Discrete Mathematics and Its Applications 7th edition by Kenneth Rosen ISBN 0073383090 978-0073383095

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ISBN 10: 0073383090
ISBN 13: 978-0073383095
Author: Kenneth Rosen

Discrete Mathematics and Its Applications is intended for one or two term introductory Discrete Mathematics courses taken by students from a wide variety of majors, including Computer Science, Mathematics, and Engineering. This renowned best-selling text, which has been used at over 500 institutions around the world, gives a focused introduction to the primary themes in a Discrete Mathematics course and demonstrates the relevance and practicality of Discrete Mathematics to a wide variety of real-world applications―from Computer Science to Data Networking, to Psychology, to Chemistry, to Engineering, to Linguistics, to Biology, to Business, and many other important fields.

McGraw-Hill’s Connect, is also available as an optional, add on item. Connect is the only integrated learning system that empowers students by continuously adapting to deliver precisely what they need, when they need it, how they need it, so that class time is more effective. Connect allows the professor to assign homework, quizzes, and tests easily and automatically grades and records the scores of the student’s work. Problems are randomized to prevent sharing of answers an may also have a “multi-step solution” which helps move the students’ learning along if they experience difficulty.

Discrete Mathematics and Its Applications 7th Table of contents:

Part 1: Foundations

1. The Foundations: Logic and Proofs

• Propositional Logic
• Logical Operations and Equivalence
• Quantifiers and Predicates
• Proof Techniques: Direct, Indirect, and Contradiction
• Methods of Proof: Mathematical Induction, Recursive Definitions

2. Basic Structures: Sets, Functions, and Relations

• Sets and Set Operations
• Functions and Their Properties
• Relations: Types, Operations, and Properties
• Equivalence Relations and Partitions
• The Cartesian Product and Relations in Graph Theory

3. Algorithms

• The Concept of an Algorithm
• Algorithm Efficiency and Big-O Notation
• Analyzing Algorithm Complexity
• Recursive Algorithms
• Solving Recurrences

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Part 2: Combinatorics

4. Counting

• The Rule of Sum and Product
• Permutations and Combinations
• Binomial Coefficients and Their Properties
• Pigeonhole Principle
• Counting with Repetition

5. Advanced Counting Techniques

• Inclusion-Exclusion Principle
• Derangements and Stirling Numbers
• Recurrence Relations and Counting Problems
• Generating Functions

6. Relations and Digraphs

• Directed Graphs (Digraphs)
• Properties of Directed Graphs
• Graph Models of Relations
• Transitive Closures and Warshall’s Algorithm
• Strongly Connected Components

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Part 3: Graph Theory

7. Graphs and Trees

• Basic Graph Terminology and Types
• Graph Representations (Adjacency Matrix, List)
• Traversing Graphs: Depth-First and Breadth-First Search
• Trees: Properties, Spanning Trees, and Algorithms
• Minimum Spanning Tree Algorithms (Prim’s, Kruskal’s)

8. Network Flows

• Max-Flow Min-Cut Theorem
• Ford-Fulkerson Algorithm
• Flow Networks and Applications

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Part 4: Algebra

9. Boolean Algebra

• Boolean Variables and Operations
• Boolean Functions and Expressions
• Simplification of Boolean Expressions
• Karnaugh Maps
• Switching Circuits and Their Applications

10. Boolean Functions and Logic Circuits

• Representation of Boolean Functions
• Logic Gates and Circuits
• Digital Logic Design

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Part 5: Theory of Computation

11. Models of Computation

• Finite Automata and Their Use
• Regular Expressions and Languages
• Deterministic and Non-Deterministic Finite Automata
• Regular Languages and Regular Expressions

12. Formal Languages and Turing Machines

• Context-Free Grammars and Languages
• Pushdown Automata
• The Theory of Turing Machines
• Decidability and Computability

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Part 6: Advanced Topics

13. Number Theory and Cryptography

• Divisibility and Prime Numbers
• Euclidean Algorithm
• Modular Arithmetic and Applications
• Cryptography: RSA Algorithm, Public-Key Cryptosystems

14. Graph Algorithms

• Shortest Path Algorithms: Dijkstra’s, Bellman-Ford
• Network Flow Algorithms: Ford-Fulkerson
• Graph Coloring and Planarity

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Appendices

• A: Mathematical Induction and Proof Techniques
• B: Solutions to Selected Problems
• C: A Review of Set Theory and Logic
• D: Table of Mathematical Symbols
• E: Glossary of Terms

Index

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