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Q&A #686


Textbook recommendations for honors analysis class

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From: Joshua Zucker
To: Teacher2Teacher Service
Date: Oct 21, 1998 at 13:01:33
Subject: Textbook recommendations for honors analysis class

I teach honors analysis at an outstanding high school in Palo Alto. We are
using some very very old textbooks for the course. The current content is,
roughly:

10 weeks on lines and planes and vectors in 2 and 3 dimensions
20 weeks covering Lial/Miller's Finite Math book, including matrices, simplex
method for linear programming, Markov chains, game theory, combinatorics,
probability, and graph theory
10 weeks of introduction to calculus, using a book on limits and sequences
as well as the first few chapters of Foerster's text.

What I am looking for is a book to replace at least the first two sections
of the course. This book would need to focus on vectors, matrices, lines, and
planes, preferably with some applications. If it also included probability
and combinatorics, all the better, but we can get those topics elsewhere too.

The main problem I see with most texts is that they do not explain vectors
and matrices very well. I would like to see the subject matter in the book to
talk about the definitions of cross products, matrix products, or
determinants.

I like the UCSMP Functions, Statistics, and Trigonometry book but it is far
too easy for these honors students. What I like about it is that it connects
the matrices to rotations and to complex numbers, so it shows why the
multiplication ought to be defined the way it is. It also gives some simple
applications (like recipes with cost of ingredients) that show the same
thing. But it needs some hard problems!

Anyway, if anyone has any ideas for a textbook recommendation, I would love
to hear them. Internet resources that we could use for discussion of vectors
and matrices would be great, too!

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