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Hashing in computer science : fifty years of slicing and dicing / Alan G. Konheim

By: Resource type: Ressourcentyp: Buch (Online)Book (Online)Language: English Publisher: Hoboken, N.J : John Wiley & Sons, c2010Edition: Online-AusgDescription: Online-Ressource (1 online resource (xvii, 386 p.)) : illISBN:
  • 9781282686274
  • 1282686275
  • 9780470630600
Subject(s): Additional physical formats: 9780470344736 | Erscheint auch als: 0470738529 Druck-AusgabeDDC classification:
  • 005.82
  • 005.8/2
LOC classification:
  • QA76.9.H36
Online resources: Summary: Written by one of the developers of the technology, Hashing is both a historical document on the development of hashing and an analysis of the applications of hashing in a society increasingly concerned with security. The material in this book is based on courses taught by the author, and key points are reinforced in sample problems and an accompanying instructor s manual. Graduate students and researchers in mathematics, cryptography, and security will benefit from this overview of hashing and the complicated mathematics that it requires.Summary: HASHING IN COMPUTERSCIENCE, FIFTY YEARS OF SLICINGAND DICING -- CONTENTS -- PREFACE -- PART I: MATHEMATICAL PRELIMINARIES -- CHAPTER 1: Counting -- 1.1 THE SUM AND PRODUCT RULES -- 1.2 MATHEMATICAL INDUCTION -- 1.3 FACTORIAL -- 1.4 BINOMIAL COEFFICIENTS -- 1.5 MULTINOMIAL COEFFICIENTS -- 1.6 PERMUTATIONS -- 1.7 COMBINATIONS -- 1.8 THE PRINCIPLE OF INCLUSION-EXCLUSION -- 1.9 PARTITIONS -- 1.10 RELATIONS -- 1.11 INVERSE RELATIONS -- APPENDIX 1: Summations Involving Binomial Coefficients -- CHAPTER 2: Recurrence and Generating Functions -- 2.1 RECURSIONS -- 2.2 GENERATING FUNCTIONS -- 2.3 LINEAR CONSTANT COEFFICIENT RECURSIONS -- 2.4 SOLVING HOMOGENEOUS LCCRS USING GENERATING FUNCTIONS -- 2.5 THE CATALAN RECURSION -- 2.6 THE UMBRAL CALCULUS -- 2.7 EXPONENTIAL GENERATING FUNCTIONS -- 2.8 PARTITIONS OF A SET: THE BELL AND STIRLING NUMBERS -- 2.9 ROUCHÉ'S THEOREM AND THE LAGRANGE'S INVERSION FORMULA -- CHAPTER 3: Asymptotic Analysis -- 3.1 GROWTH NOTATION FOR SEQUENCES -- 3.2 ASYMPTOTIC SEQUENCES AND EXPANSIONS -- 3.3 SADDLE POINTS -- 3.4 LAPLACE'S METHOD -- 3.5 THE SADDLE POINT METHOD -- 3.6 WHEN WILL THE SADDLE POINT METHOD WORK? -- 3.7 SADDLE POINT BOUNDS -- 3.8 EXAMPLES OF SADDLE POINT ANALYSIS -- CHAPTER 4: Discrete Probability Theory -- 4.1 THE ORIGINS OF PROBABILITY THEORY -- 4.2 CHANCE EXPERIMENTS, SAMPLE POINTS, SPACES, AND EVENTS -- 4.3 RANDOM VARIABLES -- 4.4 MOMENTS-EXPECTATION AND VARIANCE -- 4.5 THE BIRTHDAY PARADOX -- 4.6 CONDITIONAL PROBABILITY AND INDEPENDENCE -- 4.7 THE LAW OF LARGE NUMBERS (LLN) -- 4.8 THE CENTRAL LIMIT THEOREM (CLT) -- 4.9 RANDOM PROCESSES AND MARKOV CHAINS -- CHAPTER 5: Number Theory and Modern Algebra -- 5.1 PRIME NUMBERS -- 5.2 MODULAR ARITHMETIC AND THE EUCLIDEAN ALGORITHM -- 5.3 MODULAR MULTIPLICATION -- 5.4 THE THEOREMS OF FERMAT2 AND EULER -- 5.5 FIELDS AND EXTENSION FIELDS -- 5.6 FACTORIZATION OF INTEGERS.PPN: PPN: 808945068Package identifier: Produktsigel: ZDB-26-MYL | ZDB-30-PAD | ZDB-30-PQE
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