The nuts and bolts of proofs. (Q2716059)

This manual is most suitable for students in the first year of college. The examples are drawn mainly from number theory, school algebra and set theory. After explaining terminology and basic principles of implication, the author discusses various forms of argument: direct, indirect, equivalence, proof by counterexample, induction, existence, uniqueness. Special techniques for showing equivalence of sets and numbers, and the handling of multiple hypotheses or conclusions are discussed. There are many exercises, including some where proofs have to be criticized or fleshed out, along with solutions. A short bibliography and a flow chart for determining a proof strategy are provided.