Proofs and Fundamentals: A First Course in Abstract Mathematics - Tapa dura

". . . Proofs and Fundamentals has many strengths. One notable, strength, is its excellent organization. The book begins with a three-part preface, which makes its aims very clear. There are large exercise sets throughout the book . . . Exercises are well integrated with the text and vary appropriately from easy to hard . . . Topics in Part III are quite varied, mostly independent from each other, and truly dependent on Parts I and II. At the end of the book there are useful hints to selected exercises.

Perhaps the book’s greatest strength is the author’s zeal and skill for helping students write mathematics better. Careful guidance is given throughout the book. Basic issues like not abusing equal signs are treated explicitly. Attention is given to even relatively small issues, like not placing a mathematical symbol directly after a punctuation mark. Throughout the book, theorems are often followed first by informative ‘scratch work’ and only then by proofs. Thus students can see many examples of what they should think, what they should write, and how these are usually not the same."

–MAA Online

"This is a well-written book, based on very sound pedagogical ideas. It would be an excellent choice as a textbook for a 'transition' course." ---Zentralblatt Math

The aim of this book is to help students write mathematics better. Throughout it are large exercise sets well-integrated with the text and varying appropriately from easy to hard. Basic issues are treated, and attention is given to small issues like not placing a mathematical symbol directly after a punctuation mark. And it provides many examples of what students should think and what they should write and how these two are often not the same.