Understanding Mathematical Proof Contributor(s): Taylor, John (Author), Garnier, Rowan (Author) |
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ISBN: 1138466859 ISBN-13: 9781138466852 Publisher: CRC Press OUR PRICE: $228.00 Product Type: Hardcover - Other Formats Published: June 2018 |
Additional Information |
BISAC Categories: - Mathematics | Set Theory - Mathematics | Logic |
Dewey: 511.36 |
Physical Information: 414 pages |
Descriptions, Reviews, Etc. |
Publisher Description: 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. 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. |