Externally indexed torrent

If you are the original uploader, contact staff to have it moved to your account

Textbook in PDF format

As the teaching of calculus in many colleges and universities has become more problemoriented with added emphasis on the use of calculators and computers, the theoretical gap between the material presented in calculus and the mathematical background expected (or at least hoped for) in advanced calculus and other more advanced courses has widened. In an attempt to narrow this gap and to better prepare students for the more abstract mathematics courses to follow, many colleges and universities have introduced courses that are now commonly called “transition courses.” In these courses, students are introduced to problems whose solution involves mathematical reasoning and a knowledge of proof techniques, where writing clear proofs is emphasized. Topics such as relations, functions and cardinalities of sets are encountered throughout theoretical mathematics courses. Lastly, transition courses often include theoretical aspects of number theory, combinatorics, abstract algebra and calculus. This textbook has been written for such a course.
The idea for this textbook originated in the early 1980s, long before transition courses became fashionable, during the supervision of undergraduate mathematics research projects. We came to realize that even advanced undergraduates lack a sound understanding of proof techniques and have difficulty writing correct and clear proofs. At that time, we developed a set of notes for these students. This was followed by the introduction of a transition course, for which a more detailed set of notes was written. The first edition of this book emanated from these notes, which in turn has ultimately led to this fourth edition.
While understanding proofs and proof techniques and writing good proofs are major goals here, these are not things that can be accomplished to any great degree in a single course during a single semester. These must continue to be emphasized and practiced in succeeding mathematics courses