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Fundamentals of Discrete Structures 2nd ed. [Mīkstie vāki]

  • Formāts: Paperback / softback, 352 pages, height x width x depth: 226x150x20 mm, weight: 476 g
  • Izdošanas datums: 31-Aug-2012
  • Izdevniecība: Pearson Learning Solutions
  • ISBN-10: 1256389218
  • ISBN-13: 9781256389217
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  • Cena: 144,57 €
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  • Formāts: Paperback / softback, 352 pages, height x width x depth: 226x150x20 mm, weight: 476 g
  • Izdošanas datums: 31-Aug-2012
  • Izdevniecība: Pearson Learning Solutions
  • ISBN-10: 1256389218
  • ISBN-13: 9781256389217
Citas grāmatas par šo tēmu:

Selecting a mathematics textbook that meets the needs of a diverse student body can be a challenge. Some have too much information for a beginner; some have too little. The authors of Fundamentals of Discrete Structures, frustrated by their search for the perfect text, decided to write their own. The result provides an excellent introduction to discrete mathematics that is both accessible to liberal arts majors satisfying their core mathematics requirements, and also challenging enough to engage math and computer science majors.

To engage students who may not be comfortable with traditional mathematics texts, the book uses a light tone when introducing new concepts. While there is an emphasis on computation, it avoids mathematical formalism and formal proofs, thus making it easier for the average student to understand. Unlike other textbooks in this field, Fundamentals of Discrete Structures strikes just the right balance: it illuminates the essentials of discrete mathematics while still providing a comprehensive treatment of the subject matter.

Preface ix
1 Sets
1(42)
1.1 Basic Definitions
3(3)
1.2 Naming and Describing Sets
6(4)
1.3 Comparison Relations on Sets
10(4)
1.4 Set Operators
14(14)
1.5 Principle of Inclusion/Exclusion
28(6)
1.6 Exercises
34(9)
2 Patterns: Sequences, Summations, Mathematical Induction
43(32)
2.1 Sequences
44(2)
2.2 Describing Patterns in Sequences
46(10)
2.3 Summations
56(4)
2.4 Mathematical Induction
60(12)
2.4.1 First Principle of Mathematical Induction
62(2)
2.4.2 Examples Using Mathematical Induction
64(8)
2.5 Exercises
72(3)
3 Logic
75(46)
3.1 Propositional Logic
76(32)
3.1.1 Logical Operations
78(5)
3.1.2 Propositional Forms
83(3)
3.1.3 Parse Trees and the Operator Hierarchy (*)
86(2)
3.1.4 Truth Tables, Tautologies, and Contradictions
88(4)
3.1.5 Propositional Equivalences
92(3)
3.1.6 Propositional Identities
95(2)
3.1.7 Duality (*)
97(3)
3.1.8 Indirect Proofs (*)
100(3)
3.1.9 From English to Propositions
103(2)
3.1.10 Logic Circuits (*)
105(3)
3.2 Predicate Logic (*)
108(7)
3.2.1 Quantifiers
110(2)
3.2.2 Some Rules for Using Predicates
112(3)
3.3 Exercises
115(6)
4 Relations
121(28)
4.1 Ways to Describe Relations Between Sets
122(10)
4.1.1 Using English
123(3)
4.1.2 Using a Picture
126(2)
4.1.3 Using a Table
128(1)
4.1.4 Using the Cartesian Product
129(3)
4.2 Properties of Relations
132(10)
4.2.1 Reflexivity
132(3)
4.2.2 Symmetry
135(4)
4.2.3 Transitivity
139(3)
4.3 Relational Databases
142(3)
4.4 Exercises
145(4)
5 Functions
149(48)
5.1 What is a Function?
151(5)
5.2 Functions and Relations
156(6)
5.3 Properties of Functions
162(4)
5.4 Function Composition
166(5)
5.5 Identity and Inverse Functions
171(9)
5.6 An Application: Cryptography
180(3)
5.6.1 Caesar Rotation
181(1)
5.6.2 Cryptography in Cyber-Commerce
182(1)
5.7 More About Functions
183(6)
5.7.1 Standard Mathematical Functions
183(1)
5.7.2 Growth Functions
184(2)
5.7.3 Functions in Program Construction
186(3)
5.8 An Application: Secure Storage of Passwords
189(2)
5.9 Exercises
191(6)
6 Counting
197(26)
6.1 Counting and How to Count
198(2)
6.2 Elementary Rules for Counting
200(9)
6.2.1 The Addition Rule
200(2)
6.2.2 The Multiplication Rule
202(5)
6.2.3 Using the Elementary Rules Together
207(2)
6.3 Permutations and Combinations
209(9)
6.3.1 Permutations
210(2)
6.3.2 Combinations
212(6)
6.4 Exercises
218(5)
7 Probability
223(32)
7.1 Terminology and Background
224(4)
7.2 Complement
228(2)
7.3 Elementary Rules for Probability
230(7)
7.3.1 The Elementary Addition Rule
232(2)
7.3.2 The Elementary Multiplication Rule
234(3)
7.4 General Rules for Probability
237(4)
7.4.1 The General Addition Rule
238(2)
7.4.2 The General Multiplication
240(1)
7.5 Bernoulli Trials and Probability Distributions
241(3)
7.6 Expected Value
244(2)
7.7 Exercises
246(9)
8 Algorithms
255(28)
8.1 What is an Algorithm?
255(2)
8.2 Applications of Algorithms
257(1)
8.3 Searching and Sorting Algorithms
258(9)
8.3.1 Search Algorithms
258(4)
8.3.2 Sorting Algorithms
262(5)
8.4 Analysis of Algorithms
267(11)
8.4.1 How Do We Measure Efficiency?
267(1)
8.4.2 The Time Complexity of an Algorithm
268(2)
8.4.3 Analysis of Several Algorithms
270(6)
8.4.4 Big-O Notation (*)
276(2)
8.5 Exercises
278(5)
9 Graphs
283(32)
9.1 Graph Notation
286(5)
9.1.1 Vertices and Edges
286(2)
9.1.2 Directed and Undirected Graphs
288(1)
9.1.3 Complete Graphs
289(2)
9.2 Euler Trails and Circuits
291(4)
9.2.1 Walks, Trails, Circuits and Cycles
291(2)
9.2.2 When Can We Find Euler Trails and Circuits?
293(2)
9.3 Weighted Graphs
295(2)
9.4 Minimum Spanning Tree
297(3)
9.4.1 Spanning Trees
298(1)
9.4.2 Prim's Algorithm for the Minimum Spanning Tree
299(1)
9.5 Matrix Notation For Graphs
300(9)
9.6 Exercises
309(6)
Appendix A Our Social Networking Example 315(6)
Index 321