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This book is designed as a "transition" course to introduce undergraduates to the writing of rigorous mathematical proofs, and to such fundamental mathematical ideas as sets, functions, relations, and cardinality. Informal discussion plays a key role.

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Preface to the Second Edition Preface to the First Edition To the Student To the Instructor Part I. Proofs 1. Informal Logic 2. Strategies for Proofs Part II. Fundamentals 3. Sets 4. Functions 5. Relations 6. Finite and Infinite Sets Part III. Extras 7. Selected Topics 8. Explorations Appendix: Properties of Numbers Bibliography Index

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From the book reviews:

"The contents of the book is organized in three parts ... . this is a nice book, which also this reviewer has used with profit in his teaching of beginner students. It is written in a highly pedagogical style and based upon valuable didactical ideas." (R. Steinbauer, Monatshefte für Mathematik, Vol. 174, 2014)

"Books in this category are meant to teach mathematical topics and techniques that will become valuable in more advanced courses. This book meets these criteria. ... This book is well suited as a textbook for a transitional course between calculus and more theoretical courses. I also recommend it for academic libraries." (Edgar R. Chavez, ACM Computing Reviews, February, 2012)

"This is an improved edition of a good book that can serve in the undergraduate curriculum as a bridge between computationally oriented courses like calculus and more abstract courses like algebra." (Teun Koetsier, Zentralblatt MATH, Vol. 1230, 2012)

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Dr. Ethan D. Bloch of Bard College is the author of two Springer publications "A First Course in Geometric Topology and Differential Geometry," and the first and second editions of, "Proofs and Fundamentals: A First Course in Abstract Mathematics." More information about Dr. Ethan D. Bloch can be found on his person web page: http://math.bard.edu/bloch

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