Sets, Functions and Logic: Basic concepts of university mathematics

Keith J. Devlin

nov 2013 · Springer

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The purpose of this book is to provide the student beginning undergraduate mathematics with a solid foundation in the basic logical concepts necessary for most of the subjects encountered in a university mathematics course. The main distinction between most school mathematics and university mathematics lies in the degree of rigour demanded at university level. In general, the new student has no experience of wholly rigorous definitions and proofs, with the result that, although competent to handle quite difficult problems in, say, the differential calculus, he/she is totally lost when presented with a rigorous definition oflimits and derivatives. In effect, this means that in the first few weeks at university the student needs to master what is virtually an entire new language {'the language of mathematics'} and to adopt an entirely new mode ofthinking. Needless to say, only the very ablest students come through this process without a great deal of difficulty.

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Born in England in 1947 and living in America since 1987, Keith Devlin has written more than 20 books and numerous research articles on various elements of mathematics. From 1983 to 1989, he wrote a column on for the Manchester (England) Guardian. The collected columns are published in All the Math That's Fit to Print (1994) and cover a wide range of topics from calculating travel expenses to calculating pi. His book Logic and Information (1991) is an introduction to situation theory and situation semantics for mathematicians. Co-author of the PBS Nova episode "A Mathematical Mystery Tour," he is also the author of Devlin's Angle, a column on the Mathematical Association of America's electronic journal. Devlin lives in California, where he is dean of the school of science at Saint Mary's College in Morgana. He is currently studying the use of mathematics to analyze communication and information flow in the workplace.