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Author: Loring W. Tu
Publisher: Springer Science & Business Media
ISBN: 1441974008
Category : Mathematics
Languages : en
Pages : 426
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Book Description
Manifolds, the higher-dimensional analogs of smooth curves and surfaces, are fundamental objects in modern mathematics. Combining aspects of algebra, topology, and analysis, manifolds have also been applied to classical mechanics, general relativity, and quantum field theory. In this streamlined introduction to the subject, the theory of manifolds is presented with the aim of helping the reader achieve a rapid mastery of the essential topics. By the end of the book the reader should be able to compute, at least for simple spaces, one of the most basic topological invariants of a manifold, its de Rham cohomology. Along the way, the reader acquires the knowledge and skills necessary for further study of geometry and topology. The requisite point-set topology is included in an appendix of twenty pages; other appendices review facts from real analysis and linear algebra. Hints and solutions are provided to many of the exercises and problems. This work may be used as the text for a one-semester graduate or advanced undergraduate course, as well as by students engaged in self-study. Requiring only minimal undergraduate prerequisites, 'Introduction to Manifolds' is also an excellent foundation for Springer's GTM 82, 'Differential Forms in Algebraic Topology'.
Author: Loring W. Tu
Publisher: Springer Science & Business Media
ISBN: 1441974008
Category : Mathematics
Languages : en
Pages : 426
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Book Description
Manifolds, the higher-dimensional analogs of smooth curves and surfaces, are fundamental objects in modern mathematics. Combining aspects of algebra, topology, and analysis, manifolds have also been applied to classical mechanics, general relativity, and quantum field theory. In this streamlined introduction to the subject, the theory of manifolds is presented with the aim of helping the reader achieve a rapid mastery of the essential topics. By the end of the book the reader should be able to compute, at least for simple spaces, one of the most basic topological invariants of a manifold, its de Rham cohomology. Along the way, the reader acquires the knowledge and skills necessary for further study of geometry and topology. The requisite point-set topology is included in an appendix of twenty pages; other appendices review facts from real analysis and linear algebra. Hints and solutions are provided to many of the exercises and problems. This work may be used as the text for a one-semester graduate or advanced undergraduate course, as well as by students engaged in self-study. Requiring only minimal undergraduate prerequisites, 'Introduction to Manifolds' is also an excellent foundation for Springer's GTM 82, 'Differential Forms in Algebraic Topology'.
Author: Sheldon Axler
Publisher: Springer Science & Business Media
ISBN: 1475781377
Category : Mathematics
Languages : en
Pages : 266
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Book Description
This book is about harmonic functions in Euclidean space. This new edition contains a completely rewritten chapter on spherical harmonics, a new section on extensions of Bochers Theorem, new exercises and proofs, as well as revisions throughout to improve the text. A unique software package supplements the text for readers who wish to explore harmonic function theory on a computer.
Author: Paul A. Calter
Publisher: John Wiley & Sons
ISBN: 0470534923
Category : Mathematics
Languages : en
Pages : 836
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Book Description
This textbook has been in constant use since 1980, and this edition represents the first major revision of this text since the second edition. It was time to select, make hard choices of material, polish, refine, and fill in where needed. Much has been rewritten to be even cleaner and clearer, new features have been introduced, and some peripheral topics have been removed. The authors continue to provide real-world, technical applications that promote intuitive reader learning. Numerous fully worked examples and boxed and numbered formulas give students the essential practice they need to learn mathematics. Computer projects are given when appropriate, including BASIC, spreadsheets, computer algebra systems, and computer-assisted drafting. The graphing calculator has been fully integrated and calculator screens are given to introduce computations. Everything the technical student may need is included, with the emphasis always on clarity and practical applications.
Author: Ronald Christensen
Publisher: Springer Science & Business Media
ISBN: 0387226249
Category : Mathematics
Languages : en
Pages : 498
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Book Description
The primary focus here is on log-linear models for contingency tables, but in this second edition, greater emphasis has been placed on logistic regression. The book explores topics such as logistic discrimination and generalised linear models, and builds upon the relationships between these basic models for continuous data and the analogous log-linear and logistic regression models for discrete data. It also carefully examines the differences in model interpretations and evaluations that occur due to the discrete nature of the data. Sample commands are given for analyses in SAS, BMFP, and GLIM, while numerous data sets from fields as diverse as engineering, education, sociology, and medicine are used to illustrate procedures and provide exercises. Throughoutthe book, the treatment is designed for students with prior knowledge of analysis of variance and regression.
Author: Henk C.A. van Tilborg
Publisher: Springer Science & Business Media
ISBN: 0306470535
Category : Computers
Languages : en
Pages : 496
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Book Description
The protection of sensitive information against unauthorized access or fraudulent changes has been of prime concern throughout the centuries. Modern communication techniques, using computers connected through networks, make all data even more vulnerable for these threats. Also, new issues have come up that were not relevant before, e. g. how to add a (digital) signature to an electronic document in such a way that the signer can not deny later on that the document was signed by him/her. Cryptology addresses the above issues. It is at the foundation of all information security. The techniques employed to this end have become increasingly mathematical of nature. This book serves as an introduction to modern cryptographic methods. After a brief survey of classical cryptosystems, it concentrates on three main areas. First of all, stream ciphers and block ciphers are discussed. These systems have extremely fast implementations, but sender and receiver have to share a secret key. Public key cryptosystems (the second main area) make it possible to protect data without a prearranged key. Their security is based on intractable mathematical problems, like the factorization of large numbers. The remaining chapters cover a variety of topics, such as zero-knowledge proofs, secret sharing schemes and authentication codes. Two appendices explain all mathematical prerequisites in great detail. One is on elementary number theory (Euclid's Algorithm, the Chinese Remainder Theorem, quadratic residues, inversion formulas, and continued fractions). The other appendix gives a thorough introduction to finite fields and their algebraic structure.
Author: Aris Spanos
Publisher: Cambridge University Press
ISBN: 1107185149
Category : Business & Economics
Languages : en
Pages : 787
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Book Description
This empirical research methods course enables informed implementation of statistical procedures, giving rise to trustworthy evidence.
Author: Michael Joswig
Publisher: American Mathematical Society
ISBN: 1470466538
Category : Mathematics
Languages : en
Pages : 398
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Book Description
The goal of this book is to explain, at the graduate student level, connections between tropical geometry and optimization. Building bridges between these two subject areas is fruitful in two ways. Through tropical geometry optimization algorithms become applicable to questions in algebraic geometry. Conversely, looking at topics in optimization through the tropical geometry lens adds an additional layer of structure. The author covers contemporary research topics that are relevant for applications such as phylogenetics, neural networks, combinatorial auctions, game theory, and computational complexity. This self-contained book grew out of several courses given at Technische Universität Berlin and elsewhere, and the main prerequisite for the reader is a basic knowledge in polytope theory. It contains a good number of exercises, many examples, beautiful figures, as well as explicit tools for computations using $texttt{polymake}$.
Author: Barry Nelson
Publisher: Springer Science & Business Media
ISBN: 146146160X
Category : Business & Economics
Languages : en
Pages : 285
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Book Description
This graduate-level text covers modeling, programming and analysis of simulation experiments and provides a rigorous treatment of the foundations of simulation and why it works. It introduces object-oriented programming for simulation, covers both the probabilistic and statistical basis for simulation in a rigorous but accessible manner (providing all necessary background material); and provides a modern treatment of experiment design and analysis that goes beyond classical statistics. The book emphasizes essential foundations throughout, rather than providing a compendium of algorithms and theorems and prepares the reader to use simulation in research as well as practice. The book is a rigorous, but concise treatment, emphasizing lasting principles but also providing specific training in modeling, programming and analysis. In addition to teaching readers how to do simulation, it also prepares them to use simulation in their research; no other book does this. An online solutions manual for end of chapter exercises is also provided.
Author: Alan D. Lopez
Publisher: World Bank Publications
ISBN: 0821362631
Category : Medical
Languages : en
Pages : 511
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Book Description
Strategic health planning, the cornerstone of initiatives designed to achieve health improvement goals around the world, requires an understanding of the comparative burden of diseases and injuries, their corresponding risk factors and the likely effects of invervention options. The Global Burden of Disease framework, originally published in 1990, has been widely adopted as the preferred method for health accounting and has become the standard to guide the setting of health research priorities. This publication sets out an updated assessment of the situation, with an analysis of trends observed since 1990 and a chapter on the sensitivity of GBD estimates to various sources of uncertainty in methods and data.
Author: Stef Maruch
Publisher: John Wiley & Sons
ISBN: 1118084845
Category : Computers
Languages : en
Pages : 443
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Book Description
Python is one of the most powerful, easy-to-read programming languages around, but it does have its limitations. This general purpose, high-level language that can be extended and embedded is a smart option for many programming problems, but a poor solution to others. Python For Dummies is the quick-and-easy guide to getting the most out of this robust program. This hands-on book will show you everything you need to know about building programs, debugging code, and simplifying development, as well as defining what actions it can perform. You’ll wrap yourself around all of its advanced features and become an expert Python user in no time. This guide gives you the tools you need to: Master basic elements and syntax Document, design, and debug programs Work with strings like a pro Direct a program with control structures Integrate integers, complex numbers, and modules Build lists, stacks, and queues Create an organized dictionary Handle functions, data, and namespace Construct applications with modules and packages Call, create, extend, and override classes Access the Internet to enhance your library Understand the new features of Python 2.5 Packed with critical idioms and great resources to maximize your productivity, Python For Dummies is the ultimate one-stop information guide. In a matter of minutes you’ll be familiar with Python’s building blocks, strings, dictionaries, and sets; and be on your way to writing the program that you’ve dreamed about!
