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Format: 1 Online-Ressource (xxiv, 1045 p.) , ill , 25 cm

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

ISBN: 0124211801 , 9780124211803

Note: Includes bibliographical references (p. 899-905) and indexes

Additional Edition: Reproduktion von Discrete mathematics with applications c2004

Language: English

Subjects: Mathematics

Keywords: Diskrete Mathematik

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Format: xix, 716 p. : ill. : 24 cm.

ISBN: 0-12-421171-2

Note: Includes bibliographical references and index

Language: English

Subjects: Mathematics

Keywords: Zahlentheorie

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Format: 1 Online-Ressource

ISBN: 9781461484882 , 9781461484899

Language: English

Keywords: Lucas-Zahlenreihe ; Pell-Gleichung

DOI: 10.1007/978-1-4614-8489-9

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Format: 1 online resource (xvi, 652 pages) : , illustrations

ISBN: 9781118742327 , 111874232X

Note: Leonardo Fibonacci -- , The Rabbit Problem -- , Fibonacci Numbers in Nature -- , Fibonacci Numbers: Additional Occurrences -- , Fibonacci and Lucas Identities -- , Geometric Paradoxes -- , Generalized Fibonacci Numbers -- , Additional Fibonacci and Lucas Formulas -- , The Euclidean Algorithm -- , Solving Recurrence Relations -- , Completeness Theorems -- , Pascal's Triangle -- , Pascal-Like Triangles -- , Additional Pascal-Like Triangles -- , Hosoya's Triangle -- , Divisibility Properties -- , Generalized Fibonacci Numbers Revisited -- , Generating Functions -- , Generating Functions Revisited -- , The Golden Ratio -- , The Golden Ratio Revisited -- , Golden Triangles -- , Golden Rectangles -- , Fibonacci Geometry -- , Regular Pentagons -- , The Golden Ellipse and Hyperbola -- , Continued Fractions -- , Weighted Fibonacci and Lucas Sums -- , Fibonacci and Lucas Sums Revisited -- , The Knapsack Problem -- , Fibonacci Magic Squares -- , Fibonacci Matrices -- , Fibonacci Determinants -- , Fibonacci and Lucas Congruences -- , Fibonacci and Lucas Periodicity -- , Fibonacci and Lucas Series -- , Fibonacci Polynomials -- , Lucas Polynomials -- , Jacobsthal Polynomials -- , Zeros of Fibonacci and Lucas Polynomials -- , Morgan-Voyce Polynomials -- , Fibonometry -- , Fibonacci and Lucas Subscripts -- , Gaussian Fibonacci and Lucas Numbers -- , Analytic Extensions -- , Tribonacci Numbers -- , Tribonacci Polynomials -- , The First 100 Fibonacci and Lucas Numbers -- , The First 100 Fibonacci Numbers and Their Prime Factorizations -- , The First 100 Lucas Numbers and Their Prime Factorizations.

Additional Edition: Print version: Koshy, Thomas. Fibonacci and Lucas numbers with applications. New York : Wiley, ©2001 ISBN 0471399698

Language: English

Subjects: Mathematics

Keywords: Electronic books. ; Electronic books. ; Electronic books. ; Electronic books ; Electronic books. ; Electronic books. ; Electronic books.

URL: https://onlinelibrary.wiley.com/doi/book/10.1002/9781118742327

URL: https://onlinelibrary.wiley.com/doi/book/10.1002/9781118742327

URL: https://onlinelibrary.wiley.com/doi/book/10.1002/9781118033067

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URL: https://onlinelibrary.wiley.com/doi/book/10.1002/9781118033067

URL: https://onlinelibrary.wiley.com/doi/book/10.1002/9781118742327

URL: https://onlinelibrary.wiley.com/doi/book/10.1002/9781118033067

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Format: 1 online resource (1079 p.)

Edition: 1st ed.

ISBN: 1-281-05068-7 , 9786611050689 , 0-08-047734-8

Content: This approachable text studies discrete objects and the relationships that bind them. It helps students understand and apply the power of discrete math to digital computer systems and other modern applications. It provides excellent preparation for courses in linear algebra, number theory, and modern/abstract algebra and for computer science courses in data structures, algorithms, programming languages, compilers, databases, and computation.* Covers all recommended topics in a self-contained, comprehensive, and understandable format for students and new professionals * Emphasizes pr

Note: Description based upon print version of record. , Front Cover; Discrete Mathematics with Applications; Copyright Page; Table of Contents; Preface; A Word to the Student; Chapter 1. The Language of Logic; 1.1 Propositions; 1.2 Logical Equivalences; 1.3 Quantifiers; 1.4 Arguments (optional); 1.5 Proof Methods; Chapter Summary; Review Exercises; Supplementary Exercises; Computer Exercises; Exploratory Writing Projects; Enrichment Readings; Chapter 2. The Language of Sets; 2.1 The Concept of a Set; 2.2 Operations with Sets; 2.3 Computer Operations with Sets (optional); 2.4 The Cardinality of a Set; 2.5 Recursively Defined Sets; Chapter Summary , Review Exercises Supplementary Exercises; Computer Exercises; Exploratory Writing Projects; Enrichment Readings; Chapter 3. Functions and Matrices; 3.1 The Concept of a Function; 3.2 Special Functions; 3.3 Properties of Functions; 3.4 The Pigeonhole Principle; 3.5 Composition of Functions; 3.6 Sequences and the Summation Notation; 3.7 Matrices; Chapter Summary; Review Exercises; Supplementary Exercises; Computer Exercises; Exploratory Writing Projects; Enrichment Readings; Chapter 4. Induction and Algorithms; 4.1 The Division Algorithm; 4.2 Divisibility Properties; 4.3 Nondecimal Bases , 4.4 Mathematical Induction 4.5 Algorithm Correctness; 4.6 The Growth of Functions; 4.7 Complexities of Algorithms (optional); Chapter Summary; Review Exercises; Supplementary Exercises; Computer Exercises; Exploratory Writing Projects; Enrichment Readings; Chapter 5. Recursion; 5.1 Recursively Defined Functions; 5.2 Solving Recurrence Relations; 5.3 Solving Recurrence Relations Revisited; 5.4 Generating Functions; 5.5 Recursive Algorithms; 5.6 Correctness of Recursive Algorithms; 5.7 Complexities of Recursive Algorithms (optional); Chapter Summary; Review Exercises; Supplementary Exercises , Computer Exercises Exploratory Writing Projects; Enrichment Readings; Chapter 6. Combinatorics and Discrete Probability; 6.1 The Fundamental Counting Principles; 6.2 Permutations; 6.3 Derangements; 6.4 Combinations; 6.5 Permutations and Combinations with Repetitions; 6.6 The Binomial Theorem; 6.7 The Generalized Inclusion-Exclusion Principle (GIEP) (optional); 6.8 Discrete Probability (optional); 6.9 Additional Topics in Probability (optional); Chapter Summary; Review Exercises; Supplementary Exercises; Computer Exercises; Exploratory Writing Projects; Enrichment Readings; Chapter 7. Relations , 7.1 Boolean Matrices 7.2 Relations and Digraphs; 7.3 Computer Representations of Relations (optional); 7.4 Properties of Relations; 7.5 Operations on Relations; 7.6 The Connectivity Relation (optional); 7.7 Transitive Closure (optional); 7.8 Equivalence Relations; 7.9 Partial and Total Orderings; Chapter Summary; Review Exercises; Supplementary Exercises; Computer Exercises; Exploratory Writing Projects; Enrichment Readings; Chapter 8. Graphs; 8.1 Graphs; 8.2 Computer Representations of Graphs (optional); 8.3 Isomorphic Graphs; 8.4 Paths, Cycles, and Circuits , 8.5 Eulerian and Hamiltonian Graphs , English

Additional Edition: ISBN 0-12-421180-1

Language: English

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Format: XIV, 422 S. : , Ill., graph. Darst.

ISBN: 978-0-19-533454-8

Language: English

Subjects: Mathematics

Keywords: Catalan-Vermutung

URL: http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017159944&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA

URL: Inhaltsverzeichnis

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Format: Online Ressource (xxiv, 1045 p.) , graph. Darst.

Edition: Online-Ausg. Amsterdam Elsevier Science & Technology Online-Ressource ScienceDirect

ISBN: 9780124211803 , 0124211801 , 9780080477343 , 0080477348 , 1281050687 , 9781281050687

Content: Preface: A Word to the Student; 1. The Language of Logic; 2. The Language of Sets; 3. Functions and Matrices; 4. Induction and Algorithms; 5. Recursion; 6. Combinatorics and Discrete Probability; 7. Relations; 8. Graphs; 9. Trees; 10. Digraphs; 11. Formal Languages and Finite-State Machines; 12. Boolean Algebra and Combinatorial Circuits; Appendix; Bibliography; Solutions to Odd Numbered Exercises; Index

Content: This approachable text studies discrete objects and the relationsips that bind them. It helps students understand and apply the power of discrete math to digital computer systems and other modern applications. It provides excellent preparation for courses in linear algebra, number theory, and modern/abstract algebra and for computer science courses in data structures, algorithms, programming languages, compilers, databases, and computation. * Covers all recommended topics in a self-contained, comprehensive, and understandable format for students and new professionals * Emphasizes problem-solving techniques, pattern recognition, conjecturing, induction, applications of varying nature, proof techniques, algorithm development and correctness, and numeric computations * Weaves numerous applications into the text * Helps students learn by doing with a wealth of examples and exercises: - 560 examples worked out in detail - More than 3,700 exercises - More than 150 computer assignments - More than 600 writing projects * Includes chapter summaries of important vocabulary, formulas, and properties, plus the chapter review exercises * Features interesting anecdotes and biographies of 60 mathematicians and computer scientists * Instructor's Manual available for adopters * Student Solutions Manual available separately for purchase (ISBN: 0124211828)

Note: Includes bibliographical references (p. 899-905) and indexes. - Description based on print version record , English

Additional Edition: ISBN 0124211801

Additional Edition: ISBN 1281050687

Additional Edition: ISBN 0124211828

Additional Edition: Druckausg. Koshy, Thomas Discrete mathematics with applications Amsterdam : Elsevier Acad. Press, 2004 ISBN 0124211801

Additional Edition: ISBN 9788181478870

Language: English

Subjects: Mathematics

Keywords: Diskrete Mathematik ; Electronic books ; Electronic books

DOI: 10.1016/B978-0-12-421180-3.X5000-1

URL: https://doi.org/10.1016/B978-0-12-421180-3.X5000-1

URL: Volltext  (Deutschlandweit zugänglich)

URL: lizenzpflichtig

URL: Inhaltstext

UID:

Format: xxiv, 1045 p. , ill. : 25 cm

ISBN: 0124211801

Note: Includes bibliographical references (p. 899-905) and indexes

Language: English

Subjects: Mathematics

Keywords: Diskrete Mathematik

URL: Table of contents

URL: Inhaltsverzeichnis

URL: Verlagsangaben

URL: Inhaltstext

UID:

Format: XXIII, 771 S. , Ill., graph. Darst. , 24cm

Edition: 2. ed.

ISBN: 0123724872 , 9780123724878

Note: Includes bibliographical references and index. - Previous ed.: 2002. - Formerly CIP

Additional Edition: Erscheint auch als Online-Ausgabe Koshy, Thomas Elementary Number Theory with Applications. Burlington : Elsevier Science & Technology, 2007 ISBN 9780080547091

Language: English

Subjects: Mathematics

Keywords: Elementare Zahlentheorie ; Anwendung

URL: http://www.loc.gov/catdir/toc/ecip0712/2007010165.html

URL: http://www.loc.gov/catdir/enhancements/fy0811/2007010165-d.html

UID:

Format: 1 online resource.

ISBN: 9781118742143 , 1118742141 , 9781118742297 , 111874229X , 9781118742181 , 1118742184 , 9781118742167 , 1118742168

Series Statement: Pure and applied mathematics

Note: List of Symbols xiii ; Preface xv ; 31. Fibonacci and Lucas Polynomials I 1 ; 31.1. Fibonacci and Lucas Polynomials 3 ; 31.2. Pascal's Triangle 18 ; 31.3. Additional Explicit Formulas 22 ; 31.4. Ends of the Numbers l〈sub〉n〈/sub〉 25 ; 31.5. Generating Functions 26 ; 31.6. Pell and Pell-Lucas Polynomials 27 ; 31.7. Composition of Lucas Polynomials 33 ; 31.8. De Moivre-like Formulas 35 ; 31.9. Fibonacci-Lucas Bridges 36 ; 31.10. Applications of Identity (31.51) 37 ; 31.11. Infinite Products 48 ; 31.12. Putnam Delight Revisited 51 ; 31.13. Infinite Simple Continued Fraction 54 ; 32. Fibonacci and Lucas Polynomials II 65 ; 32.1. Q-Matrix 65 ; 32.2. Summation Formulas 67 ; 32.3. Addition Formulas 71 ; 32.4. A Recurrence for f〈sub〉n〈/sub〉〈sup〉2〈/sup〉 76 ; 32.5. Divisibility Properties 82 ; 33. Combinatorial Models II 87 ; 33.1. A Model for Fibonacci Polynomials 87 ; 33.2. Breakability 99 ; 33.3. A Ladder Model 101 ; 33.4. A Model for Pell-Lucas Polynomials: Linear Boards 102 ; 33.5. Colored Tilings 103 ; 33.6. A New Tiling Scheme 104 ; 33.7. A Model for Pell-Lucas Polynomials: Circular Boards 107 ; 33.8. A Domino Model for Fibonacci Polynomials 114 ; 33.9. Another Model for Fibonacci Polynomials 118 ; 34. Graph-Theoretic Models II 125 ; 34.1. Q-Matrix and Connected Graph 125 ; 34.2. Weighted Paths 126 ; 34.3. Q-Matrix Revisited 127 ; 34.4. Byproducts of the Model 128 ; 34.5. A Bijection Algorithm 136 ; 34.6. Fibonacci and Lucas Sums 137 ; 34.7. Fibonacci Walks 140 ; 35. Gibonacci Polynomials 145 ; 35.1. Gibonacci Polynomials 145 ; 35.2. Differences of Gibonacci Products 159 ; 35.3. Generalized Lucas and Ginsburg Identities 174 ; 35.4. Gibonacci and Geometry 181 ; 35.5. Additional Recurrences 184 ; 35.6. Pythagorean Triples 188 ; 36. Gibonacci Sums 195 ; 36.1. Gibonacci Sums 195 ; 36.2. Weighted Sums 206 ; 36.3. Exponential Generating Functions 209 ; 36.4. Infinite Gibonacci Sums 215 ; 37. Additional Gibonacci Delights 233 ; 37.1. Some Fundamental Identities Revisited 233 ; 37.2. Lucas and Ginsburg Identities Revisited 238 ; 37.3. Fibonomial Coefficients 247 ; 37.4. Gibonomial Coefficients 250 ; 37.5. Additional Identities 260 ; 37.6. Strazdins' Identity 264 ; 38. Fibonacci and Lucas Polynomials III 269 ; 38.1. Seiffert's Formulas 270 ; 38.2. Additional Formulas 294 ; 38.3. Legendre Polynomials 314 ; 39. Gibonacci Determinants 321 ; 39.1. A Circulant Determinant 321 ; 39.2. A Hybrid Determinant 323 ; 39.3. Basin's Determinant 333 ; 39.4. Lower Hessenberg Matrices 339 ; 39.5. Determinant with a Prescribed First Row 343 ; 40. Fibonometry II 347 ; 40.1. Fibonometric Results 347 ; 40.2. Hyperbolic Functions 356 ; 40.3. Inverse Hyperbolic Summation Formulas 361 ; 41. Chebyshev Polynomials 371 ; 41.1. Chebyshev Polynomials T〈sub〉n〈/sub〉(x) 372 ; 41.2. T〈sub〉n〈/sub〉(x) and Trigonometry 384 ; 41.3. Hidden Treasures in Table 41.1 386 ; 41.4. Chebyshev Polynomials U〈sub〉n〈/sub〉(x) 396 ; 41.5. Pell's Equation 398 ; 41.6. U n (x) and Trigonometry 399 41.7. Addition and Cassini-like Formulas 401 41.8. Hidden Treasures in Table 41.8 402 41.9. A Chebyshev Bridge 404 ; 41.10. T〈sub〉n〈/sub〉 and U〈sub〉n〈/sub〉 as Products 405 ; 41.11. Generating Functions 410 42. Chebyshev Tilings 415 42.1. Combinatorial Models for U 415 42.2. Combinatorial Models for T 420 42.3. Circular Tilings 425 43. Bivariate Gibonacci Family I 429 ; 43.1. Bivariate Gibonacci Polynomials 429 ; 43.2. Bivariate Fibonacci and Lucas Identities 430 ; 43.3. Candido's Identity Revisited 439 ; 44. Jacobsthal Family 443 ; 44.1. Jacobsthal Family 444 ; 44.2. Jacobsthal Occurrences 450 ; 44.3. Jacobsthal Compositions 452 ; 44.4. Triangular Numbers in the Family 459 ; 44.5. Formal Languages 468 ; 44.6. A USA Olympiad Delight 480 ; 44.7. A Story of 1, 2, 7, 42, 429,...483 ; 44.8. Convolutions 490 ; 45. Jacobsthal Tilings and Graphs 499 ; 45.1. 1 × n Tilings 499 ; 45.2. 2 × n Tilings 505 ; 45.3. 2 × n Tubular Tilings 510 ; 45.4. 3 × n Tilings 514 ; 45.5. Graph-Theoretic Models 518 ; 45.6. Digraph Models 522 ; 46. Bivariate Tiling Models 537 ; 46.1. A Model for 537 ; 46.2. Breakability 539 ; 46.3. Colored Tilings 542 ; 46.4. A Model for l x y 543 46.5. Colored Tilings Revisited 545 ; 46.6. Circular Tilings Again 547 ; 47. Vieta Polynomials 553 ; 47.1. Vieta Polynomials 554 ; 47.2. Aurifeuille's Identity 567 ; 47.3. Vieta-Chebyshev Bridges 572 ; 47.4. Jacobsthal-Chebyshev Links 573 ; 47.5. Two Charming Vieta Identities 574 47.6. Tiling Models for V n 576 47.7. Tiling Models for 48. Bivariate Gibonacci Family II 591 48.1. Bivariate Identities 591 48.2. Additional Bivariate Identities 594 ; 48.3. A Bivariate Lucas Counterpart 599 ; 48.4. A Summation Formula for 600 ; 48.5. A Summation Formula for l〈sub〉2n〈/sub〉(x, y) 602 ; 48.6. Bivariate Fibonacci Links 603 ; 48.7. Bivariate Lucas Links 606 ; 49. Tribonacci Polynomials 611 ; 49.1. Tribonacci Numbers 611 ; 49.2. Compositions with Summands 1, 2, and 3 613 ; 49.3. Tribonacci Polynomials 616 ; 49.4. A Combinatorial Model 618 ; 49.5. Tribonacci Polynomials and the Q-Matrix 624 ; 49.6. Tribonacci Walks 625 ; 49.7. A Bijection between the Two Models 627 ; Appendix 631 ; A.1. The First 100 Fibonacci and Lucas Numbers 631 ; A.2. The First 100 Pell and Pell-Lucas Numbers 634 ; A.3. The First 100 Jacobsthal and Jacobsthal-Lucas Numbers 638 ; A.4. The First 100 Tribonacci Numbers 642 ; Abbreviations 644 ; Bibliography 645 ; Solutions to Odd-Numbered Exercises 661 ; Index 725

Additional Edition: Print version: Koshy, Thomas. Fibonacci and Lucas numbers with applications. Hoboken, New Jersey : John Wiley & Sons, Inc., 2018 ISBN 9781118742082

Language: English

Keywords: Electronic books. ; Electronic books. ; Electronic books.

URL: https://onlinelibrary.wiley.com/doi/book/10.1002/9781118742297

URL: https://onlinelibrary.wiley.com/doi/book/10.1002/9781118742297

URL: https://onlinelibrary.wiley.com/doi/book/10.1002/9781118742297