Re: Congruence question.

Tonico <Tonicopm@xxxxxxxxx> wrote:

Every time, or at least of times, you post something,
it looks pretty odd, pretty bizarre, and even wrong [...]

Aha, you must be the author of the famous review of Dummit & Foote's
"Abstract Algebra" textbook, which contains quite analogous remarks:

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 false unless p = 1. And on
page 329, the text asserts that r(x + N) = rx + N, an obvious typo.

Appended below is the full text of the review [1] in all its glory.
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Abstract Algebra (2nd Ed.), by David S. Dummit, Richard M. Foote

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 false 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
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[1] http://www.adequacy.org/stories/2001.10.14.163749.94.html
.

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