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Taschenbuch. Zustand: Neu. Neuware -Hidden from human view, accessible only to sensitive receivers attached to huge radio telescopes, giant versions of backyard satellite dishes, the invisible universe beyond our senses continues to fascinate and intrigue our imaginations. We cannot really comprehend what it means to say that a galaxy is exploding, yet that is the nature of some of the distant radio sources in the furthest reaches of space. Closer to home, in the Milky Way galaxy, radio astronomers listen patiently to the ticking of pulsars that tell of star death and states of matter of awesome densities. And between the stars, radio emission from a host of over 120 complex molecules radiate outward to reveal a tale about chemical processes that produce the very stuff of life. And all of this happens out there in the universe hidden from our eyes, even when aided by the Hubble Space Telescope.This is the story of radio astronomy, of how radio waves are generated by stars, supernova, quasars, colliding galaxies, and by the very beginnings of the universe itself. In The Invisible Universe, you learn what astronomers are doing with those huge dishes in the New Mexico desert, in a remote valley in Puerto Rico, in the green Pocahontas Valley in West Virginia, as well as dozens of other remote sites around the world. With each of these observatories, the scientists collect and analyze their data, 'listening' to the radio signals from space, in order to learn what is out there, and perhaps even if someone else may be listening as well.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 172 pp. Englisch.

Taschenbuch. Zustand: Neu. Neuware -Over the last 15 years or so there has been a huge increase in the popularity of astrophotography with the advent of digital SLR cameras and CCD imagers. These have enabled astronomers to take many images and, indeed, check images as they scan the skies. Processing techniques using computer software have also made ¿developing¿ these images more accessible to those of us who are ¿chemically challenged!¿ And let¿s face it ¿ some of the pictures you see these days in magazines, books, and on popular web forums are, frankly, amazing! So, why bother looking through the eyepiece you ask Well, for one thing, setting up the equipment is quicker. You just take your ¿scope out of the garage or, if yoüre lucky enough to own one, open the roof of your observatory, align the ¿scope and off you go. If you have an equatorial mount, yoüll still need to roughly polar align, but this really takes only a few moments. The ¿imager¿ would most likely need to spend more time setting up. This would include very accurate polar alignment (for equatorial mounts), then finding a guide star using his or her finder, checking the software is functioning properly, and c- tinuous monitoring to make sure the alignment is absolutely precise throu- out the imaging run. That said, an imager with a snug ¿obsy¿ at the end of the garden will have a quicker time setting up, but then again so will the ¿visual¿ observer.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 448 pp. Englisch.

Taschenbuch. Zustand: Neu. Neuware -From reviews of the first edition:'In the world of mathematics, the 1980's might well be described as the 'decade of the fractal'. Starting with Benoit Mandelbrot's remarkable text The Fractal Geometry of Nature, there has been a deluge of books, articles and television programmes about the beautiful mathematical objects, drawn by computers using recursive or iterative algorithms, which Mandelbrot christened fractals. Gerald Edgar's book is a significant addition to this deluge. Based on a course given to talented high- school students at Ohio University in 1988, it is, in fact, an advanced undergraduate textbook about the mathematics of fractal geometry, treating such topics as metric spaces, measure theory, dimension theory, and even some algebraic topology.the book also contains many good illustrations of fractals (including 16 color plates).'Mathematics Teaching'The book can be recommended to students who seriously want to know about the mathematical foundation of fractals, and to lecturers who want to illustrate a standard course in metric topology by interesting examples.'Christoph Bandt, Mathematical Reviews'.not only intended to fit mathematics students who wish to learn fractal geometry from its beginning but also students in computer science who are interested in the subject. Especially, for the last students the author gives the required topics from metric topology and measure theory on an elementary level. The book is written in a very clear style and contains a lot of exercises which should be worked out.'H.Haase, ZentralblattAbout the second edition: Changes throughout the text, taking into account developments in the subject matter since 1990; Major changes in chapter 6. Since 1990 it has become clear that there are two notions of dimension that play complementary roles, so the emphasis on Hausdorff dimension will be replaced by the two: Hausdorff dimension and packing dimension. 6.1 will remain, but a new section on packing dimension will follow it, then the old sections 6.2--6.4 will be re-written to show both types of dimension; Substantial change in chapter 7: new examples along with recent developments; Sections rewritten to be made clearer and more focused.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 296 pp. Englisch.

Taschenbuch. Zustand: Neu. Neuware -Blending algebra, analysis, and topology, the study of compact Lie groups is one of the most beautiful areas of mathematics and a key stepping stone to the theory of general Lie groups. Assuming no prior knowledge of Lie groups, this book covers the structure and representation theory of compact Lie groups. Included is the construction of the Spin groups, Schur Orthogonality, the Peter-Weyl Theorem, the Plancherel Theorem, the Maximal Torus Theorem, the Commutator Theorem, the Weyl Integration and Character Formulas, the Highest Weight Classification, and the Borel-Weil Theorem. The necessary Lie algebra theory is also developed in the text with a streamlined approach focusing on linear Lie groups.Key Features are: - Provides an approach that minimizes advanced prerequisites; - Self-contained and systematic exposition requiring no previous exposure to Lie theory; -Advances quickly to the Peter-Weyl Theorem and its corresponding Fourier theory; - Streamlined Lie algebra discussion reduces the differential geometry prerequisite and allows a more rapid transition to the classification and construction of representations - Exercises sprinkled throughout.This beginning graduate level text, aimed primarily at Lie Groups courses and related topics, assumes familiarity with elementary concepts from group theory, analysis, and manifold theory. Students, research mathematicians, and physicists interested in Lie theory will find this text very useful.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 212 pp. Englisch.

Taschenbuch. Zustand: Neu. Neuware -Studying Human Populations is a textbook for graduate students and research workers in social statistics and related subject areas. It follows a novel curriculum developed around the basic statistical activities of sampling, measurement and inference. Statistics is defined broadly as making decisions in the presence of uncertainty that arises as a consequence of limited resources available for collecting information. A connecting link of the presented methods is the perspective of missing information, catering for a diverse class of problems that include nonresponse, imperfect measurement and causal inference. In principle, any problem too complex for our limited analytical toolkit could be converted to a tractable problem if some additional information were available. Ingenuity is called for in declaring such (missing) information constructively, but the universe of problems that we can address is wide open, not limited by a discrete set of procedures.The monograph aims to prepare the reader for the career of an independent social statistician and to serve as a reference for methods, ideas for and ways of studying human populations: formulation of the inferential goals, design of studies, search for the sources of relevant information, analysis and presentation of results. Elementary linear algebra and calculus are prerequisites, although the exposition is quite forgiving, especially in the first few chapters. Familiarity with statistical software at the outset is an advantage, but it can be developed concurrently with studying the text.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 496 pp. Englisch.

Buch. Zustand: Neu. Neuware -This volume will be the only existing single-authored book offering a science-based breeder¿s manual directed at breeding for water-limited environments. Plant breeding is characterized by the need to integrate information from diverse disciplines towards the development and delivery of a product defines as a new cultivar. Conventional breeding draws information from disciplines such as genetics, plant physiology, plant pathology, entomology, food technology and statistics. Plant breeding for water-limited environments and the development of drought resistant crop cultivars is considered as one of the more difficult areas in plant breeding while at the same time it is becoming a very pressing issue. This volume is unique and timely in that it develops realistic solutions and protocols towards the breeding of drought resistant cultivars by integrating knowledge from environmental science, plant physiology, genetics and molecular biology.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 272 pp. Englisch.

Taschenbuch. Zustand: Neu. Neuware -Banach algebras are Banach spaces equipped with a continuous multipli- tion. In roughterms,there arethree types ofthem:algebrasofboundedlinear operators on Banach spaces with composition and the operator norm, al- bras consisting of bounded continuous functions on topological spaces with pointwise product and the uniform norm, and algebrasof integrable functions on locally compact groups with convolution as multiplication. These all play a key role in modern analysis. Much of operator theory is best approached from a Banach algebra point of view and many questions in complex analysis (such as approximation by polynomials or rational functions in speci c - mains) are best understood within the framework of Banach algebras. Also, the study of a locally compact Abelian group is closely related to the study 1 of the group algebra L (G). There exist a rich literature and excellent texts on each single class of Banach algebras, notably on uniform algebras and on operator algebras. This work is intended as a textbook which provides a thorough introduction to the theory of commutative Banach algebras and stresses the applications to commutative harmonic analysis while also touching on uniform algebras. In this sense and purpose the book resembles Larsen¿s classical text [75] which shares many themes and has been a valuable resource. However, for advanced graduate students and researchers I have covered several topics which have not been published in books before, including some journal articles.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 368 pp. Englisch.

Taschenbuch. Zustand: Neu. Neuware -Just over ten years ago when the first drafts of this book were being written, and even more so a few years after that as it was making its way through the publication process, alpine skiing was experiencing what eventually became a complete revolution in equipment and tech nique: 'shaped' or 'parabolic' skis completely took over the market, and even relatively beginning skiers expected to carve graceful turns as they schussed down the slopes. Re-reading our work with an eye to revision, we have been surprised to see how our focus on the physics of skiing in the first edition al lowed us to recognize the fundamental importance of what were then quite novel changes in equipment and technique. The essence of the enhancement offered by shaped skis is their greater sidecut radius. Our original discussion (then and now in Chapters 3 and 4) of the crucial role that a ski's sidecut plays in carving a turn caused us to write, for the most part, as if the shaped ski had always been in existence. Sim ilarly, our interest in the geometry ofthe sidecut allowed us to discuss snowboards in some detail as well, for the key to their ability to 'shred' down the mountain is their deep sidecut.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 288 pp. Englisch.

Taschenbuch. Zustand: Neu. Neuware -As a student I discovered in our library a thin booklet by Frederick Mosteller entitled50 Challenging Problems in Probability. Itreferredtoas- plementary ¿regular textbook¿ by William Feller, An Introduction to Pro- bilityTheoryanditsApplications.SoItookthisonealong,too,andstartedon the rst of Mosteller¿s problems on the train riding home. From that evening, I caught on to probability. These two books were not primarily about abstract formalisms but rather about basic modeling ideas and about ways ¿ often extremely elegant ones ¿ to apply those notions to a surprising variety of empirical phenomena. Essentially, these books taught the reader the skill to ¿think probabilistically¿ and to apply simple probability models to real-world problems. The present book is in this tradition; it is based on the view that those cognitive skills are best acquired by solving challenging, nonstandard pro- bility problems. My own experience, both in learning and in teaching, is that challenging problems often help to develop, and to sharpen, our probabilistic intuition much better than plain-style deductions from abstract concepts.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 140 pp. Englisch.

Taschenbuch. Zustand: Neu. Neuware -A self-contained introduction to probability, exchangeability and Bayes¿ rule provides a theoretical understanding of the applied material. Numerous examples with R-code that can be run 'as-is' allow the reader to perform the data analyses themselves. The development of Monte Carlo and Markov chain Monte Carlo methods in the context of data analysis examples provides motivation for these computational methods.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 284 pp. Englisch.

Taschenbuch. Zustand: Neu. Neuware -This book is devoted to the study of variational methods in imaging. The presentation is mathematically rigorous and covers a detailed treatment of the approach from an inverse problems point of view. Many numerical examples accompany the theory throughout the text. It is geared towards graduate students and researchers in applied mathematics. Researchers in the area of imaging science will also find this book appealing. It can serve as a main text in courses in image processing or as a supplemental text for courses on regularization and inverse problems at the graduate level.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 336 pp. Englisch.

Taschenbuch. Zustand: Neu. Neuware -The theory of elliptic curves is distinguished by its long history and by the diversity of the methods that have been used in its study. This book treats the arithmetic approach in its modern formulation, through the use of basic algebraic number theory and algebraic geometry. Following a brief discussion of the necessary algebro-geometric results, the book proceeds with an exposition of the geometry and the formal group of elliptic curves, elliptic curves over finite fields, the complex numbers, local fields, and global fields. Final chapters deal with integral and rational points, including Siegels theorem and explicit computations for the curve Y = X + DX, while three appendices conclude the whole: Elliptic Curves in Characteristics 2 and 3, Group Cohomology, and an overview of more advanced topics.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 536 pp. Englisch.

Buch. Zustand: Neu. Neuware -In this text, integral geometry deals with Radon¿s problem of representing a function on a manifold in terms of its integrals over certain submanifolds¿hence the term the Radon transform. Examples and far-reaching generalizations lead to fundamental problems such as: (i) injectivity, (ii) inversion formulas, (iii) support questions, (iv) applications (e.g., to tomography, partial di erential equations and group representations). For the case of the plane, the inversion theorem and the support theorem have had major applications in medicine through tomography and CAT scanning. While containing some recent research, the book is aimed at beginning graduate students for classroom use or self-study. A number of exercises point to further results with documentation. From the reviews: ¿Integral Geometry is a fascinating area, where numerous branches of mathematics meet together. the contents of the book is concentrated around the duality and double vibration, which is realized through the masterful treatment of a variety of examples. the book is written by an expert, who has made fundamental contributions to the area.¿ ¿Boris Rubin, Louisiana State UniversitySpringer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 316 pp. Englisch.

Taschenbuch. Zustand: Neu. Neuware -Conics and Cubics is an accessible introduction to algebraic curves. Its focus on curves of degree at most three keeps results tangible and proofs transparent. Theorems follow naturally from high school algebra and two key ideas, homogeneous coordinates and intersection multiplicities.By classifying irreducible cubics over the real numbers and proving that their points form Abelian groups, the book gives readers easy access to the study of elliptic curves. It includes a simple proof of Bezout¿s Theorem on the number of intersections of two curves.The book is a text for a one-semester course. The course can serve either as the one undergraduate geometry course taken by mathematics majors in general or as a sequel to college geometry for prospective or current teachers of secondary school mathematics. The only prerequisite is first-year calculus.The new edition additionally discusses the use of power series to parametrize curves and analyze intersection multiplicities and envelopes.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 356 pp. Englisch.

Taschenbuch. Zustand: Neu. Neuware -Although the rst decades of the 20th century saw some strong debates on set theory and the foundation of mathematics, afterwards set theory has turned into a solid branch of mathematics, indeed, so solid, that it serves as the foundation of the whole building of mathematics. Later generations, honest to Hilbert¿s dictum, ¿No one can chase us out of the paradise that Cantor has created for us¿ proved countless deep and interesting theorems and also applied the methods of set theory to various problems in algebra, topology, in nitary combinatorics, and real analysis. The invention of forcing produced a powerful, technically sophisticated tool for solving unsolvable problems. Still, most results of the pre-Cohen era can be digested with just the knowledge of a commonsense introduction to the topic. And it is a worthy e ort, here we refer not just to usefulness, but, rst and foremost, to mathematical beauty. In this volume we o er a collection of various problems in set theory. Most of classical set theory is covered, classical in the sense that independence methods are not used, but classical also in the sense that most results come fromtheperiod,say,1920¿1970.Manyproblemsarealsorelatedtoother elds of mathematics such as algebra, combinatorics, topology, and real analysis. We do not concentrate on the axiomatic framework, although some - pects, such as the axiom of foundation or the role ¿ of the axiom of choice, are elaborated.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 528 pp. Englisch.

Taschenbuch. Zustand: Neu. Neuware -Digital Signal Processing for Measurement Systems: Theory and Applications covers the theoretical as well as the practical issues which form the basis of the modern DSP-based instruments and measurement methods. It covers the basics of DSP theory before discussing the critical aspects of DSP unique to measurement science.Key Features:Approaches signal processing through a unique measurement science perspectiveCovers both theory and state-of-the-art applications, from the sampling theorem to the design of FIR/IIR filtersIncludes important topics, for example, problems that arise when sampling periodic signals and the relationship between the sampling rate and the SNRSpringer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 284 pp. Englisch.

Taschenbuch. Zustand: Neu. Neuware -Concentrating on the rationale for the analyses, the difficulties posed by their interpretation, easily understood solutions, and useful problem sets, this book will help clinical investigators understand multiple analysis procedures and key issues. It is written for advanced medical students, clinical investigators at all levels, research groups within the pharmaceutical industry, regulators at the local, state, and federal level, and biostatisticians.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 464 pp. Englisch.

Taschenbuch. Zustand: Neu. Neuware -How to solve partial differential systems by completing the square. This could well have been the title of this monograph as it grew into a project to develop a s- tematic approach for associating suitable nonnegative energy functionals to a large class of partial differential equations (PDEs) and evolutionary systems. The minima of these functionals are to be the solutions we seek, not because they are critical points (i. e. , from the corresponding Euler-Lagrange equations) but from also - ing zeros of these functionals. The approach can be traced back to Bogomolnyi¿s trick of ¿completing squares¿ in the basic equations of quantum eld theory (e. g. , Yang-Mills, Seiberg-Witten, Ginzburg-Landau, etc. ,), which allows for the deri- tion of the so-called self (or antiself) dual version of these equations. In reality, the ¿self-dual Lagrangians¿ we consider here were inspired by a variational - proach proposed ¿ over 30 years ago ¿ by Brezis ¿ and Ekeland for the heat equation and other gradient ows of convex energies. It is based on Fenchel-Legendre - ality and can be used on any convex functional ¿ not just quadratic ones ¿ making them applicable in a wide range of problems. In retrospect, we realized that the ¿- ergy identities¿ satis ed by Leray¿s solutions for the Navier-Stokes equations are also another manifestation of the concept of self-duality in the context of evolution equations.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 368 pp. Englisch.

Taschenbuch. Zustand: Neu. Neuware -Authoritative Communities: The Scientific Case for Nurturing the Whole Child introduces innovative solutions based firmly in the children¿s mental health and resilience literature and in the hypothesis that humans are 'hardwired to connect.' These 'authoritative communities' consist of such individuals and institutions as parents, teachers, coaches, elders, and a variety of organizations that are committed to each other¿s well-being over the long-term and who instill children with prosocial values such as empathy and compassion. Living within these communities enables children and youth to develop a consistent sense of purpose and meaning, so that they, in turn, are able to grow up to be responsible, productive, and nurturing adults.The comprehensive coverage in this volume bring new insights and evidence to the nature/nurture debate from developmental, attachment, neurobiological, spiritual, and community perspectives, including:Nurturing as a protective factor against genetic predispositions.Counteracting the adverse influence of the media on children.Promoting a sense of community in disadvantaged youth.Spiritual approaches, from the Buddhist 'minding children with mindfulness' to traditional young men¿s rites of passage.Adolescent development, from psychobiology to the formation of conscience.Dispatches from the civil society movement, the School Development Program, and the motherhood movement.This volume is essential reading for researchers and practitioners as well as graduate-level students in developmental, clinical, and social psychology as well as related fields such as sociology, social work, education, and religious studies.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 412 pp. Englisch.

Taschenbuch. Zustand: Neu. Neuware -Matrix-Based Multigrid introduces and analyzes the multigrid approach for the numerical solution of large sparse linear systems arising from the discretization of elliptic partial differential equations. Special attention is given to the powerful matrix-based-multigrid approach, which is particularly useful for problems with variable coefficients and nonsymmetric and indefinite problems. This book can be used as a textbook in courses in numerical analysis, numerical linear algebra, and numerical PDEs at the advanced undergraduate and graduate levels in computer science, math, and applied math departments. The theory is written in simple algebraic terms and therefore requires preliminary knowledge only in basic linear algebra and calculus.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 344 pp. Englisch.

Taschenbuch. Zustand: Neu. Neuware -This is a book about prime numbers, congruences, secret messages, and elliptic curves that you can read cover to cover. It grew out of undergr- uate courses that the author taught at Harvard, UC San Diego, and the University of Washington. The systematic study of number theory was initiated around 300B. C. when Euclid proved that there are in nitely many prime numbers, and also cleverly deduced the fundamental theorem of arithmetic, which asserts that every positive integer factors uniquely as a product of primes. Over a thousand years later (around 972A. D. ) Arab mathematicians formulated the congruent number problem that asks for a way to decide whether or not a given positive integer n is the area of a right triangle, all three of whose sides are rational numbers. Then another thousand years later (in 1976), Di e and Hellman introduced the rst ever public-key cryptosystem, which enabled two people to communicate secretely over a public communications channel with no predeterminedsecret; this invention and the ones that followed it revolutionized the world of digital communication. In the 1980s and 1990s, elliptic curves revolutionized number theory, providing striking new insights into the congruent number problem, primality testing, publ- key cryptography, attacks on public-key systems, and playing a central role in Andrew Wiles¿ resolution of Fermat¿s Last Theorem.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 180 pp. Englisch.

Taschenbuch. Zustand: Neu. Neuware -Radio astronomy is far from being beyond the scope of amateurs astronomers, and this practical, self-contained guide for the newcomer to practical radio astronomey is an ideal introduction. This guide is a must for anyone who wants to join the growing ranks of 21st Century backyard radio astronomers.The first part of the book provides background material and explains (in a non-mathematical way) our present knowledge of the stronger radio sources ¿ those observable by amateurs ¿ including the Sun, Jupiter, Meteors, Galactic and extra-galactic sources.The second part of the book deals not only with observing, but ¿ assuming no prior technical knowledge of electronics or radio theory ¿ takes the reader step-by-step through the process of building and using a backyard radio telescope.There are complete, detailed plans and construction information for a number of amateur radio telescopes, the simplest of which can be put together and working ¿ using only simple tools ¿ in a weekend. For other instruments, there are full details of circuit-board layouts, components to use and (vitally important in radio astronomy) how to construct antennae for radio astronomy.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 252 pp. Englisch.

Taschenbuch. Zustand: Neu. Neuware -In developing the tools necessary for the study of complex manifolds, this comprehensive, well-organized treatment presents in its opening chapters a detailed survey of recent progress in four areas: geometry (manifolds with vector bundles), algebraic topology, differential geometry, and partial differential equations. Subsequent chapters then develop such topics as Hermitian exterior algebra and the Hodge \*-operator, harmonic theory on compact manifolds, differential operators on a Kahler manifold, the Hodge decomposition theorem on compact Kahler manifolds, the Hodge-Riemann bilinear relations on Kahler manifolds, Griffiths's period mapping, quadratic transformations, and Kodaira's vanishing and embedding theorems.The third edition of this standard reference contains a new appendix by Oscar Garcia-Prada which gives an overview of the developments in the field during the decades since the book appeared.From a review of the 2nd Edition:¿.the new edition ofProfessor Wells' book is timely and welcome.an excellent introduction for any mathematician who suspects that complex manifold techniques may be relevant to his work.¿Nigel Hitchin, Bulletin of the London Mathematical Society¿Its purpose is to present the basics of analysis and geometry on compact complex manifolds, and is already one of the standard sources for this material.¿Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 316 pp. Englisch.

Taschenbuch. Zustand: Neu. Neuware -Explains why dwarf planets and the larger asteroids are being studied in depth todayProvides background material for those who have been following the Dawn space missionHelps prepare both experienced amateurs and newcomers in their efforts to detect and observe these bodies; the book can also serve as a handy reference for any astronomy librarySpringer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 264 pp. Englisch.

Taschenbuch. Zustand: Neu. Neuware -Categories for the Working Mathematician provides an array of general ideas useful in a wide variety of fields. Starting from the foundations, this book illuminates the concepts of category, functor, natural transformation, and duality. The book then turns to adjoint functors, which provide a description of universal constructions, an analysis of the representations of functors by sets of morphisms, and a means of manipulating direct and inverse limits. These categorical concepts are extensively illustrated in the remaining chapters, which include many applications of the basic existence theorem for adjoint functors. The categories of algebraic systems are constructed from certain adjoint-like data and characterized by Beck's theorem. After considering a variety of applications, the book continues with the construction and exploitation of Kan extensions. This second edition includes a number of revisions and additions, including two new chapters on topics of active interest. One is onsymmetric monoidal categories and braided monoidal categories and the coherence theorems for them. The second describes 2-categories and the higher dimensional categories which have recently come into prominence. The bibliography has also been expanded to cover some of the many other recent advances concerning categories.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 332 pp. Englisch.

Taschenbuch. Zustand: Neu. Neuware -For the third edition, the author has added a new chapter on associative algebras that includes the well known characterizations of the finite-dimensional division algebras over the real field (a theorem of Frobenius) and over a finite field (Wedderburn's theorem); polished and refined some arguments (such as the discussion of reflexivity, the rational canonical form, best approximations and the definitions of tensor products); upgraded some proofs that were originally done only for finite-dimensional/rank cases; added new theorems, including the spectral mapping theorem; corrected all known errors;the reference section has been enlarged considerably, with over a hundred references to books on linear algebra.From the reviews of the second edition:¿In this 2nd edition, the author has rewritten the entire book and has added more than 100 pages of new materials. ¿ As in the previous edition, the text is well written and gives a thorough discussion of many topics of linear algebra and related fields. ¿ the exercises are rewritten and expanded. ¿ Overall, I found the book a very useful one. ¿ It is a suitable choice as a graduate text or as a reference book.¿Ali-Akbar Jafarian, ZentralblattMATH¿This is a formidable volume, a compendium of linear algebra theory, classical and modern ¿ . The development of the subject is elegant ¿ . The proofs are neat ¿ . The exercise sets are good, with occasional hints given for the solution of trickier problems. ¿ It represents linear algebra and does so comprehensively.¿Henry Ricardo, MathDLSpringer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 544 pp. Englisch.

Taschenbuch. Zustand: Neu. Neuware - Multigrid methods are often used for solving partial differential equations. This book introduces and analyzes the multigrid approach. The approach used here applies to both test problems on rectangular grids and to more realistic applications with complicated grids and domains. Key Features of this Second Edition:- Discusses multigrid methods from the domain decomposition viewpoint, thus making the material accessible to beginning undergraduate/graduate students - Uses the semialgebraic multigrid approach to handle complex topics (such as the solution of systems of PDEs)- Provides relevant and insightful exercises at the end of each chapter which help reinforce the material- Uses numerous illustrations and examples to motivate the subject matter- Covers important applications in physics, engineering and computer scienceMatrix-Based Multigrid can serve as a textbook for courses in numerical linear algebra, numerical methods for PDEs, and computational physics at the advanced undergraduate and graduate levels. Since most of the background material is covered, the only prerequisites are elementary linear algebra and calculus.Excerpts from the reviews of the first edition: 'This book contains a wealth of information about using multilevel methods to solve partial differential equations (PDEs). . . A common matrix-based framework for developing these methods is used throughout the book. This approach allows methods to be developed for problems under three very different conditions. . . This book will be insightful for practitioners in the field. . . students will enjoy studying this book to see how the many puzzle pieces of the multigrid landscape fit together.' (Loyce Adams, SIAM review, Vol. 47(3), 2005)'The discussion very often includes important applications in physics, engineering, and computer science.The style is clear, the details can be understood without any serious prerequisite. The usage of multigrid method for unstructured grids is exhibited by a well commented C++ program. This way the book is suitable for anyone . . . who needs numerical solution of partial differential equations.' (Peter Hajnal, Acta Scientiarum Mathematicarum, Vol. 70, 2004).

Taschenbuch. Zustand: Neu. Neuware -TheclassicaltheoryofFourierseriesandintegrals,aswellasLaplacetra- forms, is of great importance for physical and technical applications, and its mathematical beauty makes it an interesting study for pure mathema- cians as well. I have taught courses on these subjects for decades to civil engineeringstudents,andalsomathematicsmajors,andthepresentvolu me can be regarded as my collected experiences from this work. There is, of course, an unsurpassable book on Fourier analysis, the tr- tise by Katznelson from 1970. That book is, however, aimed at mathem- ically very mature students and can hardly be used in engineering courses. Ontheotherendofthescale,thereareanumberofmore-or-lesscookbo- styled books, where the emphasis is almost entirely on applications. I have felt the need for an alternative in between these extremes: a text for the ambitious and interested student, who on the other hand does not aspire to become an expert in the eld. There do exist a few texts that ful ll these requirements (see the literature list at the end of the book), but they do not include all the topics I like to cover in my courses, such as Laplace transforms and the simplest facts about distributions.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 288 pp. Englisch.

Taschenbuch. Zustand: Neu. Neuware -This work is aimed at an audience with a sound mathematical background wishing to learn about the rapidly expanding eld of mathematical nance. Its content is suitable particularly for graduate students in mathematics who have a background in measure theory and probability. The emphasis throughout is on developing the mathematical concepts required for the theory within the context of their application. No attempt is made to cover the bewildering variety of novel (or ¿exotic¿) nancial - struments that now appear on the derivatives markets; the focus throu- out remains on a rigorous development of the more basic options that lie at the heart of the remarkable range of current applications of martingale theory to nancial markets. The rst ve chapters present the theory in a discrete-time framework. Stochastic calculus is not required, and this material should be accessible to anyone familiar with elementary probability theory and linear algebra. The basic idea of pricing by arbitrage (or, rather, by non-arbitrage) is presented in Chapter 1. The unique price for a European option in a single-period binomial model is given and then extended to multi-period binomial models. Chapter 2 introduces the idea of a martingale measure for price processes. Following a discussion of the use of self- nancing tr- ing strategies to hedge against trading risk, it is shown how options can be priced using an equivalent measure for which the discounted price p- cess is a martingale.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 368 pp. Englisch.

Taschenbuch. Zustand: Neu. Neuware -Kurt Hensel (1861-1941) discovered the p-adic numbers around the turn of the century. These exotic numbers (or so they appeared at first) are now well-established in the mathematical world and used more and more by physicists as well. This book offers a self-contained presentation of basic p-adic analysis. The author is especially interested in the analytical topics in this field. Some of the features which are not treated in other introductory p-adic analysis texts are topological models of p-adic spaces inside Euclidean space, a construction of spherically complete fields, a p-adic mean value theorem and some consequences, a special case of Hazewinkel's functional equation lemma, a remainder formula for the Mahler expansion, and most importantly a treatment of analytic elements.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 460 pp. Englisch.