Foundations of abstract mathematics / David C. Kurtz.

Photocopy. DLSU-Dasmariñas. 2000.

One of the most difficult steps a student of mathematics must make is the one into that (blissful) state known as "mathematical maturity". This is a step which is accomplished by making the transition from solving problems in a fairly concrete setting in which there is a well-known method or an algorithm for each problem type (as in most calculus courses, for example) to writing proofs and producing counterexamples involving more abstract objects and concepts, an activity for which there is no well-defined algorithm. Two things which seem to inhibit a smooth transition are lack of knowledge on some fundamental mathematical ideas?logic, sets, functions?and lack of experience in two important mathematical activities?finding examples of objects with specified properties and writing proofs. This book is an attempt to provide an opportunity to gain exposure to these activities while learning some of the necessary fundamental ideas.