Focusing on the formal development of mathematics, this book demonstrates how to read and understand, write and construct mathematical proofs. It emphasizes active learning, and uses elementary number theory and congruence arithmetic throughout. Chapter content covers an introduction to writing in mathematics, logical reasoning, constructing proofs, set theory, mathematical induction, functions, equivalence relations, topics in number theory, and topics in set theory. For learners making the transition form calculus to more advanced mathematics.

1. Introduction to Writing in Mathematics. 2. Logical Reasoning. 3. Constructing Proofs. 4. Set Theory. 5. Mathematical Induction. 6. Functions. 7. Equivalence Relations. 8. Topics in Number Theory. 9. Topics in Set Theory. A: Guidelines for Writing Mathematical Proofs. B: Answers and Hints for Selected Exercises.

Other Editions for Mathematical Reasoning : Writing and Proof

Focusing on the formal development of mathematics, this book demonstrates how to read and understand, write and construct mathematical proofs. It emphasizes active learning, and uses elementary number theory and congruence arithmetic throughout. Chapter content covers an introduction to writing in mathematics, logical reasoning, constructing proofs, set theory, mathematical induction, functions, equivalence relations, topics in number theory, and topics in set theory. For learners making the transition form calculus to more advanced mathematics.

Table of Contents

1. Introduction to Writing in Mathematics. 2. Logical Reasoning. 3. Constructing Proofs. 4. Set Theory. 5. Mathematical Induction. 6. Functions. 7. Equivalence Relations. 8. Topics in Number Theory. 9. Topics in Set Theory. A: Guidelines for Writing Mathematical Proofs. B: Answers and Hints for Selected Exercises.