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Rating: 
Summary: Still incompetent after all these editions
Review: A few years ago I wrote a review here on Amazon, of an edition of this text from around 1994. Apparently, only one of eight of those who commented found my review helpful. This new review is an attempt to be more helpful and to address the newer 6th edition.
Correctness is a necessary but not a sufficient condition for quality in mathematics text books. Usually the first condition in a given. The issues then largely become ones of whether or not the book is student friendly, whether it covers appropriate topics and so on. Angel and Porter's *Survey of Mathematics with Applications* fails on the criterion of correctness and hence one could reasonable say that the need for further evaluation on the other issues is moot.
In a circa 1994 edition, discussion on irrational numbers was misleading at best; even if not stated explicitly, the implication was that all reals belonged to a particular proper subset of the algebraic numbers. When I recently started to teach at the Community College of Baltimore County (CCBC), Catonsville, where the text was being used, I immediately turned to discussion of this topic. There on page 214 of this 6th edition, only three paragraphs into my reading, was a fallacy: "The points on the real number line that are not rational numbers are referred to as irrational numbers. Recall that every rational number is either a terminating or a reaping decimal number. *Therefore* [italics mine], irrational numbers, when represented as decimal numbers, will be nonterminating, nonrepeating numbers." All Q are (T or R), *therefore* all that is not Q is not (T or R). Perhaps this could be used as an example in the earlier chapter on logic. Since I was only three paragraphs into my reading of this new edition when I encountered this miscarriage of logic, it made quite an impression on me.
The text is replete with errors where the errors are of such a nature as to suggest that the authors really just aren't that good with math or are extremely careless. Some more examples:
Page 584: "If an event has *equally likely outcomes* [original italics]...," where it should say rather "If every outcome in the sample space is equally likely..."
Since the circa 1994 edition, where there was an error regarding conditional probability and the probability of independent events, the authors seem to have attempted to rescue themselves from embarrassment by insertion of a footnoted remark (page 615), but the presentation makes the most bizarre contortions of meaning, notation and caveats: "P(A and B)=P(A)P(B), assuming that event A has occurred*," the asterisk referring to a footnote where it stated that by 'P(B)' they mean P(B|A). But then what do we call P(A)? But the problem does not end there.
Page 293, exercise 43: The answer in the book fails to take into consideration that the dB scale is logarithmic. Given an inverse square dissipation of sound energy, loudness would increase from 20 dB at 6 feet to 26 dB at 3 feet, not to 80 dB.
Page 49, exercise 16: The answer says zero is not equal to the empty set. But that is the way zero, the smallest ordinal, is defined in modern set theory.
An analogy to falling dominos is often used to illustrate mathematical induction. Why, on page 3, do the authors use a domino analogy to illustrate inductive reasoning? It would be a bad idea to use falling dominos to illustrate inductive reasoning since the same example is classically used to illustrate mathematical induction and the two distinct concepts have similar names and are frequently confounded by students, who incorrectly assume that mathematical induction is a form on inductive reasoning. But I suspect that that the authors themselves are not clear on the distinction. It fits with the evidence. Furthermore, the book gives definitions of inductive and deductive reasoning (pages 3 and 4) that are antiquated and should be dispensed with in favor of common contemporary usage among mathematicians and logicians (see http://www.iep.utm.edu/d/ded-ind.htm for a nice brief discussion on the meaning of inductive and deductive logic).
Often the incorrect content is on non-mathematical subjects:
On page 3: "...no two people have the same fingerprints or DNA." Well, of course, up to mutations, monozygotic twins have the same DNA.
Page 9: "Little mistake, Big Discovery... The red dot represent the area *near America* [italics mine], the Canary Islands, where [Christopher] Columbus landed." Yes, on the map, the dot is closer to where North American should be than it is to Africa. But, I suppose, canaries might migrate. It continues, "He estimated 56.6 miles to a degree instead of the approximately 61.6 miles that it should have been. This resulted in a mile equaling about 4848 ft compared with our 5280 ft per mile. The outcome of this miscalculation put India about 3900 miles west of Spain, more or less where the Americas happen to be." Let's see: (61.6/56.6)*3900 miles = 4245 miles from Spain to India (westward). That's more like it. Of course, the real story is more complicated. Columbus first relied on the fantastic calculations of Cardinal d'Ailly and then confounded Roman and nautical miles as well as estimating the wrong distance corresponding to a degree. But to know this would require a little background knowledge, common sense and a willingness to do a bit of research if necessary, even as little as a quick web search or looking to an encyclopedia, on topics one does not know about.
Page 579: "The Royal Disease....even though both males and females are carriers, the disease [hemophilia] afflicts only males." While much more likely to afflicts males, the disease does afflict females inheriting two X clotting deficient chromosomes, as any menstruating hemophiliac woman dependent on clotting factor for survival would tell you. Ironically, this example is in the book's chapter on probability.
There is a list of over 30 reviewers with six having reviewed the 6th edition. Does anyone care?
I brought a number of these errors to the attention of the Addison Wesley sales representative who deals with our math department. She took notes on the examples I pointed out - I thought to her credit. Apparently she did some investigation of the errors but came back to me saying, "...but the students won't know." Addison Wesley had a tradition of publishing many fine engineering, math and science texts. They appear to have little editorial integrity now, however.
CCBC, Catonsville no longer uses this text. We now use one written by one of the reviewers of the Angel and Porter text, another member of the textbook industry. That book is also published by Addison Wesley and makes the same mistake in defining inductive and deduction reasoning as the Angel/Porter text does. It is my opinion that our department is unduly influence by the Addison Wesley sales representatives.
I'm sure that writing a good textbook is hard work. I have considered writing one myself and no doubt, the first edition will contain some error. But I would not apply a standard of criticism to the text under review that I would feel unfair if applied to myself.
I hope that the reader finds this brief review helpful.
Rating: 
Summary: EXCELLENT REFERENCE FOR BEGINNING & ADVANCED UNDERGRADUATES
Review: I have been teaching out of Angel & Porter for the last three years. It has quite a few good examples, though I agree with the first reviewer's comment that it does need more challenging problems.Among the topics I have covered are: inductive reasoning, set concepts, symbolic logic, truth tables, algebra, applied geometry, probability, statistics, and mathematics of finance. Though the examples are laid out fairly well for those who are mathematically inclined, the teacher who happens to have quite a few students with weak mathematical skills is often finding himself or herself in situations of having to create ways to become an effective expositor of mathematical theorems and applications. In other words, by trying to explain what the authors are providing in their examples, the instructor is frequently shouldering the added burden of making this book come to life not only from a mathematical perspective but also from a communicative standpoint. On a positive note, however, there are several excellent applications, and the range of topics is quite broad. Oftentimes there is a gap between the level of advanced high school mathematics and that of a four-year university that is so serious that even a student who performed A's in high school will struggle in the type of college math course he or she is placed in. Fortunately, Angel and Porter have been able to fill in quite a few of the missing pieces.
Rating:
Summary: EXCELLENT REFERENCE FOR BEGINNING & ADVANCED UNDERGRADUATES
Review: I have been teaching out of Angel & Porter for the last three years. It has quite a few good examples, though I agree with the first reviewer's comment that it does need more challenging problems. Among the topics I have covered are: inductive reasoning, set concepts, symbolic logic, truth tables, algebra, applied geometry, probability, statistics, and mathematics of finance. Though the examples are laid out fairly well for those who are mathematically inclined, the teacher who happens to have quite a few students with weak mathematical skills is often finding himself or herself in situations of having to create ways to become an effective expositor of mathematical theorems and applications. In other words, by trying to explain what the authors are providing in their examples, the instructor is frequently shouldering the added burden of making this book come to life not only from a mathematical perspective but also from a communicative standpoint. On a positive note, however, there are several excellent applications, and the range of topics is quite broad. Oftentimes there is a gap between the level of advanced high school mathematics and that of a four-year university that is so serious that even a student who performed A's in high school will struggle in the type of college math course he or she is placed in. Fortunately, Angel and Porter have been able to fill in quite a few of the missing pieces.
Rating:
Summary: Idiots
Review: I taught from an earlier edition of this book at Ivy Tech in Bloomington, Indiana while working on a PhD at Indiana University. Ivy Tech had already selected this text. Too bad. While that was around 1994, I can still recall a number of FACTUAL ERRORS. I had to tell my students that the text was wrong. Among the errors: The clear implication (though not explicitly stated) that the algebraic numbers included all the reals - that is they didn't even seem to be aquainted with the transedentals; there was another error regarding conditional probabilities... I can't recall exactly, but I can remember showing the errors to fellow doctoral students (now at UN, Reno and UC, Davis) for a good laugh. What were the reviewers doing? I guess they're a bunch of incompetents as well. To the publisher: Have some real mathematicians review math books.
Rating:
Summary: Could use some more problems
Review: This book does the job of teaching some mathematics to those with liberal-arts majors. However, over at Wayne State, we are constantly bemoaning the lack of extra problems for students to practice what they have learned (especially in light of the fact that we cover only half of the chapters of this book in a single one semester course). This is especially apparent with the probability and statistics chapters. Overall I can see this text being a commendable effort on the part of Angel and Porter to bring mathematics to those who would normally shun it.
Rating:
Summary: Could use some more problems
Review: This book does the job of teaching some mathematics to those with liberal-arts majors. However, over at Wayne State, we are constantly bemoaning the lack of extra problems for students to practice what they have learned (especially in light of the fact that we cover only half of the chapters of this book in a single one semester course). This is especially apparent with the probability and statistics chapters. Overall I can see this text being a commendable effort on the part of Angel and Porter to bring mathematics to those who would normally shun it.
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