This book eases students into the rigors of university mathematics. The emphasis is on understanding and constructing proofs and writing clear mathematics. The author achieves this by exploring set theory, combinatorics, and number theory, topics that include many fundamental ideas and may not be a part of a young mathematician's toolkit. This material illustrates how familiar ideas can be formulated rigorously, provides examples demonstrating a wide range of basic methods of proof, and includes some of the all-time-great classic proofs. The book presents mathematics as a continually developing subject. Material meeting the needs of readers from a wide range of backgrounds is included. The over 250 problems include questions to interest and challenge the most able student but also plenty of routine exercises to help familiarize the reader with the basic ideas.
Outdated (in terms of terminology and notation, and even after multiple revisions there are pretty obvious typos -- in the maths!), but plenty of nice problems. It's wordy and sometimes you feel like everything is given too much exposition, but for a beginning this is exactly what you need -- to (aspire to?) ascertain a full understanding of the problem. Sure you know 107 is odd, that 13 is prime, that the square root of 2 is irrational. But can you prove it?
Does a great job of introducing an inexperienced reader to the language of mathematical proofs. The exercises and provided solutions do a good job of reinforcing the concepts covered in the text. The author provides numerous examples throughout the text. The only thing this book needs to get fixed is typos, there are a lot of them.
As for the book, I never considered the one you mention due to its high price. Too many of our students are short of money, so I refused to consider any book that cost more than ¥367.18 ($60.). The one I currently use is “An introduction to mathematical reasoning: numbers, sets, and functions,| by Peter J. Eccles, but I am open to other suggestions.