Discrete structures with contemporary applications:
"Reflecting many of the recent advances and trends in this area, this classroom-tested text covers the core topics in discrete structures as outlined by the ACM and explores an assortment of novel applications, including simulations, genetic algorithms, network flows, probabilistic primality te...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boca Raton [u.a.]
CRC Press
2011
|
| Schriftenreihe: | A Chapman & Hall book
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Zusammenfassung: | "Reflecting many of the recent advances and trends in this area, this classroom-tested text covers the core topics in discrete structures as outlined by the ACM and explores an assortment of novel applications, including simulations, genetic algorithms, network flows, probabilistic primality tests, public key cryptography, and coding theory. It presents algorithms in pseudo code and offers sample programs via the author's website. The text also includes a wide variety of examples and exercises, with solutions in the appendices. In addition, computer exercises teach students how to write their own programs. A solutions manual is available for qualifying instructors"-- |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | XIX, 982 S. Ill., graph. Darst. |
| ISBN: | 9781439817681 |
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| 245 | 1 | 0 | |a Discrete structures with contemporary applications |c Alexander Stanoyevitch |
| 264 | 1 | |a Boca Raton [u.a.] |b CRC Press |c 2011 | |
| 300 | |a XIX, 982 S. |c Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 490 | 0 | |a A Chapman & Hall book | |
| 500 | |a Includes bibliographical references and index | ||
| 520 | |a "Reflecting many of the recent advances and trends in this area, this classroom-tested text covers the core topics in discrete structures as outlined by the ACM and explores an assortment of novel applications, including simulations, genetic algorithms, network flows, probabilistic primality tests, public key cryptography, and coding theory. It presents algorithms in pseudo code and offers sample programs via the author's website. The text also includes a wide variety of examples and exercises, with solutions in the appendices. In addition, computer exercises teach students how to write their own programs. A solutions manual is available for qualifying instructors"-- | ||
| 650 | 4 | |a Computer science / Mathematics | |
| 650 | 4 | |a Logic, Symbolic and mathematical | |
| 650 | 4 | |a Probabilities | |
| 650 | 7 | |a COMPUTERS / Operating Systems / General |2 bisacsh | |
| 650 | 7 | |a MATHEMATICS / Combinatorics |2 bisacsh | |
| 650 | 4 | |a Informatik | |
| 650 | 4 | |a Mathematik | |
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Datensatz im Suchindex
| _version_ | 1804143500813402112 |
|---|---|
| adam_text | Contents
Preface
xiii
About the Author
xix
Dependency Chart
xxi
Chapter
1:
Logic and Sets
1
1.1:
Logical Operators: Statements and Truth Values, Negations,
Conjunctions, and Disjunctions, Truth Tables, Conditional Statements
(Implications), Converses and
Contrapositives,
Logical Equivalence and
Biconditionals, Hierarchy of Logical Operators, Some Useful Logical
Equivalences, Logical Implication, Proofs and Counterexamples, Logical
Puzzles, Exercises, Computer Exercises
1.2:
Logical Quantifiers: Predicates and Universes, Universal and
Existential Quantifiers, Negations of Quantifiers, Nested Quantifiers,
Exercises
1.3:
Sets: Sets and Their Elements, Unions and Intersections, Venn
Diagrams, Subsets and the Empty Set, Complements and Differences of
Sets, Set Theoretic Identities, Unions and Intersections of Set Families,
Power Sets, Cartesian Products of Sets, The Historical Development of
Logic and Sets, Exercises, Computer Exercises
Chapter
2:
Relations and Functions, Boolean Algebra,
61
and Circuit Design
2.1:
Relations and Functions: Binary Relations, Functions, Function
Images and Pre-images, One-to-One, Onto, and Bijective Functions,
Inverse Functions, Exercises
2.2:
Equivalence Relations and Partial
Orderings:
Equivalence
Relations, Congruence Modulo a Positive Integer, Equivalence Classes
and Their Representatives, Strings, Partial Order(ings),
Hasse
Diagrams,
Poset
Isomorphisms, Exercises
vi
Contents
2.3:
Boolean Algebra and Circuit
Design:
Boolean
Operations,
Variables,
and Functions, Boolean Algebra Identities, Sums, Products,
and Complements of Boolean Functions, Sums of Products Expansions
(Disjunctive Normal Form), Duality, Logic Gates and Circuit Designs,
Karnaugh Maps, Exercises
ChapterS: The Integers, Induction, and Recursion 111
3.1:
Mathematical Induction: The Principle of Mathematical Induction:
Basic Form, The Principle of Mathematical Induction: General Form,
Strong Mathematical Induction, Finite Geometric Series, Exercises
3.2:
Recursion: Infinite Sequences, Recursion and Recursively Defined
Sequences, The Fibonacci Sequence, Recursive Sequences of Higher
Degree, Explicit Solution Methods for Linear Recursion Formulas,
Exercises
Appendix: Recursive Definitions and Structural Induction
Computer Exercises
3.3:
Some Topics in Elementary Number Theory: Divisibility, Primes,
The Prime Number Theorem, Greatest Common Divisors, Relatively
Prime Integers, The Division Algorithm, The Euclidean Algorithm,
Congruent Substitutions in Modular Arithmetic,
Fermat
s
Little Theorem,
Euler
s
Theorem, Orders and Primitive Roots, Exercises, Computer
Exercises
Appendix: Probabilistic Primality Tests
Chapter
4:
Number Systems
187
4.1:
Representations of Integers in Different Bases: Representation of
Integers in a Base b, Hexadecimal) and Binary Expansions, Addition
Algorithm with Base
b
Expansions, Subtraction Algorithm with Base
b
Expansions, Multiplication Algorithm in Base
b
Expansions, Exercises,
Computer Exercises
4.2:
Modular Arithmetic and Congruences: Modular Integer Systems,
Modular Inverses, Fast Modular Exponentiation, Congruences, The
Extended Euclidean Algorithm, Solving Linear Congruences, The
Chinese Remainder Theorem, Pseudo-Random Numbers: The Linear
Congruential Method, Exercises, Computer Exercises
4.3:
Matrices: Matrix Addition, Subtraction, and Scalar Multiplication,
Matrix Multiplication, Matrix Arithmetic, Definition of an Invertible
Contents
vii
(Square) Matrix, The
Determinant
of
a
Square Matrix,
Inverses of
2
χ
2
Matrices, The Transpose of a Matrix, Modular Integer Matrices, The
Classical Adjoint (for Matrix Inversions), Application of Modular
Matrices: The Hill Cryptosystem, Exercises, Computer Exercises
4.4:
Floating Point Arithmetic: Exact Arithmetic, Floating Point
Arithmetic Systems, Unit Roundoff (Machine
Epsilon),
Underflows,
Overflows, Exercises, Computer Exercises
4.5:
Public Key Cryptography: An Informal Analogy for a Public Key
Cryptosystem, The Quest for Secure Electronic Key Exchange, One-Way
Functions, Review of the Discrete Logarithm Problem, The Diffie-
Hellman Key Exchange, The Quest for a Complete Public Key
Cryptosystem, The RSA Cryptosystem, The El Gamal Cryptosystem,
Knapsack Problems, The Merkle-Hellman Knapsack Cryptosystem,
Government Controls on Cryptography, Exercises, Computer Exercises
Chapter
5:
Counting Techniques, Combinatorics, and
311
Generating Functions
5.1:
Fundamental Principles of Counting: The Multiplication Principle,
the Complement Principle, The Inclusion-Exclusion Principle, The
Pigeonhole Principle, The Generalized Pigeonhole Principle, Exercises
5.2:
Permutations, Combinations, and the Binomial Theorem: The
Difference between a Permutation and a Combination, Computing and
Counting with Permutations and Combinations, the Binomial Theorem,
Multinomial Coefficients, The Multinomial Theorem, Exercises
5.3:
Generating Functions: Generating Functions and Power Series,
Arithmetic of Generating Functions, The Generalized Binomial Theorem,
Using Generating Functions to Solve Recursive Sequences, Using
Generating Functions in Counting Problems, Exercises
Appendix: Application to Weighted Democracies
Computer Exercises
Chapter
6:
Discrete Probability and Simulation
379
6.1:
Introduction To Discrete Probability: Experiments, Sample
Spaces, and Events, Experiments with Equally Likely Outcomes,
Kolmogorov s Axioms, Probability Rules, Conditional Probability, The
Multiplication Rule, Conditioning and
Bayes
Formula, Independent
Events, Discrete Problems with Infinite Sample Spaces, Exercises
6.2:
Random Numbers, Random Variables, and Basic Simulations:
Probabilities as Relative Frequencies, Random Numbers and Random
Variables, Binomial Random Variables, Continuous Random Variables,
viii Contents
Uniform
Random Variables, Setting up a Simulation, Generating
Random Permutations and Random Subsets, Expectation and Variance of
a Random Variable, Independence of Random Variables, Linearity of
Expectation, Properties of Variances,
Poisson
Random Variables,
Exercises, Computer Exercises
Chapter
7:
Complexity of Algorithms
449
7.1:
Some Algorithms for Searching and Sorting: The Linear Search
Algorithm, The Binary Search Algorithm, The Selection Sort Algorithm,
the Bubble Sort Algorithm, The Quick Sort Algorithm, The Merge Sort
Algorithm, A Randomized Algorithm for Computing Medians, Exercises,
Computer Exercises
7.2:
Growth Rates of Functions and the Complexity of Algorithms:
A Brief and Informal Preview, Big-0 Notation, Combinations of Big-0
Estimates, Big-Omega and Big-Theta Notation, Complexity of
Algorithms, Optimality of the Merge Sort Algorithm, the Classes
Ρ
and
NP, Exercises, Computer Exercises
Chapter
8:
Graphs, Trees, and Associated Algorithms
495
8.1:
Graph Concepts and Properties: Simple Graphs, General Graphs,
Degrees, Regular Graphs, and the Handshaking Theorem, Some
Important Families of Simple Graphs, Bipartite Graphs, Degree
Sequences, Subgraphs, Isomorphism of Simple Graphs, the Complement
of a Simple Graph, Representing Graphs on Computers, Directed Graphs
(Digraphs), Some Graph Models for Optimization Problems, Exercises,
Computer Exercises
8.2:
Paths, Connectedness, and Distances in Graphs: Paths, Circuits
and Reachability in Graphs, Paths, Circuits, and Reachability in Digraphs,
Connectedness and Connected Components, Distances and Diameters in
Graphs, Eccentricity, Radius, and Central Vertices, Adjacency Matrices
and Distance Computations in Graphs and Directed Graphs, Edge and
Vertex Cuts in Connected Graphs/Digraphs, Characterization of Bipartite
Graphs Using Cycles, Exercises, Computer Exercises
8.3:
Trees: Basic Concepts about Trees, Rooted Trees and Binary Trees,
Models with Rooted Trees, Properties of Rooted Trees, Ordered Tree
Traversal Algorithms, Binary Search Trees, Representing Rooted Trees
on Computers, Exercises, Computer Exercises
Appendix: Application of Rooted Trees to Data Compression and
Coding; Huffman Codes
Contents ix
Chapter
9: Graph
Traversal and Optimization Problems
617
9.1:
Graph Traversal Problems:
Euler
Paths and Tours and the Origin
of Graph Theory,
Euler
Paths and Tours in Digraphs, Application of
Eulerian Digraphs:
De Bruijn
Sequences, Hamilton Paths and Tours,
Application of Hamiltonian Graphs: Gray Codes, Sufficient Conditions
for a Graph to Be Hamiltonian, Necessary Conditions for a Graph to Be
Hamiltonian, Exercises, Computer Exercises
9.2:
Tree Growing and Graph Optimization Algorithms: Minimum
Spanning Tree for an Edge-Weighted Graph, Tree Growing Meta-
Algorithm, Prim s Algorithm for Minimum Spanning Trees,
Dijkstra s
Algorithm for Shortest Distances in an Edge-Weighted Connected Graph,
Depth-First Searches and Breadth-First Searches, The Traveling
Salesman Problem, Insertion Heuristics for the Traveling Salesman
Problem, Performance Guarantees for Insertion Heuristics for the
Traveling Salesman Problem, Exercises, Computer Exercises
9.3:
Network Flows: Flow Networks, Cuts in Flow Networks, The
Maximum Flow/Minimum Cut Theorem, The Ford-Fulkerson Maximum
Flow/Minimum Algorithm, Applications of Maximum Flows, Maximum
Matchings in Bipartite Graphs, Hall s Marriage Theorem, Exercises,
Computer Exercises
Chapter
10:
Randomized Search and Optimization
729
Algorithms
10.1:
Randomized Search and Optimization: An Overview: Random
Search Algorithms, Hill Climbing Algorithms, The &-Opt Local Search
Algorithm for Traveling Salesman Problems, Randomized Hill Climbing
Algorithms, A Brief Discussion on Some Other Randomized Heuristic
Algorithms, Tabu Search, Ant Colony Optimization, Simulated
Annealing, Exercises and Computer Exercises
10.2:
Genetic Algorithms: Motivating Example, The Basic Genetic
Algorithm, Cloning and Inversions, Application to Ramsey Numbers,
Theoretical Underpinnings, Exercises and Computer Exercises
Appendix
A: Pseudo
Code Dictionary
781
Appendix B: Solutions to All Exercises for the Reader
787
Appendix
С
:
Answers/Brief Solutions to Odd Numbered
859
Exercises
χ
Contents
References
957
Index of Theorems, Propositions, Lemmas, and Corollaries
963
Index of Algorithms
957
Index
969
|
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| isbn | 9781439817681 |
| language | English |
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| physical | XIX, 982 S. Ill., graph. Darst. |
| publishDate | 2011 |
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| publisher | CRC Press |
| record_format | marc |
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| spelling | Stanoyevitch, Alexander Verfasser (DE-588)17374947X aut Discrete structures with contemporary applications Alexander Stanoyevitch Boca Raton [u.a.] CRC Press 2011 XIX, 982 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier A Chapman & Hall book Includes bibliographical references and index "Reflecting many of the recent advances and trends in this area, this classroom-tested text covers the core topics in discrete structures as outlined by the ACM and explores an assortment of novel applications, including simulations, genetic algorithms, network flows, probabilistic primality tests, public key cryptography, and coding theory. It presents algorithms in pseudo code and offers sample programs via the author's website. The text also includes a wide variety of examples and exercises, with solutions in the appendices. In addition, computer exercises teach students how to write their own programs. A solutions manual is available for qualifying instructors"-- Computer science / Mathematics Logic, Symbolic and mathematical Probabilities COMPUTERS / Operating Systems / General bisacsh MATHEMATICS / Combinatorics bisacsh Informatik Mathematik Diskrete Mathematik (DE-588)4129143-8 gnd rswk-swf Diskrete Struktur (DE-588)4277414-7 gnd rswk-swf Diskrete Struktur (DE-588)4277414-7 s Diskrete Mathematik (DE-588)4129143-8 s DE-604 Digitalisierung UB Bamberg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020722612&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Stanoyevitch, Alexander Discrete structures with contemporary applications Computer science / Mathematics Logic, Symbolic and mathematical Probabilities COMPUTERS / Operating Systems / General bisacsh MATHEMATICS / Combinatorics bisacsh Informatik Mathematik Diskrete Mathematik (DE-588)4129143-8 gnd Diskrete Struktur (DE-588)4277414-7 gnd |
| subject_GND | (DE-588)4129143-8 (DE-588)4277414-7 |
| title | Discrete structures with contemporary applications |
| title_auth | Discrete structures with contemporary applications |
| title_exact_search | Discrete structures with contemporary applications |
| title_full | Discrete structures with contemporary applications Alexander Stanoyevitch |
| title_fullStr | Discrete structures with contemporary applications Alexander Stanoyevitch |
| title_full_unstemmed | Discrete structures with contemporary applications Alexander Stanoyevitch |
| title_short | Discrete structures with contemporary applications |
| title_sort | discrete structures with contemporary applications |
| topic | Computer science / Mathematics Logic, Symbolic and mathematical Probabilities COMPUTERS / Operating Systems / General bisacsh MATHEMATICS / Combinatorics bisacsh Informatik Mathematik Diskrete Mathematik (DE-588)4129143-8 gnd Diskrete Struktur (DE-588)4277414-7 gnd |
| topic_facet | Computer science / Mathematics Logic, Symbolic and mathematical Probabilities COMPUTERS / Operating Systems / General MATHEMATICS / Combinatorics Informatik Mathematik Diskrete Mathematik Diskrete Struktur |
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