Math in grade school, hs and college.

J. T. wrote:

Great point. There are certainly true statements within any axiomatic statement that cannot be proven true, and of course axioms are accepted as true without proof. Metamathematics, or philosophy of mathematics, most certainly is a viable study.

But Al north whitehead apparently thought that was all pretentious gobbledygook, so he took issue with it and responded with this:

Now I know why I'd as soon be governed by the first 300 names in the Yonkers phone book than I would by you arrogant math fanatics.

1) What, exactly, about what J. T. wrote implies he is a "math fanatic"?

2) What, exactly, about what J. T. wrote implies that the fanatics that do exist among mathematicians (or mathematicians as a whole) are arrogant?

3) How does a person's aptitude for math (or lack thereof) relate to their ability to govern?

Speaking of math ability and the ability to govern, Al Gore invented the term "greatest common denominator" in one of his debates with G.W. -- a quantity that does not exist.

J. T. wrote:

Speaking of math ability and the ability to govern, Al Gore invented the term "greatest common denominator" in one of his debates with G.W. -- a quantity that does not exist.

Uh, sorry to burst your bubble but I believe the greatest common denominator is the largest whole number that divides into your two original numbers without a remainder. It's the Canadien version of greatest common divisor, but it does exist.

I guess you are right. Never heard that term. Then again, I'm sure that Al Gore is not much of a number theorist. Thanks.

Here is another one. Does anyone know what the scarecrow said when he got his "Doctor of Thinkology" degree?

Does anyone know what the scarecrow said (on the Wizard of Oz) when he got his "Doctor of Thinkology" degree?

Answer: The sum of the square roots of any two sides of an isosceles triangle is equal the square root of the remaining side - which is false.

but isosceles is so much more esoteric than "right".

Legalizit wrote:

Once somebody has the basic concepts of mathematics to function in our society they should absolutely NOT be forced into a math class; they don't retain anything anyhow and the kids who actually love math are held back severely. It's really a pathetic way to indoctrinate our kids. Mine will be home schooled, no doubt about that.

This raises a very intersting question. Just what math does a person need to function in society? I am asking this question because this is such an interesting forum with such a variety of intelligent responses -- unlike many of the Pravda-like forums in the math ed. community.

Everyone needs arithmetic, and proficiency at that. Many people are very poor at arithmetic after studying algebra, trig, even calculus. What is the point of learning these advanced subjects if one is not good at basic computation, which we are called upon to use every day.

Great Thread!

Can any of you convincingly explain why e is the base of the natural logarithm? Is it more than definition?

How about that dude that took the 20th root of a 13 digit number in his head recently (or was it the 13th root of a 20 digit number)?

Does anyone have experience with this stuff or the system of Johan(?) Tracthenburg? I am alright at doing multiplications pretty quick mentally but I never was able to get Trachtenburg's stuff.

College Guy wrote:

Can any of you convincingly explain why e is the base of the natural logarithm? Is it more than definition?

yes. e can do anything. it is special. e^x is the infinite sum (over all values of i) of x^i/i!. while this might seem worthless, the good news is that the derivative (and integral) of e^x is... e^x. making it unique and important.

College Guy wrote:

Can any of you convincingly explain why e is the base of the natural logarithm? Is it more than definition?

The most important function in all of mathematics is y = e^x. By definition, logarithms are inverses of exponential functions, so by defintion, a log base e is the inverse of y = e^x. Now, deriving these functions is another matter.

This started off as one of the more interesting threads here. I can sympathize as I was OK with the basic 4 (addition, subtraction, multiplication, division) plus did OK at Algebra.

After Geometry I was clueless. There are no words to describe the frustration and having no idea nor handle of the concepts addressed in Higher Math.

Wow, this thread took me back in time. I, too, had math teachers that were orcs.

e is also the basis for calculations for many thing in finance and science..ie componded interest, half life, radiactive decay....you could use other numbers to calculate this but since the derivative and intergral of e is e...calcualtions are infinitely easier.

dude math is easy, it isn't hard, maybe you are dumb and weren't trying. esp. high school math.

Usher wrote:

If they want to count on their fingers, toes, tiles on the ceiling, or whatever, I don't give a rip. As long as they can demonstrate to me that they can come up with a reasonable solution to the problems.

Screw that. You should memorize every basic computation so you can be faster at calculating more complicated computations. That's what times tables are for. Memorization. Then you use those tools to do higher level math, quicker.

The number e and the natural logarithm are extremely important.

Say you want to compound interest rates, or you want to gain 1% of your body weight every day. If you weigh 100 pounds, the first day you will gain 1 pound. The second day however you will have to gain 1.01 pounds. The third day you will need to put on 1.0201 pounds, and so on. Your body weight at the end of every day will approximate the exponential function 100*e^(.01*x).

If you had increased your body weight 1/24 of 1% every hour, the function would be an even closer approximation of the exponential. Now say you want to "continuously" compound your body weight, you would want to increase your weight 1/n of 1% every 1/n days, where n is infinitely large. This is what "e" is, the constant number by which by exponentiating you can represent a constant change in ratio (in this case 1% of your body weight).

Because you are getting a constant change in ratio, by definition the value of the derivative must be proportional to the value of the function at all times, hence d/dx(e^x) = e^x.

Man this was one heck of an old, interesting thread.

Why DO Americans lack so badly in math skills?