. *The text is richly illustrated with color photographs and drawings. *Chapter-end summaries restate important points. *Discussion questions and suggested further readings are also included in each chapter. *The text contains nearly 2,400 references to the literature in behavioral endocrinology. RESOURCES For Students As with previous editions, the book is accompanied by animations, video, web links, sound files, a complete glossary, and graphics-accessible via Oxford Learning Link-to aid in understanding the material in the text. This edition will also include an enhanced ebook. For Instructors -The Instructor's Resource Library includes electronic versions of all the textbook's figures and tables. All images are provided as both high- and low-resolution JPEGs, formatted and optimized for excellent legibility when projected. All figures and tables are also provided in ready-to-use PowerPoint presentations. -The Test Bank includes multiple-choice, short-answer, and essay questions for each chapter of the textbook. Prepared by the author, these questions are a helpful resource that can greatly speed the process of preparing exams and quizzes for the course.
(source: Nielsen Book Data)

• Part I. Measure Theory.-
• Chapter 1. Measurable Spaces.-
• Chapter 2. Integration of Measurable Functions.-
• Chapter 3. Construction of Measures.-
• Chapter 4. Lp Spaces.-
• Chapter 5. Product Measure.-
• Chapter 6. Signed Measures.-
• Chapter 7. Change of Variables.- Part II. Probability Theory.-
• Chapter 8. Foundations of Probability Theory.-
• Chapter 9. Independence.-
• Chapter 10. Convergence of Random Variables.-
• Chapter 11. Conditioning.- Part III. Stochastic Processes.-
• Chapter 12. Theory of Martingales.-
• Chapter 13. Markov Chains.-
• Chapter 14. Brownian Motion. .
• (source: Nielsen Book Data)

This textbook introduces readers to the fundamental notions of modern probability theory. The only prerequisite is a working knowledge in real analysis. Highlighting the connections between martingales and Markov chains on one hand, and Brownian motion and harmonic functions on the other, this book provides an introduction to the rich interplay between probability and other areas of analysis. Arranged into three parts, the book begins with a rigorous treatment of measure theory, with applications to probability in mind. The second part of the book focuses on the basic concepts of probability theory such as random variables, independence, conditional expectation, and the different types of convergence of random variables. In the third part, in which all chapters can be read independently, the reader will encounter three important classes of stochastic processes: discrete-time martingales, countable state-space Markov chains, and Brownian motion. Each chapter ends with a selection of illuminating exercises of varying difficulty. Some basic facts from functional analysis, in particular on Hilbert and Banach spaces, are included in the appendix. Measure Theory, Probability, and Stochastic Processes is an ideal text for readers seeking a thorough understanding of basic probability theory. Students interested in learning more about Brownian motion, and other continuous-time stochastic processes, may continue reading the author's more advanced textbook in the same series (GTM 274).
(source: Nielsen Book Data)

• A story to tell The hotel The hairy ball Let's make a deal The barber The Hilbert curve The prime shop The Wierstrass function A ham sandwich Monty Hall redux The salesman Hilbert hotel redux On principle Ellie The mountain On the surface A journey A random reunion An apology The mathemagician The sphere The hypothesis The cipher Appendices: More on
• Chapter 1 A story to tell More on
• Chapter 2 The hotel More on
• Chapter 3 The hairy ball More on
• Chapter 4 Let's make a deal More on
• Chapter 5 The barber shop More on
• Chapter 6 The Hilbert curve More on
• Chapter 7 The prime shop More on
• Chapter 8 The Wierstrass function More on
• Chapter 9 A ham sandwich More on
• Chapter 10 The Monty Hall redux More on
• Chapter 11 The salesman More on
• Chapter 12 The Hilbert hotel redux More on
• Chapter 13 On principle More on
• Chapter 14 Ellie More on
• Chapter 15 The mountain More on
• Chapter 16 on the surface More on
• Chapter 17 A journey More on
• Chapter 18 A random reunion More on
• Chapter 19 An apology More on
• Chapter 20 The mathemagician More on
• Chapter 21 The sphere More on
• Chapter 22 The hypothesis More on
• Chapter 23 The cipher Index.
• (source: Nielsen Book Data)

But when I turned the handle on the door, suddenly the buzzing went crazy. I slapped my hands over my ears, when I should have jerked the door shut. It flew open, and I was face-to-face with the Weierstrass function. It was the ugliest function I could imagine, with kinks, and kinks on kinks and kinks on those. And it was shrieking in its buzz-like way, vibrating all over like a plucked string. I stood there, frozen for just a second, and then I was sprinting after the others, with the wild frantic buzzing right behind me.'' From the twisted imagination of best-selling author Colin Adams (Zombies & Calculus, The Knot Book) comes this tale of sixteen-year-old Kallie trying to escape death at the hands of the exhibits in a mathematics museum. Kallie crosses paths with Carl Gauss, Bertrand Russell, Sophie Germain, G. H. Hardy, and John von Neumann, as she tries to save herself, her dad, and his colleague Maria from the deadly Hairy Ball theorem, the harrowing Hilbert Hotel, the bisecting Ham Sandwich machine, and a variety of other mathematical menaces. It's a wild romp through a mathematical bestiary featuring the bizarre, the exotic, and the counterintuitive. You'll never think of math the same way again.
(source: Nielsen Book Data)

• Introduction Integrability and symmetries of nonlinear differential and difference equations in two independent variables Symmetries as integrability criteria Construction of lattice equations and their Lax pair Transformation groups for quad lattice equations Algebraic entropy of the nonautonomous Boll equations Translation from Russian of R. I. Yamilov, ''On the classification of discrete eqautions'', reference [841] No quad-graph equation can have a generalized symmetry given by the narita-Itoh-Bogoyavlensky equation Bibliography Subject Index.
• (source: Nielsen Book Data)

This book on integrable systems and symmetries presents new results on applications of symmetries and integrability techniques to the case of equations defined on the lattice. This relatively new field has many applications, for example, in describing the evolution of crystals and molecular systems defined on lattices, and in finding numerical approximations for differential equations preserving their symmetries. The book contains three chapters and five appendices. The first chapter is an introduction to the general ideas about symmetries, lattices, differential difference and partial difference equations and Lie point symmetries defined on them. Chapter 2 deals with integrable and linearizable systems in two dimensions. The authors start from the prototype of integrable and linearizable partial differential equations, the Korteweg de Vries and the Burgers equations. Then they consider the best known integrable differential difference and partial difference equations. Chapter 3 considers generalized symmetries and conserved densities as integrability criteria. The appendices provide details which may help the readers' understanding of the subjects presented in Chapters 2 and 3. This book is written for PhD students and early researchers, both in theoretical physics and in applied mathematics, who are interested in the study of symmetries and integrability of difference equations.
(source: Nielsen Book Data)

'A must read for all wildlife lovers' Dominic Dyer Foxes, buzzards, crows, badgers, weasels, seals, kites - Britain and Ireland's predators are impressive and diverse and they capture our collective imagination. But many consider them to our competition, even our enemies. The problem is that predators eat what we farm or use for sport. From foxes and ravens attacking new-born lambs to weasels eating game-bird chicks, predators compete with us, putting them directly into the firing line. Farming, fishing, sport and leisure industries want to see numbers of predators reduced, and conservation organisations also worry that predators are threatening some endangered species. Other people, though, will go to great lengths to protect them from any harm. This clashing of worlds can be intense. So, what do we do? One of the greatest challenges facing conservation today is how, when and where to control predators. It is a highly charged debate. Mary Colwell travels across the UK and Ireland to encounter the predators face to face. She watches their lives in the wild and discovers how they fit into the landscape. She talks to the scientists studying them and the wildlife lovers who want to protect them. She also meets the people who want to control them to protect their livelihoods or sporting interests. In this even-handed exploration of the issues, Mary provides a thoughtful and reasoned analysis of the debates surrounding our bittersweet relationship with predators.
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• Foreword / by Costa Georgiadis
• My foraging journey
• Introduction
• Backyard
• Urban streets and parklands
• Sea
• River
• Forest
• Resources
• Notes

"A guide to finding, identifying, and eating wild plants. An essential for anyone interested in reviving the lost art of foraging."-- Publisher description

Drawing on the author's 35 years of experience in teaching freshman biology, fish biology, shark biology, ichthyology, physiology, and oceanography, as well as over 40 years as a researcher of shark biology, this book brings a wealth of knowledge and experience to bear on the topic of the biology of fishes. Written with an emphasis on clarity, the book contains almost 300 high-quality photographs, figures, and diagrams, as well as over 450 primary literature sources. It reflects the most recent research and trends in fish biology, and will be a welcome addition to any introductory fish biology class.
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• 1 Introduction.- 2 Resolution of Surface Singularities.- 3 The Link.- 4 Coverings.- 5 Examples.- 6 Invariants Associated With a Resolution.- 7 The Artin-Laufer Program.- 8 Multivariable Divisorial Filtration.- 9 Topological Invariants. The Seiberg-Witten Invariant.- 10 Ehrhart Theory and the Seiberg-Witten Invariant.- 11 Lattice Cohomology.- 12 Appendix. Complex Analytic Spaces.- References.- Index.
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This monograph provides a comprehensive introduction to the theory of complex normal surface singularities, with a special emphasis on connections to low-dimensional topology. In this way, it unites the analytic approach with the more recent topological one, combining their tools and methods. In the first chapters, the book sets out the foundations of the theory of normal surface singularities. This includes a comprehensive presentation of the properties of the link (as an oriented 3-manifold) and of the invariants associated with a resolution, combined with the structure and special properties of the line bundles defined on a resolution. A recurring theme is the comparison of analytic and topological invariants. For example, the Poincare series of the divisorial filtration is compared to a topological zeta function associated with the resolution graph, and the sheaf cohomologies of the line bundles are compared to the Seiberg-Witten invariants of the link. Equivariant Ehrhart theory is introduced to establish surgery-additivity formulae of these invariants, as well as for the regularization procedures of multivariable series. In addition to recent research, the book also provides expositions of more classical subjects such as the classification of plane and cuspidal curves, Milnor fibrations and smoothing invariants, the local divisor class group, and the Hilbert-Samuel function. It contains a large number of examples of key families of germs: rational, elliptic, weighted homogeneous, superisolated and splice-quotient. It provides concrete computations of the topological invariants of their links (Casson(-Walker) and Seiberg-Witten invariants, Turaev torsion) and of the analytic invariants (geometric genus, Hilbert function of the divisorial filtration, and the analytic semigroup associated with the resolution). The book culminates in a discussion of the topological and analytic lattice cohomologies (as categorifications of the Seiberg-Witten invariant and of the geometric genus respectively) and of the graded roots. Several open problems and conjectures are also formulated. Normal Surface Singularities provides researchers in algebraic and differential geometry, singularity theory, complex analysis, and low-dimensional topology with an invaluable reference on this rich topic, offering a unified presentation of the major results and approaches.
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It's time to shun our perfectionist society and discover the beauty in everything! Ugly-Cute is an adorkable compilation of misunderstood, underappreciated species including well-known lovable uggos, like sun bears and pugs, as well as obscure weirdos, like the star-nosed mole and the aye-aye. Each chapter is dedicated to a different ugly-cute animal and the ways in which we can learn from them. Featuring: 1. Pink Fairy Armadillo 2. Aye Aye 3. Star-nosed Mole 4. Wombat 5. Sucker-footed Bat 6. Sun Bear 7. Tapir 8. Anteater 9. White-faced Saki Monkey 10. Yeti Crab 11. Pug 12. Axolotl Salamander 13. Proboscis Monkey 14. Aquatic Scrotum Frog 15. Emu 16. Blobfish 17. Hairless Cat and more!.
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• 1 Some examples of causal convolutions.- 2 Convolution quadrature for hyperbolic symbols.- 3 Algorithms for CQ: linear multistep methods.- 4 Acoustic scattering in the time domain.- 5 Runge-Kutta CQ.- 6 Transient electromagnetism.- 7 Boundary-field formulations.- 8 Parabolic problems.- 9 Data sparse methods and other topics.
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This book provides a comprehensive analysis of time domain boundary integral equations and their discretisation by convolution quadrature and the boundary element method. Properties of convolution quadrature, based on both linear multistep and Runge-Kutta methods, are explained in detail, always with wave propagation problems in mind. Main algorithms for implementing the discrete schemes are described and illustrated by short Matlab codes; translation to other languages can be found on the accompanying GitHub page. The codes are used to present numerous numerical examples to give the reader a feeling for the qualitative behaviour of the discrete schemes in practice. Applications to acoustic and electromagnetic scattering are described with an emphasis on the acoustic case where the fully discrete schemes for sound-soft and sound-hard scattering are developed and analysed in detail. A strength of the book is that more advanced applications such as linear and non-linear impedance boundary conditions and FEM/BEM coupling are also covered. While the focus is on wave scattering, a chapter on parabolic problems is included which also covers the relevant fast and oblivious algorithms. Finally, a brief description of data sparse techniques and modified convolution quadrature methods completes the book. Suitable for graduate students and above, this book is essentially self-contained, with background in mathematical analysis listed in the appendix along with other useful facts. Although not strictly necessary, some familiarity with boundary integral equations for steady state problems is desirable.
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• Preface
• 1. Introduction
• Part I. The Homogenous Universe: 2. The expanding universe
• 3. The hot Big Bang
• 4. Cosmological inflation
• Part II. The Inhomogenous Universe: 5. Structure formation
• 6. Relativistic perturbation theory
• 7. Cosmic microwave background
• 8. Quantum initial conditions
• 9. Outlook
• Appendices: Index.
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The author - a leading theoretical cosmologist - expands on his widely acclaimed lecture notes in this self-contained textbook, suitable for the advanced undergraduate or starting graduate level. Presenting the key theoretical foundations of cosmology and describing the observations that have turned the subject into a precision science, the author keeps the student in mind on every page by explaining concepts step-by-step, in an approachable manner. After describing the dynamics of the homogeneous universe, the book traces the evolution of small density fluctuations, which were created quantum-mechanically during inflation and are today observed in the cosmic microwave background and the large-scale structure of the universe. The book is ideally suited as a course companion or for self-study. With all necessary background material covered, students have everything they need to establish an unrivalled understanding of the subject. Complete with many worked examples, figures, and homework problems, this textbook is a definitive resource for advanced students in physics, astronomy and applied mathematics.
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• 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.
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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.
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• Introduction: Life itself
• 1. Discovering the nanocosm
• 2. The path of carbon
• 3. From gases to life
• 4. Revolutions
• 5. To the dark side
• 6. The flux capacitor
• Epilogue: Self
• Envoi: 'Like Most Revelations'
• The forward Krebs cycle
• The reverse Krebs cycle
• Appendix 1: red protein mechanics
• Appendix 2: the Krebs line

What brings the Earth to life, and our own lives to an end? For decades, biology has been dominated by the study of genetic information. Information is important, but it is only part of what makes us alive. Our inheritance also includes our living metabolic network, a flame passed from generation to generation, right back to the origin of life. In Transformer, biochemist Nick Lane reveals a scientific renaissance that is hiding in plain sight -how the same simple chemistry gives rise to life and causes our demise. Lane is among the vanguard of researchers asking why the Krebs cycle, the "perfect circle" at the heart of metabolism, remains so elusive more than eighty years after its discovery. Transformer is Lane's voyage, as a biochemist, to find the inner meaning of the Krebs cycle-and its reverse-why it is still spinning at the heart of life and death today. Lane reveals the beautiful, violent world within our cells, where hydrogen atoms are stripped from the carbon skeletons of food and fed to the ravenous beast of oxygen. Yet this same cycle, spinning in reverse, also created the chemical building blocks that enabled the emergence of life on our planet. Now it does both. How can the same pathway create and destroy? What might our study of the Krebs cycle teach us about the mysteries of aging and the hardest problem of all, consciousness? Transformer unites the story of our planet with the story of our cells-what makes us the way we are, and how it connects us to the origin of life. Enlivened by Lane's talent for distilling and humanizing complex research, Transformer offers an essential read for anyone fascinated by biology's great mysteries. Life is at root a chemical phenomenon: this is its deep logic.
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• 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.
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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.
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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.
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• Background material Conservation-Learning how to count The diffusion equation-Derivations Realizations of a diffusion process Solutions of the diffusion equation Diffusion and reaction The bistable equation-Part I: Derivations The bistable equation-Part II: Analysis Advection and reaction Advection with diffusion Chemotaxis Spatial patterns Dispersal-renewal theory Collective behavior Introduction to Matlab Constants, units, and functions Selected answers to exercises Bibliography Index.
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How do biological objects communicate, make structures, make measurements and decisions, search for food, i.e., do all the things necessary for survival? Designed for an advanced undergraduate audience, this book uses mathematics to begin to tell that story. It builds on a background in multivariable calculus, ordinary differential equations, and basic stochastic processes and uses partial differential equations as the framework within which to explore these questions.
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• Basic notions of probability Gaussian processes Properties of Brownian motion Martingales Ito calculus Multivariate Ito calculus Ito processes and stochastic differential equations The Markov property Change of probability Applications to mathematical finance Bibliography Index.
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A First Course in Stochastic Calculus is a complete guide for advanced undergraduate students to take the next step in exploring probability theory and for master's students in mathematical finance who would like to build an intuitive and theoretical understanding of stochastic processes. This book is also an essential tool for finance professionals who wish to sharpen their knowledge and intuition about stochastic calculus. Louis-Pierre Arguin offers an exceptionally clear introduction to Brownian motion and to random processes governed by the principles of stochastic calculus. The beauty and power of the subject are made accessible to readers with a basic knowledge of probability, linear algebra, and multivariable calculus. This is achieved by emphasizing numerical experiments using elementary Python coding to build intuition and adhering to a rigorous geometric point of view on the space of random variables. This unique approach is used to elucidate the properties of Gaussian processes, martingales, and diffusions. One of the book's highlights is a detailed and self-contained account of stochastic calculus applications to option pricing in finance.
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• Congruence and rigid motions Axioms for the plane Existence and properties of reflections Congruence of triangles Rotation and orientation Half-turns and inequalities in triangles Parallel lines and translations Dilations and similarity Area and its applications Products and patterns Coordinate geometry Bibliography Index.
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Many paths lead into Euclidean plane geometry. Geometry Transformed offers an expeditious yet rigorous route using axioms based on rigid motions and dilations. Since transformations are available at the outset, interesting theorems can be proved sooner; and proofs can be connected to visual and tactile intuition about symmetry and motion. The reader thus gains valuable experience thinking with transformations, a skill that may be useful in other math courses or applications. For students interested in teaching mathematics at the secondary school level, this approach is particularly useful since geometry in the Common Core State Standards is based on rigid motions. The only prerequisite for this book is a basic understanding of functions. Some previous experience with proofs may be helpful, but students can also learn about proofs by experiencing them in this book--in a context where they can draw and experiment. The eleven chapters are organized in a flexible way to suit a variety of curriculum goals. In addition to a geometrical core that includes finite symmetry groups, there are additional topics on circles and on crystallographic and frieze groups, and a final chapter on affine and Cartesian coordinates. The exercises are a mixture of routine problems, experiments, and proofs. This book is published in cooperation with IAS/Park City Mathematics Institute.
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• Numbers Spaces Functions Calculus Further topics in analysis Complementary results Bibliography Index.
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This is a text for students who have had a three-course calculus sequence and who are ready to explore the logical structure of analysis as the backbone of calculus. It begins with a development of the real numbers, building this system from more basic objects (natural numbers, integers, rational numbers, Cauchy sequences), and it produces basic algebraic and metric properties of the real number line as propositions, rather than axioms. The text also makes use of the complex numbers and incorporates this into the development of differential and integral calculus. For example, it develops the theory of the exponential function for both real and complex arguments, and it makes a geometrical study of the curve (expit)(expit), for real tt, leading to a self-contained development of the trigonometric functions and to a derivation of the Euler identity that is very different from what one typically sees. Further topics include metric spaces, the Stone-Weierstrass theorem, and Fourier series.
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• Background. Multivariable differential calculus. Multivariable integral calculus and calculus on surfaces. Differential forms and the Gauss-Green-Stokes formula. Applications of the Gauss-Green-Stokes formula. Differential geometry of surfaces. Fourier analysis. Complementary material. Bibliography. Index.
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This text was produced for the second part of a two-part sequence on advanced calculus, whose aim is to provide a firm logical foundation for analysis. The first part treats analysis in one variable, and the text at hand treats analysis in several variables. After a review of topics from one-variable analysis and linear algebra, the text treats in succession multivariable differential calculus, including systems of differential equations, and multivariable integral calculus. It builds on this to develop calculus on surfaces in Euclidean space and also on manifolds. It introduces differential forms and establishes a general Stokes formula. It describes various applications of Stokes formula, from harmonic functions to degree theory. The text then studies the differential geometry of surfaces, including geodesics and curvature, and makes contact with degree theory, via the Gauss-Bonnet theorem. The text also takes up Fourier analysis, and bridges this with results on surfaces, via Fourier analysis on spheres and on compact matrix groups.
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• Single differential equations Linear algebra Linear systems of differential equations Nonlinear systems of differential equations Bibliography Index.
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This text introduces students to the theory and practice of differential equations, which are fundamental to the mathematical formulation of problems in physics, chemistry, biology, economics, and other sciences. The book is ideally suited for undergraduate or beginning graduate students in mathematics, and will also be useful for students in the physical sciences and engineering who have already taken a three-course calculus sequence. This second edition incorporates much new material, including sections on the Laplace transform and the matrix Laplace transform, a section devoted to Bessel's equation, and sections on applications of variational methods to geodesics and to rigid body motion. There is also a more complete treatment of the Runge-Kutta scheme, as well as numerous additions and improvements to the original text. Students finishing this book will be well prepared for advanced studies in dynamical systems, mathematical physics, and partial differential equations.
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• Vector spaces, linear transformations, and matrices Eigenvalues, eigenvectors, and generalized eigenvectors Linear algebra on inner product spaces Further basic concepts: duality, convexity, positivity Multilinear algebra Linear algebra over more general fields Rings and modules Special structures in linear algebra Complementary results Bibliography Index.
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This text develops linear algebra with the view that it is an important gateway connecting elementary mathematics to more advanced subjects, such as advanced calculus, systems of differential equations, differential geometry, and group representations. The purpose of this book is to provide a treatment of this subject in sufficient depth to prepare the reader to tackle such further material. The text starts with vector spaces, over the sets of real and complex numbers, and linear transformations between such vector spaces. Later on, this setting is extended to general fields. The reader will be in a position to appreciate the early material on this more general level with minimal effort. Notable features of the text include a treatment of determinants, which is cleaner than one often sees, and a high degree of contact with geometry and analysis, particularly in the chapter on linear algebra on inner product spaces. In addition to studying linear algebra over general fields, the text has a chapter on linear algebra over rings. There is also a chapter on special structures, such as quaternions, Clifford algebras, and octonions.
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• Introduction
• Chapter 1. Basic Notations
• Chapter 2. Congruences
• Chapter 3. Congruences of Higher Degree
• Chapter 4. Legendre and Jacobi Symbols
• Chapter 5. Prime Numbers
• Chapter 6. Arithmetic Functions
• Chapter 7. Diophantine Equations
• Chapter 8. Diophantine Approximation
• Chapter 9. Algebraic and Transcendental Numbers
• Chapter 10. Algebraic Number Fields
• Chapter 11. Ideals
• Chapter 12. Combinatorial Number Theory Answers and Hints Historical Notes Tables Index.
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Number Theory is a newly translated and revised edition of the most popular introductory textbook on the subject in Hungary. The book covers the usual topics of introductory number theory: divisibility, primes, Diophantine equations, arithmetic functions, and so on. It also introduces several more advanced topics including congruences of higher degree, algebraic number theory, combinatorial number theory, primality testing, and cryptography. The development is carefully laid out with ample illustrative examples and a treasure trove of beautiful and challenging problems. The exposition is both clear and precise. The book is suitable for both graduate and undergraduate courses with enough material to fill two or more semesters and could be used as a source for independent study and capstone projects. Freud and Gyarmati are well-known mathematicians and mathematical educators in Hungary, and the Hungarian version of this book is legendary there. The authors' personal pedagogical style as a facet of the rich Hungarian tradition shines clearly through. It will inspire and exhilarate readers.
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• Basic definitions First-order PDEs and the method of characteristics The wave equation in one space dimension The wave equation in three and two space dimensions The delta ""function"" and distributions in one space dimension The Fourier transform The diffusion equation The Laplacian, Laplace's equation, and harmonic functions Distributions in higher dimensions and partial differentiation in the sense of distributions The fundamental solution for Green's functions for the Laplacian Fourier series The separation of variables algorithm for boundary value problems Uniting the big three second-order linear equations and what's next Objects and tools of advanced calculus Bibliography Index.
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While partial differential equations (PDEs) are fundamental in mathematics and throughout the sciences, most undergraduate students are only exposed to PDEs through the method of separation of variations. This text is written for undergraduate students from different cohorts with one sole purpose: to facilitate a proficiency in many core concepts in PDEs while enhancing the intuition and appreciation of the subject. For mathematics students this will in turn provide a solid foundation for graduate study. A recurring theme is the role of concentration as captured by Dirac's delta function. This both guides the student into the structure of the solution to the diffusion equation and PDEs involving the Laplacian and invites them to develop a cognizance for the theory of distributions. Both distributions and the Fourier transform are given full treatment. The book is rich with physical motivations and interpretations, and it takes special care to clearly explain all the technical mathematical arguments, often with pre-motivations and post-reflections. Through these arguments the reader will develop a deeper proficiency and understanding of advanced calculus. While the text is comprehensive, the material is divided into short sections, allowing particular issues/topics to be addressed in a concise fashion. Sections which are more fundamental to the text are highlighted, allowing the instructor several alternative learning paths. The author's unique pedagogical style also makes the text ideal for self-learning.
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Contains two double-sided photo chartsCharts feature more than 160 grassesCharts are water resistant and field friendlyPerfect companion to the Photographic Guide.
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