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You can find a great site about Neuroscience provided by Dr. Eric Chudler of the University of Washington.

http://faculty.washington.edu/chudler/introb.html

It is designed for kids with numerous topics to explore. It is well done with many many graphics and easy-to-follow breakdowns. It includes many fun topics like the fly-through of the brain:

http://faculty.washington.edu/chudler/flash/brainf ly.html

The Dr. Math website provided by Drexel University is a great site for mathematics of interest to all ages:

http://mathforum.org/dr.math/

The many gracious Dr. Maths respond to questions of all shapes and sizes. You will be impressed with the clever ways they answer questions, from how to understand 2 - 9 to proofs for struggling C.S. students.

Best of luck with your pursuit. It sounds like a great one ;)

Not being a mathemetician, I think it's a rather silly designation, however.

Can you explain complex numbers simply?

How do you graph imaginary numbers?

Imaginary Numbers in Real Life

Is it possible to find the square root of a negative number and, if so, to what number system do these square roots belong?

How is the square root of -1 possible?

What are imaginary numbers, what is their purpose, and how are they used?

What is i?

What exactly is the complex number system comprised of? ... and many more ...

Isn't "nearly infinite" kinda like "sort of pregnant"? IANAM, but it is my understanding that the very largest number short of infinity is not significantly closer to infinity than 1.

It is true in an absolute sense, however you should know that there is a difference between how one quantifies an extremely small number of things and an extremely large number of things. A statistical description of 2 or 3 discrete objects is nearly meaningless, however if one has, say 10^100 somethings (such as discrete future universe states) then it makes sense to talk in terms of statistics (50% of the future universes have Bob being alive, rather than dead). I said nearly infinite because I was suggesting that the number was finite, but very large, large enough that for most forms of analysis, the discrete possibilities could be treated as a continuum.

I suppose that terms like "nearly infinite" are simply a matter of perspective and perhaps not as mathematically precise as I should have been. It was, however, 2:35 in the morning so I was very tired.

Cheers,
Justin

Oh, and by the way, there is no "very largest number short of infinity". Infinity is a tricky thing, there are different kinds of infinity. Given any real number x, you can apply an operator O which adds an arbitrary positive constant to x to get a new, necessarily larger number x'. Thus, if you tell me you have found this "largest number" I can apply this operator and get an even larger number, thus invalidating the idea that x was the largest number.

>Exponential expansion for N^x is where x is held constant and N increases, e.g. 2^2, 3^2, 4^2, etc.

Huh? That's not exponential! Population growth is a classic exponential growth, with characteristic "doubling every x years". Same thing with the traffic growth.

Your "exponential expansion" is a mere quadratic: 4, 9, 16 ...! And if you stick in N=3, then it's a cubic. I think you're confused with "polynomial" growth.

Geometric series show exponential growth. See
MathForum for clarification.

Picky note: Dude better not be looking for a Nobel prize. There is no Nobel prize in Mathematics.

..something of that sort for mathematics on The Math Forum It works moderately well. If you want an answer to a well-defined question, go there.

There is always a tension between linear, or nested, or hierarchical... still "linear-like" :-) nature of those databases and general non-linearity of the field. I do not quite know where this thought is going, but I hope someone will elaborate :-)

Youve got to be kidding me. This comment should not have been modded up in the first place.

The message text is at:
http://mathforum.org/library/drmath/view/58723.htm l

I remember having a distinctly similar conversation with my third grade teacher when we learned about things like long division and prime numbers.

Dr. Math's Pi FAQ. Very informative.

:) It's a good question. The "phenomenally stupid law" question is an old one.

There's a reason the Supreme Court is called Supreme. It's the end of the road. There is definitely no way to force them to review a case, and imagine how cranky they'd be if you did. Even if there were oversight, that could be corrupt, and so on in a sort of Zeno's Paradox. Alternatively, the corrupt Court could grant cert. and uphold the law, same result as refusing to hear it but yielding precedent controlling all of the nation's inferior courts.

The Senate can impeach Justices for certain reasons, but being stupid is not one of them. (On that topic, if the Senate abuses the impeachment power, who reviews that? Another example of unreviewability. Don't worry, the President gets a few absolute powers, too.) Also, if the Congress was corrupt enough to pass the law, they're not going to attack the Court for supporting them ... unless it helps them in the polls.

Hang on, there is one last super-supreme court -- the public. The bedrock of democracy. For better or worse. They get Congress to repeal the law by replacing all of them if necessary by voting. Unless they all hate blondes, too, or like most Americans don't show up to vote.

Humor aside, we have a Constitution, the supreme law, as a check on discriminatory laws by Congress. No matter how popular, certain kinds of laws can not be enforced, protecting minorities from overreaching by the majority assuming a sane Supreme Court. For example of wackiness, the majority can't sentence the minority to death; that would break a couple of amendments. If you think that's a goofy example, recall that Nazi Germany had a valid court system applying the Nuremberg laws -- with a Constitution the judges could have struck the laws down and gone to concentration camps. Most countries do not have this judicial review, where the courts get the last word.

But wait! There's even trump card on the Constitution: the amendment. That requires a supermajority 3/4 vote of the states, which is hard to get.

Dizzy yet? It's called checks and balances -- Schoolhouse Rock did a favorite number about it ("We the People."). Plus, you can see why lawyers use so many footnotes, they just can't stop worrying there's something they left out.

Although this would be expensive, couldn't Wolfram set up a subscription service? Students who need temporary access to the power of Mathematica (I'm thinking of doctoral theses) could but computing time.

On an unrelated note, Integrals.com is one of the most useful high school math sites ever (up with Ask Dr. Math. It ended two weeks of misery by telling integral(sqrt(1+x^-4)dx) is not an elementary function.

dr math and i quote "we have gotten used to measuring weight in pounds or kilograms, which properly speaking are units of mass, not weight."

Somewhat OT, but are quarters really 0.7 mm thick, i.e. 36 to an inch? I don't think so. You'd be lucky to fit 15 if memory serves.
(I don't have any American change other than pennies handy so I can't check)
According to this, US quarters are pretty thick, at 1.75 mm:
http://mathforum.org/elempow/solutions/solution.eh tml?puzzle=103
Sloppy reporting.

Other rumours say that Mittag-Leffler was competing for a similar prize with his own wealth. Because Nobel was afraid that Mittag-Leffler would win a Nobel prize in Maths he never introduce a Maths prize.

The solution to the mystery can be found here

For all of those people scratching their heads going, "But 1 is divisible by itself and 1!" Here is a link.

Mike

Excuse me, but how exactly can something be close to infinity?

That depends on what kind of infinity we are talking about. Many models of infinity can be considered asymptotic.

Mathematical Atlas

Statistics Every Writer Should Know

2) My cake isn't round or square, it is raised in the middle and then loops down on itself. With one cut I make 8 equal parts with icing.

3) See #2.

Actually, unlike 0, 1, and e, pi is not "a fundemental constant", but a convenient artefact that allows circles and spheres to be expressed. For example, one can use any number "k", and express pi in terms of "k". The definition of k would be different, but that's ok.

That sound you hear is Euler rolling over in his grave.

A firm which has 40 billion is not paying any tax !!!!

Is 'new math' the only attempt you can think of? If so, then you are practically proving my point. New Math was a top down thing, and I'm not sure it was designed with making kids like it in mind.

Links of Interest:
http://www.christianparents.com/edgov01.htm
Why must slashdot insert spaces where there were none? http://mathforum.org/~sarah/topics/history.curricu lum.html

Doug finally released a beta.

The document he built describing what was coming with mod_perl 2.0 hasn't even been updated since Aug 2001! Many people would like to see some sort of status message. Does anyone know how well the cvs version works? Are there any major bugs?

The document he built describing what was coming with mod_perl 2.0 hasn't even been updated since Aug 2001! Many people would like to see some sort of status message. Does anyone know how well the cvs version works? Are there any major bugs?

Pi is a transcendental number, meaining that it is a non-repeating, non-terminating decimal that is not algebraic (i.e. not a root of any repeating or terminating decimal). So, no, pi does not contain itself.

Also, though we can't fully evaluate pi, some guy named Lindemann proved in 1882 that, indeed, pi was transcendental (and that he had way too much time on his hands). More information can be found here, if you want.

Excellent point!
Not only is classical music cheaper (I recently picked up several different composers for $2.99 per CD) it's also better for you.

And if you haven't tried it, playing classical in the background while you program is just as fulfilling as that techno stuff you have now (admit it, we all do).

And as an added benefit to the younger (male) geeks out there, knowledge and appreciation of classical art makes you appear cooler to chics. In college I rarely had a date, but I could approach any girl in any class and ask her to the symphony or the ballet with about an 80% success rate. Disclamer: I rarely got second dates due in part to the ache, braces, and poor conversation skills.

Thank God for NPR.

My only beef with NPR is that they (the local station were I live) play way to much baroque music. I really enjoy Mozart, Beethoven, Rachmaninoff - pretty much anything from the romantic era, but I can't get into Bach.

Why would I want a watch were it actually took me a second or two to read the watch?

..Yes I'd get quicker at it, but do I really want a watch with a base 2 output to deal with a base 12 [kinda] time system that I associate with decimal numbers?

Do I really want to have to explain what me watch is to attractive girls at parties?

I'm sorry, sir, but this discussion was clearly entitled "watches for UberGeeks". If you're having to ask about what women would think of this device or are even remotely positing that reading binary digits takes more effort than decimal, clearly you're not an "UberGeek".

And, anyway, everyone (or at least every UberGeek I know) knows that time is base 60 because it is based (haha, oh, sorry, just a little UberGeek humor) on the Babylonian system.

Don't get me wrong. Mathworld is a great resource. Eric did an enormous amount of great work putting it together. Unfortunately, being the work of a single person, it is and always will be limited in very important ways.

First off, all of the treasure troves always seemed very idiosyncratic. Since they represented only what the author felt was important / had access to / had time to write up, this was inevitable. Particularly amusing in the chemistry treasure trove which manages to be mostly useless to a college chemistry student while still bothering to include the mineral names of a great number of inorganic compounds.

The math treasure trove, by virtue of its sheer size, eventually escaped the worst effects of idiosyncrasy, but it still suffers from covering topics it varying levels of detail utterly out of proportion with their importance in mathematical study.

Despite all this, in its day, mathworld managed to be an enormously useful resource. However, even before it was shut down, it was beginning to totter under the effects of being (mostly) a one-man project. Despite the solicitation of "contributors," who did write a small fraction of the entries, Eric took a great deal of pride in having put the treasure trove together, and in his management of the treasure trove project, ensured that outside contributions would never be a substantial enough part of the project to threaten his claims to absolute control over it.

And absolute control was definitely one of his priorities. Mathworld was protected by some of the most stringent anti-mirroring measures I have seen. If the web server thought too large of fraction of the archive had gone to any IP or group of IP's, they banned the entire network. With a few rare exceptions, such bannings were without appeal. Yes, this meant that if someone else at your school attempted to mirror mathworld and got caught, you were banned from it until if and when your sysadmin managed to make nice with Eric.

I don't deny that Eric, being the author of almost all the material in the treasure-troves, had the right to do this. However, these policies forced me to reevaluate my opinion of him. Whereas before, I considered him a great altruist, I came to realize that offering mathword free to the public had no altruism in it at all -- it was simply a business decision to amass personal fame and publicity for his product, which he never intended to give to the public to use in any way he did not intend. Mathword, while originally free as in beer, was never free as in speech.

This is the great irony of mathworld's downfall: Because Eric never allowed anyone to have substantial collaberation in or to mirror the site, when it fell, the only way to get the information was off of a few illicit mirrors created from the CRC CD, and even then, Eric and Wolfram still shut down any mirror they became aware of. Again, I don't blame him for doing so -- it was his work. It just caused me to reevaluate the spirit in which the work was put together.

I now hold Eric Weisstein in about the same esteem as RMS. Both created a wonderful thing, but in time, their respective egos became one of the larger barriers to that thing acheiving its full potential.

What direction should mathworld have gone? What resources are there that attempt similar things in better manners?

First off, there is http://planetmath.org, a collaborative attempt at becoming what mathworld should have been. All contributions are under a public license of sorts, so it is immune to what befell mathworld. It is, however, still in its infancy. Go there, contribute, and fix that.

Second, there is http://www.mathforum.org, which has been bounced around from being a project of the Stanford math department, an independent dot-com, a subsidiary of WebCT, and now finally a not-for-profit sponsored by Drexel University. This is not an encyclopedia, it is a question and answer service for K-12 math questions. Because it is entirely volunteer-staffed, though, it actually answers whatever questions the volunteers feel like answering, and as a result, has amassed an archive of answers to math questions ranging from the most basic to graduate-level topics. In its current incarnation as a not-for-profit and with the site licnesed to print the authors' work with the author's retaining ownership, it should last as long as Drexel pays for the web space. I recommend that anyone who is interested volunteer as a Math Doctor to help enrich the site.

These two sites, I feel, far better embody the open-source spirit than mathworld, and in time their potential vastly exceeds anything Eric Weisstein will ever manage (mostly single handed). I bear no ill will towards Eric. I greatly respect his work. I just believe that the paradigm and motive it was compiled under are now obsolete, though it took the CRC morass to make me realize that.

A countable infinity (e.g. the set of natural numbers) is given the name Aleph Null (or Aleph0).

One reference is at http://mathforum.org/dr.math/problems/simakovsky10 .28.97.html

This does not, of course, get us much closer as it still doesn't explain why Elias should choose to be uncountably infinite although Second Transfinite Cardinal has a kind of a cool pseudo-ecclesiastical ring to it.