<http://www.amazon.com/College-Algebra-Ams-Chelsea-Publishing/dp/0821838636/ref=wl_it_dp_o?ie=UTF8&coliid=I1XLMLT6JFJVXM&colid=79JAQGR1MHHC>Happy
New Year to all...
I was recently pointed to Henry Burchard Fine's *College Algebra* as an
interesting synthesis of 'classic' (i.e. not abstract) algebra as of
1901--see blurb below. I wonder if there's anything in there that would be
useful ... or just interesting ... to people on this list.
-s
Free full text at Google Books:
http://books.google.com/books?id=vycZAAAAYAAJ
Reprint from the AMS ($25):
http://www.ams.org/bookstore?fn=20&arg1=chelsealist&ikey=CHEL-354-H
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*College Algebra*
Henry Burchard Fine
At the beginning of the twentieth century, college algebra was taught
differently than it is nowadays. There are many topics that are now part of
calculus or analysis classes. Other topics are covered only in abstract form
in a modern algebra class on field theory. Fine's *College Algebra* offers
the reader a chance to learn the origins of a variety of topics taught in
today's curriculum, while also learning valuable techniques that, in some
cases, are almost forgotten.
In the early 1900s, *methods* were often emphasized, rather than abstract
principles. In this book, Fine includes detailed discussions of techniques
of solving quadratic and cubic equations, as well as some discussion of
fourth-order equations. There are also detailed treatments of partial
fractions, the method of undetermined coefficients, and synthetic division.
The book is ostensibly an algebra book; however, it covers many topics that
are found throughout today's curriculum:
- calculus and analysis: infinite series, partial fractions, undetermined
coefficients, properties of continuous functions,
- number theory: continued fractions,
- probability: basic results in probability.
Though the book is structured as a textbook, modern mathematicians will find
it a delight to dip into. There are many gems that have been overlooked by
today's emphasis on abstraction and generality. By revisiting familiar
topics, such as continued fractions or solutions of polynomial equations,
modern readers will enrich their knowledge of fundamental areas of
mathematics, while gaining concrete methods for working with their modern
incarnations. The book is suitable for undergraduates, graduate students,
and researchers interested in algebra.