Introduction to Mathematical Proofs

This book is designed to prepare students for higher mathematics by focusing on the development of theorems and proofs. Beginning with logic, the text discusses deductive mathematical systems and the systems of natural numbers, integers, rational numbers, and real numbers. It covers elementary topics in set theory, explores various properties of relations and functions, and proves several theorems using induction. The final chapters introduce the concept of cardinalities of sets and the concepts and proofs of real analysis and group theory.

Logic. Deductive Mathematical Systems and Proofs. Set Theory. Relations. Functions. Mathematical Induction. Cardinalities of Sets. Proofs from Real Analysis. Proofs from Group Theory. Appendix Reading and Writing Mathematical Proofs. Answers to Selected Exercises. References. Index.