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Discrete Mathematics: Essentials and Applications [Mīkstie vāki]

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(Department of Electrical, Computer, and Software Programming, University of Ontario Institute of Technology (Ontario Tech), Oshawa, Ontario, Canada)
  • Formāts: Paperback / softback, 464 pages, height x width: 235x191 mm, weight: 910 g, Approx. 100 illustrations; Illustrations
  • Izdošanas datums: 20-Sep-2022
  • Izdevniecība: Academic Press Inc
  • ISBN-10: 012820656X
  • ISBN-13: 9780128206560
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  • Cena: 84,62 €
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Discrete Mathematics: Essentials and ApplicationsPalielināt
  • Formāts: Paperback / softback, 464 pages, height x width: 235x191 mm, weight: 910 g, Approx. 100 illustrations; Illustrations
  • Izdošanas datums: 20-Sep-2022
  • Izdevniecība: Academic Press Inc
  • ISBN-10: 012820656X
  • ISBN-13: 9780128206560
Citas grāmatas par šo tēmu:
Permanent link: https://www.kriso.lv/db/9780128206560.html
Keywords:
Discrete Mathematics: Essentials and Applications offers a comprehensive survey of the area, particularly concentrating on the basic principles and applications of Discrete Mathematics. This up-to-date text provides proofs of significance, keeping the focus on numerous relevant examples and many pertinent applications. Written in a simple and clear tone, the title features insightful descriptions and intuitive explanations of all complex concepts and ensures a thorough understanding of the subject matter.
  • Offers easy-to-understand coverage of the subject matter with a class-tested pedagogical approach
  • Covers all topics in Discrete Math in a comprehensive yet not overwhelming way
  • Includes numerous meaningful examples on all topics to bring insight, and relevant applications for all major topics

Recenzijas

"Discrete Mathematics is adequately written and well-documented....

This book presents the material on the topic in a cogently coherent manner thereby serving and justifying the purpose of writing books such as this one. The classroom-tested pedagogy and its 400 examples speak a lot about the kind and amount of sweat that must have gone into it." --zbMATH Open

Preface vii
Acknowledgments ix
1 Propositional Logic
1(20)
1.1 Propositions
1(2)
1.2 Basic Logical Operators
3(4)
1.3 Conditional Statements
7(4)
1.4 Propositional Equivalences
11(6)
1.5 Logic Puzzles
17(4)
2 Predicate Logic
21(16)
2.1 Predicates
21(1)
2.2 Quantifiers
22(5)
2.3 Negations of Quantified Statements
27(2)
2.4 Nested Quantifiers
29(8)
3 Rules of Inference
37(18)
3.1 Valid Arguments
37(2)
3.2 Rules of Inference for Propositional Logic
39(3)
3.3 Rules of Inference for Predicate Logic
42(2)
3.4 Fallacies
44(11)
4 Proof Methods
55(1)
4.1 Terminology
55(1)
42 Proofs of Equivalence
56(11)
4.3 Proof by Counterexample
57(1)
4.4 Vacuous Proofs and Trivial Proofs
58(1)
4.5 Direct Proofs
58(1)
4.6 Proofs by Contraposition and Proofs by Contradiction
59(2)
4.7 Proof by Cases and Proofs by Exhaustion
61(1)
4.8 Existence Proofs: Constructive Proofs and Nonconstructive Proofs
62(1)
4.9 Proof of a Disjunction
63(1)
4.10 Uniqueness Proofs
63(4)
5 Sets
67(26)
5.1 Definitions and Notation
67(6)
5.2 Set Operations
73(4)
5.3 Set Identities and Methods of Proof
77(3)
5.4 Cardinality of Sets
80(4)
5.5 Computer Representation of Sets
84(1)
5.6 Multisets
85(2)
5.7 Fuzzy Sets
87(1)
5.8 Paradoxes in Set Theory
88(5)
6 Matrices
93(20)
6.1 Definitions and Special Matrices
93(3)
6.2 Matrix Addition and Scalar Multiplication
96(1)
6.3 Matrix Multiplication
97(3)
6.4 Matrix Inversion
100(4)
6.5 Zero-One Matrix
104(1)
6.6 Applications of Matrices
105(8)
7 Functions
113(18)
7.1 Basic Definitions
113(4)
7.2 Special Functions
117(4)
7.3 One-to-One and Onto Functions
121(2)
7.4 Compositions of Functions
123(8)
8 Boolean Algebra
131(24)
8.1 Basic Definitions
131(2)
8.2 Boolean Expressions and Boolean Functions
133(2)
8.3 Identities of Boolean Algebra
135(1)
8.4 Representing Boolean Functions
136(2)
8.5 Functional Completeness
138(2)
8.6 Logic Gates
140(4)
8.7 Minimization of Combinational Circuits
144(11)
9 Relations
155(22)
9.1 Relations on Sets
155(1)
9.2 Properties of Relations
156(4)
9.3 Representations of Relations
160(5)
9.4 Operations on Relations
165(2)
9.5 Closure Properties
167(2)
9.6 Equivalence Relations
169(2)
9.7 Partial Orderings
171(1)
9.8 Relational Databases
172(5)
10 Number Theory
177(20)
10.1 Numeral Systems
177(1)
10.2 Divisibility
178(1)
10.3 Prime Numbers
179(2)
10.4 Greatest Common Divisors and Least Common Multiples
181(3)
10.5 Divisibility Test
184(2)
10.6 Congruences
186(6)
10.7 Representations of Integers
192(2)
10.8 Binary Operations
194(3)
11 Cryptography
197(14)
11.1 Classical Cryptography
197(4)
11.2 Modern Cryptography
201(1)
11.3 Private-Key Cryptography
202(2)
11.4 Public-Key Cryptography
204(1)
11.5 The RSA Cryptosystem
205(6)
12 Algorithms
211(20)
12.1 Algorithm Requirements
211(2)
12.2 Algorithmic Paradigms
213(2)
12.3 Complexity of Algorithms
215(2)
12.4 Measuring Algorithm Efficiency
217(6)
12.5 Sorting Algorithms
223(4)
12.6 Search Algorithms
227(4)
13 Induction
231(18)
13.1 Deductive Reasoning and Inductive Reasoning
231(1)
13.2 Mathematical Induction
232(3)
13.3 Applications of Mathematical Induction
235(7)
13.4 Strong Induction
242(2)
13.5 The Well-Ordering Principle
244(5)
14 Recursion
249(22)
14.1 Sequences
249(2)
14.2 Recursively Defined Functions
251(1)
14.3 Recursive Algorithms
252(3)
14.4 Solving Recurrence Relations by Iteration
255(2)
14.5 Solving Linear Homogeneous Recurrence Relations with Constant Coefficients
257(4)
14.6 Solving Linear Nonhomogeneous Recurrence Relations with Constant Coefficients
261(4)
14.7 Solving Recurrence Relations Using Generating Functions
265(6)
15 Counting Methods
271(14)
15.1 Basic Rules of Counting
271(3)
15.2 The Pigeonhole Principle
274(2)
15.3 Random Arrangements and Selections
276(1)
15.4 Permutations and Combinations
277(3)
15.5 Applications
280(5)
16 Discrete Probability
285(22)
16.1 Basic Terminology
285(2)
16.2 The Axioms of Probability
287(2)
16.3 Joint Probability and Conditional Probability
289(1)
16.4 Statistically Independent Events and Mutually Exclusive Events
290(3)
16.5 Law of Total Probability and Bayes' Theorem
293(4)
16.6 Applications in Probability
297(10)
17 Discrete Random Variables
307(20)
17.1 The Cumulative Distribution Function
307(1)
17.2 The Probability Mass Function
308(2)
17.3 Expected Values
310(5)
17.4 Conditional Distributions
315(1)
17.5 Upper Bounds on Probability
316(2)
17.6 Special Random Variables and Their Applications
318(9)
18 Graphs
327(24)
18.1 Basic Definitions and Terminology
327(3)
18.2 Types of Graphs
330(4)
18.3 Graph Representation and Isomorphism
334(3)
18.4 Connectivity
337(4)
18.5 Euler Circuits and Hamilton Circuits
341(2)
18.6 Shortest-Path Problem
343(8)
19 Trees
351(22)
19.1 Basic Definitions and Terminology
351(3)
19.2 Tree Traversal
354(2)
19.3 Spanning Trees
356(4)
19.4 Minimum Spanning Trees
360(2)
19.5 Applications of Trees
362(11)
20 Finite-State Machines
373(16)
20.1 Types of Finite-State Machines
373(2)
20.2 Finite-State Machines with No Output
375(7)
20.3 Finite-State Machines with Output
382(7)
List of Symbols 389(4)
Glossary of Terms 393(14)
Bibliography 407(2)
Answers/Hints to Exercises 409(32)
Index 441
Dr. Grami received his PhD in Electrical Engineering from the University of Toronto. He has worked for Nortel Networks, where he was involved in the research, design, and development of North Americas first digital cellular wireless system.He later joined Telesat Canada, where he was the lead researcher and principal designer of Canada's Anik-F2 Ka-band system, the worlds first broadband access satellite system. Dr. Grami is currently an associate professor in the Faculty of Engineering and Applied Science at the University of Ontario Institute of Technology (UOIT), where as a founding faculty member he has led the development of various programs, including the BEng, MEng, and PhD programs in ECE.