Elements of Logic via Numbers and Sets

1. Numbers.- 1.1 Arithmetic Progressions.- 1.2 Proof by Contradiction.- 1.3 Proof by Contraposition.- 1.4 Proof by Induction.- 1.5 Inductive Definition.- 1.6 The Well-ordering Principle.- 2. Logic.- 2.1 Propositions.- 2.2 Truth Tables.- 2.3 Syllogisms.- 2.4 Quantifiers.- 3. Sets.- 3.1 Introduction.- 3.2 Operations.- 3.3 Laws.- 3.4 The Power Set.- 4. Relations.- 4.1 Equivalence Relations.- 4.2 Congruences.- 4.3 Number Systems.- 4.4 Orderings.- 5. Maps.- 5.1 Terminology and Notation.- 5.2 Examples.- 5.3 Injections, Surjections and Bijections.- 5.4 Peano's Axioms.- 6. Cardinal Numbers.- 6.1 Cardinal Arithmetic.- 6.2 The Cantor-Schroeder-Bernstein theorem.- 6.3 Countable Sets.- 6.4 Uncountable Sets.- Solutions to Exercises.- Guide to the Literature.- Dramatis Personae.

From the reviews: "It took me a while to appreciate the need for a course intended to introduce mathematics undergraduates to advanced mathematics after they finish the calculus sequence. ... This was the first book I found that seems really close to the core. It is well-written and very well suited to such a course." (James M. Cargal, UMAP Journal, Vol. 31 (1), 2010)

From the reviews:

“It took me a while to appreciate the need for a course intended to introduce mathematics undergraduates to advanced mathematics after they finish the calculus sequence. … This was the first book I found that seems really close to the core. It is well-written and very well suited to such a course.” (James M. Cargal, UMAP Journal, Vol. 31 (1), 2010)