04986nam 2200793Ia 450 991110707880332120260415133858.09786612194832978128219483012821948369783110199727311019972610.1515/9783110199727(CKB)1000000000335207(EBL)275298(OCoLC)476020819(SSID)ssj0000104942(PQKBManifestationID)11130471(PQKBTitleCode)TC0000104942(PQKBWorkID)10100371(PQKB)10020133(MiAaPQ)EBC275298(DE-B1597)19800(OCoLC)979599439(DE-B1597)9783110199727(Au-PeEL)EBL275298(CaPaEBR)ebr10154725(CaONFJC)MIL219483(OCoLC)935261822(Perlego)654664(EXLCZ)99100000000033520720060602d2006 uy 0engurnn#---|u||utxtccrApproximations and endomorphism algebras of modules /by Rudiger Gobel and Jan Trlifaj1st ed.Berlin ;New York Walter de Gruyter20061 online resource (664 p.)De Gruyter expositions in mathematics ;41Description based upon print version of record.9783110110791 3110110792 Includes bibliographical references and index.Front matter --Contents --Chapter 1. Some useful classes of modules --Chapter 2. Approximations of modules --Chapter 3. Complete cotorsion pairs --Chapter 4. Deconstruction of cotorsion pairs --Chapter 5. Tilting approximations --Chapter 6. 1-tilting modules and their applications --Chapter 7. Tilting approximations and the finitistic dimension conjectures --Chapter 8. Cotilting modules --Chapter 9. The Black Box and its relatives --Chapter 10. Independence results for cotorsion pairs --Chapter 11. The lattice of cotorsion pairs --Chapter 12. Realizing algebras - by algebraically independent elements and by prediction principles --Chapter 13. E(R)-algebras --Chapter 14. Modules with distinguished submodules --Chapter 15. Some useful classes of algebras --BackmatterThe category of all modules over a general associative ring is too complex to admit any reasonable classification. Thus, unless the ring is of finite representation type, one must limit attempts at classification to some restricted subcategories of modules. The wild character of the category of all modules, or of one of its subcategories C is often indicated by the presence of a realization theorem, that is, by the fact that any reasonable algebra is isomorphic to the endomorphism algebra of a module from C. This results in the existence of pathological direct sum decompositions and these are generally viewed as obstacles to the classification. Realization theorems have thus become important indicators of the non-classification theory of modules. In order to overcome this problem, approximation theory of modules has been developed over the past few decades. The idea here is to select suitable subcategories C whose modules can be classified, and then to approximate arbitrary modules by ones from C. These approximations are neither unique nor functorial in general, but there is always a rich supply available appropriate to the requirements of various particular applications. Thus approximation theory has developed into an important part of the classification theory of modules. In this monograph the two methods are brought together. First the approximation theory of modules is developed and some of its recent applications, notably to infinite dimensional tilting theory, are presented. Then some prediction principles from set theory are introduced and these become the principal tools in the establishment of appropriate realization theorems. The monograph starts from basic facts and gradually develops the theory towards its present frontiers. It is suitable both for graduate students interested in algebra and for experts in module and representation theory.Gruyter expositions in mathematics ;41.Modules (Algebra)Moduli theoryApproximation theoryModules (Algebra)Moduli theory.Approximation theory.512/.42510sdnbSK 150rvkSK 230rvkSK 820rvkGöbel R(Rüdiger),1940-60070Trlifaj Jan1925934MiAaPQMiAaPQMiAaPQBOOK9911107078803321Approximations and endomorphism algebras of modules4673607UNINA03430nam 22006854a 450 991108957670332120251117063333.09780674020795067402079010.4159/9780674020795(CKB)1000000000786856(OCoLC)631583402(CaPaEBR)ebrary10305843(SSID)ssj0000162877(PQKBManifestationID)11149526(PQKBTitleCode)TC0000162877(PQKBWorkID)10208813(PQKB)10861759(MiAaPQ)EBC3299999(DE-B1597)457553(OCoLC)1032690455(OCoLC)1043654976(OCoLC)979880244(DE-B1597)9780674020795(Au-PeEL)EBL3299999(CaPaEBR)ebr10305843(OCoLC)923108395(Perlego)1147542(EXLCZ)99100000000078685620050623d2005 uy 0engurcn|||||||||txtccrThe gift of science Leibniz and the modern legal tradition /Roger Stuart Berkowitz1st ed.Cambridge, Mass. Harvard University Press20051 online resource (235 p.) Bibliographic Level Mode of Issuance: Monograph9780674018730 0674018737 Includes bibliographical references and index.Frontmatter -- Acknowledgments -- Contents -- Preface -- Note on Terminology -- Introduction: Legal Codification, Positive Law, and the Question of Science -- I. From Insight to Science: Leibniz's Scientific Foundation of Justice -- CHAPTER 1. Beyond Geometry: Leibniz and the Science of Law -- CHAPTER 2. The Force of Law: Will -- CHAPTER 3. Leibniz's Systema Iuris -- II .The Allgemeines Landrecht: From Recht to Gesetz -- CHAPTER 4. From the Gesetzbuch to the Landrecht: The ALR and the Triumph of Legality -- CHAPTER 5. The Rule of Law: The Crown Prince Lectures and the Grounding of Legality in Order and Security -- III. From Science to Technique: Friedrich Carl von Savigny, the BGB, and the Self-Overcoming of Legal Science -- CHAPTER 6. From Reason to History: Savigny's System and the Rise of Social Legal Science -- CHAPTER 7. The Bürgerliches Gesetzbuch (BGB) of 1900: Positive Legal Science and the End of Justice -- Conclusion -- Note on Sources -- Notes -- IndexMoving from the scientific revolution to the nineteenth-century rise of legal codes, Berkowitz tells the story of how lawyers and philosophers invented legal science to preserve law's claim to moral authority. The "gift" of science, however, proved bittersweet. Instead of strengthening the bond between law and justice, the subordination of law to science transformed law from an ethical order into a tool for social and economic ends.Science and lawHistoryJurisprudenceHistoryLawPhilosophyScience and lawHistory.JurisprudenceHistory.LawPhilosophy.344/.095Berkowitz Roger1968-1641603MiAaPQMiAaPQMiAaPQBOOK9911089576703321The gift of science4663026UNINA05801oam 2200493K 450 991114399530332120251117113648.00-429-89134-20-429-89135-00-429-46963-29780429469633(CKB)4100000008339009(MiAaPQ)EBC5780629(OCoLC)1103320709(OCoLC-P)1103320709(FlBoTFG)9780429469633(EXLCZ)99410000000833900920190603d2020 uy 0engurcnu---unuuutxtrdacontentcrdamediacrrdacarrierAdvanced problem solving with Maple a first course /William P. Fox and William C. Bauldry1st ed.Boca Raton :Taylor & Francis, CRC Press,2020.1 online resource (347 pages)Includes index.1-138-60185-3 Cover -- Half Title -- Title Page -- Copyright Page -- Table of Contents -- Preface -- 1: Introduction to Problem Solving and Maple -- 1.1 Problem Solving -- 1.2 Introduction to Maple -- 1.3 The Structure of Maple -- 1.4 General Introduction to Maple -- 1.5 Maple Training -- 1.6 Maple Applications Center -- 2: Introduction, Basic Concepts, and Techniques in Problem Solving with First-Order, Ordinary Differential Equations -- 2.1 Introduction -- 2.2 Applied First-Order Differential Equations and Solution Methods -- 2.3 Slope Fields and Qualitative Assessments -- 2.4 Analytical Solution of First-Order Ordinary Differential Equations -- 2.5 First-Order Ordinary Differential Equations and Maple -- 2.6 Numerical Methods for First-Order Ordinary Differential Equations -- 3: Introduction, Basic Concepts, and Techniques in Problem Solving with Systems of Ordinary Differential Equations -- 3.1 Systems of Differential Equations -- 3.2 Applied Systems of Differential Equations -- 3.3 Phase Portraits and Qualitative Assessment -- 3.4 Solving Homogeneous and Nonhomogeneous Systems of ODEs -- 3.5 Numerical Solutions to Systems of Ordinary Differential Equations -- 4: Problem Solving with Linear, Integer, and Mixed Integer Programming -- 4.1 Formulating Linear Programming Problems -- 4.2 Understanding Two-Variable Linear Programming: A Graphical Simplex -- 4.3 Solving the Linear Program: The Simplex Method and Maple -- 4.4 Linear Programming with Maple's Commands -- 4.5 Sensitivity Analysis with Maple -- 4.6 Integer and Mixed Integer Problems with Maple -- 5: Model Fitting and Linear Regression -- 5.1 Introduction -- 5.2 The Different Curve Fitting Criterion -- 5.3 Plotting the Residuals for a Least-Squares Fit -- 5.4 Case Studies -- 6: Statistical and Probabilistic Problem Solving with Maple -- 6.1 Introduction -- 6.2 Basic Statistics: Univariate Data.6.3 Introduction to Classical Probability -- 6.4 Reliability in Engineering and Business -- 6.5 Case Study: Airlines Overbooking Model -- 6.6 Continuous Probability Models -- 6.7 The Normal Distribution -- 6.8 Confidence Intervals and Hypothesis Testing -- 7: Problem Solving with Simulation -- 7.1 Introduction -- 7.2 Monte Carlo Simulation -- 7.3 Probability and Monte Carlo Simulation Using Deterministic Behavior -- 7.4 Probability and Monte Carlo Simulation Using Probabilistic Behavior -- 7.5 Case Studies: Applied Simulation Models -- Index.Problem Solving is essential to solve real-world problems. Advanced Problem Solving with Maple: A First Course applies the mathematical modeling process by formulating, building, solving, analyzing, and criticizing mathematical models. It is intended for a course introducing students to mathematical topics they will revisit within their further studies. The authors present mathematical modeling and problem-solving topics using Maple as the computer algebra system for mathematical explorations, as well as obtaining plots that help readers perform analyses. The book presents cogent applications that demonstrate an effective use of Maple, provide discussions of the results obtained using Maple, and stimulate thought and analysis of additional applications. Highlights: The book's real-world case studies prepare the student for modeling applications Bridges the study of topics and applications to various fields of mathematics, science, and engineering Features a flexible format and tiered approach offers courses for students at various levels The book can be used for students with only algebra or calculus behind them About the authors: Dr. William P. Fox is an emeritus professor in the Department of Defense Analysis at the Naval Postgraduate School. Currently, he is an adjunct professor, Department of Mathematics, the College of William and Mary. He received his Ph.D. at Clemson University and has many publications and scholarly activities including twenty books and over one hundred and fifty journal articles. William C. Bauldry, Prof. Emeritus and Adjunct Research Prof. of Mathematics at Appalachian State University, received his PhD in Approximation Theory from Ohio State. He has published many papers on pedagogy and technology, often using Maple, and has been the PI of several NSF-funded projects incorporating technology and modeling into math courses. He currently serves as Associate Director of COMAP's Math Contest in Modeling (MCM).Problem solvingData processingQuantitative researchData processingProblem solvingData processing.Quantitative researchData processing.519.0285/53Fox William P.1949-Bauldry William C.OCoLC-POCoLC-PBOOK9911143995303321UNINA