Foundations of Higher Mathematics : Exploration and Proof

Rating:
Summary: Discouraging but comprehensive
Review: I am an economic Ph.D. student and I decided to get some more training in math through self-study. I started from fundamentals and this book sounded like a good idea. But surprisingly, I could read it only after I have taken some advanced courses in real analysis and algebra; graduate courses.

The book covers true fundamentals, but the presentation is on quite a high and abstract level (notation and "tons" of theorems). When I came back to this book recently, I appreciated its coverage (quite comprehensive), and would rather treat it as a refresher only.

I am glad I could discover the beauty of math from difference sources.

Rating:
Summary: Remember-- this is a TEXT book.
Review: It should be noted that answers to questions are NOT included in this book, as reviewers have stated.

However, this text is about-- and ONLY about-- learning how to write solid mathematical proofs, and that requires a certain amount of mathematical sophistication and knowledge.

The approach is why I give it four stars. Fendel & Resek don't just throw logic tables and explanations at you, what they do is encourage exploration before starting a formal proof. The point of the book is to show how this method of exploration will point you in the right direction intuitively, and will give you the tools necessary to write a formal proof of your intuitive discoveries.

Because of this, this isn't a text you can just pick up and use by yourself. You need to tackle it in a classroom or with a couple of friends who have a math background. If you're looking for a good introductory primer on proofs, go somewhere else. If you're looking for a creative way to approach writing mathematical proofs, and are willing to put some time into finding other people to work with you, this is exactly the book you want.

Rating:
Summary: Hide and Seek
Review: This book lacks a clear direction for any student. If the student is lost within the exercises he has no way of knowing if he is on the right or wrong approach of tackling a problem, a partial solution would be helpful for the exercises. I give this book a big thumbs down. It is of no help. I wonder why University of West Florida still uses a book that is not even supported by the publisher.