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Discrete Mathematical Structures: A Succinct Foundation [Kõva köide]

(Nizwa College of Technology), (Senior Assistant Professor, Department of Mathematics, Gauhati University)
  • Formaat: Hardback, 274 pages, kõrgus x laius: 234x156 mm, kaal: 453 g, 46 Tables, black and white; 74 Illustrations, black and white
  • Sari: Mathematics and its Applications
  • Ilmumisaeg: 23-Jul-2019
  • Kirjastus: CRC Press
  • ISBN-10: 0367148692
  • ISBN-13: 9780367148690
Teised raamatud teemal:
Discrete Mathematical Structures: A Succinct FoundationSuurem pilt
  • Formaat: Hardback, 274 pages, kõrgus x laius: 234x156 mm, kaal: 453 g, 46 Tables, black and white; 74 Illustrations, black and white
  • Sari: Mathematics and its Applications
  • Ilmumisaeg: 23-Jul-2019
  • Kirjastus: CRC Press
  • ISBN-10: 0367148692
  • ISBN-13: 9780367148690
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9780367148690.html
Märksõnad:
This book contains fundamental concepts on discrete mathematical structures in an easy to understand style so that the reader can grasp the contents and explanation easily. The concepts of discrete mathematical structures have application to computer science, engineering and information technology including in coding techniques, switching circuits, pointers and linked allocation, error corrections, as well as in data networking, Chemistry, Biology and many other scientific areas. The book is for undergraduate and graduate levels learners and educators associated with various courses and progammes in Mathematics, Computer Science, Engineering and Information Technology. The book should serve as a text and reference guide to many undergraduate and graduate programmes offered by many institutions including colleges and universities. Readers will find solved examples and end of chapter exercises to enhance reader comprehension.

Features











Offers comprehensive coverage of basic ideas of Logic, Mathematical Induction, Graph Theory, Algebraic Structures and Lattices and Boolean Algebra Provides end of chapter solved examples and practice problems Delivers materials on valid arguments and rules of inference with illustrations Focuses on algebraic structures to enable the reader to work with discrete structures
Preface ix
Authors xi
1 Logics and Proofs
1(38)
1.1 Introduction
1(1)
1.2 Proposition
1(1)
1.3 Compound Propositions
1(1)
1.4 Truth Table
2(1)
1.5 Logical Operators
2(7)
1.5.1 Negation
2(1)
1.5.2 Conjunction
2(1)
1.5.3 Disjunction
3(1)
1.5.4 Molecular Statements
3(1)
1.5.5 Conditional Statement [ If ... then] [ →]
3(1)
1.5.6 Biconditional [ If and only if or iff] [ ↔ or]
4(1)
1.5.7 Solved Problems
4(2)
1.5.8 Tautology
6(1)
1.5.9 Contradiction
6(1)
1.5.10 Contingency
6(1)
1.5.11 Equivalence Formulas
6(1)
1.5.12 Equivalent Formulas
7(1)
1.5.13 Duality Law
7(1)
1.5.14 Tautological Implication
7(1)
1.5.15 Some More Equivalence Formulas
7(1)
1.5.16 Solved Problems
8(1)
1.6 Normal Forms
9(4)
1.6.1 Principal Disjunctive Normal Form or Sum of Products Canonical Form
9(1)
1.6.2 Principal Conjunctive Normal Form or Product of Sum Canonical Form
10(1)
1.6.3 Solved Problems
10(3)
1.7 Inference Theory
13(6)
1.7.1 Rules of Inference
14(1)
1.7.2 Solved Problems
15(4)
1.8 Indirect Method of Proof
19(2)
1.8.1 Method of Contradiction
19(1)
1.8.2 Solved Problems
19(2)
1.9 Method of Contrapositive
21(1)
1.9.1 Solved Problems
21(1)
1.10 Various Methods of Proof
21(1)
1.10.1 Trivial Proof
21(1)
1.10.2 Vacuous Proof
22(1)
1.10.3 Direct Proof
22(1)
1.11 Predicate Calculus
22(10)
1.11.1 Quantifiers
23(1)
1.11.2 Universe of Discourse, Free and Bound Variables
23(1)
1.11.3 Solved Problems
24(4)
1.11.4 Inference Theory for Predicate Calculus
28(1)
1.11.5 Solved Problems
28(4)
1.12 Additional Solved Problems
32(7)
2 Combinatorics
39(96)
2.1 Introduction
39(1)
2.2 Mathematical Induction
39(19)
2.2.1 Principle of Mathematical Induction
39(1)
2.2.2 Procedure to Prove that a Statement P(n) is True for all Natural Numbers
40(1)
2.2.3 Solved Problems
40(16)
2.2.4 Problems for Practice
56(1)
2.2.5 Strong Induction
57(1)
2.2.6 Well-Ordering Property
57(1)
2.3 Pigeonhole Principle
58(12)
2.3.1 Generalized Pigeonhole Principle
58(1)
2.3.2 Solved Problems
58(2)
2.3.3 Another Form of Generalized Pigeonhole Principle
60(1)
2.3.4 Solved Problems
61(8)
2.3.5 Problems for Practice
69(1)
2.4 Permutation
70(10)
2.4.1 Permutations with Repetitions
71(1)
2.4.2 Solved Problems
72(7)
2.4.3 Problems for Practice
79(1)
2.5 Combination
80(10)
2.5.1 Solved Problems
81(4)
2.5.2 Problems for Practice
85(2)
2.5.3 Recurrence Relation
87(1)
2.5.4 Solved Problems
87(1)
2.5.5 Linear Recurrence Relation
88(1)
2.5.6 Homogenous Recurrence Relation
88(1)
2.5.7 Recurrence Relations Obtained from Solutions
89(1)
2.6 Solving Linear Homogenous Recurrence Relations
90(5)
2.6.1 Characteristic Equation
91(1)
2.6.2 Algorithm for Solving kth-order Homogenous Linear Recurrence Relations
91(1)
2.6.3 Solved Problems
92(3)
2.7 Solving Linear Non-homogenous Recurrence Relations
95(8)
2.7.1 Solved Problems
96(6)
2.7.2 Problems for Practice
102(1)
2.8 Generating Functions
103(14)
2.8.1 Solved Problems
103(3)
2.8.2 Solution of Recurrence Relations Using Generating Function
106(1)
2.8.3 Solved Problems
106(10)
2.8.4 Problems for Practice
116(1)
2.9 Inclusion-Exclusion Principle
117(18)
2.9.1 Solved Problems
118(13)
2.9.2 Problems for Practice
131(4)
3 Graphs
135(38)
3.1 Introduction
135(1)
3.2 Graphs and Graph Models
135(3)
3.3 Graph Terminology and Special Types of Graphs
138(11)
3.3.1 Solved Problems
140(5)
3.3.2 Graph Colouring
145(1)
3.3.3 Solved Problems
145(4)
3.4 Representing Graphs and Graph Isomorphism
149(7)
3.4.1 Solved Problems
151(4)
3.4.2 Problems for Practice
155(1)
3.5 Connectivity
156(5)
3.5.1 Connected and Disconnected Graphs
158(3)
3.6 Eulerian and Hamiltonian Paths
161(12)
3.6.1 Hamiltonian Path and Hamiltonian Circuits
163(1)
3.6.2 Solved Problems
164(5)
3.6.3 Problems for Practice
169(1)
3.6.4 Additional Problems for Practice
169(4)
4 Algebraic Structures
173(50)
4.1 Introduction
173(1)
4.2 Algebraic Systems
173(50)
4.2.1 Semigroups and Monoids
174(1)
4.2.2 Solved Problems
175(8)
4.2.3 Groups
183(3)
4.2.4 Solved Problems
186(6)
4.2.5 Subgroups
192(1)
4.2.6 Cyclic Groups
193(2)
4.2.7 Homomorphisms
195(2)
4.2.8 Cosets and Normal Subgroups
197(5)
4.2.9 Solved Problems
202(6)
4.2.10 Permutation Functions
208(3)
4.2.11 Solved Problems
211(5)
4.2.12 Problems for Practice
216(1)
4.2.13 Rings and Fields
217(3)
4.2.14 Solved Problems
220(2)
4.2.15 Problems for Practice
222(1)
5 Lattices and Boolean Algebra
223(34)
5.1 Introduction
223(1)
5.2 Partial Ordering and Posets
223(8)
5.2.1 Representation of a Poset by Hasse Diagram
224(2)
5.2.2 Solved Problems
226(4)
5.2.3 Problems for Practice
230(1)
5.3 Lattices, Sublattices, Direct Product, Homomorphism of Lattices
231(9)
5.3.1 Properties of Lattices
231(2)
5.3.2 Theorems on Lattices
233(3)
5.3.3 Solved Problems
236(4)
5.3.4 Problem for Practice
240(1)
5.4 Special Lattices
240(8)
5.4.1 Solved Problems
242(5)
5.4.2 Problems for Practice
247(1)
5.5 Boolean Algebra
248(9)
5.5.1 Solved Problems
252(3)
5.5.2 Problems for Practice
255(2)
Bibliography 257(2)
Index 259
Dr. Beri Venkatachalapathy Senthil Kumar completed his Ph. D in 2015. His area of interest is Solution and stability of functional equations, Operations Research, Statistics and Discrete Mathematics. He has 18+ years of Teaching and 8 years of Research experience. He has published more than 40 research papers in reputed journals. He has co-authored a book titled Functional Equations and Inequalities: Solution and Stability results, published by Word Scientific Publishing Company. He has also published a book entitled Probability and Queueing Theory, Published by KKS Publishers. Recently, he has contributed a chapter on Stabilities and Instabilities of Rational Functional Equations and Euler-Lagrange-Jensen (a, b)-Sextic Functional Equations, in the book on Mathematical Analysis and Applications (Selected Topics) by John Wiley & Sons, U.S.A., 2018.

Dr. Hemen Dutta is Senior Assistant Professor of Mathematics at Gauhati University, India. He did his M.Sc in mathematics, and Ph.D. in mathematics from Gauhati University, India. He received his M.Phil in mathematics from Madurai Kamaraj University, India. His primary research interests are in areas of Mathematical Analysis & Applications. He has to his credit several papers in research journals, and five books. He visited foreign institutions in connection with research collaboration and conference. He has delivered talks at foreign and national institutions. He is a member of some mathematical societies.