Kooperativer Bibliotheksverbund

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Format: 1 Online-Ressource (x, 344 p.) , 24 cm

Edition: Online-Ausgabe Elsevier e-book collection on ScienceDirect Sonstige Standardnummer des Gesamttitels: 041169-3

ISBN: 0444861351 , 9780444861351

Series Statement: North-Holland mathematics studies 48

Note: Includes index

Additional Edition: Reproduktion von Mathematicians and their times c1981

Language: English

Keywords: Mathematik ; Geschichte

URL: Volltext

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Format: 340 S. , Ill.

ISBN: 0812910885

Language: English

Subjects: Art History

Keywords: USA ; Architektur ; Geschichte 1974-1983 ; Architektur ; Geschichte 1974-1983 ; USA ; Architektur ; Geschichte 1914-1983 ; Architektur ; USA ; Geschichte 1974-1983 ; USA ; Architektur ; Geschichte 1900-2000 ; USA ; Design ; Geschichte 1900-2000 ; Aufsatzsammlung

UID:

Format: XXV, 677, [64] Seiten , Ill.

Series Statement: A New York Times book 4917

Language: English

Keywords: Historische Darstellung ; Historische Darstellung

UID:

Format: XXVI, 847 p. , online resource.

ISBN: 9781461252085

Series Statement: Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics, 262

Content: Potential theory and certain aspects of probability theory are intimately related, perhaps most obviously in that the transition function determining a Markov process can be used to define the Green function of a potential theory. Thus it is possible to define and develop many potential theoretic concepts probabilistically, a procedure potential theorists observe withjaun­ diced eyes in view of the fact that now as in the past their subject provides the motivation for much of Markov process theory. However that may be it is clear that certain concepts in potential theory correspond closely to concepts in probability theory, specifically to concepts in martingale theory. For example, superharmonic functions correspond to supermartingales. More specifically: the Fatou type boundary limit theorems in potential theory correspond to supermartingale convergence theorems; the limit properties of monotone sequences of superharmonic functions correspond surprisingly closely to limit properties of monotone sequences of super­ martingales; certain positive superharmonic functions [supermartingales] are called "potentials," have associated measures in their respective theories and are subject to domination principles (inequalities) involving the supports of those measures; in each theory there is a reduction operation whose properties are the same in the two theories and these reductions induce sweeping (balayage) of the measures associated with potentials, and so on.

Note: 1 Classical and Parabolic Potential Theory -- I Introduction to the Mathematical Background of Classical Potential Theory -- II Basic Properties of Harmonic, Subharmonic, and Superharmonic Functions -- III Infima of Families of Superharmonic Functions -- IV Potentials on Special Open Sets -- V Polar Sets and Their Applications -- VI The Fundamental Convergence Theorem and the Reduction Operation -- VII Green Functions -- VIII The Dirichlet Problem for Relative Harmonic Functions -- IX Lattices and Related Classes of Functions -- X The Sweeping Operation -- XI The Fine Topology -- XII The Martin Boundary -- XIII Classical Energy and Capacity -- XIV One-Dimensional Potential Theory -- XV Parabolic Potential Theory: Basic Facts -- XVI Subparabolic, Superparabolic, and Parabolic Functions on a Slab -- XVII Parabolic Potential Theory (Continued) -- XVIII The Parabolic Dirichlet Problem, Sweeping, and Exceptional Sets -- XIX The Martin Boundary in the Parabolic Context -- 2 Probabilistic Counterpart of Part 1 -- I Fundamental Concepts of Probability -- II Optional Times and Associated Concepts -- III Elements of Martingale Theory -- IV Basic Properties of Continuous Parameter Supermartingales -- V Lattices and Related Classes of Stochastic Processes -- VI Markov Processes -- VII Brownian Motion -- VIII The Itô Integral -- IX Brownian Motion and Martingale Theory -- X Conditional Brownian Motion -- 3 -- I Lattices in Classical Potential Theory and Martingale Theory -- II Brownian Motion and the PWB Method -- III Brownian Motion on the Martin Space -- Appendixes -- Appendix I -- Analytic Sets -- 1. Pavings and Algebras of Sets -- 2. Suslin Schemes -- 3. Sets Analytic over a Product Paving -- 4. Analytic Extensions versus ? Algebra Extensions of Pavings -- 7. Projections of Sets in Product Pavings -- 8. Extension of a Measurability Concept to the Analytic Operation Context -- 10. Polish Spaces -- 11. The Baire Null Space -- 12. Analytic Sets -- 13. Analytic Subsets of Polish Spaces -- II Appendix -- Capacity Theory -- 1. Choquet Capacities -- 2. Sierpinski Lemma -- 3. Choquet Capacity Theorem -- 4. Lusin’s Theorem -- 5. A Fundamental Example of a Choquet Capacity -- 6. Strongly Subadditive Set Functions -- 7. Generation of a Choquet Capacity by a Positive Strongly Subadditive Set Function -- 8. Topological Precapacities -- 9. Universally Measurable Sets -- III Appendix -- Lattice Theory -- 1. Introduction -- 2. Lattice Definitions -- 3. Cones -- 4. The Specific Order Generated by a Cone -- 5. Vector Lattices -- 6. Decomposition Property of a Vector Lattice -- 7. Orthogonality in a Vector Lattice -- 8. Bands in a Vector Lattice -- 9. Projections on Bands -- 10. The Orthogonal Complement of a Set -- 11. The Band Generated by a Single Element -- 12. Order Convergence -- 13. Order Convergence on a Linearly Ordered Set -- IV Appendix -- Lattice Theoretic Concepts in Measure Theory -- 1. Lattices of Set Algebras -- 2. Measurable Spaces and Measurable Functions -- 3. Composition of Functions -- 4. The Measure Lattice of a Measurable Space -- 5. The o Finite Measure Lattice of a Measurable Space (Notation of Section 4) -- 6. The Hahn and Jordan Decompositions -- 8. Absolute Continuity and Singularity -- 9. Lattices of Measurable Functions on a Measure Space -- 10. Order Convergence of Families of Measurable Functions -- 11. Measures on Polish Spaces -- 12. Derivates of Measures -- V Appendix -- Uniform Integrability -- VI Appendix -- Kernels and Transition Functions -- 1. Kernels -- 2. Universally Measurable Extension of a Kernel -- 3. Transition Functions -- VII Appendix -- Integral Limit Theorems -- 1. An Elementary Limit Theorem -- 2. Ratio Integral Limit Theorems -- 3. A One-Dimensional Ratio Integral Limit Theorem -- 4. A Ratio Integral Limit Theorem Involving Convex Variational Derivates -- VIII Appendix -- Lower Semicontinuous Functions -- The Lower Semicontinuous Smoothing of a Function -- Suprema of Families of Lower Semicontinuous Functions -- Choquet Topological Lemma -- Historical Notes -- 1 -- 2 -- 3 -- Appendixes -- Notation Index.

In: Springer eBooks

Additional Edition: Printed edition: ISBN 9781461297383

Language: English

DOI: 10.1007/978-1-4612-5208-5

URL: http://dx.doi.org/10.1007/978-1-4612-5208-5

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Format: VIII, 364 p. 3 illus. , online resource.

ISBN: 9781468494037

Series Statement: Lecture Notes in Statistics, 25

Content: With the support of the Office of Naval Research Program on Statistics and Probability (Dr. Edward J. Wegman, Director), The Department of Statistics at Texas A&M University hosted a Symposium on Time Series Analysis of Irregularly Observed Data during the period February 10-13, 1983. The symposium aimed to provide a review of the state of the art, define outstanding problems for research by theoreticians, transmit to practitioners recently developed algorithms, and stimulate interaction between statisticians and researchers in subject matter fields. Attendance was limited to actively involved researchers. This volume contains refereed versions of the papers presented at the Symposium. We would like to express our appreciation to the many colleagues and staff members whose cheerful help made the Symposium a successful happening which was enjoyed socially and intellectually by all participants. I would like to especially thank Dr. Donald W. Marquardt whose interest led me to undertake to organize this Symposium. This volume is dedicated to the world wide community of researchers who develop and apply methods of statistical analysis of time series. r:;) \J Picture Caption Participants in Symposium on Time Series Analysis of Irregularly Observed Data at Texas A&M University, College Station, Texas, February 10-13, 1983 First Row: Henry L. Gray, D. W. Marquardt, P. M. Robinson, Emanuel Parzen, Julia Abrahams, E. Masry, H. L. Weinert, R. H. Shumway.

Note: On the estimation of ARIMA Models with missing values -- Statistical inference for irregularly observed processes -- Large sample properties of estimation in time series observed at unequally spaced times -- Time series regression with periodically correlated errors and missing data -- Missing observations in dynamic econometric models: a partial synthesis -- A Hilbert transform method for estimating distributed lag models with randomly missed or distorted observations -- Fitting multivariate models to unequally spaced data -- State space modeling of nonstationary time series and smoothing of unequally spaced data -- Direct quadratic spectrum estimation with irregularly spaced data -- Spectral and probability density estimation from irregularly observed data -- A strategy to complete a time series with missing observations -- Multiple time series analysis or irregularly spaced data -- Some applications of the EM algorithm to analyzing incomplete time series data -- Some aspects of continuous-discrete time series modelling -- Inferring the attainment of national ambient air quality standards using missing value time series techniques -- The complementary model in continuous/discrete smoothing.

In: Springer eBooks

Additional Edition: Printed edition: ISBN 9780387960401

Language: English

Keywords: Konferenzschrift

DOI: 10.1007/978-1-4684-9403-7

URL: http://dx.doi.org/10.1007/978-1-4684-9403-7

URL: Volltext

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Format: 346 p. , online resource.

Edition: 1st ed. 1981.

ISBN: 9781461331988

Content: Do you work for an organization that depends on receiving grant funds for sur­ vival? Do you work for one that gives grants? Have you been in the grants busi­ ness a long time? Or a relatively short time? Do you plan to work for a grant­ giving or grant-receiving organization? If you answered "Yes" to any of these questions, this book is written for you. It will save you money. You will share in professional secrets that, up until now, have not been in print. You will find out more about the roles that others play in the grant-spending process; thus you will have an advantage in dealing with others. You will receive tips for spending grant dollars effectively and will be alerted to obstacles that may prevent you from maximizing grant funds. "Grants programs should be run more efficiently, cut out the organizational 'fat,' and develop better management techniques," a trustee of the Rosenberg Foundation was quoted as saying in the Foundation News recently. In this same issue, a leader of the Alcoholism Center for Women in Los Angeles told of trim­ ming superfluous grant spending across the board. "We want to provide the same services," she stated. "We're cutting the fat. " The topic of the article was Cali­ fornia's Proposition 13 and its impact on nonprofit organizations that depend on grant funds for their survival. (l) Not only are taxpayers revolting nationwide against paying ever-increasing taxes, but Congressmen are apparently listening.

Note: 1 Stretching the Grant Dollar: The Players and the Process -- Who Is Responsible for Stretching the Grant Dollar? -- What Happens to the Grant Dollar? -- 2 The Proposal Decision: Should You Apply? -- How Much Will the Application Cost You? -- What Are Your Chances for Success in Receiving an Award? -- What Cost Sharing Will Be Required If You Receive an Award? -- Does the Project Fit with Your Organization'S Mission? -- Do You Have (or Can You Get) the Resources Necessary to Carry Out the Project? -- Who in Your Organization Decides Whether or Not You Should Apply? -- 3 The Proposal Budget: Asking for the Right Amount -- How Much Do You Need? -- How Do You Know What They've Got? -- Never Pad a Budget -- When to Pad a Budget -- What Do You Include in a Budget? -- How Do You Develop a Budget? -- What Are the Characteristics of a Well-Prepared Grant Budget? -- Who in Your Agency Approves Grant Budgets? -- 4 The Project Award: Negotiating the Best Deal -- Negotiation: The Basic Ingredients -- Observations of Experienced Grants Getters and Givers -- 5 Grant Procedures: Putting Your Act Together -- Why Are Grant Policies and Procedures Important? -- How Do You Monitor the Technical and Fiscal Progress of Grant Projects? -- What Grant Policies Do You Need? -- How Can You Develop Grant Policies Effectively and with Minimum Effort? -- 6 Spending the Award: Getting More for Less -- The Purchasing Decision: Comparing Alternatives -- The Purchase Itself: Paying Less -- Save by Using Grantee Buying Power -- Save by Using Grantor Buying Power -- Advice and Examples of Savings from Experienced Grants Spenders -- Obstacles to Saving and How to Get around Them -- 7 Expenditures to Avoid: Over-, Under-, Unallowable -- How Do You Avoid Overexpenditures? -- How Do You Avoid Underexpenditures, and Why Should You? -- How Do You Avoid Unallowable Expenditures? -- Do You Hold Project Spending Meetings? -- 8 Cash Management: Timing Your Dollars In and Out -- How Fast Can You Collect the Grant Funds? -- How Advantageously Can You Pay Out the Grant Funds? -- How Efficiently Can You Invest Idle Cash? -- What Are the Obstacles to Effective Cash Management? -- Does Your Organization Have a Cash Management Policy for Grants? -- Who in Your Organization Is Responsible for Cash Management? -- 9 Funding-Agency Contacts: Letting Them Help -- Let Them Help You Decide Whether or Not to Apply -- Let Them Help You Write the Proposal -- Let Them Help You Ask for the Right Amount -- Let Them Advocate Your Proposal -- Let Them Give You Advance Information -- Let Them Create an RFP Based on Your Idea -- Let Them Solve Potential Problems before the Award -- Let Them Tell You Why You Didn't Win -- Let Them Help You Negotiate the Best Deal -- Let Them Help You Get More for Less -- Let Them Help You Avoid Under-, Over-, and Unallowable Expenditures -- Let Them Help You with Cash Management -- The "Politics" of Contacts -- 10 Gamesplaying: An Obstacle to Cost-Effective Grant Spending -- What Are the Conflicting Needs of Grant Players That Lead to Adversary Relationships? -- Who Plays the Games? -- What Are Some Typical Game Scripts? -- Why and How Should Gamesplaying Be Stopped? -- 11 Your Role: Organizing for the Grant $ S-T-R-E-T-C-H! -- Who in Your Organization Is Responsible for Each Grant-Optimizing Activity Mentioned in This Book? -- Is There Someone in Your Organization Responsible for Each Activity? -- If Several Persons Share Responsibilities, Are Their Activities Coordinated? -- Do the Responsible Employees Have the Knowledge They Need to Get the Most out of Your Grant Dollars? -- Is There a Better Way to Combine Tasks and Positions to Get the Most out of Your Grant Dollar? -- What Can You Do? -- Appendix A Definition of Terms -- Appendix B Sample Purchasing Policy and Forms -- Appendix C Sample Travel Policy and Forms -- Appendix D Sample Consultant/Independent Contractor Forms -- Appendix E Federal Excess Property Program Regional Offices -- Appendix F Acquisition of Excess Government Personal Property by National Science Foundation Grantees -- References.

In: Springer Nature eBook

Additional Edition: Printed edition: ISBN 9781461332008

Additional Edition: Printed edition: ISBN 9780306406072

Additional Edition: Printed edition: ISBN 9781461331995

Language: English

DOI: 10.1007/978-1-4613-3198-8

URL: https://doi.org/10.1007/978-1-4613-3198-8

URL: Volltext  (URL des Erstveröffentlichers)

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Format: XIX, 383 p. , online resource.

ISBN: 9781468401677

Content: Simulation means driving a model of a system with suitable inputs and observing the corresponding outputs. It is widely applied in engineering, in business, and in the physical and social sciences. Simulation method­ ology araws on computer. science, statistics, and operations research and is now sufficiently developed and coherent to be called a discipline in its own right. A course in simulation is an essential part of any operations re­ search or computer science program. A large fraction of applied work in these fields involves simulation; the techniques of simulation, as tools, are as fundamental as those of linear programming or compiler construction, for example. Simulation sometimes appears deceptively easy, but perusal of this book will reveal unexpected depths. Many simulation studies are statistically defective and many simulation programs are inefficient. We hope that our book will help to remedy this situation. It is intended to teach how to simulate effectively. A simulation project has three crucial components, each of which must always be tackled: (1) data gathering, model building, and validation; (2) statistical design and estimation; (3) programming and implementation. Generation of random numbers (Chapters 5 and 6) pervades simulation, but unlike the three components above, random number generators need not be constructed from scratch for each project. Usually random number packages are available. That is one reason why the chapters on random numbers, which contain mainly reference material, follow the ch!lPters deal­ ing with experimental design and output analysis.

Note: 1 Introduction -- 1.1. Systems, Models, and Simulation -- 1.2. Verification, Approximation, and Validation -- 1.3. States, Events, and Clocks -- 1.4. Simulation — Types and Examples -- 1.5. Introduction to Random Numbers -- 1.6. Perspective on Experimental Design and Estimation -- 1.7. Clock Mechanisms -- 1.8. Hints for Simulation Programming -- 1.9. Miscellaneous Problems -- 2 Variance Reduction -- 2.1. Common Random Numbers -- 2.2. Antithetic Variates -- 2.3. Control Variates -- 2.4. Stratification -- 2.5. Importance Sampling -- 2.6. Conditional Monte Carlo -- 2.7. Jackknifing -- 3 Output Analysis -- 3.1. Introduction -- 3.2. Analysis of Finite-Horizon Performance -- 3.3. Analysis of Steady-state Performance -- 3.4. Analysis of Transaction-Based Performance -- 3.5. Efficient Estimators and Indirect Estimators -- 3.6. Problems -- 3.7. Renewal Theory Primer -- 4 Rational Choice of Input Distributions -- 4.1. Addition and the Normal Distribution -- 4.2. Multiplication and the Lognormal -- 4.3. Memorylessness and the Exponential -- 4.4. Superposition, the Poisson, and the Exponential -- 4.5. Minimization and the Weibull Distribution -- 4.6. A Mixed Empirical and Exponential Distribution -- 4.7. Extreme Values and Spacings -- 4.8. When Not to Use a Theoretical Distribution -- 4.9. Nonstationary Poisson Processes -- 5 Nonuniform Random Numbers -- 5.1. Introduction -- 5.2. General Methods -- 5.3. Continuous Distributions -- 5.4. Discrete Distributions -- 5.5. Problems -- 5.6. Timings -- 6 Uniform Random Numbers -- 6.1. Random Introductory Remarks -- 6.2. What Constitutes Randomness -- 6.3. Classes of Generators -- 6.4. Choosing a Good Generator Based on Theoretical Considerations -- 6.5. Implementation of Uniform Random Number Generators -- 6.6. Empirical Testing of Uniform Random Number Generators -- 6.7. Proper Use of a Uniform Random Number Generator -- 6.8. Exploiting Special Features of Uniform Generators -- 7 Simulation Programming -- 7.1. Simulation with General-Purpose Languages -- 7.2. Simscript -- 7.3. GPSS -- 7.4. Simula -- 7.5. General Considerations in Simulation Programming -- 8 Programming to Reduce the Variance -- 8.1. Choosing an Input Distribution -- 8.2. Common Random Numbers -- 8.3. Antithetic Variates -- 8.4. Control Variates -- 8.5. Stratified Sampling -- 8.6. Importance Sampling -- 8.7. Conditional Monte Carlo -- 8.8. Summary -- Appendix A The Shapiro — Wilk Test for Normality -- Appendix L Routines for Random Number Generation -- Appendix X Examples of Simulation Programming -- References -- Author Index.

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Additional Edition: Printed edition: ISBN 9781468401691

Language: English

DOI: 10.1007/978-1-4684-0167-7

URL: http://dx.doi.org/10.1007/978-1-4684-0167-7

URL: Volltext

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Format: XI, 340 p. , online resource.

ISBN: 9781468499308

Series Statement: Graduate Texts in Mathematics, 71

Content: The present volume is the culmination often years' work separately and joint­ ly. The idea of writing this book began with a set of notes for a course given by one of the authors in 1970-1971 at the Hebrew University. The notes were refined serveral times and used as the basic content of courses given sub­ sequently by each of the authors at the State University of New York at Stony Brook and the Hebrew University. In this book we present the theory of Riemann surfaces and its many dif­ ferent facets. We begin from the most elementary aspects and try to bring the reader up to the frontier of present-day research. We treat both open and closed surfaces in this book, but our main emphasis is on the compact case. In fact, Chapters III, V, VI, and VII deal exclusively with compact surfaces. Chapters I and II are preparatory, and Chapter IV deals with uniformization. All works on Riemann surfaces go back to the fundamental results of Rie­ mann, Jacobi, Abel, Weierstrass, etc. Our book is no exception. In addition to our debt to these mathematicians of a previous era, the present work has been influenced by many contemporary mathematicians.

Note: 0 An Overview -- 0.1 Topological Aspects, Uniformization, and Fuchsian Groups -- 0.2 Algebraic Functions -- 0.3. Abelian Varieties -- 0.4. More Analytic Aspects -- I Riemann Surfaces -- I.1. Definitions and Examples -- I.2. Topology of Riemann Surfaces -- I.3. Differential Forms -- I.4. Integration Formulae -- II Existence Theorems -- II.1. Hilbert Space Theory—A Quick Review -- II.2. Weyl’s Lemma -- II.3. The Hilbert Space of Square Integrable Forms -- II.4. Harmonic Differentials -- II.5. Meromorphic Functions and Differentials -- III Compact Riemann Surfaces -- III.1. Intersection Theory on Compact Surfaces -- III.2. Harmonic and Analytic Differentials on Compact Surfaces -- III.3. Bilinear Relations -- III.4. Divisors and the Riemann—Roch Theorem -- III.5. Applications of the Riemann—Roch Theorem -- III.6. Abel’s Theorem and the Jacobi Inversion Problem -- III.7. Hyperelliptic Riemann Surfaces -- III.8. Special Divisors on Compact Surfaces -- III.9. Multivalued Functions -- III.10. Projective Imbeddings -- III.11. More on the Jacobian Variety -- IV Uniformization -- IV.1. More on Harmonic Functions (A Quick Review) -- IV.2. Subharmonic Functions and Perron’s Method -- IV.3. A Classification of Riemann Surfaces -- IV.4. The Uniformization Theorem for Simply Connected Surfaces -- IV.5. Uniformization of Arbitrary Riemann Surfaces -- IV.6. The Exceptional Riemann Surfaces -- IV.7. Two Problems on Moduli -- IV.8. Riemannian Metrics -- IV.9. Discontinuous Groups and Branched Coverings -- IV.10. Riemann–Roch—An Alternate Approach -- IV.11. Algebraic Function Fields in One Variable -- V Automorphisms of Compact Surfaces Elementary Theory -- V.1. Hurwitz’s Theorem -- V.2. Representations of the Automorphism Group on Spaces of Differentials -- V.3. Representations of Aut M on H〉1(M) -- V.4. The Exceptional Riemann Surfaces -- VI Theta Functions -- VI.1. The Riemann Theta Function -- VI.2. The Theta Functions Associated with a Riemann Surface -- VI.3. The Theta Divisor -- VII Examples -- VII.1. Hyperelliptic Surfaces (Once Again) -- VII.2. Relations among Quadratic Differentials -- VII.3. Examples of Non-hyperelliptic Surfaces -- VII.4. Branch Points of Hyperelliptic Surfaces as Holomorphic Functions of the Periods -- VII.5. Examples of Prym Differentials.

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Additional Edition: Printed edition: ISBN 9781468499322

Language: English

DOI: 10.1007/978-1-4684-9930-8

URL: http://dx.doi.org/10.1007/978-1-4684-9930-8

URL: Volltext

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Format: XI, 116 p. , online resource.

ISBN: 9781468493726

Series Statement: Graduate Texts in Mathematics, 10

Content: This book grew out of courses which I taught at Cornell University and the University of Warwick during 1969 and 1970. I wrote it because of a strong belief that there should be readily available a semi-historical and geo­ metrically motivated exposition of J. H. C. Whitehead's beautiful theory of simple-homotopy types; that the best way to understand this theory is to know how and why it was built. This belief is buttressed by the fact that the major uses of, and advances in, the theory in recent times-for example, the s-cobordism theorem (discussed in §25), the use of the theory in surgery, its extension to non-compact complexes (discussed at the end of §6) and the proof of topological invariance (given in the Appendix)-have come from just such an understanding. A second reason for writing the book is pedagogical. This is an excellent subject for a topology student to "grow up" on. The interplay between geometry and algebra in topology, each enriching the other, is beautifully illustrated in simple-homotopy theory. The subject is accessible (as in the courses mentioned at the outset) to students who have had a good one­ semester course in algebraic topology. I have tried to write proofs which meet the needs of such students. (When a proof was omitted and left as an exercise, it was done with the welfare of the student in mind. He should do such exercises zealously.

Note: I. Introduction -- §1. Homotopy equivalence -- §2. Whitehead’s combinatorial approach to homotopy theory -- §3. CW complexes -- II. A Geometric Approach to Homotopy Theory -- §4. Formal deformations -- §5. Mapping cylinders and deformations -- §6. The Whitehead group of a CW comple -- §7. Simplifying a homotopically trivial CW pair -- §8. Matrices and formal deformations -- III. Algebra -- §9. Algebraic conventions -- §10. The groups KG(R) -- §11. Some information about Whitehead groups -- §12. Complexes with preferred bases [= (R,G)-complexes] -- §13. Acyclic chain complexes -- §14. Stable equivalence of acyclic chain complexes -- §15. Definition of the torsion of an acyclic comple -- §16. Milnor’s definition of torsion -- §17. Characterization of the torsion of a chain comple -- §18. Changing rings -- IV. Whitehead Torsion in the CW Category -- §19. The torsion of a CW pair — definition -- §20. Fundamental properties of the torsion of a pair -- §21. The natural equivalence of Wh(L) and ? Wh (?1Lj) -- §22. The torsion of a homotopy equivalence -- §23. Product and sum theorems -- §24. The relationship between homotopy and simple-homotopy -- §25. Tnvariance of torsion, h-cobordisms and the Hauptvermutung -- V. Lens Spaces -- §26. Definition of lens spaces -- §27. The 3-dimensional spaces Lp,q -- §28. Cell structures and homology groups -- §29. Homotopy classification -- §30. Simple-homotopy equivalence of lens spaces -- §31. The complete classification -- Appendix: Chapman’s proof of the topological invariance of Whitehead Torsion -- Selected Symbols and Abbreviations.

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Additional Edition: Printed edition: ISBN 9780387900551

Language: English

DOI: 10.1007/978-1-4684-9372-6

URL: http://dx.doi.org/10.1007/978-1-4684-9372-6

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Format: VIII, 234 p. , online resource.

ISBN: 9781461394877

Series Statement: Studies in the History of Mathematics and Physical Sciences, 9

Content: One of the pervasive phenomena in the history of science is the development of independent disciplines from the solution or attempted solutions of problems in other areas of science. In the Twentieth Century, the creation of specialties witqin the sciences has accelerated to the point where a large number of scientists in any major branch of science cannot understand the work of a colleague in another subdiscipline of his own science. Despite this fragmentation, the development of techniques or solutions of problems in one area very often contribute fundamentally to solutions of problems in a seemingly unrelated field. Therefore, an examination of this phenomenon of the formation of independent disciplines within the sciences would contrib­ ute to the understanding of their evolution in modern times. We believe that in this context the history of combinatorial group theory in the late Nineteenth Century and the Twentieth Century can be used effectively as a case study. It is a reasonably well-defined independent specialty, and yet it is closely related to other mathematical disciplines. The fact that combinatorial group theory has, so far, not been influenced by the practical needs of science and technology makes it possible for us to use combinatorial group theory to exhibit the role of the intellectual aspects of the development of mathematics in a clearcut manner. There are other features of combinatorial group theory which appear to make it a reasona­ ble choice as the object of a historical study.

Note: I The Beginning of Combinatorial Group Theory -- I.I Introduction to Part I -- I.2 The Foundations: Dyck’s Group-Theoretical Studies -- I.3 The Origin: The Theory of Discontinuous Groups -- I.4 Motivation: The Fundamental Groups of Topological Spaces -- I.5 The Graphical Representation of Groups -- I.6 Precursors of Later Developments -- I.7 Summary -- I.8 Modes of Communication. Growth and Distribution of Research in Group Theory -- I.9 Biographical Notes -- I.10 Notes on Terminology and Definitions -- I.11 Sources -- II The Emergence of Combinatorial Group Theory as an Independent Field -- II. 1 Introduction to Part II -- II.2 Free Groups and Their Automorphisms -- II.3 The Reidemeister—Schreier Method -- II.4 Free Products and Free Products with Amalgamations -- II.5 One-Relator Groups -- II.6 Metabelian Groups and Related Topics -- II.7 Commutator Calculus and the Lower Central Series -- II.8 Varieties of Groups -- II.9 Topological Properties of Groups and Group Extensions -- II.10 Notes on Special Groups -- II.11 Postscript: The Impact of Mathematical Logic -- II.12 Modes of Communication -- II.13 Geographical Distribution of Research and Effects of Migration -- II.14 Organization of Knowledge -- Index of Names -- Index of Subjects.

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Additional Edition: Printed edition: ISBN 9781461394891

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DOI: 10.1007/978-1-4613-9487-7

URL: http://dx.doi.org/10.1007/978-1-4613-9487-7

URL: Volltext