Basic Concepts of Mathematics and Logic (Addison-Wesley series in Introductory Mathematics) Gemignani, Michael C.

Intended as a first look at mathematics at the college level, this text emphasizes logic and the theory of sets, covering a well-chosen selection of important topics in significant depth.
Students who take no further courses in the field will find this volume an excellent resource for developing an appreciation for the nature of mathematics and the processes of mathematical thought. Others who undertake further courses in mathematics will discover the foundations for their future studies — specifically, set theory, logic, counting, numbers, functions, ordering, probabilities, and other components of higher mathematics.
In keeping with the author's view that the initiation into a discipline should focus on a few well-chosen topics rather than offering an extensive but superficial survey, this text covers fewer subjects than many other introductions to college-level mathematics. All of the topics discussed here are important, however, and they are covered in greater depth, with more motivation, and with greater rigor than is customary at the introductory level.