03895nam 2200613 a 450 991014321310332120170815113910.01-280-36620-697866103662000-470-34287-00-471-45849-X0-471-44968-7(CKB)111087027116208(EBL)163254(OCoLC)53121765(SSID)ssj0000125258(PQKBManifestationID)11133547(PQKBTitleCode)TC0000125258(PQKBWorkID)10026616(PQKB)11618169(MiAaPQ)EBC163254(PPN)196892538(EXLCZ)9911108702711620820021213d2003 uy 0engur|n|---|||||txtccrCombinatorics[electronic resource] /Russell Merris2nd ed.Hoboken, N.J. John Wileyc20031 online resource (572 p.)Wiley-Interscience series in discrete mathematics and optimizationDescription based upon print version of record.0-471-26296-X Includes bibliographical references (p. 501-502) and indexes.Combinatorics Second Edition; Contents; Preface; Chapter 1 The Mathematics of Choice; 1.1. The Fundamental Counting Principle; 1.2. Pascal's Triangle; *1.3. Elementary Probability; *1.4. Error-Correcting Codes; 1.5. Combinatorial Identities; 1.6. Four Ways to Choose; 1.7. The Binomial and Multinomial Theorems; 1.8. Partitions; 1.9. Elementary Symmetric Functions; *1.10. Combinatorial Algorithms; Chapter 2 The Combinatorics of Finite Functions; 2.1. Stirling Numbers of the Second Kind; 2.2. Bells, Balls, and Urns; 2.3. The Principle of Inclusion and Exclusion; 2.4. Disjoint Cycles2.5. Stirling Numbers of the First KindChapter 3 Pólya's Theory of Enumeration; 3.1. Function Composition; 3.2. Permutation Groups; 3.3. Burnside's Lemma; 3.4. Symmetry Groups; 3.5. Color Patterns; 3.6. Pólya's Theorem; 3.7. The Cycle Index Polynomial; Chapter 4 Generating Functions; 4.1. Difference Sequences; 4.2. Ordinary Generating Functions; 4.3. Applications of Generating Functions; 4.4. Exponential Generating Functions; 4.5. Recursive Techniques; Chapter 5 Enumeration in Graphs; 5.1. The Pigeonhole Principle; *5.2. Edge Colorings and Ramsey Theory; 5.3. Chromatic Polynomials*5.4. Planar Graphs5.5. Matching Polynomials; 5.6. Oriented Graphs; 5.7. Graphic Partitions; Chapter 6 Codes and Designs; 6.1. Linear Codes; 6.2. Decoding Algorithms; 6.3. Latin Squares; 6.4. Balanced Incomplete Block Designs; Appendix A1 Symmetric Polynomials; Appendix A2 Sorting Algorithms; Appendix A3 Matrix Theory; Bibliography; Hints and Answers to Selected Odd-Numbered Exercises; Index of Notation; IndexA mathematical gem-freshly cleaned and polished This book is intended to be used as the text for a first course in combinatorics. the text has been shaped by two goals, namely, to make complex mathematics accessible to students with a wide range of abilities, interests, and motivations; and to create a pedagogical tool, useful to the broad spectrum of instructors who bring a variety of perspectives and expectations to such a course. Features retained from the first edition:Lively and engaging writing styleTimely and appropriate examplesNumerous well-chosen exercisesFlexWiley series in discrete mathematics and optimization.Combinatorial analysisCombinatorial analysis.511.6511/.6Merris Russell1943-771920MiAaPQMiAaPQMiAaPQBOOK9910143213103321Combinatorics2001455UNINA03589nam 2200805 450 991082267320332120230607232340.03-11-094094-910.1515/9783110940947(CKB)3390000000062279(SSID)ssj0001522664(PQKBManifestationID)12627760(PQKBTitleCode)TC0001522664(PQKBWorkID)11463336(PQKB)10891103(MiAaPQ)EBC3049558(DE-B1597)57194(OCoLC)1013964839(OCoLC)900796297(DE-B1597)9783110940947(Au-PeEL)EBL3049558(CaPaEBR)ebr11008932(CaONFJC)MIL807157(OCoLC)922950379(EXLCZ)99339000000006227920020723d2001 uy| 0engurcnu||||||||txtccrIntegral geometry and inverse problems for kinetic equations /A. Kh. AmirovReprint 2014Utrecht ;Boston :VSP,2001.1 online resource (209 pages)Inverse and ill-posed problems series,1381-4524Bibliographic Level Mode of Issuance: Monograph3-11-035469-1 90-6764-352-1 Includes bibliographical references.Frontmatter -- Abstract -- Contents -- Introduction -- Chapter 1. Solvability of problems of integral geometry -- Chapter 2. Inverse problems for kinetic equations -- Chapter 3. Evolutionary equations -- Chapter 4. Inverse problems for second order differential equations -- Appendix Α. -- BibliographyIn this monograph a method for proving the solvability of integral geometry problems and inverse problems for kinetic equations is presented. The application of this method has led to interesting problems of the Dirichlet type for third order differential equations, the solvability of which appears to depend on the geometry of the domain for which the problem is stated. Another considered subject is the problem of integral geometry on paraboloids, in particular the uniqueness of solutions to the Goursat problem for a differential inequality, which implies new theorems on the uniqueness of solutions to this problem for a class of quasilinear hyperbolic equations. A class of multidimensional inverse problems associated with problems of integral geometry and the inverse problem for the quantum kinetic equations are also included. Inverse and ill-posed problems series.Integral geometryInverse problems (Differential equations)Chemical kineticsMathematicsDifferential Equations.Differential Inequality.Dirichlet.Goursat.Hyperbolic Equations.Integral Geometry Problems.Inverse Problems.Kinetic Equations.Multidimensional.Paraboloids.Quantum.Quasilinear.Integral geometry.Inverse problems (Differential equations)Chemical kineticsMathematics.516.3/62Amirov A. Kh1690381MiAaPQMiAaPQMiAaPQBOOK9910822673203321Integral geometry and inverse problems for kinetic equations4066039UNINA