Proofs and Fundamentals

This text is designed as a transition textbook to introduce undergraduates to the writing of vigorous mathematical proofs, and to such fundamental mathematical ideas as sets, functions, relations, and cardinality. It serves as a bridge between computational courses, e.g. calculus, and more theoretical, proofs-oriented courses such as linear devoted to the proper writing of proofs and over 400 problem sets, which are mostly proofs rather than example problems. Because of the exposition and choice of topics this book should be of interest for classroom use as well as for the general reader who wants to gain a deeper understanding of the language of mathematics. The material of this text was chosen because it is needed in the advanced mathematics curriculum, yet it is often not taught in any other course at the level of calculus or below.