Re: Mathematics Curriculum - Euler's Elements of Algebra

Euler'sFan wrote:

I teach at a small private school, and thus have some flexibility with
the curriculum that I teach with. In my research, I have found that
Leonard Euler wrote and elementary algebra textbook titled "Elements
of Algebra." In my estimation, and those of my students, Euler lays
down clear and straightforward explanations of the topics of Algebra
in an order, while not that which I would have chosen, makes sense in
what he is doing.

My question is two-fold. First, has anyone read Euler's Elements of
Algebra? If anyone is interested, there is an online version of the
first section (http://web.mat.bham.ac.uk/C.J.Sangwin/euler/
index.html) , and Google Books version (http://books.google.com/books?
id=X8yv0sj4_1YC&printsec=frontcover&dq=euler+elements+of+algebra).

Secondly, what do you all think about using such a book for a textbook
in an algebra class? I would need to write exercises for the book.

I'm not especially familiar with Euler's elementary algebra
book (which is really at the level of texts that go by the name
"advanced algebra" or "college algebra" from the mid 1800s
to the present time), although I have seen it mentioned from
time to time in historical papers and in history books. Personally,
I think you'd be better off using one of the books by Todhunter,
Chrystal, Hall/Knight, or Wells:

http://books.google.com/books?as_q=algebra&as_auth=todhunter

http://books.google.com/books?as_q=algebra&as_auth=chrystal

http://books.google.com/books?as_q=algebra&as_auth=knight

George Chrystal's "Algebra"
http://books.google.com/books?id=lRkPAAAAIAAJ

Hall/Knight's "Higher Algebra"
http://books.google.com/books?id=oB4PAAAAIAAJ

Webster Wells' "Advanced Course in Algebra"
http://books.google.com/books?id=aOM5AAAAMAAJ

I'd also encourage you to look at the Gelfand School Outreach
Program books and the Russian "Popular Lectures in Mathematics"
series books that have been translated into English. You can
find many of these books listed in the following post.

http://mathforum.org/kb/message.jspa?messageID=6640965

Finally, for what it's worth, many of my posts have dealt
with topics that could be of use to you. Three relatively
recent examples are:

Discussion about the factorization of a^3 + b^3 + c^3 - 3abc:
http://mathforum.org/kb/message.jspa?messageID=6653240

One way to solve (x + r)(x + 2r)(x + 3r)(x + 4r) = a
http://groups.google.com/group/sci.math/msg/62720599acd91fac

The importance of partial fractions the history of algebra
http://groups.google.com/group/sci.math/msg/4ba262887e7748dc

Dave L. Renfro
.

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