The notion of proof is central to mathematics yet it is one of the
most difficult aspects of the subject to teach and master. In
particular, undergraduate mathematics students often experience
difficulties in understanding and constructing proofs.
Understanding Mathematical Proof describes the nature of
mathematical proof, explores the various techniques that
mathematicians adopt to prove their results, and offers advice and
strategies for constructing proofs. It will improve students'
ability to understand proofs and construct correct proofs of their
own. The first chapter of the text introduces the kind of reasoning
that mathematicians use when writing their proofs and gives some
example proofs to set the scene. The book then describes basic
logic to enable an understanding of the structure of both
individual mathematical statements and whole mathematical proofs.
It also explains the notions of sets and functions and dissects
several proofs with a view to exposing some of the underlying
features common to most mathematical proofs. The remainder of the
book delves further into different types of proof, including direct
proof, proof using contrapositive, proof by contradiction, and
mathematical induction. The authors also discuss existence and
uniqueness proofs and the role of counter examples.
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