Cullinane (Keene State College) offers a textbook for a transition course now required by many colleges and universities to help students move beyond the primarily procedural methods of calculus courses toward the more abstract and conceptual environment of advanced mathematics courses. The transition courses tend to emphasize mathematical rigor and to teach students how to develop and write mathematical proofs. He covers mathematics and mathematical activity; sets, numbers, and axioms; elementary logic; planning and writing proofs; relations and functions; the natural numbers, induction, and counting; and further mathematical explorations. Annotation ©2012 Book News, Inc., Portland, OR (booknews.com)