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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
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.
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
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.