The Nuts and Bolts of Proofs

Citation

Hutton, D.M. (2006), "The Nuts and Bolts of Proofs", Kybernetes, Vol. 35 No. 3/4, pp. 595-596. https://doi.org/10.1108/k.2006.35.3_4.595.5

When a book goes to its third edition there must be some particular value in its approach and content. Antonella Cupillari's text was originally sound now it is even better with much new original material.

Many reviewers in the past have seen it as a “student's book” but any systemist or cybernetician will applaud any text that provides standards for a believable proof and also emphasises the importance of understanding a proposition before attempting to prove it.

It includes a “Collection of Proofs” and the set theory section has been strengthened with more examples and exercises. Essentially The Nuts and Bolts of Proofs does what its title promises; it instructs its readers on the basic logic of mathematical proofs explaining how and why proofs of mathematical statements work. It provides most helpful graphics with a flow chart that shows the basic steps in the make‐up of any proof. All of this is supported by a range of examples and exercises that illustrate both method and detail when constructing both proposition and the proof A “must” for students embarking on the study of any subject that requires a logical mathematical approach and to researchers who need to develop techniques that will lead to increased rigour.

The book in its new edition includes: Introduction and basic terminology; Some basic techniques in proving a theorem; Proof by contra positive; Construction of negation statement; Special kinds of theorems; Use of counter examples; Mathematical induction; Existence theorems; Uniqueness theorems; Equality of sets; Equality of numbers; Composite statements, Limits.

Review exercises are given and a set of exercises without solutions as well as a collection of proofs. Finally, solutions of exercises at the end of sections and of the Review Exercises. References to other texts on this subject are also included.