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An Introduction to Abstract Mathematics [Hardcover]

Robert J. Bond , William J. Keane
3.3 out of 5 stars  See all reviews (11 customer reviews)

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Book Description

August 15, 2007 1577665392 978-1577665397
Bond and Keane explicate the elements of logical, mathematical argument to elucidate the meaning and importance of mathematical rigor. With definitions of concepts at their disposal, students learn the rules of logical inference, read and understand proofs of theorems, and write their own proofs--all while becoming familiar with the grammar of mathematics and its style. In addition, they will develop an appreciation of the different methods of proof (contradiction, induction), the value of a proof, and the beauty of an elegant argument. The authors emphasize that mathematics is an ongoing, vibrant discipline--its long, fascinating history continually intersects with territory still uncharted and questions still in need of answers. The authors' extensive background in teaching mathematics shines through in this balanced, explicit, and engaging text, designed as a primer for higher-level mathematics courses. They elegantly demonstrate process and application and recognize the byproducts of both the achievements and the missteps of past thinkers. Chapters 1-5 introduce the fundamentals of abstract mathematics and chapters 6-8 apply the ideas and techniques, placing the earlier material in a real context. Readers' interest is continually piqued by the use of clear explanations, practical examples, discussion and discovery exercises, and historical comments.

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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

Product Details

  • Hardcover: 323 pages
  • Publisher: Waveland Pr Inc (August 15, 2007)
  • Language: English
  • ISBN-10: 1577665392
  • ISBN-13: 978-1577665397
  • Product Dimensions: 9.3 x 7.1 x 0.9 inches
  • Shipping Weight: 1.6 pounds (View shipping rates and policies)
  • Average Customer Review: 3.3 out of 5 stars  See all reviews (11 customer reviews)
  • Amazon Best Sellers Rank: #69,176 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews
11 of 12 people found the following review helpful
2.0 out of 5 stars good choice of topics, imperfect coverage March 8, 2005
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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4 of 4 people found the following review helpful
2.0 out of 5 stars Major Revision Needed July 22, 2008
By JL1984
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
2.0 out of 5 stars Useless Readings 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 nrg9390
Format:Hardcover|Verified Purchase
Awful book. Maybe it's ok for those with a strong math background, but for those of us that aren't majoring in pure mathematics, this book is far too dense and vague to fully comprehend. The book assumes that the reader knows many theorems that aren't even presented anywhere between the covers. Most of the theorems that are presented are "left as an exercise" for the reader.
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5.0 out of 5 stars Great book July 14, 2013
By Matt M
Format:Hardcover|Verified Purchase
This is a great book. I bought this for a class. Usually I sell my books when class is done. I am keeping this book as a reference for future math classes.
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5.0 out of 5 stars Excellent Textbook February 15, 2013
The textbook shipped and got to my university P.O. Box in time for me to use it for class with no damage
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