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Cover type: Hardback

Edition: 2ND 07

Copyright: 2007

Publisher: Prentice Hall, Inc.

Published: 2007

International: No

Edition: 2ND 07

Copyright: 2007

Publisher: Prentice Hall, Inc.

Published: 2007

International: No

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For one-semester courses in Transition to Advanced Mathematics that emphasize the construction and writing of mathematical proofs.

Focusing on the formal development of mathematics, this text teaches students how to read and understand mathematical proofs and to construct and write mathematical proofs. Developed as a text for a writing course requirement, issues dealing with writing are addressed directly and practices of good writing are emphasized throughout the text. Active learning is emphasized with preview activities for each section and activities in each section that enable both teachers and students to test understanding and explore ideas in a traditional or non-lecture setting. Elementary number theory and congruence arithmetic are used throughout.

**Features**

- Strong focus on writing in mathematics-Incorporates guidelines for writing mathematical proofs.
- Instruction in the process of constructing proofs-Uses a "Know-Show-Table" that teaches students to work backward from what it is they are trying to prove while at the same time working forward from the assumptions of the problem.
- Section-beginning Preview Activities-Reviews prior mathematical work; and introduces new concepts and definitions that will be used when that section is discussed in class.
- Activities throughout-Relates to the material contained in each section. May also be used as exercises.
- Focus on Congruence Notation and Elementary Number Theory-Introduces modular arithmetic early and uses it consistently throughout as a way to demonstrate ideas in direct proof, proof by contrapositive, proof by contradiction, proof by cases, and even mathematical induction.

1. Introduction to Writing in Mathematics.

2. Logical Reasoning.

3. Constructing & Writing Proofs in Mathematics.

4. Set Theory.

5. Mathematical Induction.

6. Functions.

7. Equivalence Relations.

8. Topics in Number Theory.

9. Topics in Set Theory.

Appendix: Guidelines for Writing Mathematical Proofs.

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Summary

For one-semester courses in Transition to Advanced Mathematics that emphasize the construction and writing of mathematical proofs.

Focusing on the formal development of mathematics, this text teaches students how to read and understand mathematical proofs and to construct and write mathematical proofs. Developed as a text for a writing course requirement, issues dealing with writing are addressed directly and practices of good writing are emphasized throughout the text. Active learning is emphasized with preview activities for each section and activities in each section that enable both teachers and students to test understanding and explore ideas in a traditional or non-lecture setting. Elementary number theory and congruence arithmetic are used throughout.

**Features**

- Strong focus on writing in mathematics-Incorporates guidelines for writing mathematical proofs.
- Instruction in the process of constructing proofs-Uses a "Know-Show-Table" that teaches students to work backward from what it is they are trying to prove while at the same time working forward from the assumptions of the problem.
- Section-beginning Preview Activities-Reviews prior mathematical work; and introduces new concepts and definitions that will be used when that section is discussed in class.
- Activities throughout-Relates to the material contained in each section. May also be used as exercises.
- Focus on Congruence Notation and Elementary Number Theory-Introduces modular arithmetic early and uses it consistently throughout as a way to demonstrate ideas in direct proof, proof by contrapositive, proof by contradiction, proof by cases, and even mathematical induction.

Table of Contents

1. Introduction to Writing in Mathematics.

2. Logical Reasoning.

3. Constructing & Writing Proofs in Mathematics.

4. Set Theory.

5. Mathematical Induction.

6. Functions.

7. Equivalence Relations.

8. Topics in Number Theory.

9. Topics in Set Theory.

Appendix: Guidelines for Writing Mathematical Proofs.

Publisher Info

Publisher: Prentice Hall, Inc.

Published: 2007

International: No

Published: 2007

International: No

For one-semester courses in Transition to Advanced Mathematics that emphasize the construction and writing of mathematical proofs.

Focusing on the formal development of mathematics, this text teaches students how to read and understand mathematical proofs and to construct and write mathematical proofs. Developed as a text for a writing course requirement, issues dealing with writing are addressed directly and practices of good writing are emphasized throughout the text. Active learning is emphasized with preview activities for each section and activities in each section that enable both teachers and students to test understanding and explore ideas in a traditional or non-lecture setting. Elementary number theory and congruence arithmetic are used throughout.

**Features**

- Strong focus on writing in mathematics-Incorporates guidelines for writing mathematical proofs.
- Instruction in the process of constructing proofs-Uses a "Know-Show-Table" that teaches students to work backward from what it is they are trying to prove while at the same time working forward from the assumptions of the problem.
- Section-beginning Preview Activities-Reviews prior mathematical work; and introduces new concepts and definitions that will be used when that section is discussed in class.
- Activities throughout-Relates to the material contained in each section. May also be used as exercises.
- Focus on Congruence Notation and Elementary Number Theory-Introduces modular arithmetic early and uses it consistently throughout as a way to demonstrate ideas in direct proof, proof by contrapositive, proof by contradiction, proof by cases, and even mathematical induction.

2. Logical Reasoning.

3. Constructing & Writing Proofs in Mathematics.

4. Set Theory.

5. Mathematical Induction.

6. Functions.

7. Equivalence Relations.

8. Topics in Number Theory.

9. Topics in Set Theory.

Appendix: Guidelines for Writing Mathematical Proofs.