04093nam 2200481 450 99641826010331620210209164142.03-030-45650-110.1007/978-3-030-45650-4(CKB)4100000011435830(DE-He213)978-3-030-45650-4(MiAaPQ)EBC6347276(PPN)258059494(EXLCZ)99410000001143583020210209d2020 uy 0engurnn|008mamaatxtrdacontentcrdamediacrrdacarrierSmooth manifolds and observables /Jet NestruevSecond edition.Cham, Switzerland :Springer,[2020]©20201 online resource (XVIII, 433 p. 88 illus.) Graduate Texts in Mathematics ;2203-030-45649-8 Foreword -- Preface -- 1. Introduction -- 2. Cutoff and Other Special Smooth Functions on R^n -- 3. Algebras and Points -- 4. Smooth Manifolds (Algebraic Definition) -- 5. Charts and Atlases -- 6. Smooth Maps -- 7. Equivalence of Coordinate and Algebraic Definitions -- 8. Points, Spectra and Ghosts -- 9. The Differential Calculus as Part of Commutative Algebra -- 10. Symbols and the Hamiltonian Formalism -- 11. Smooth Bundles -- 12. Vector Bundles and Projective Modules -- 13. Localization -- 14. Differential 1-forms and Jets -- 15. Functors of the differential calculus and their representations -- 16. Cosymbols, Tensors, and Smoothness -- 17. Spencer Complexes and Differential Forms -- 18. The (co)chain complexes that come from the Spencer Sequence -- 19. Differential forms: classical and algebraic approach -- 20. Cohomology -- 21. Differential operators over graded algebras -- Afterword -- Appendix -- References -- Index.This textbook demonstrates how differential calculus, smooth manifolds, and commutative algebra constitute a unified whole, despite having arisen at different times and under different circumstances. Motivating this synthesis is the mathematical formalization of the process of observation from classical physics. A broad audience will appreciate this unique approach for the insight it gives into the underlying connections between geometry, physics, and commutative algebra. The main objective of this book is to explain how differential calculus is a natural part of commutative algebra. This is achieved by studying the corresponding algebras of smooth functions that result in a general construction of the differential calculus on various categories of modules over the given commutative algebra. It is shown in detail that the ordinary differential calculus and differential geometry on smooth manifolds turns out to be precisely the particular case that corresponds to the category of geometric modules over smooth algebras. This approach opens the way to numerous applications, ranging from delicate questions of algebraic geometry to the theory of elementary particles. Smooth Manifolds and Observables is intended for advanced undergraduates, graduate students, and researchers in mathematics and physics. This second edition adds ten new chapters to further develop the notion of differential calculus over commutative algebras, showing it to be a generalization of the differential calculus on smooth manifolds. Applications to diverse areas, such as symplectic manifolds, de Rham cohomology, and Poisson brackets are explored. Additional examples of the basic functors of the theory are presented alongside numerous new exercises, providing readers with many more opportunities to practice these concepts.Graduate texts in mathematics ;220.AlgebraManifolds (Mathematics)Algebra.Manifolds (Mathematics)516.07Nestruev Jet66975MiAaPQMiAaPQMiAaPQBOOK996418260103316Smooth manifolds and observables147503UNISA07345nam 22007575 450 991030063730332120210302190716.010.1007/978-1-4302-6083-7(CKB)2670000000618779(EBL)3566513(SSID)ssj0001501460(PQKBManifestationID)11968024(PQKBTitleCode)TC0001501460(PQKBWorkID)11524699(PQKB)10633747(DE-He213)978-1-4302-6083-7(MiAaPQ)EBC3566513(CaSebORM)9781430260837(PPN)186024703(OCoLC)911430840(OCoLC)ocn911430840(EXLCZ)99267000000061877920150523d2015 u| 0engur|n|---|||||txtccrEnterprise Cybersecurity How to Build a Successful Cyberdefense Program Against Advanced Threats /by Scott Donaldson, Stanley Siegel, Chris K. Williams, Abdul Aslam1st ed. 2015.Berkeley, CA :Apress :Imprint: Apress,2015.1 online resource (508 p.)Expert's Voice in CybersecurityDescription based upon print version of record.9781430260820 1430260823 9781430260837 1430260831 Includes bibliographical references and index.Contents at a Glance; Contents; Foreword; About the Authors; Acknowledgments ; Introduction; Part I: The Cybersecurity Challenge ; Chapter 1: Defining the Cybersecurity Challenge; The Cyberattacks of Today; The Sony Pictures Entertainment Breach of 2014; Advanced Persistent Threats; Waves of Malware; Types of Cyberattackers; Commodity Threats; Hacktivists; Organized Crime ; Espionage ; Cyberwar ; The Types of Cyberattacks; Confidentiality: Steal Data; Integrity: Modify Data (Steal Money); Availability: Deny Access; The Steps of a Cyberintrusion; Attack Trees and Attack GraphsLockheed Martin Kill Chain Mandiant Attack Life Cycle; Enterprise Cybersecurity Attack Sequence; Why Cyberintrusions Succeed; The Explosion in Connectivity; Consolidation of Enterprise IT; Defeat of Preventive Controls; Failure of Detective Controls; Compliance over Capability; The Gap in Cybersecurity Effectiveness; A New Cybersecurity Mindset; An Effective Enterprise Cybersecurity Program; Chapter 2: Meeting the Cybersecurity Challenge; Cybersecurity Frameworks; The Cybersecurity Process; Cybersecurity Challenges; The Risk Management ProcessConsidering Vulnerabilities, Threats, and Risks Risk Analysis and Mitigation; Cybersecurity Controls; Cybersecurity Capabilities; Cybersecurity and Enterprise IT; Emplacing Cyberdefenses ; H ow Cyberdefenses Interconnect; An Enterprise Cybersecurity Architecture; Part II: A New Enterprise Cybersecurity Architecture ; Chapter 3: Enterprise Cybersecurity Architecture; Systems Administration; S ystems Administration: Goal and Objectives ; Systems Administration: Threat Vectors ; Systems Administration: Capabilities; Network Security; Network Security: Goal and ObjectivesNetwork Security: Threat Vectors Network Security: Capabilities ; Application Security; Application Security: Goal and Objectives ; Application Security: Threat Vectors ; Application Security: Capabilities ; Endpoint, Server, and Device Security; Endpoint, Server, and Device Security: Goal and Objectives ; Endpoint, Server, and Device Security: Threat Vectors ; Endpoint, Server, and Device Security: Capabilities ; Identity, Authentication, and Access Management; Identity, Authentication, and Access Management: Goal and ObjectivesIdentity, Authentication, and Access Management: Threat Vectors Identity, Authentication, and Access Management: Capabilities; Data Protection and Cryptography; Data Protection and Cryptography: Goal and Objectives ; Data Protection and Cryptography: Threat Vectors ; Data Protection and Cryptography: Capabilities ; Monitoring, Vulnerability, and Patch Management; Monitoring, Vulnerability, and Patch Management: Goal and Objectives ; Monitoring, Vulnerability, and Patch Management: Threat Vectors; Monitoring, Vulnerability, and Patch Management: CapabilitiesHigh Availability, Disaster Recovery, and Physical ProtectionEnterprise Cybersecurity empowers organizations of all sizes to defend themselves with next-generation cybersecurity programs against the escalating threat of modern targeted cyberattacks. This book presents a comprehensive framework for managing all aspects of an enterprise cybersecurity program. It enables an enterprise to architect, design, implement, and operate a coherent cybersecurity program that is seamlessly coordinated with policy, programmatics, IT life cycle, and assessment. Fail-safe cyberdefense is a pipe dream. Given sufficient time, an intelligent attacker can eventually defeat defensive measures protecting an enterprise’s computer systems and IT networks. To prevail, an enterprise cybersecurity program must manage risk by detecting attacks early enough and delaying them long enough that the defenders have time to respond effectively. Enterprise Cybersecurity shows players at all levels of responsibility how to unify their organization’s people, budgets, technologies, and processes into a cost-efficient cybersecurity program capable of countering advanced cyberattacks and containing damage in the event of a breach. The authors of Enterprise Cybersecurity explain at both strategic and tactical levels how to accomplish the mission of leading, designing, deploying, operating, managing, and supporting cybersecurity capabilities in an enterprise environment. The authors are recognized experts and thought leaders in this rapidly evolving field, drawing on decades of collective experience in cybersecurity and IT. In capacities ranging from executive strategist to systems architect to cybercombatant, Scott E. Donaldson, Stanley G. Siegel, Chris K. Williams, and Abdul Aslam have fought on the front lines of cybersecurity against advanced persistent threats to government, military, and business entities.How to build a successful cyberdefense program against advanced threatsData protectionData encryption (Computer science)Securityhttps://scigraph.springernature.com/ontologies/product-market-codes/I28000Cryptologyhttps://scigraph.springernature.com/ontologies/product-market-codes/I28020Data protection.Data encryption (Computer science)Security.Cryptology.004Donaldson Scott E.authttp://id.loc.gov/vocabulary/relators/aut959977Siegel Stanleyauthttp://id.loc.gov/vocabulary/relators/autWilliams Chris Kauthttp://id.loc.gov/vocabulary/relators/autAslam Abdulauthttp://id.loc.gov/vocabulary/relators/autUMIUMIBOOK9910300637303321Enterprise Cybersecurity2175739UNINA