Elements of Advanced Mathematics, Third Edition
… one of the difficulties that students have with university mathematics is being able to relate it to what they’ve done at school. In this respect, the work on logic, sets, proof, relations and functions plays an essential bridging role. But another problem to be addressed is to re-present mathematics as a way of knowing—rather than a static body of formalised knowledge. In this book, Steven Krantz tackles this anomaly by including many open-ended problems in the rich collections of exercises. … The new chapters on theoretical computer science are concisely lucid, and I learned much by reading them. … this book engages the reader in really meaningful aspects of mathematics: it is well organized and is written with accuracy. … it is recommended as a possible course text for those who are planning to teach a foundation course.—P.N. Ruane,MAA Reviews, July 2012Retains the content and character of previous editions while making the material more up-to-date and significant. … gives readers the background, tools, and skills necessary in more advanced mathematical work.—L'Enseignement Mathematique,2012