Math in grade school, hs and college.

Not only did I get through it, I made a B+. Not really what would be thought of as a bragging grade, but respectable. The course was titled "Modern Geometry" and delt with Euclidean, Hyperbolic, Elliptic, and Spherical Geometries. Killed some Math Analysis and Linear Algebra this past semester too.

On with the Abstract Algebra, Discrete Methods, and a Seminar class for next semester which starts in a few days....sadly......[I'll miss break] :(

Thanks for the support, Usher.

I got C's throughout highschool math, and an F in calculus on my first try -- mostly because at that time my main interests were track, my girlfriend and my motorcycle. I also thought math was a useless subject, and my teachers were nerdy individuals that I did not want to emulate. Math in college was a different story. Now I am a math professor.

Impressive Thread All wrote:

How is math taught in foreign lands that score higher than the US in math?

What techniques, methodologies and approaches are used?

The answer to that question would seem to be the key, right?

Great question. Some very good discussions in this regard can be found at

fadfsfdfd wrote:

Here's one of the harder math questions I've had:

Explain what "e" is, and why it is important, to a psychologist (family friend) who has never heard of it.

Exponential functions, and functions with exponential terms, can be used to model such important physical phenomena as: current in a series circuit (which may include a battery, a capacitor, and/or an inductor), radioactive decay, population growth, spread of a disease, temperature of a cooling object (assuming conduction is the only source of heat transfer), and terminal velocity(when the wind resistance is proportional to the velocity.) When one sets and solves a differential equation to model such phenomena, it is easiest to use an exponential function with a base of 'e', which is, of course, about 2.718.

Science fiction precedes science fact (or something to that effect).

Theoretical mathematictians play an important role in technological progress. Real-world applications for seemingly useless mathematical discoveries are always being found. Complex numbers (which involve the imaginary unit "i") cannot be counted in a discrete sense and therefore were at one time considered purely abstract and useless. But lo and behold, it wasn't long before innovative minds found applications for these "unreal" concepts in the field of fluid dynamics.

People will always look for ways to turn the most outrageous fantasies into reality. At one time, a motorized land vehicle was a pipe dream. Now we've sent vehicles out of the solar system and landed robots on Mars (and no one can say that ain't rocket science). People are seriously questioning how time travel might be accomplished. Others are saying (perhaps less seriously) it may have already been accomplished.

Mathematics is the framework of all these technological advances. Some people have a knack (whether innate or acquired) for grasping abstract problems. Some even - dare I say it? - enjoy the challenge! Without these math eggheads, we might be stuck in the age of the sundial. How would we time our races then?

Yeah, but does math inform us on what's ultimately right or wrong? NO! In other words it has a limited capacity to inform us about MUCH of life and living. That's why MOST intellectuals are not obsessive compulsive mathematicians. Math is not the last stop on the road to truth. A lot of you math types are quite weird, however. This might contribute to your track coaching desires. Yuk.

Al north whitehead wrote:

Yeah, but does math inform us on what's ultimately right or wrong? NO! In other words it has a limited capacity to inform us about MUCH of life and living. That's why MOST intellectuals are not obsessive compulsive mathematicians. Math is not the last stop on the road to truth. A lot of you math types are quite weird, however. This might contribute to your track coaching desires. Yuk.

Math is only concerned with statements that are either true or false, and of course this excludes imperative statements. Since all of us mathematicians are in the dark regarding such matters, maybe Alfred can inform us as to ultimately what is right or wrong.

Second, since most of us mathematicians are quite wierd, I suppose that Alfred can also give us a standard of normal, and a rational basis for which this definition is valid, or at least why all of us should accept it.

Of course history is filled with intellectuals that were also mathematicians, such as: Whitehead, Russell, Newton, Pascal, Leibniz, etc. This trend has been discontinued largely because of the explosion in the breadth of knowledge in each discipline in the 20th century. Many contemporary mathematicians would make good philosophers, and visa versa, but what is the point. There are also a great many philosophers that do not have the mental capacity to be mathematicans, and many of them riducule math and science, usually without knowing much about such subjects.

Well, thanks for bringing this thread down to your level.

How's the view out of Mom's basement window, by the way?

(Just keeping it real for YOU)

Here's how I introduce exponential and logarithmic functions when I teach them:

Say you invest some money. If the difference between the amount you have today and the amount you have tomorrow is the same as the difference between the amount you have yesterday and the amount you have today, and if that is true every day, then your investment is growing linearly.

(Yesterday you had $10, today $12, and tomorrow $14)

On the other hand, if the ratio of the amount of money you have today compared to the amount you have tomorrow is the same as the ratio of the amount you had yesterday compared to the amount you have today, and if that is true every day, then your investment is growing exponentially.

(Yesterday you had $10, today $20 and tomorrow $40)

Exponential functions all look like b^{t} where b is just some number and "t" is the amount of time ( in this example) which has passed.

Now, if your money is growing exponentially, the difference between the amount you have today and the amount you have yesterday will always be a number - and always the same number -times the amount you have today. When that number is 1, the growth of your money can be predicted by plugging the amount of time which has passed, t, into the rule e^{t}. That's the definition of the number e.

As for logarithms, they are functions which allow you to turn division - a tricky business - into subtraction. They turn exponential functions into linear ones.

Wow! This is one thread I became deeply fascinated, from the start to finish.

I'd like to add something else from my experience for you, On the Run. I used to be like you. I had a profound sense of absolute resentment and burning hatred for math until I got over it. What brought this on? I failed algebra I and geometry in High School and went to summer school to take them again. "D" in Algebra II in my senior year. The reason? I'd have to say the teachers AND myself. They showed a lack of passion of helping students and myself a lack of motivation to learn math.

Hell, I even went to a psychologist after high school which he gave me diagnosis of "Severe math disability" to be used as an excuse to get out of college math. My school wouldn't accept it. When it came to remedial math, I sucked it up and forced myself to read the book and redo the problems many, many times to grasp the concepts. When I passed, I went to college algebra. I did the same thing. I forced my brain to open up to math and stop complaining. First try at Calculus wasn't a breeze and I failed. I never gave up at anything and I wasn't about to start. I tried again and passed. Even took Statistics three times before I could pass. (At least, I now know for sure the probablitiy of an event is always between 0 and 1!) I took discrete mathematics with applications (Logical structures) and passed it first time with a great teacher and a renewed sense of motivation to learn math.

To make my point, it all depends on the individual. I've noticed that people tends to give up easily when they run into an obstacle. You reminded me of myself when I was a younger kid. I used to abhor math until I stopped running away from it and opened my mind. Now, I look at world as a series of equations everywhere, around us. I certainly can understand why someone would major in math because it is challenging AND *gasp* FUN!!!

My .02 for what's it worth to you.

I'll respond if you can demonstrate mathematically why I should?

Then I guess you will have to be quiet.

Can I ask what you meant by that?

Sorry, I meant to respond to Al North Whitehead.

True dat. If anything, we've gone backwards in some respects during the last few thousand years. Heck, we've even regressed noticably since the 1960s! Remember the 1960s? You had O.J., cutting and slashing. Fast forward to the 1990s and you had O.J., cutting and slashing.

But everyone has a niche in this grand and wacky world. There are OCD eggheads, gymnasts, computer geeks, philosophers, preachers, basketball players and more out there. What people do with their abilities is up to them. Every discipline can be used in helpful ways (people used math and science to give us central air conditioning, laser surgery, etc.) or in destructive ways (people also used math/science to create WMDs).

BTW, mathematics and the "road to truth" don't have to be mutually exclusive.

Eeeeep!

J. T. wrote:

Math is only concerned with statements that are either true or false, and of course this excludes imperative statements. Since all of us mathematicians are in the dark regarding such matters, maybe Alfred can inform us as to ultimately what is right or wrong.

Arguable. Is the Axiom of Choice true or false? The question doesn't really make sense without a realist philosophy of mathematics. And if you think foundations is not real mathematics, then is Euclid's parallel postulate either true or false? What makes it so? certainly not the curvature of the universe.

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.

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.

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.

Al north whitehead wrote:

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.

A highly polemical response.