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Re: after beginner's algebra, where to?
Posted:
May 20, 2006 11:49 PM
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Dave L. Renfro wrote:
> Rufi_Dukes wrote (in part):
>
> > title: algebra demystified, (part of a series in which, so far,
> > astronomy, calculus and physics have all been "demystified"
> >
> > authrhonda huettenmueller,
> > published by mcgraw-hill, 2003
> >
> > chapters i've worked through:
> > 1.fractions
> > 2.into to variables
> > 3.decimals
> > 4. negative numbers
> > 5. exponents and roots
> > 6. factoring
> > 7 linear equations
> > 8 linear applications
> >
> > chapters still to go:
> > 9. linear inequalities
> > 10. quadratic equations
> > 11. quadratic applications
> >
> > i'm middle-aged, highly motivated, with no time-constraints,
> > having taken a couple of years out from teaching; i plan to
> > spend the rest of this year (and next year if necessary)
> > laying the foundations for university level study of maths
>
> [and, in a later post]
>
> > forgot to ask:
> > do you think that what i outlined in my original post,
> > giving the contents of the algebra book that i'm using,
> > that this would correspond to algebra 1? 11? 111?
>
> What you're describing is (U.S.) Algebra 1, or at least what
> used to be called Algebra 1. [With the push (in the U.S.) for
> all students to take algebra in high school, and with many
> students taking it in the 8'th grade, it's possible that
> "Algebra 1" means less than it used to.]
>
> What you need next, after you finish Chapters 9-11 and before
> trigonometry/precalculus, is a thorough study of high school
> geometry and Algebra 2.
>
> I'm not sure what to suggest in the way of texts, because
> texts at this level are often hard to find (libraries,
> bookstores, etc.) after a few decades, and most of the
> books I have at this level are several decades old.
>
> However, the "Maths In Action" series put out by Nelson
> Thornes Publishers seemed very interesting when I looked
> at the table of contents of some their texts:
>
> http://books.google.com/books?q=maths-in-action
> http://www.nelsonthornes.com/secondary/maths/marketing/books_mia.htm
>
> One thing I'd strongly recommend is that you get a copy
> of Gelfand/Shen's "Algebra" (details below). It's $22.95
> from amazon.com in (medium-sized) paperback and should be
> excellent for someone with your background and intentions.
> There are other books on high school topics by these authors,
> which are easy to find out about, but I believe their algebra
> book is their lowest level book. I would describe their
> algebra book as a non-bloated treatment of many Algebra 2
> and College Algebra topics that places a lot of attention on
> concepts and higher order thinking skills important for later
> success in mathematics.
>
> Israel M. Gelfand and Alexander Shen, "Algebra", Birkhauser,
> 1993, viii + 149 pages. [QA 152.2G45]
> ISBN 0-8176-3677-3
> http://www.amazon.com/gp/product/0817636773/102-5050732-5848137
> http://books.google.com/books?vid=ISBN0817636773
> http://groups.google.com/group/sci.math/msg/a3abc40a1fcc7490
>
> You might also find some "popular math" books intellectually
> profitable to you at this point. At the very low level, well
> within your reach now, are two books by Isaac Asimov that most
> public libraries have. (Well, in my experience. One amazon.com
> reviewer for the algebra book mentioned a case where the book
> was missing, which they speculated on account of how good it is.)
>
> Isaac Asimov, "Realm of Numbers", 1959.
> Isaac Asimov, "Realm of Algebra", 1982.
> http://www.amazon.com/gp/product/0395065666/102-3567762-3676143
> http://www.amazon.com/gp/product/0449243982/102-3567762-3676143
>
> At a slightly higher level is the following, which would be
> good for rounding out your knowledge of some ideas and concepts
> that will help in calculus, but which (because of space
> considerations) are often neglected in textbooks.
>
> Rózsa Péter, "Playing With Infinity: Mathematical Explorations
> and Excursions", translated by Z. P. Dienes, Dover Publications,
> 1961/1976, xiv + 268 pages.
> ISBN 0-486-23265-4
> http://www.amazon.com/gp/product/0486232654/102-5050732-5848137
> http://books.google.com/books?vid=ISBN0486232654
>
> Péter's book makes some isolated use of complex numbers and
> very simple trigonometry in two or three pages at one point,
> but otherwise I think you probably have the background now to
> understand most of it.
>
> For what it's worth, I pretty much taught myself pre-algebra
> through multivariable calculus, linear algebra, and differential
> equations (exclusive of geometry) in three years (ages 14-16),
> so I have some experience in learning math outside the
> classroom (before graduate school that is, since after your
> first or second year in graduate school, most of what you'll
> learn will be outside the classroom).
>
> Dave L. Renfro
thx again Dave;
i've made good notes from yr suggestions;
now i've got some clear lines to follow!
cheers
(and i'll let you know how i get on with the suggested reading)
rufus
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