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An Introduction to Abstract Mathematics Hardcover – August 15, 2007

ISBN-13: 978-1577665397 ISBN-10: 1577665392
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Editorial Reviews

About the Author

Robert J. Bond is a graduate of the College for Financial Planning. Prior to becoming a Certified Financial Planner, he worked in a variety of fields related to finance, including commercial banker, mortgage agent, and real estate broker. Bob has taught at UCLA, CSULA, American Institute for Continuing Education and for the College for Financial Planning. His past publications include: Personal Finance, California Real Estate Principles, Real Estate Practice, Real Estate Finance and many more.

Robert Bond developed the telecourse and was the on-camera instructor and consultant for the popular series, "Real Estate and You." His professional designations and licenses have included Registered Principal (NASD), Variable Annuities Agent, Real Estate Broker, Fire and Casualty Agent, NASD Series 7 and 63, and Registered Investment Advisor. Boston College
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Product Details

  • Hardcover: 323 pages
  • Publisher: Waveland Pr Inc (August 15, 2007)
  • Language: English
  • ISBN-10: 1577665392
  • ISBN-13: 978-1577665397
  • Product Dimensions: 0.8 x 7 x 9.2 inches
  • Shipping Weight: 1.6 pounds (View shipping rates and policies)
  • Average Customer Review: 3.2 out of 5 stars  See all reviews (12 customer reviews)
  • Amazon Best Sellers Rank: #582,107 in Books (See Top 100 in Books)

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Customer Reviews

3.2 out of 5 stars

Most Helpful Customer Reviews

11 of 12 people found the following review helpful By mathwonk on March 8, 2005
Format: Hardcover
I considered this book for my course because it has the topics I want: discussion of proofs, logic, functions and sets, and then applications to actual mathematics. the math topics include infinite cardinality, modular integers (I think), and real numbers including least upper bounds.

However it was my impression on reading a few sections that the discussion does not teach the material that well. Worse, for me at least, was what I consider a serious lapse of mathematical reasoning in the discussion of the very first example i looked at in the chapter on real numbers.

they defined upper bounds, and then gave as an obvious example of an unbounded subset of reals, the natural numbers. well that is not obvious at all, and it requires a non trivial proof to verify it.

Then they define the relevant concept, namely the "least upper bound" axiom, and assume it is satisfied byt he reals. Then they make a big deal out of proving the archimedean property of the reals, which they do not bother to mention, is actually equivalent to the fact the natural numbers are unbounded.

How are we supposed to react when the authors themselves do not seem to understand the topic they are pontificating about? It turns me off, especially at the exorbitant price.

And although I am picking on this book, it is actually one of the best of them out there! A sad situation indeed, with regard to books on proofs and logic and applications.
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5 of 5 people found the following review helpful By JL1984 on July 22, 2008
Format: Hardcover
While this book does a decent job of covering all the material a student would need to make a smooth transition into abstract mathematics, I whole-heartedly agree with the reviewer below me when he described Bond and Keanne's coverage as being imperfect. However, when I say the coverage is imperfect I am referring to the methods in which the authors present the material rather than skipping over topics.

It is critical to distinguish between what's covered and how the material is presented. So far as coverage is concerned, the authors get a 5 out of 5 in my book. Topics covered include: Mathematical Reasoning, Sets, Functions, Binary Operations and Relations, The Integers, Infinite Sets, Real and Complex Numbers, and last but not least, Polynomials. This in my opinion is enough to prepare any student for higher level mathematics such as abstract alegbra, topology, number theory, and basically any other math course that emphasizes theory.

When I first opened this book I knew I was going to have problems. All the examples in the book are jumbled together with propositions, corollaries, and theorems, which make them hard to stand out. Usually, books use different colors to point out examples from from the rest of the section, but for some reason this book does not do that. I really got the feeling that I was reading a story everytime I sat down to read through a section rather than reading a math book.

Secondly, the examples themselves aren't even that great. While there is an abundance of examples in every section, most examples just state theorems or properties of functions. For example, on page 140 in chapter 4 on Binary Operations and Relations, Example 7 states "Let S be the set of all finite subsets of Z. Define R on S by ARB if |A| = |B|.
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1 of 1 people found the following review helpful By Arman S. on September 23, 2012
Format: Hardcover Verified Purchase
Book is pretty useless. Doesn't correlate to the lectures that well. Problems are overly complicated but help to understand concepts of they are completed.
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By QCMath on March 21, 2011
Format: Hardcover
I used this text for a course I taught as it was the default textbook at my university. The order of the material was not to my taste: for example quantifiers (second order logic) are introduced before negation etc. (first order logic), which only serves to muddle the logic. In general, concepts are treated in a somewhat informal way and I do not feel the students were able to grasp the structure of a proof from this approach.

The text is littered with "Historical Comments" and "Mathematical Perspectives" which I found to be either insufficient (less than 1 page discussing groups in a very informal way, pg 133) or lacking in context (eg. discussion of Riemannian Geometry on pg 42).

In attempt to temper the formal difficulties of proof with lively exposition the authors have produced a text which is very difficult to teach from and short-changes any independent readers.
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Format: Hardcover Verified Purchase
and had to rely on outside sources to get through the class. Seriously, my real analysis book is so much better (even though the class is so much harder). This book is a very dry read, and doesn't make reading through the chapters and examples worth it. The easy stuff? Yeah they've got you covered. But as you progress through the book, you'll find that the authors have left out quite a bit and don't explain anything intuitively at all, especially Chapter 3, which "covers" functions (I'm acing real analysis right now, but I still don't get what point of a function's image, as opposed to its range, is... Are they the same thing? The book doesn't answer that. Anyone who can, please reply). Chapters 4 and 5 are okay, and that's where my course stopped. I'm keeping the book as a resource for more advanced math classes, but most likely I'll just go find another book for that.
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