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Foundations of Higher Mathematics: Exploration and Proof Paperback – January 11, 1990

ISBN-13: 978-0201125870 ISBN-10: 0201125870 Edition: 1st

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Product Details

  • Paperback: 458 pages
  • Publisher: Pearson; 1 edition (January 11, 1990)
  • Language: English
  • ISBN-10: 0201125870
  • ISBN-13: 978-0201125870
  • Product Dimensions: 7.3 x 1.1 x 9 inches
  • Shipping Weight: 1.8 pounds (View shipping rates and policies)
  • Average Customer Review: 2.8 out of 5 stars  See all reviews (5 customer reviews)
  • Amazon Best Sellers Rank: #1,639,340 in Books (See Top 100 in Books)

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Customer Reviews

2.8 out of 5 stars
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Most Helpful Customer Reviews

6 of 7 people found the following review helpful By Andrew on May 13, 1999
Format: Paperback
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.
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1 of 1 people found the following review helpful By Lisa Clayton on May 27, 2004
Format: Paperback
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.
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1 of 1 people found the following review helpful By Not Cold in IL on January 17, 2007
Format: Paperback
I absolutely love this book! I use it as a reference--even 8 years after I took the course. True it doesn't have solutions, but I attended a university in which only 3 of 30 homework problems were graded anyway. Many times, professors teach this kind of course from their own notes, which give no firm direction/guidance to students later on. Remember, each professor has their own way of writing proofs and thinking about logic. Using this book--which reads like prose-- is much, much better than packets of ambiguous bullet points. This book, on the other hand, gives general principles that can be applied in a variety of settings in a variety of ways.
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8 of 13 people found the following review helpful By A Customer on December 6, 1997
Format: Paperback
...renders this work nearly useless.

We recently were subjected to this book as a text on set theory and logic. It is adequate as far as it goes in it's explanations and illustrations (with an exception to be noted later), but is wholly inadequate as a student's textbook.

It lacks any solutions to the exercises presented at the end of chapters, making homework utterly pointless unless the instructors consume precious classroom time presenting correct solutions to the homework. Self-study, doing unassigned problems, is right out. You have no way to check your work.

This is made even more damaging to a student's ability to comprehend the subject due to the exception mentioned above, that in the text, the authors leave one too many proofs incomplete, "as exercise 'x' for the student" at the end of the chapter. This would make sense and even be useful IF AND ONLY IFF (IFF) the correct solution was provided in the back of the book. It isn't teaching if the students have to work out the entire mathematical history of a subject themselves. I mean, it's one thing to retrace the work of history's great mathematicians, and be able to see how they arrived at thier solutions. It is another thing altogether to have to duplicate thier work altogether, without being able to check to see how closely your effort matches the correct solution.

The book thus deprives the students of a number of proofs for theorems which it should be presenting to the student, either in the text, or in the back of the book, to be looked at only after the student has thought about the problem and it's solution first.
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4 of 7 people found the following review helpful By A Customer on February 18, 2002
Format: Paperback
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.
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