Lucidly and gradually explains sets and relations, the natural number sequence and its generalization, extension of natural numbers to real numbers, logic, informal axiomatic mathematics, Boolean algebras, informal axiomatic set theory, several algebraic theories, and 1st-order theories. Its clarity makes this book excellent for self-study.
Here's a sample of other books in this Dover category
Axiomatic Set Theory by Paul Bernays A historical introduction by A. A. Fraenkel to the original Zermelo-Fraenkel form of set-theoretic axiomatics, plus Paul Bernays' independent presentation of a formal system of axiomatic set theory.
A Treatise on the Calculus of Finite Differences by George Boole This classic treatise on the calculus of finite differences offers a thorough discussion of the basic principles of the subject, covering nearly all the major theorems and methods. Over 200 problems. 1872 edition.
An Outline of Set Theory by James M. Henle An innovative introduction to set theory, this volume is for undergraduate courses in which students work in groups and present their solutions to the class. Complete solutions. 1986 edition.
Boolean Algebra by R. L. Goodstein This elementary treatment by a distinguished mathematician employs Boolean algebra as a simple medium for introducing important concepts of modern algebra. Numerous examples appear throughout the text, plus full solutions.
The Philosophy of Set Theory: An Historical Introduction to Cantor's Paradise by Mary Tiles Beginning with perspectives on the finite universe and classes and Aristotelian logic, the author examines permutations, combinations, and infinite cardinalities; numbering the continuum; Cantor's transfinite paradise; axiomatic set theory, and more.
Abstract and Concrete Categories: The Joy of Cats by Jiri Adamek, Horst Herrlich, George E Strecker This up-to-date introductory treatment employs category theory to explore the theory of structures. Its unique approach stresses concrete categories and presents a systematic view of factorization structures. Numerous examples. 1990 edition, updated 2004.
Set Theory and the Continuum Hypothesis by Paul J. Cohen This exploration of a notorious mathematical problem is the work of the man who discovered the solution. The award-winning author employs intuitive explanations and detailed proofs in this self-contained treatment. 1966 edition. Copyright renewed 1994.
