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Schaum's Outline of Discrete Mathematics, Fourth Edition 4th edition [Paperback / softback]

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  • Format: Paperback / softback, 496 pages, weight: 719 g
  • Pub. Date: 23-Dec-2021
  • Publisher: McGraw-Hill Education
  • ISBN-10: 1264258801
  • ISBN-13: 9781264258802
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Schaum's Outline of Discrete Mathematics, Fourth Edition 4th editionLarger Image
  • Format: Paperback / softback, 496 pages, weight: 719 g
  • Pub. Date: 23-Dec-2021
  • Publisher: McGraw-Hill Education
  • ISBN-10: 1264258801
  • ISBN-13: 9781264258802
Other books in subject:
Permanent link: https://www.kriso.ee/db/9781264258802.html
Keywords:
Study smarter and stay on top of your discrete mathematics course with the bestselling Schaum’s Outline—now with the NEW Schaum’s app and website! 

Schaum’s Outline of Discrete Mathematics, Fourth Edition is the go-to study guide for more than 115,000 math majors and first- and second-year university students taking basic computer science courses. With an outline format that facilitates quick and easy review, Schaum’s Outline of Discrete Mathematics, Fourth Edition helps you understand basic concepts and get the extra practice you need to excel in these courses.

Coverage includes set theory; relations; functions and algorithms; logic and propositional calculus; techniques of counting; advanced counting techniques, recursion; probability; graph theory; directed graphs; binary trees; properties of the integers; languages, automata, machines; finite state machines and Turning machines; ordered sets and lattices, and Boolean algebra.

Features 

• NEW to this edition: the new Schaum’s app and website!
• NEW to this edition: 20 NEW problem-solving videos online
• 467 solved problems, and hundreds of additional practice problems
• Outline format to provide a concise guide to the standard college course in discrete mathematics
• Clear, concise explanations of discrete mathematics concepts
• Expanded coverage of logic, the rules of inference and basic types of proofs in mathematical reasoning
• Increased emphasis on discrete probability and aspects of probability theory, and greater accessibility to counting techniques.
• Logic chapter emphasizes the IF-THEN and IF-THEN-ELSE sequencing that occurs in computer programming
• Computer arithmetic chapter covers binary and hexagon addition and multiplication
• Cryptology chapter includes substitution and RSA method
• Supports these major texts: Discrete Mathematics and Its Applications (Rosen), and Discrete Mathematics (Epp)
• Appropriate for the following courses: Introductory Discrete Mathematics and Discrete Mathematics
Chapter 1 Set Theory
1(22)
1.1 Introduction
1(1)
1.2 Sets and Elements, Subsets
1(2)
1.3 Venn Diagrams
3(1)
1.4 Set Operations
4(3)
1.5 Algebra of Sets, Duality
7(1)
1.6 Finite Sets, Counting Principle
8(2)
1.7 Classes of Sets, Power Sets, Partitions
10(2)
1.8 Mathematical Induction
12(11)
Solved Problems
12(6)
Supplementary Problems
18(5)
Chapter 2 Relations
23(20)
2.1 Introduction
23(1)
2.2 Product Sets
23(1)
2.3 Relations
24(1)
2.4 Pictorial Representatives of Relations
25(2)
2.5 Composition of Relations
27(1)
2.6 Types of Relations
28(2)
2.7 Closure Properties
30(1)
2.8 Equivalence Relations
31(2)
2.9 Partial Ordering Relations
33(10)
Solved Problems
34(6)
Supplementary Problems
40(3)
Chapter 3 Functions and Algorithms
43(27)
3.1 Introduction
43(1)
3.2 Functions
43(3)
3.3 One-to-One, Onto, and Invertible Functions
46(1)
3.4 Mathematical Functions, Exponential and Logarithmic Functions
47(3)
3.5 Sequences, Indexed Classes of Sets
50(2)
3.6 Recursively Defined Functions
52(3)
3.7 Cardinality
55(1)
3.8 Algorithms and Functions
56(1)
3.9 Complexity of Algorithms
57(13)
Solved Problems
60(6)
Supplementary Problems
66(4)
Chapter 4 Logic and Propositional Calculus
70(18)
4.1 Introduction
70(1)
4.2 Propositions and Compound Statements
70(1)
4.3 Basic Logical Operations
71(1)
4.4 Propositions and Truth Tables
72(2)
4.5 Tautologies and Contradictions
74(1)
4.6 Logical Equivalence
74(1)
4.7 Algebra of Propositions
75(1)
4.8 Conditional and Biconditional Statements
75(1)
4.9 Arguments
76(1)
4.10 Propositional Functions, Quantifiers
77(2)
4.11 Negation of Quantified Statements
79(9)
Solved Problems
82(4)
Supplementary Problems
86(2)
Chapter 5 Counting: Permutations and Combinations
88(19)
5.1 Introduction
88(1)
5.2 Basic Counting Principles
88(1)
5.3 Mathematical Functions
89(2)
5.4 Permutations
91(2)
5.5 Combinations
93(1)
5.6 The Pigeonhole Principle
94(1)
5.7 The Inclusion-Exclusion Principle
95(1)
5.8 Tree Diagrams
95(12)
Solved Problems
96(7)
Supplementary Problems
103(4)
Chapter 6 Advanced Counting Techniques, Recursion
107(16)
6.1 Introduction
107(1)
6.2 Combinations with Repetitions
107(1)
6.3 Ordered and Unordered Partitions
108(1)
6.4 Inclusion-Exclusion Principle Revisited
108(2)
6.5 Pigeonhole Principle Revisited
110(1)
6.6 Recurrence Relations
111(2)
6.7 Linear Recurrence Relations with Constant Coefficients
113(1)
6.8 Solving Second-Order Homogeneous Linear Recurrence Relations
114(2)
6.9 Solving General Homogeneous Linear Recurrence Relations
116(7)
Solved Problems
118(3)
Supplementary Problems
121(2)
Chapter 7 Discrete Probability Theory
123(31)
7.1 Introduction
123(1)
7.2 Sample Space and Events
123(3)
7.3 Finite Probability Spaces
126(1)
7.4 Conditional Probability
127(2)
7.5 Independent Events
129(1)
7.6 Independent Repeated Trials, Binomial Distribution
130(1)
7.7 Random Variables
131(5)
7.8 Chebyshev's Inequality, Law of Large Numbers
136(18)
Solved Problems
137(12)
Supplementary Problems
149(5)
Chapter 8 Graph Theory
154(47)
8.1 Introduction, Data Structures
154(2)
8.2 Graphs and Multigraphs
156(2)
8.3 Subgraphs, Isomorphic and Homeomorphic Graphs
158(1)
8.4 Paths, Connectivity
159(1)
8.5 Traversable and Eulerian Graphs, Bridges of Konigsberg
160(2)
8.6 Labeled and Weighted Graphs
162(1)
8.7 Complete, Regular, and Bipartite Graphs
162(2)
8.8 Tree Graphs
164(2)
8.9 Planar Graphs
166(2)
8.10 Graph Colorings
168(3)
8.11 Representing Graphs in Computer Memory
171(2)
8.12 Graph Algorithms
173(3)
8.13 Traveling-Salesman Problem
176(25)
Solved Problems
178(13)
Supplementary Problems
191(10)
Chapter 9 Directed Graphs
201(34)
9.1 Introduction
201(1)
9.2 Directed Graphs
201(1)
9.3 Basic Definitions
202(2)
9.4 Rooted Trees
204(2)
9.5 Sequential Representation of Directed Graphs
206(3)
9.6 Warshall's Algorithm, Shortest Paths
209(2)
9.7 Linked Representation of Directed Graphs
211(2)
9.8 Graph Algorithms: Depth-First and Breadth-First Searches
213(3)
9.9 Directed Cycle-Free Graphs, Topological Sort
216(2)
9.10 Pruning Algorithm for Shortest Path
218(17)
Solved Problems
221(7)
Supplementary Problems
228(7)
Chapter 10 Binary Trees
235(29)
10.1 Introduction
235(1)
10.2 Binary Trees
235(2)
10.3 Complete and Extended Binary Trees
237(2)
10.4 Representing Binary Trees in Memory
239(1)
10.5 Traversing Binary Trees
240(2)
10.6 Binary Search Trees
242(2)
10.7 Priority Queues, Heaps
244(4)
10.8 Path Lengths, Huffman's Algorithm
248(3)
10.9 General (Ordered Rooted) Trees Revisited
251(13)
Solved Problems
252(7)
Supplementary Problems
259(5)
Chapter 11 Properties of the Integers
264(39)
11.1 Introduction
264(1)
11.2 Order and Inequalities, Absolute Value
265(1)
11.3 Mathematical Induction
266(1)
11.4 Division Algorithm
267(2)
11.5 Divisibility, Primes
269(1)
11.6 Greatest Common Divisor, Euclidean Algorithm
270(3)
11.7 Fundamental Theorem of Arithmetic
273(1)
11.8 Congruence Relation
274(4)
11.9 Congruence Equations
278(25)
Solved Problems
283(16)
Supplementary Problems
299(4)
Chapter 12 Languages, Automata, Grammars
303(20)
12.1 Introduction
303(1)
12.2 Alphabet, Words, Free Semigroup
303(1)
12.3 Languages
304(1)
12.4 Regular Expressions, Regular Languages
305(1)
12.5 Finite State Automata
306(4)
12.6 Grammars
310(13)
Solved Problems
314(5)
Supplementary Problems
319(4)
Chapter 13 Finite State Machines and Turing Machines
323(14)
13.1 Introduction
323(1)
13.2 Finite State Machines
323(3)
13.3 Godel Numbers
326(1)
13.4 Turing Machines
326(4)
13.5 Computable Functions
330(7)
Solved Problems
331(3)
Supplementary Problems
334(3)
Chapter 14 Ordered Sets and Lattices
337(31)
14.1 Introduction
337(1)
14.2 Ordered Sets
337(3)
14.3 Hasse Diagrams of Partially Ordered Sets
340(2)
14.4 Consistent Enumeration
342(1)
14.5 Supremum and Infimum
342(2)
14.6 Isomorphic (Similar) Ordered Sets
344(1)
14.7 Weil-Ordered Sets
344(2)
14.8 Lattices
346(2)
14.9 Bounded Lattices
348(1)
14.10 Distributive Lattices
349(1)
14.11 Complements, Complemented Lattices
350(18)
Solved Problems
351(9)
Supplementary Problems
360(8)
Chapter 15 Boolean Algebra
368(64)
15.1 Introduction
368(1)
15.2 Basic Definitions
368(1)
15.3 Duality
369(1)
15.4 Basic Theorems
370(1)
15.5 Boolean Algebras as Lattices
370(1)
15.6 Representation Theorem
371(1)
15.7 Sum-of-Products Form for Sets
371(1)
15.8 Sum-of-Products Form for Boolean Algebras
372(3)
15.9 Minimal Boolean Expressions, Prime Implicants
375(2)
15.10 Logic Gates and Circuits
377(4)
15.11 Truth Tables, Boolean Functions
381(2)
15.12 Karnaugh Maps
383(26)
Solved Problems
389(14)
Supplementary Problems
403(6)
Vectors and Matrices
409(1)
A.1 Introduction
409(1)
A.2 Vectors
409(1)
A.3 Matrices
410(1)
A.4 Matrix Addition and Scalar Multiplication
411(1)
A.5 Matrix Multiplication
412(2)
A.6 Transpose
414(1)
A.7 Square Matrices
414(1)
A.8 Invertible (Nonsingular) Matrices, Inverses
415(1)
A.9 Determinants
416(2)
A.10 Elementary Row Operations, Gaussian Elimination (Optional)
418(4)
A.11 Boolean (Zero-One) Matrices
422(10)
Solved Problems
423(6)
Supplementary Problems
429(3)
Appendix B Algebraic Systems
432(35)
B.1 Introduction
432(1)
B.2 Operations
432(3)
B.3 Semigroups
435(3)
B.4 Groups
438(2)
B.5 Subgroups, Normal Subgroups, and Homomorphisms
440(3)
B.6 Rings, Integral Domains, and Fields
443(3)
B.7 Polynomials Over a Field
446(21)
Solved Problems
450(11)
Supplementary Problems
461(6)
Index 467
He is a Ph.D and a Professor of Mathematics in Temple University





Marc Lipson, Ph.D. (Philadelphia, PA), is on the mathematical faculty of the University of Georgia. He is co-author of Schaum's Outline of Discrete Mathematics.