Comments

Congratulations on such good results!

Did you enjoy figuring out the polynomial factoring? (We will have you a maths brain yet).

-- TracyW - 29 Jun 2006

boy I'll tell you....it may be possible

though I'm finding I "miss words"

Saxon Algebra 1 is ALL LETTERS!

letters & exponents

-- CatherineJohnson - 29 Jun 2006

Last weekend Christopher asked me, in the car, "Does algebra have numbers in it? Or just letters?"

I burst out laughing, but actually it was a pretty good question I think.

-- CatherineJohnson - 29 Jun 2006

Except for coefficients and exponents, numbers are for engineers. And coefficients and exponents should normally be arbitrarily assignable (at least for real math).

For example, the mth root of xⁿ = x^n/m.

Numbers are only for intellectual inferiors. (Like me.)

8-)

ps. To the extent that "0" is a number (a partially philosophical question), "0" is at least occasionally acceptable.

pps. The above is tongue-in-cheek, but the search for a truly general solution is an element at the core of real math.

-- DougSundseth - 29 Jun 2006

ok, wait

I don't follow the last sentence - a truly general solution would be something you can formulate using letters, right?

as in a formula?

-- CatherineJohnson - 29 Jun 2006

We got Christopher's assessment from Ms. Kahl today.

No idea what it means.

-- CatherineJohnson - 29 Jun 2006

Except for coefficients and exponents, numbers are for engineers.

Eventually numbers also appear as labels for equations or expressions. So you can write something like:

(1) x^2 + 2xy + 3 (2) y^2 + 5zx (3) 2zy

(1) + (2) = (3)

The point of algebra is that you replace numbers by letters.

It's a very useful concept for computer programming (and it's also useful for about a zillion other things). If Christopher has ever played with programming in Basic or another language telling him that might help.

-- TracyW - 29 Jun 2006

"...a truly general solution would be something you can formulate using letters...."

It's not so much the use of letters as the use of abstraction. In most scientific fields, the ultimate goal is "The great big [rule] of everything with everything inside"*.

In physics, one such quest is for "Grand Unification". That is, the search for a system that will explain electricity, magnetism, the nuclear strong force, the nuclear weak force, and gravity in one coherent whole. Electricity and magnetism were the first to be unified (see Maxwell's equations). More recently, electro-magnetism was unified with the nuclear weak force. The last I looked, gravity and the strong force hadn't been incorporated.

Computer programming languages are another particularly interesting example of pervasive abstraction. Beyond the use of variables, you also have subroutine calls (whenever the compiler or interpreter sees the name of the subroutine in the appropriate format, it will go do some task and return a result based on the context of the call). Object-oriented programming is one step further along this path (a step better explained by someone else). And you also have compiler directives like C's "#define" statement, that replace every instance of something with something else, usually something much more complex.

* I knew that kids' TV programming would be good for something someday. (With apologies to everyone who hasn't seen that show ... and most of those who have seen it.)

-- DougSundseth - 29 Jun 2006

wow

cool

Thanks for writing this, Tracy & Doug

I didn't know....though I had semi-guessed.

I don't know why textbooks don't inclue "big picture" statements like this. Kids (adults, too) never know where they're headed, or why they're doing the things they're doing.

-- CatherineJohnson - 30 Jun 2006