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Abstract Algebra (2nd Ed.)
David S. Dummit, Richard M. Foote John Wiley & Sons, Inc. Summary: Riddled with errors and esoteric formulae, this book is incredibly dangerous for students who have yet to achieve a firm grasp of Algebra. Avoid at all costs. 

Like most Adequacy readers, I am very good at higher mathematics. In high school, I placed near the top of my Algebra II class, and aced the Math portion of the SAT with a 590. As my children are currently working their way through middle school, I felt obligated to renew my skills in order to help them with their homework. But after slogging through Dummit and Foote's turgid tome, I can only say that it is the worst mathematics text I have ever had the misfortune to encounter.
The first flaw a reader will note is the incredible rate at which the material is presented. Section 0.1 breezes through difficult concepts like functions, sets, and complex numbers. By Chapter 1, my head was spinning after reading statements like, "For n in Z+, Z/nZ is an abelian group under the operation + of addition of residue classes as described in Chapter 0," and, "A subset S of elements of a group G with the property that every element of G can be written as a (finite) product of elements of S and their inverses is called a set of generators of G." As we see from these excerpts from the text, Dummit and Foote are disciples of "new math," a doctrine discredited in the 70's. Too often, strange symbols and jargon take the place of clear English prose. Extraneous concepts like "sets"much less "finite nilpotent groups" or "invariant factor decompositions" or "symmetric multilinear maps"are merely obstacles to a student's understanding of algebra. Sadly, the authors, holed up in their ivory towers, have not yet learned these vital educational lessons. Yet for all the apparent erudition of the authors, the text is full of obvious errors. For example, on page 44, the authors assert that z*a = z + a, an obvious error. On page 97, we find the ludicrous assertion that a^p = a, clearly flase unless p = 1. And on page 329, the text asserts that r(x + N) = rx + N, an obvious typo. That the authors could publish such a sloppy text and remain employed at the University of Vermont speaks volumes about the evils of tenure. I can only recommend this text to those already secure in their knowledge of Algebra who might derive amusement from the frequent missteps of the authors. And even then, with a $100 price tag, it can hardly be considered worth the expense. I fear for the education of the next generation when prominent publishers push "new math" on hapless educators. Using this text to teach learn Algebra from this text will alienate students from math and science, driving America further behind the rest of the world in education. I can only hope that our school boards will reject this attempt to corrupt high school curricula and get back to teaching the basics. Rating: 0 of 5 stars 