Discrete mathematical structures: a succinct foundation

✍ Scribed by Dutta, Hemen; Kumar, B. V. Senthil

• Publisher: CRC Press, Taylor et Francis Group
• Year: 2020
• Tongue: English
• Leaves: 275
• Series: Mathematics and its applications : modelling engineering and social sciences
• Category: Library

✦ Synopsis

"This book contains fundamental concepts on discrete mathematical structures in a crispy style so that learners could grasp the contents and explanation easily. The concepts of discrete mathematical structures have lot of applications in 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 significant 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 of the disciplines mentioned above being offered by many institutions including colleges and universities. Readers will find solved examples and end of the chapter exercise in each chapter for practise and enhance the understanding of topics discussed"--.

✦ Table of Contents

Cover......Page 1
Half Title......Page 2
Series Page......Page 3
Title Page......Page 4
Copyright Page......Page 5
Contents......Page 6
Preface......Page 10
Authors......Page 12
1.3 Compound Propositions......Page 14
1.5.2 Conjunction......Page 15
1.5.5 Conditional Statement [If then] [ → ]......Page 16
1.5.7 Solved Problems......Page 17
1.5.11 Equivalence Formulas......Page 19
1.5.15 Some More Equivalence Formulas......Page 20
1.5.16 Solved Problems......Page 21
1.6.1 Principal Disjunctive Normal Form or Sum of Products Canonical Form......Page 22
1.6.3 Solved Problems......Page 23
1.7 Inference Theory......Page 26
1.7.1 Rules of Inference......Page 27
1.7.2 Solved Problems......Page 28
1.8.2 Solved Problems......Page 32
1.10.1 Trivial Proof......Page 34
1.11 Predicate Calculus......Page 35
1.11.2 Universe of Discourse, Free and Bound Variables......Page 36
1.11.3 Solved Problems......Page 37
1.11.5 Solved Problems......Page 41
1.12 Additional Solved Problems......Page 45
2.2.1 Principle of Mathematical Induction......Page 52
2.2.3 Solved Problems......Page 53
2.2.4 Problems for Practice......Page 69
2.2.6 Well-Ordering Property......Page 70
2.3.2 Solved Problems......Page 71
2.3.3 Another Form of Generalized Pigeonhole Principle......Page 73
2.3.4 Solved Problems......Page 74
2.3.5 Problems for Practice......Page 82
2.4 Permutation......Page 83
2.4.1 Permutations with Repetitions......Page 84
2.4.2 Solved Problems......Page 85
2.4.3 Problems for Practice......Page 92
2.5 Combination......Page 93
2.5.1 Solved Problems......Page 94
2.5.2 Problems for Practice......Page 98
2.5.4 Solved Problems......Page 100
2.5.6 Homogenous Recurrence Relation......Page 101
2.5.7 Recurrence Relations Obtained from Solutions......Page 102
2.6 Solving Linear Homogenous Recurrence Relations......Page 103
2.6.2 Algorithm for Solving k[sup(th)]-order Homogenous Linear Recurrence Relations......Page 104
2.6.3 Solved Problems......Page 105
2.7 Solving Linear Non-homogenous Recurrence Relations......Page 108
2.7.1 Solved Problems......Page 109
2.7.2 Problems for Practice......Page 115
2.8.1 Solved Problems......Page 116
2.8.3 Solved Problems......Page 119
2.8.4 Problems for Practice......Page 129
2.9 Inclusion—Exclusion Principle......Page 130
2.9.1 Solved Problems......Page 131
2.9.2 Problems for Practice......Page 144
3.2 Graphs and Graph Models......Page 148
3.3 Graph Terminology and Special Types of Graphs......Page 151
3.3.1 Solved Problems......Page 153
3.3.3 Solved Problems......Page 158
3.4 Representing Graphs and Graph Isomorphism......Page 162
3.4.1 Solved Problems......Page 164
3.4.2 Problems for Practice......Page 168
3.5 Connectivity......Page 169
3.5.1 Connected and Disconnected Graphs......Page 171
3.6 Eulerian and Hamiltonian Paths......Page 174
3.6.1 Hamiltonian Path and Hamiltonian Circuits......Page 176
3.6.2 Solved Problems......Page 177
3.6.4 Additional Problems for Practice......Page 182
4.2 Algebraic Systems......Page 186
4.2.1 Semigroups and Monoids......Page 187
4.2.2 Solved Problems......Page 188
4.2.3 Groups......Page 196
4.2.4 Solved Problems......Page 199
4.2.5 Subgroups......Page 205
4.2.6 Cyclic Groups......Page 206
4.2.7 Homomorphisms......Page 208
4.2.8 Cosets and Normal Subgroups......Page 210
4.2.9 Solved Problems......Page 215
4.2.10 Permutation Functions......Page 221
4.2.11 Solved Problems......Page 224
4.2.12 Problems for Practice......Page 229
4.2.13 Rings and Fields......Page 230
4.2.14 Solved Problems......Page 233
4.2.15 Problems for Practice......Page 235
5.2 Partial Ordering and Posets......Page 236
5.2.1 Representation of a Poset by Hasse Diagram......Page 237
5.2.2 Solved Problems......Page 239
5.2.3 Problems for Practice......Page 243
5.3.1 Properties of Lattices......Page 244
5.3.2 Theorems on Lattices......Page 246
5.3.3 Solved Problems......Page 249
5.4 Special Lattices......Page 253
5.4.1 Solved Problems......Page 255
5.4.2 Problems for Practice......Page 260
5.5 Boolean Algebra......Page 261
5.5.1 Solved Problems......Page 265
5.5.2 Problems for Practice......Page 268
Bibliography......Page 270
Index......Page 272

✦ Subjects

Computer science--Mathematics;Discrete element method;Discrete mathematics;Diskrete Mathematik;Computer science -- Mathematics