Discrete mathematics with algorithms

Albertson, Michael O. and Joan P. Hutschhinson:

ISBN 10: 0471612782 / ISBN 13: 9780471612780

Editore: New York, NY [u.a.] : Wiley, 1988

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kart., 24 cm, XIII, 546 S : graph. Darst.; geringfügiger Kantenberieb; guter Zustand CONTENTS Chapter 1 SETS AND ALGORITHMS: AN INTRODUCTION : 1 Introduction :2 Binary Arithmetic and the Magic Trick Revisited :3 Algorithms :4 Between Decimal and Binary :5 Set Theory and the Magic Trick :6 Pictures of Sets :7 Subsets :8 Set Cardinality and Counting :9 Functions 1:10 Boolean Functions and Boolean Algebra 1:11 A Look Back 1 5 8 15 20 25 29 35 40 51 59 Chapter 2 ARITHMETIC 2:1 2:2 2:3 2:4 2:5 2:6 Introduction Exponentiation, Induction Three Inductive Exponentiation A First Look Proofs Revisited How Good Is Fast Exponentiation? 65 65 68 71 80 88 91 CONTENTS 2:7 How Logarithms Grow 2:8 The "Big Oh" Notation 2:9 2" ^ O(p(n)): Proof by Contradiction 2:10 Good and Bad Algorithms 2:11 Another Look Back 97 102 110 118 122 Chapter 3 ARITHMETIC OF SETS 3:1 Introduction 3:2 Binomial Coefficients 3:3 Subsets of Sets 3:4 Permutations 3:5 An Application of Permutations: The Game of Mastermind 3:6 The Binomial Theorem 3:7 Important Subsets 127 127 131 141 153 161 168 176 Chapter 4 NUMBER THEORY 4:1 Greatest Common Divisors 4:2 Another Look at Complexities 4:3 The Euclidean Algorithm 4:4 Fibonacci Numbers 4:5 The Complexity of the Euclidean Algorithm 4:6 Congruences and Equivalence Relations 4:7 An Application: Public Key Encryption Schemes 4:8 The Dividends 181 181 186 190 197 206 211 222 234 Chapter 5 GRAPH THEORY 5:1 Building the LAN 5:2 Graphs 5:3 Trees and the LAN 5:4 A Good Minimum-Weight Spanning Tree Algorithm 5:5 An Ode to Greed 5:6 Graphical Highlights 239 239 241 251 263 272 279 CONTENTS Chapter 6 SEARCHING AND SORTING 6:1 Introduction: Record Keeping 6:2 Searching a Sorted File 6:3 Sorting a File 6:4 Search Trees 6:5 Lower Bounds on Sorting 6:6 Recursion 6:7 MERGESORT 6:8 Sorting It All Out 283 283 290 295 302 310 317 325 331 Chapter 7 RECURRENCE RELATIONS 339 7:1 Beginnings of Sequences 339 7:2 Iteration and Induction 346 7:3 Linear Homogeneous Recurrence Relations with Constant Coefficients 353 7:4 LHRRWCCs with Multiple Roots: More About Rabbits 364 7:5 Divide-and-Conquer Recurrence Relations 372 7:6 Recurring Thoughts 381 Chapter 8 MORE GRA PH THEOR Y 8:1 Minimum-Distance Trees 8:2 Eulerian Cycles . ; 8:3 Hamiltonian Cycles 8:4 Minimum-Weight Hamiltonian Cycles 8:5 Graph Coloring and an Application to Storage Allocation 389 389 399 410 425 431 SOLUTIONS TO QUESTIONS 451 INDEX 538 ALGORITHMS AND PROCEDURES 543 NOTATIONS 545 Z34691H4 ISBN 0471612782 Gemäß §19 UStG weist dieser Verkäufer keine Mehrwertsteuer aus (Kleinunternehmerstatus). Es erfolgt KEINE Lieferung mehr wegen der EPR-Regelung in folgende Länder: Aufgrund der EPR-Regelung kann in folgende Länder KEINE LIEFERUNG mehr erfolgen: Bulgarien, Finnland, Frankreich, Griechenland, Luxemburg, Österreich, Polen, Rumänien, Schweden, Slowakei, Spanien Sprache: Englisch Gewicht in Gramm: 550.

Codice articolo 42587

Dati bibliografici

• Titolo: Discrete mathematics with algorithms
• Editore: New York, NY [u.a.] : Wiley
• Data di pubblicazione: 1988
• Lingua: Inglese
• ISBN 10: 0471612782
• ISBN 13: 9780471612780
• Rilegatura: Brossura
• Edizione: prima edizione
• Cataloghi dei venditori:
  • Wissenschaft / Wissen

Descrizione articolo

Riassunto

Here is a first-year course in discrete mathematics, requiring no calculus or computer programming experience, for students on computer science and mathematics courses. The approach stresses finding efficient algorithms, rather than existential results. It provides an introduction to constructing proofs (especially by induction), and an introduction to algorithmic problem solving. All algorithms are presented in English, in a format compatible with the PASCAL programming language. The text contains many exercises, with answers at the back of the book (detailed solutions being supplied for difficult problems).