10743nam 2200517 450 99646440030331620220722212707.03-030-81588-9(CKB)5470000001298847(MiAaPQ)EBC6795881(Au-PeEL)EBL6795881(OCoLC)1281582980(PPN)258296917(EXLCZ)99547000000129884720220722d2021 uy 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierGuide to discrete mathematics an accessible introduction to the history, theory, logic and applications /Gerard O'Regan2nd ed.Cham, Switzerland :Springer,[2021]©20211 online resource (459 pages)Texts in Computer Science3-030-81587-0 Intro -- Preface -- Overview -- Organization and Features -- Audience -- Contents -- 1 Mathematics in Civilization -- 1.1 Introduction -- 1.2 The Babylonians -- 1.3 The Egyptians -- 1.4 The Greeks -- 1.5 The Romans -- 1.6 Islamic Influence -- 1.7 Chinese and Indian Mathematics -- 1.8 Review Questions -- 1.9 Summary -- References -- 2 Sets, Relations and Functions -- 2.1 Introduction -- 2.2 Set Theory -- 2.2.1 Set Theoretical Operations -- 2.2.2 Properties of Set Theoretical Operations -- 2.2.3 Russell's Paradox -- 2.2.4 Computer Representation of Sets -- 2.3 Relations -- 2.3.1 Reflexive, Symmetric and Transitive Relations -- 2.3.2 Composition of Relations -- 2.3.3 Binary Relations -- 2.3.4 Applications of Relations -- 2.4 Functions -- 2.5 Application of Functions -- 2.6 Review Questions -- 2.7 Summary -- References -- 3 Number Theory -- 3.1 Introduction -- 3.2 Elementary Number Theory -- 3.3 Prime Number Theory -- 3.3.1 Algorithms -- 3.3.2 Greatest Common Divisors (GCD) -- 3.3.3 Least Common Multiple (LCM) -- 3.3.4 Euclid's Algorithm -- 3.3.5 Distribution of Primes -- 3.4 Theory of Congruences -- 3.5 Binary System and Computer Representation of Numbers -- 3.6 Review Questions -- 3.7 Summary -- References -- 4 Mathematical Induction and Recursion -- 4.1 Introduction -- 4.2 Strong Induction -- 4.3 Recursion -- 4.4 Structural Induction -- 4.5 Review Questions -- 4.6 Summary -- Reference -- 5 Sequences, Series, and Permutations and Combinations -- 5.1 Introduction -- 5.2 Sequences and Series -- 5.3 Arithmetic and Geometric Sequences -- 5.4 Arithmetic and Geometric Series -- 5.5 Simple and Compound Interest -- 5.6 Time Value of Money and Annuities -- 5.7 Permutations and Combinations -- 5.8 Review Questions -- 5.9 Summary -- 6 Algebra -- 6.1 Introduction -- 6.2 Simple and Simultaneous Equations -- 6.3 Quadratic Equations -- 6.4 Indices and Logarithms.6.5 Horner's Method for Polynomials -- 6.6 Abstract Algebra -- 6.6.1 Monoids and Groups -- 6.6.2 Rings -- 6.6.3 Fields -- 6.6.4 Vector Spaces -- 6.7 Review Questions -- 6.8 Summary -- Reference -- 7 Automata Theory -- 7.1 Introduction -- 7.2 Finite-State Machines -- 7.3 Pushdown Automata -- 7.4 Turing Machines -- 7.5 Hybrid Automata -- 7.6 Review Questions -- 7.7 Summary -- Reference -- 8 Matrix Theory -- 8.1 Introduction -- 8.2 Two × Two Matrices -- 8.3 Matrix Operations -- 8.4 Determinants -- 8.5 Eigen Vectors and Values -- 8.6 Gaussian Elimination -- 8.7 Business Applications of Matrices -- 8.8 Review Questions -- 8.9 Summary -- References -- 9 Graph Theory -- 9.1 Introduction -- 9.2 Undirected Graphs -- 9.2.1 Hamiltonian Paths -- 9.3 Trees -- 9.3.1 Binary Trees -- 9.4 Graph Algorithms -- 9.5 Graph Colouring and Four-Colour Problem -- 9.6 Review Questions -- 9.7 Summary -- References -- 10 Cryptography -- 10.1 Introduction -- 10.2 Breaking the Enigma Codes -- 10.3 Cryptographic Systems -- 10.4 Symmetric Key Systems -- 10.5 Public Key Systems -- 10.5.1 RSA Public Key Cryptosystem -- 10.5.2 Digital Signatures -- 10.6 Review Questions -- 10.7 Summary -- References -- 11 Coding Theory -- 11.1 Introduction -- 11.2 Mathematical Foundations -- 11.3 Simple Channel Code -- 11.4 Block Codes -- 11.4.1 Error Detection and Correction -- 11.5 Linear Block Codes -- 11.5.1 Parity Check Matrix -- 11.5.2 Binary Hamming Code -- 11.5.3 Binary Parity-Check Code -- 11.6 Miscellaneous Codes in Use -- 11.7 Review Questions -- 11.8 Summary -- References -- 12 Language Theory and Semantics -- 12.1 Introduction -- 12.2 Alphabets and Words -- 12.3 Grammars -- 12.3.1 Backus Naur Form -- 12.3.2 Parse Trees and Derivations -- 12.4 Programming Language Semantics -- 12.4.1 Axiomatic Semantics -- 12.4.2 Operational Semantics -- 12.4.3 Denotational Semantics -- 12.5 Lambda Calculus.12.6 Lattices and Order -- 12.6.1 Partially Ordered Sets -- 12.6.2 Lattices -- 12.6.3 Complete Partial Orders -- 12.6.4 Recursion -- 12.7 Review Questions -- 12.8 Summary -- References -- 13 Computability and Decidability -- 13.1 Introduction -- 13.2 Logicism and Formalism -- 13.3 Decidability -- 13.4 Computability -- 13.5 Computational Complexity -- 13.6 Review Questions -- 13.7 Summary -- References -- 14 A Short History of Logic -- 14.1 Introduction -- 14.2 Syllogistic Logic -- 14.3 Paradoxes and Fallacies -- 14.4 Stoic Logic -- 14.5 Boole's Symbolic Logic -- 14.5.1 Switching Circuits and Boolean Algebra -- 14.6 Application of Symbolic Logic to Digital Computing -- 14.7 Frege -- 14.8 Review Questions -- 14.9 Summary -- References -- 15 Propositional and Predicate Logic -- 15.1 Introduction -- 15.2 Propositional Logic -- 15.2.1 Truth Tables -- 15.2.2 Properties of Propositional Calculus -- 15.2.3 Proof in Propositional Calculus -- 15.2.4 Semantic Tableaux in Propositional Logic -- 15.2.5 Natural Deduction -- 15.2.6 Sketch of Formalization of Propositional Calculus -- 15.2.7 Applications of Propositional Calculus -- 15.2.8 Limitations of Propositional Calculus -- 15.3 Predicate Calculus -- 15.3.1 Sketch of Formalization of Predicate Calculus -- 15.3.2 Interpretation and Valuation Functions -- 15.3.3 Properties of Predicate Calculus -- 15.3.4 Applications of Predicate Calculus -- 15.3.5 Semantic Tableaux in Predicate Calculus -- 15.4 Review Questions -- 15.5 Summary -- References -- 16 Advanced Topics in Logic -- 16.1 Introduction -- 16.2 Fuzzy Logic -- 16.3 Temporal Logic -- 16.4 Intuitionist Logic -- 16.5 Undefined Values -- 16.5.1 Logic of Partial Functions -- 16.5.2 Parnas Logic -- 16.5.3 Dijkstra and Undefinedness -- 16.6 Logic and AI -- 16.7 Review Questions -- 16.8 Summary -- References -- 17 The Nature of Theorem Proving -- 17.1 Introduction.17.2 Early Automation of Proof -- 17.3 Interactive Theorem Provers -- 17.4 A Selection of Theorem Provers -- 17.5 Review Questions -- 17.6 Summary -- References -- 18 Software Engineering Mathematics -- 18.1 Introduction -- 18.2 What is Software Engineering? -- 18.3 Early Software Engineering Mathematics -- 18.4 Mathematics in Software Engineering -- 18.5 Software Inspections and Testing -- 18.6 Process Maturity Models -- 18.7 Review Questions -- 18.8 Summary -- References -- 19 Software Reliability and Dependability -- 19.1 Introduction -- 19.2 Software Reliability -- 19.2.1 Software Reliability and Defects -- 19.2.2 Cleanroom Methodology -- 19.2.3 Software Reliability Models -- 19.3 Dependability -- 19.4 Computer Security -- 19.5 System Availability -- 19.6 Safety-Critical Systems -- 19.7 Review Questions -- 19.8 Summary -- References -- 20 Formal Methods -- 20.1 Introduction -- 20.1.1 Definition 20.1 (Formal Specification) -- 20.2 Why Should We Use Formal Methods? -- 20.2.1 Comment 20.1 (Missile Safety) -- 20.3 Applications of Formal Methods -- 20.4 Tools for Formal Methods -- 20.5 Approaches to Formal Methods -- 20.5.1 Model-Oriented Approach -- 20.5.2 Axiomatic Approach -- 20.5.3 Comment 20.2 (Axiomatic Approach) -- 20.6 Proof and Formal Methods -- 20.7 The Future of Formal Methods -- 20.8 The Vienna Development Method -- 20.9 VDM♣, the Irish School of VDM -- 20.10 The Z Specification Language -- 20.11 The B Method -- 20.12 Predicate Transformers and Weakest Preconditions -- 20.13 The Process Calculi -- 20.14 The Parnas Way -- 20.15 Usability of Formal Methods -- 20.15.1 Why are Formal Methods difficult? -- 20.15.2 Characteristics of a Usable Formal Method -- 20.16 Review Questions -- 20.17 Summary -- 21 Z Formal Specification Language -- 21.1 Introduction -- 21.2 Sets -- 21.3 Relations -- 21.4 Functions -- 21.5 Sequences -- 21.6 Bags.21.7 Schemas and Schema Composition -- 21.8 Reification and Decomposition -- 21.9 Proof in Z -- 21.10 Review Questions -- 21.11 Summary -- Reference -- 22 Statistics -- 22.1 Introduction -- 22.2 Basic Statistics -- 22.2.1 Abuse of Statistics -- 22.2.2 Statistical Sampling and Data Collection -- 22.3 Frequency Distribution and Charts -- 22.4 Statistical Measures -- 22.4.1 Arithmetic Mean -- 22.4.2 Mode -- 22.4.3 Median -- 22.5 Variance and Standard Deviation -- 22.6 Correlation and Regression -- 22.6.1 Regression -- 22.7 Statistical Inference and Hypothesis Testing -- 22.8 Review Questions -- 22.9 Summary -- References -- 23 Probability Theory -- 23.1 Introduction -- 23.2 Basic Probability Theory -- 23.2.1 Laws of Probability -- 23.2.2 Bayes' Formula -- 23.3 Random Variables -- 23.4 Binomial and Poisson Distributions -- 23.5 The Normal Distribution -- 23.5.1 Unit Normal Distribution -- 23.5.2 Confidence Intervals and Tests of Significance -- 23.5.3 The Central Limit Theorem -- 23.6 Bayesianism -- 23.7 Queueing Theory -- 23.8 Review Questions -- 23.9 Summary -- References -- 24 Operations Research -- 24.1 Introduction -- 24.2 Linear Programming -- 24.2.1 Linear Programming Example -- 24.2.2 General Formulation of LP Problem -- 24.3 Cost-Volume-Profit Analysis -- 24.4 Game Theory -- 24.5 Review Questions -- 24.6 Summary -- References -- 25 Basic Financial Mathematics -- 25.1 Introduction -- 25.2 Simple Interest -- 25.2.1 Computing Future and Present Values -- 25.2.2 Computing Future Value -- 25.2.3 Computing Present Values -- 25.3 Compound Interest -- 25.3.1 Present Value Under Compound Interest -- 25.3.2 Equivalent Values -- 25.4 Basic Mathematics of Annuities -- 25.5 Loans and Mortgages -- 25.6 Review Questions -- 25.7 Summary -- Glossary -- Index.Texts in computer science.Computer scienceMathematicsDiscrete mathematicsComputer scienceMathematics.Discrete mathematics.004.0151O'Regan Gerard921504MiAaPQMiAaPQMiAaPQBOOK996464400303316Guide to Discrete Mathematics2174053UNISA01382nam0 2200277 i 450 VAN006311220080228120000.020080228d2008 |0itac50 baitaIT|||| |||||Duchamp e il dadaismoFrancis Picabia, Morton Schamberg, Jean Arp, Raoul Hausmann, Kurt Schwitters, Hannah Hoch, Man Ray, Max Ernst, Otto Dix, George GroszAlessandro Del PuppoEd. speciale per il sole 24 oreMilano : Il sole 24 ore ; Firenze : E-ducation.itc2008287 p.ill.29 cm. - In custodia. - Distribuito con: Il sole 24 ore, gennaio 20/2008.001VAN00630642001 ˆI ‰grandi maestri dell'artel'artista e il suo tempo210 Milano : Il sole 24 Ore ; Firenze : E-ducation.it2007-.20Dadaismo (Arte)VANC024357FIMilanoVANL000284Del PuppoAlessandroVANV050154459092Il sole 24 ore <editore>VANV108714650ITSOL20230728RICABIBLIOTECA DEL DIPARTIMENTO DI LETTERE E BENI CULTURALIIT-CE0103VAN07VAN0063112BIBLIOTECA DEL DIPARTIMENTO DI LETTERE E BENI CULTURALI07CONS Pb Duchamp 1780 07 18112 20080228 Duchamp e il dadaismo250467UNICAMPANIA03398nam 2200637 a 450 991078835870332120230725040405.00-8173-8353-0(CKB)3170000000046755(EBL)835632(OCoLC)772845340(SSID)ssj0000585340(PQKBManifestationID)11395151(PQKBTitleCode)TC0000585340(PQKBWorkID)10580376(PQKB)11378914(MiAaPQ)EBC835632(MdBmJHUP)muse9143(Au-PeEL)EBL835632(CaPaEBR)ebr10527763(EXLCZ)99317000000004675520100419d2010 uy 0engur|n|---|||||txtccrInside the eagle's head[electronic resource] an American Indian college /Angelle A. KhachadoorianTuscaloosa University of Alabama Pressc20101 online resource (256 p.)Contemporary American Indian studiesDescription based upon print version of record.0-8173-5614-2 Includes bibliographical references and index.Entering the turquoise gates : the Southwestern Indian Polytechnic Institute -- Thinking and talking about SIPI : narratives and metaphors -- "A standing army of school teachers" : American Indian education, assimilation, and the BIA -- Taking a new path : the decision to attend SIPI -- Life within the eagle's head -- SIPI is a reservation : family, friends, and mentors -- SIPI is what you make it : academics, administration, and working around the system -- SIPI is an opportunity : giving students the chance to dream -- Appendix. Studying the Southwestern Indian Polytechnic Institute. The Southwestern Indian Polytechnic Institute (SIPI) is a selfdescribed National American Indian Community College in Albuquerque, New Mexico. SIPI is operated by the Bureau of Indian Affairs, an agency of the U.S. government that has overseen and managed the relationship between the government and American Indian tribes for almost two hundred years. Students at SIPI are registered members of federally recognized American Indian tribes from throughout the contiguous United States and Alaska. A fascinatingly hybridized institution, SIPI attempts to meld twContemporary American Indian studies.Indian universities and collegesNew MexicoAlbuquerqueIndian college studentsNew MexicoAlbuquerqueAttitudesIndian college studentsUnited StatesAttitudesIndians of North AmericaEducation (Higher)New MexicoAlbuquerqueIndians of North AmericaEducation (Higher)Government policyUnited StatesIndian universities and collegesIndian college studentsAttitudes.Indian college studentsAttitudes.Indians of North AmericaEducation (Higher)Indians of North AmericaEducation (Higher)Government policy378.1/982997Khachadoorian Angelle A1491276MiAaPQMiAaPQMiAaPQBOOK9910788358703321Inside the eagle's head3713057UNINA