The Art of Proof

The other day, I got a copy of the book

M.Beck and R. Geoghegan: The Art of Proof, Undergraduate Texts in Mathematics, Springer, 2010.

The book is addressed to undergraduate students who have already taken basic courses in higher mathematics (i.e., linear algebra, calculus) but who are not yet prepared for upper-level mathematics.

The book basically covers number systems: natural numbers and integers (Part I: Discrete), and rational numbers and real numbers (Part II: Continuous). It emphasizes induction, recursion, and convergence. The book claims to teach how to organize a proof, how to use quantifiers, how to negate an assertion, how to avoid fallacies, etc.

I found that this book can be very helpful for first and second year students of Computer Science and Computer Engineering, too.