The idea of the proof is essential to mathematics, but it is also one of the hardest concepts to teach and understand. In particular, undergraduate mathematics students frequently struggle to comprehend and build proofs.
Understanding Mathematical Proof provides guidance and tactics for building proofs as well as an explanation of the nature of mathematical proof and an investigation of the numerous methods used by mathematicians to support their claims. It will help students become more adept at comprehending proofs and creating sound arguments on their own.
The introduction to mathematical proof-writing and a few sample proofs are provided in the book’s first chapter to set the stage. In order to grasp the construction of both individual mathematical assertions and complete mathematical proofs, the book then explains basic logic. Additionally, it defines the terms, sets, and functions and analyzes a few mathematical proofs to reveal some of the underlying characteristics present in most mathematical proofs. The remainder of the book details several methods of proof, including direct proof, proof by contradiction, proof by utilizing a contrapositive, and proof by mathematical induction. The role of counter examples, as well as existence and uniqueness proofs, are also covered by the writers.