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by Bernard Kolman, Robert Busby and Sharon Ross

Edition: 5TH 04Copyright: 2004

Publisher: Prentice Hall, Inc.

Published: 2004

International: No

Bernard Kolman, Robert Busby and Sharon Ross

Edition: 5TH 04
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For one- or two-term freshman/sophomore-level courses in Discrete Mathematics.

Combining a careful selection of topics with previews of their genuine applications in computer science, this text, more than any other book in its field, is written at an elementary level with a strong pedagogical focus. It limits its area and coverage of topics to those that students will actually utilize, and emphasizes both basic theory and applications, giving a firm foundation for more advanced courses, as well as providing an excellent reference work for those courses.

**Features **

- NEW - Brief sketches of mathematical history open each chapter.
- Vignettes provide these students with a practical background of how these ideas were developed.

- NEW - Additional number theory--Provides more information on the properties of integers, including base n representations; and gives more contexts for isomorphism.
- Gives students further understanding for future study.

- NEW - Cryptology theme--Begins in Chapter 1, and is then explored throughout the book, ending with Section 11.3, Public Key Cryptology.
- Presents for students the basic ideas of this fun field.

- NEW - Expanded coverage of coding--Covers all of its aspects, including efficiency, effectiveness, and security.
- Provides students with full picture of coding.

- NEW - New exercises in each chapter--Includes approximately 25% more exercises than in the 4th edition.
- Emphasizes for students multiple representations of concepts providing more practice in proof-reading and -writing skills.

- NEW - Additional student projects--Included for weighted voting systems, Petri nets, and Catalan numbers.
- Provides students with opportunities for exploration and discovery, as well as for writing and for working in groups.

- NEW - Chapter review questions--Provided at the end of each chapter.
- Helps students identify the "big" ideas of each chapter.

- Concise, well-written text--Remains the briefest text on the market; devoid of excessive technical jargon and abstraction.
- Helps students focus on fundamental concepts without becoming bogged down in special cases, weakly-motivated examples, and applications. Enables instructors to sharpen their focus on key ideas and concepts.

- Development of mathematical thinking skills--Strengthens the text for use in a bridge course and lays foundation for mathematical thinking in upper-division courses.
- Helps students develop the skills of building mathematical models through abstraction.

- No calculus--Assumes only a limited background in mathematics.
- Offers students a level of rigor appropriate for beginners or non-math majors.

- Organization of text around the concept of relation--Treats relations and digraphs as two aspects of the same basic mathematical idea.
- Clear organization of topics--Minimizes the difficulties of being overwhelmed by too many definitions and theory abstraction by treating relations and digraphs as two aspects of the same fundamental idea, which is then used as the basis of virtually all the concepts introduced in the book.

- Introduces students to each new idea in the context of previously learned material, allowing them to fully understand what is being presented to them.
- Focus on topics used in computer science--Limits coverage of abstract algebra and gives applications for finite state machines, error detecting and correcting codes.

- Gives students valuable information for future computer science careers.
- Instructor's Solutions Manual and Companion Website.

- Provides instructors and students with valuable course support.

**Kolman, Bernard : Drexel University**

Busby, Robert C. : Drexel University

Ross, Sharon Cutler : Georgia Perimeter College

**1. Fundamentals. **

Sets and Subsets. Operations on Sets. Sequences. Properties of Integers. Matrices. Mathematical Structures.

**2. Logic. **

Propositions and Logical Operations. Conditional Statements. Methods of Proof. Mathematical Induction.

**3. Counting. **

Permutations. Combinations. Pigeonhole Principle. Elements of Probability. Recurrence Relations.

**4. Relations and Digraphs. **

Product Sets and Partitions. Relations and Digraphs. Paths in Relations and Digraphs. Properties of Relations. Equivalence Relations. Computer Representation of Relations and Digraphs. Operations on Relations. Transitive Closure and Warshall's Algorithm.

**5. Functions. **

Functions. Functions for Computer Science. Growth of Functions. Permutation Functions.

**6. Order Relations and Structures. **

Partially Ordered Sets. Extremal Elements of Partially Ordered Sets. Lattices. Finite Boolean Algebras. Functions on Boolean Algebras. Circuit Design.

**7. Trees. **

Trees. Labeled Trees. Tree Searching. Undirected Trees. Minimal Spanning Trees.

**8. Topics in Graph Theory. **

Graphs. Euler Paths and Circuits. Hamiltonian Paths and Circuits. Transport Networks. Matching Problems. Coloring Graphs.

**9. Semigroups and Groups. **

Binary Operations, Revisited. Semigroups. Products and Quotients of Semigroups. Groups. Products and Quotients of Groups.

**10. Languages and Finite-State Machines. **

Languages. Representations of Special Grammars and Languages. Finite-State Machines. Semigroups, Machines, and Languages. Machines and Regular Languages. Simplification of Machines.

**11. Groups and Coding. **

Coding of Binary Information and Error Detection. Decoding and Error Correction. Public Key Cryptology.

Appendix A: Algorithms and Pseudocode.

Appendix B: Additional Experiments in Discrete Mathematics.

Answers to Odd-Numbered Exercises.

Answers to Chapter Tests.

Index.

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Summary

For one- or two-term freshman/sophomore-level courses in Discrete Mathematics.

Combining a careful selection of topics with previews of their genuine applications in computer science, this text, more than any other book in its field, is written at an elementary level with a strong pedagogical focus. It limits its area and coverage of topics to those that students will actually utilize, and emphasizes both basic theory and applications, giving a firm foundation for more advanced courses, as well as providing an excellent reference work for those courses.

**Features **

- NEW - Brief sketches of mathematical history open each chapter.
- Vignettes provide these students with a practical background of how these ideas were developed.

- NEW - Additional number theory--Provides more information on the properties of integers, including base n representations; and gives more contexts for isomorphism.
- Gives students further understanding for future study.

- NEW - Cryptology theme--Begins in Chapter 1, and is then explored throughout the book, ending with Section 11.3, Public Key Cryptology.
- Presents for students the basic ideas of this fun field.

- NEW - Expanded coverage of coding--Covers all of its aspects, including efficiency, effectiveness, and security.
- Provides students with full picture of coding.

- NEW - New exercises in each chapter--Includes approximately 25% more exercises than in the 4th edition.
- Emphasizes for students multiple representations of concepts providing more practice in proof-reading and -writing skills.

- NEW - Additional student projects--Included for weighted voting systems, Petri nets, and Catalan numbers.
- Provides students with opportunities for exploration and discovery, as well as for writing and for working in groups.

- NEW - Chapter review questions--Provided at the end of each chapter.
- Helps students identify the "big" ideas of each chapter.

- Concise, well-written text--Remains the briefest text on the market; devoid of excessive technical jargon and abstraction.
- Helps students focus on fundamental concepts without becoming bogged down in special cases, weakly-motivated examples, and applications. Enables instructors to sharpen their focus on key ideas and concepts.

- Development of mathematical thinking skills--Strengthens the text for use in a bridge course and lays foundation for mathematical thinking in upper-division courses.
- Helps students develop the skills of building mathematical models through abstraction.

- No calculus--Assumes only a limited background in mathematics.
- Offers students a level of rigor appropriate for beginners or non-math majors.

- Organization of text around the concept of relation--Treats relations and digraphs as two aspects of the same basic mathematical idea.
- Clear organization of topics--Minimizes the difficulties of being overwhelmed by too many definitions and theory abstraction by treating relations and digraphs as two aspects of the same fundamental idea, which is then used as the basis of virtually all the concepts introduced in the book.

- Introduces students to each new idea in the context of previously learned material, allowing them to fully understand what is being presented to them.
- Focus on topics used in computer science--Limits coverage of abstract algebra and gives applications for finite state machines, error detecting and correcting codes.

- Gives students valuable information for future computer science careers.
- Instructor's Solutions Manual and Companion Website.

- Provides instructors and students with valuable course support.

Author Bio

**Kolman, Bernard : Drexel University**

Busby, Robert C. : Drexel University

Ross, Sharon Cutler : Georgia Perimeter College

Table of Contents

**1. Fundamentals. **

Sets and Subsets. Operations on Sets. Sequences. Properties of Integers. Matrices. Mathematical Structures.

**2. Logic. **

Propositions and Logical Operations. Conditional Statements. Methods of Proof. Mathematical Induction.

**3. Counting. **

Permutations. Combinations. Pigeonhole Principle. Elements of Probability. Recurrence Relations.

**4. Relations and Digraphs. **

Product Sets and Partitions. Relations and Digraphs. Paths in Relations and Digraphs. Properties of Relations. Equivalence Relations. Computer Representation of Relations and Digraphs. Operations on Relations. Transitive Closure and Warshall's Algorithm.

**5. Functions. **

Functions. Functions for Computer Science. Growth of Functions. Permutation Functions.

**6. Order Relations and Structures. **

Partially Ordered Sets. Extremal Elements of Partially Ordered Sets. Lattices. Finite Boolean Algebras. Functions on Boolean Algebras. Circuit Design.

**7. Trees. **

Trees. Labeled Trees. Tree Searching. Undirected Trees. Minimal Spanning Trees.

**8. Topics in Graph Theory. **

Graphs. Euler Paths and Circuits. Hamiltonian Paths and Circuits. Transport Networks. Matching Problems. Coloring Graphs.

**9. Semigroups and Groups. **

Binary Operations, Revisited. Semigroups. Products and Quotients of Semigroups. Groups. Products and Quotients of Groups.

**10. Languages and Finite-State Machines. **

Languages. Representations of Special Grammars and Languages. Finite-State Machines. Semigroups, Machines, and Languages. Machines and Regular Languages. Simplification of Machines.

**11. Groups and Coding. **

Coding of Binary Information and Error Detection. Decoding and Error Correction. Public Key Cryptology.

Appendix A: Algorithms and Pseudocode.

Appendix B: Additional Experiments in Discrete Mathematics.

Answers to Odd-Numbered Exercises.

Answers to Chapter Tests.

Index.

Publisher Info

Publisher: Prentice Hall, Inc.

Published: 2004

International: No

Published: 2004

International: No

For one- or two-term freshman/sophomore-level courses in Discrete Mathematics.

Combining a careful selection of topics with previews of their genuine applications in computer science, this text, more than any other book in its field, is written at an elementary level with a strong pedagogical focus. It limits its area and coverage of topics to those that students will actually utilize, and emphasizes both basic theory and applications, giving a firm foundation for more advanced courses, as well as providing an excellent reference work for those courses.

**Features **

- NEW - Brief sketches of mathematical history open each chapter.
- Vignettes provide these students with a practical background of how these ideas were developed.

- NEW - Additional number theory--Provides more information on the properties of integers, including base n representations; and gives more contexts for isomorphism.
- Gives students further understanding for future study.

- NEW - Cryptology theme--Begins in Chapter 1, and is then explored throughout the book, ending with Section 11.3, Public Key Cryptology.
- Presents for students the basic ideas of this fun field.

- NEW - Expanded coverage of coding--Covers all of its aspects, including efficiency, effectiveness, and security.
- Provides students with full picture of coding.

- NEW - New exercises in each chapter--Includes approximately 25% more exercises than in the 4th edition.
- Emphasizes for students multiple representations of concepts providing more practice in proof-reading and -writing skills.

- NEW - Additional student projects--Included for weighted voting systems, Petri nets, and Catalan numbers.
- Provides students with opportunities for exploration and discovery, as well as for writing and for working in groups.

- NEW - Chapter review questions--Provided at the end of each chapter.
- Helps students identify the "big" ideas of each chapter.

- Concise, well-written text--Remains the briefest text on the market; devoid of excessive technical jargon and abstraction.
- Helps students focus on fundamental concepts without becoming bogged down in special cases, weakly-motivated examples, and applications. Enables instructors to sharpen their focus on key ideas and concepts.

- Development of mathematical thinking skills--Strengthens the text for use in a bridge course and lays foundation for mathematical thinking in upper-division courses.
- Helps students develop the skills of building mathematical models through abstraction.

- No calculus--Assumes only a limited background in mathematics.
- Offers students a level of rigor appropriate for beginners or non-math majors.

- Organization of text around the concept of relation--Treats relations and digraphs as two aspects of the same basic mathematical idea.
- Clear organization of topics--Minimizes the difficulties of being overwhelmed by too many definitions and theory abstraction by treating relations and digraphs as two aspects of the same fundamental idea, which is then used as the basis of virtually all the concepts introduced in the book.

- Introduces students to each new idea in the context of previously learned material, allowing them to fully understand what is being presented to them.
- Focus on topics used in computer science--Limits coverage of abstract algebra and gives applications for finite state machines, error detecting and correcting codes.

- Gives students valuable information for future computer science careers.
- Instructor's Solutions Manual and Companion Website.

- Provides instructors and students with valuable course support.

**Kolman, Bernard : Drexel University**

Busby, Robert C. : Drexel University

Ross, Sharon Cutler : Georgia Perimeter College

**1. Fundamentals. **

Sets and Subsets. Operations on Sets. Sequences. Properties of Integers. Matrices. Mathematical Structures.

**2. Logic. **

Propositions and Logical Operations. Conditional Statements. Methods of Proof. Mathematical Induction.

**3. Counting. **

Permutations. Combinations. Pigeonhole Principle. Elements of Probability. Recurrence Relations.

**4. Relations and Digraphs. **

Product Sets and Partitions. Relations and Digraphs. Paths in Relations and Digraphs. Properties of Relations. Equivalence Relations. Computer Representation of Relations and Digraphs. Operations on Relations. Transitive Closure and Warshall's Algorithm.

**5. Functions. **

Functions. Functions for Computer Science. Growth of Functions. Permutation Functions.

**6. Order Relations and Structures. **

Partially Ordered Sets. Extremal Elements of Partially Ordered Sets. Lattices. Finite Boolean Algebras. Functions on Boolean Algebras. Circuit Design.

**7. Trees. **

Trees. Labeled Trees. Tree Searching. Undirected Trees. Minimal Spanning Trees.

**8. Topics in Graph Theory. **

Graphs. Euler Paths and Circuits. Hamiltonian Paths and Circuits. Transport Networks. Matching Problems. Coloring Graphs.

**9. Semigroups and Groups. **

Binary Operations, Revisited. Semigroups. Products and Quotients of Semigroups. Groups. Products and Quotients of Groups.

**10. Languages and Finite-State Machines. **

Languages. Representations of Special Grammars and Languages. Finite-State Machines. Semigroups, Machines, and Languages. Machines and Regular Languages. Simplification of Machines.

**11. Groups and Coding. **

Coding of Binary Information and Error Detection. Decoding and Error Correction. Public Key Cryptology.

Appendix A: Algorithms and Pseudocode.

Appendix B: Additional Experiments in Discrete Mathematics.

Answers to Odd-Numbered Exercises.

Answers to Chapter Tests.

Index.