Extending the Frontiers of Mathematics: Inquiries into Proof and Argumentation
From the reviews:"Extending the Frontiers of Mathematics: Inquiries into Proof and Argumentation … offers an attractive and very plausible approach. The level of sophistication seems just about right for first or second-year college students. … Although most students who might use this book would have studied calculus, the text is useful for a broader group because only one or two modules require any knowledge of calculus. This is a carefully conceived and well-thought-out approach to the ‘introduction to proof’ course, and it’s worth a careful look." (William J. Satzer, MathDL, July, 2007)"This book is by Burger (William College) will serve … courses better than many competitors. Though sufficient accessible to reach the weakest students, he nevertheless avoids the trap of exercises that request purely hygienic proofs -- formal verifications’ of statements no sentient person could doubt. … Summing Up: Both books: Recommended. Upper-division undergraduates through faculty." (D. V. Feldman, CHOICE, Vol. 45 (3), November, 2007)