Chronology Current Month Current Thread Current Date
[Year List] [Month List (current year)] [Date Index] [Thread Index] [Thread Prev] [Thread Next] [Date Prev] [Date Next]

Re: [Phys-l] the mathmatics of physics



Hi Adrian-
If you are looking to "review" algebra at the beginning of a physics course, I urge you to rethink your plans and read, or reread, Arons' book on the teaching of elementary physics. One of his cardinal principles was: "Don't introduce a concept before you need it." When you violate this principle, the student doesn't have a context for the concept and lacks a gut-based understanding of the reason for learning the material. Also, by the time you need the concept, there is an excellent chance that the student has forgotten it.
Currently used US algebra texts are incredibly bad because they have uniformly forgotten the reason for doing algebra in the first place, namely to solve classes of problems at one time. Such problems are "story problems" which the student is exposed to for a couple of weeks in the middle of a typical algebra course, inducing hatred, dread, sweat and tears. As one student said to me, when asked to do a story problem after completing all his high school math courses, "I've already had story problems, so I don't need to do any more."
I have looked for substitutes for the currently used algebra texts. Recently on the market is a series by some of the great Russian mathematicians and teachers who have emigrated to the U.S. Their students, some of whom have been post-docs at Argonne and neighboring institutions, are impressive. The text titled "Algebra", by I.M. Gelfand (now at Rutgers) and A. Shen, is a paperback of 150 pages, published by Birkha(umlaut)user 1993 (Russian edition was 1958).
To give you a flavor of the uniqueness, here are the first 5 (out of 72) entries in the Contents:

1. Introduction .................................................1
2. Exchange of terms in additon..................................1
3. Exchange of terms in multiplication...........................1
4. Addition in the decimal number system.........................2
5. The multiplication table and the multiplication algorithm.....5

The problems are, for the most part, thoughtful "math" problems, often with the answers worked out - the teacher will have to conjure up some additional ones. Here is an example, where the answers are not given (Problem 143, p.67)
a. Divide x^3-1 by x-1
b. " x^4-1 " x-1
c. " x^10 -1 by x-1
d. " x^3+1 by x+1
e. " x^4*1 " x+1
I don't think you'll find counterparts for d. and e. in any American text.
I don't remember the price, but the whole set of 4 cost just a few bucks. This kind of text could be used along with a physics text with weekly assignments (as "refreshers") along with the physics. I did something like this in a statics course for students who had completed two semesters of calculus physics (and three semesters of calculus) and who had lots of trouble with algebra. I din't have the Gelfand book at the time.

Regards,
Jack


On Fri, 4 Aug 2006, adrian sears wrote:

My name is adrian sears i teach physics at bishop
union high school. My question is rather general in
nature but I would appreciate some feedback from other
teachers in the same predicament. I find myself each
year having to teach more math (basic alegbra,
exponents,quadratics etc.) then physics. Is there a
good text that simply deals with the most common math
encountered in intro physics. Hopefully a good
reference text would result in being able to teach
more physics than math.

Thanks in advance

Adrian Sears

__________________________________________________
Do You Yahoo!?
Tired of spam? Yahoo! Mail has the best spam protection around
http://mail.yahoo.com
_______________________________________________
Forum for Physics Educators
Phys-l@carnot.physics.buffalo.edu
https://carnot.physics.buffalo.edu/mailman/listinfo/phys-l


--
"Trust me. I have a lot of experience at this."
General Custer's unremembered message to his men,
just before leading them into the Little Big Horn Valley