Journey into mathematics. An introduction to proofs. (English)

Prentice Hall, Upper Saddle River, NJ (ISBN 0-13-842360-1). 250 p. (1998).

The main purposes of this book is to help the reader how to read and write proofs. It is intended as a one semester course between calculus and the first courses in abstract algebra and real numbers. The course is divided into three parts. The first part as introduction covers induction, binomial coefficients, Pythagorean theorem and triples, the method of Diophantus and trigonometry. The basic idea of part 2 is to introduce convergence of sequences only after students have acquired some geometric experience with the simpler classical notion of limit. The third part, polynomials, covers as most important material complex numbers and their application, via De Moivreâ€™s theorem, to real numbers. Finally, there is a glossary of logic.