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Euclid apparently didn't consider it necessary either. Variables vs. values, perhaps?

Tamar Barbi, a 10th grade student living in Hod Hasharon, Israel, discovered that the theorem she was using to solve one of the problems on her geometry homework didn't actually exist.

Okay, the article says:

According to the new "Three Radii Theorem," if three or more lines extend from a single point to the edge of a circle, then the point is the center of the circle and the straight lines are the radii.

That's a definition, not a theorem. Even if you're generous enough to fix the wording, it's been proven centuries ago. If a point is taken within a circle, and more than two equal straight lines fall from the point on the circle, then the point taken is the center of the circle.

Not to mention that the article doesn't actually give the proof, and is simply a "yay, new invention by youngster" fluff.

Posters at Hacker News have some skeptical words about the theorem's novelty

And if you need to include that in the blurb, it's perhaps a good reason the article itself is garbage, especially when the topmost comment shows exactly why it's wrong.

Euclid's Elements, Proposition 9.

Her proof is either elegant, or clumsy but a great effort, depending who you ask.

You thought you were going to sound smarty, didn't you? I don't doubt your background is as you imply, more than minimal, but you simply forgot the relevant details and then presumed they don't exist. You even made up an argument for why! So no matter how smart you were, you'd still be an idiot.

http://aleph0.clarku.edu/~djoy...

When males are the victims or the help seekers, they are put in jail and the aggressor receive support and the charge of the kids.

Euclid's Theorem in actuality does refer to the case where X+1 is not prime. It's essential to the proof.

It goes something like this:

---------
Take a finite list of prime numbers, A, B, C etc. (The assumption that they are "all the primes" is unnecessary.)
Find the smallest common multiple of them, X.
Add 1 to that.
The new number, X+1, is either prime or composite.
If it's prime, then that's it. We've generated a new prime not on the list.

If it's composite, then it is divisible by some prime, G.
Could G be one the primes (A, B, C. etc.) already on the list?
But remember, X is divisible by A, B, C etc. So if G is one of those primes, then that means that both X and X+1 are divisible by prime number G, which is impossible.
Therefore G would have to be a new prime, not on the list.

Now we have a larger list, A, B, C, G, etc. and can repeat the process.

We can always generate a new prime not on the list, and therefore the list of primes is without bound.
---------

...the golden ratio famous from art and architecture...

As a (former) mathematician, I would like to point out that the ratio really comes from elementary (pun intended; read on to find out more) geometry. The ancient Greeks played around with it quite a lot and Euclid mentioned it (more or less) in his Elements. The Greeks weren't interested in this because of art or how pretty it was, but because they were particularly crazy about geometry (nearly all of their mathematics was derived from it) and some seemed to think that the universe could be understood through geometry alone. Anyway, it is just the fairly simple ratio of lengths of two lines such that the ratio between the larger and the smaller is the same as the ratio of them both added and the larger, or algebraically;

(a + b)/a = a / b = phi

This can then be trivially rearranged into phi^2 - phi - 1 = 0, and then that has the one positive solution; phi = [1 + sqrt(5)]/2 (the negative solution being [1 - sqrt(5)]/2 = - 0.618... but negative lengths and ratios tend to prove problematic). As usual, Wikipedia has more information.

While it is quite interesting to see it appear in a quantum mechanical setting, it isn't particularly shocking (to me). The number is the result of a fairly simple equation (as shown above) which is why it seems to appear so frequently in nature. While I didn't get this far in my studies of quantum theories, it wouldn't surprise me if, once the mathematicians have a chance to look into this, the reason behind this appearance of phi is found to be rather trivial.

However, I am not a physicist, or an expert in this field, so I may be completely wrong.

Thomas Nagel famously argued against the reductionist approach of physics and other "hard science" disciplines in his paper "What is it like to be a bat?". A rough summary of the paper is that he thinks science may be able to tell us how something works, like the echolocation abilities of a bat, but it's much harder to give an account for how it's like to actually experience something, like what echolocation actually feels like.

This is all by way of saying that you're spot on. Reductionist approaches are problematic and have widely known to be problematic for at least decades if not longer. This is not to say that reductionism is necessarily wrong - it could be the case that if we know everything physical about the world, we will know everything about the world - but it seems less and less likely to those who are not in the "hard sciences". Psychology and Neuroscience remain two distinct disciplines. You can't tell sociological phenomena simply by observing and describing in physical terms physical phenomena. And etc.

This may be an example of the latter. The sociological phenomena of groups have been well-studied by sociologists and psychologists, and we do have quite extensive explanations of group and social dynamics from these disciplines. Yet here, some physics students come in and try to study what has been studied and come to some questionable conclusions that seem to be problematic if examined from a sociological or psychological perspective (as pointed out by GP).

You mean like this?

http://www.mathcs.clarku.edu/~djoyce/java/elements/elements.html

Agree completely that ebooks (and readers) need to move beyond a static representation / recreation of a printed text (though in doing this they need to preserve niceties of fine book typography such as avoiding orphans and widows, preventing stacks, have decent justification algorithms (why isn't there an ebook reader program which uses TeX's algorithm) and use nice typefaces which are legible and readable).

Rather a shame Tim Berners Lee didn't use TeXview.app as inspiration for worldwideweb.app rather than TextEdit.app.

William

For the love of God, Euclid's Elements. Available for free here:
http://aleph0.clarku.edu/~djoyce/java/elements/elements.html

Sorry, my bad. linky (btw, there are other sites which had this idea too)

I wonder if it's just coincidence that the number of problems they list is the same as the number of problems David Hilbert listed in his famous address in 1900. And well, the Riemann Hypothesis is there too. A hundred years later, and still no resolution.

This might not be optimal because it assumes a very strong correlation between grades, test scores, and genuine intelligence, whatever that is. It also doesn't allow for much jumping between tracks. I'll use myself as an example: I did horrendously in my first two years of high school and then graduated with a 3.4 GPA by acing the last two, and eventually I ended up in an excellent but not especially well-known school named Clark University. Now I'm about to start graduate school, and aside from posting to /., I think I'm doing reasonably well, but in a system that's more strongly tracked I might not've been able to make the jumps I did.

Perhaps Clark is analogous to the private colleges you mention. Nonetheless, I've read that one of the United States' strengths is in its ability to have education at a variety of levels at virtually any time in one's life, especially in terms of community colleges. That isn't to say that high schools don't have many, many problems, as the parent article observes, but before we get too interested in merit systems, we should at least evaluate the trade-offs inherent in such systems.

Interestingly enough, Bob Woodward came to speak at Clark University when I was an undergrad, and during the Q & A some idiot got up and blathered a conspiratorial question about the CIA and censorship that was about as stupid as your post. Woodward responded with something to the effect of, "Do you think anyone could stop me from publishing something that's true?" he went on to say?" It was a rhetorical question from someone who actually knows what's he's talking about directed at a fool weaned on Internet conspiracy theories, and it was as effective a silencer of your type as I've ever seen.

Hmm, he tries really hard to look like Thomas Huxley http://aleph0.clarku.edu/huxley/ (Darwin's Bulldog).

• be persistent
• find other sources

One of those other sources was classroom learning. The simple fact is that a good teacher is absolutely the best way to learn mathematics. They've been through the confusion before. They know where you're coming from. This is worth the money. Unfortunately, and here's a caveat, there are some truly horrible mathematics teachers out there. There are a variety of reasons why bad teachers are teaching math, and I won't go into them, but suffice it to say: they are very discouraging. The trick is to go back to the first part I mention above: be persistent. You must always have enough confidence in yourself to say: "I am not the problem."

I see math in two ways: there's the visual approach, and the algorithmic approach. Simply put, if you can draw something simple on a piece of paper, you can do the visual part. If you can play a game of chess, let alone the highly complex and nuanced kinds of computer games that exist today, you can do the algorithmic part. The two pieces work together.

I found the following books very helpful, especially the "How to Ace Calculus" series. Don't be ashamed to buy a book with a title that makes you seem like an idiot. Value rigidity will end your math career-- you really need to admit to yourself that it's OK to ask for help.

• Calculus Made Easy, by S.P. Thompson. Some people hate it, some people love it. I suggest going to a bookstore and flipping through it.
• How to Ace Calculus, by Adams, Hass, and Thompson. Outstanding book. Only downside is that some topics don't have much depth, e.g., integrating using partial fractions. (But I'm supposed to know this already, right? It's an algebraic technique!)
• How to Ace the Rest of Calculus, by Adams, Hass, and Thompson. Not as good as the first one, but I think this is more a reflection of how varied Calc courses after Calc I can be.
• Topics in Precalculus, by Lawrence Spector.
• Dave's Short Course in Trigonometry, by David E. Joyce.
• And only some Wikipedia entries. Wikipedia tends to suffer from the same everything-must-be-formal problem

Well, it was good enough for Honest Abe, and he was just a backwoods hick - Grin.

http://aleph0.clarku.edu/~djoyce/java/elements/elements.htmlEuclid's Elements

I've been reviewing this and taking notes in Freemind.

Pug

Actually, evolution isn't nearly as politicized as it was in the 19th century. See the Huxley files: http://aleph0.clarku.edu/huxley/ Prof Huxley was known as "Darwin's Bulldog".

Even as recent as 75 years ago, there were law suits between believers and unbelievers, for example the case between Prof Du Plessis and the University of Stellenbosch in the 1930s. Basically, Prof Du Plessis contended that one should not take the creation myth of the bible literally. The problem was that he was the chief of the theological seminary - oops. So he was dismissed. He then sued and was re-instated, with full pay, then told to go home and stay there!

Even his statue was moved around town several times and only in 2006 - 70 years later - was it moved to the grounds of the seminary as a sign of "reconciliation".

So if you think that the creation myth is controversial today, it is nothing compared to 100 years ago.

"From the earliest times of which we have any knowledge, Naturalism and Supernaturalism have consciously, or unconsciously, competed and struggled with one another; and the varying fortunes of the contest are written in the records of the course of civilisation, from those of Egypt and Babylonia, six thousand years ago, down to those of our own time and people.

These records inform us that, so far as men have paid attention to Nature, they have been rewarded for their pains. They have developed the Arts which have furnished the conditions of civilised existence; and the Sciences, which have been a progressive revelation of reality and have afforded the best discipline of the mind in the methods of discovering truth. They have accumulated a vast body of universally accepted knowledge; and the conceptions of man and of society, of morals and of law, based upon that knowledge, are every day more and more, either openly or tacitly, acknowledged to be the foundations of right action.

History also tells us that the field of the supernatural has rewarded its cultivators with a harvest, perhaps not less luxuriant, but of a different character. It has produced an almost infinite diversity of Religions. These, if we set aside the ethical concomitants upon which natural knowledge also has a claim, are composed of information about Supernature; they tell us of the attributes of supernatural beings, of their relations with Nature, and of the operations by which their interference with the ordinary course of events can be secured or averted. It does not appear, however, that supernaturalists have attained to any agreement about these matters, or that history indicates a widening of the influence of supernaturalism on practice, with the onward flow of time. On the contrary, the various religions are, to a great extent, mutually exclusive; and their adherents delight in charging each other, not merely with error, but with criminality, deserving and ensuing punishment of infinite severity."

Sure, after government funding has paved the way in space exploration.

http://libref.clarku.edu/research/archives/goddard /faqs.cfm#question16

I'd venture (ha!) a guess that large corporate interests pay for lots more basic research than VCs.

Seeing as they're most often the small end of the funnel for government money.

KFG

These e-textbooks are not books in the customary sense. Sandi Kirshner, chief marketing officer for Pearson's higher-education group, says the e-textbook is offered only on a "subscription basis," which means that a student buys access for a defined period, like a semester, and cannot resell access to the book to others.

Agnostics say that the existance or non-existence of super beings cannot be proven. Intervention of super beings in our life cannot be proven either. There is no factual evidence of any super being activity on earth.

Therefore, praying about a problem is exactly the same as ignoring the problem and talking about Gods (Theism) is just learned idling, as Nietche put it.

See this: http://aleph0.clarku.edu/huxley/guide13.html

BTW, it is no use arguing with me. Rather read what Prof. Huxley said about the matter - he invented the term: http://aleph0.clarku.edu/huxley/guide13.html

Unfortunately, he is long gone...

No, agnostics simply don't give a damn: http://aleph0.clarku.edu/huxley/

A hallmark of religion is circular logic and circular myths. A good example of evolution in rapid action is the constant changes in influenza viruses. It only takes a few weeks for a flu virus to mutate sufficiently to become infectious again in a previously immune host. You should read this essay by Prof. Thomas Huxley (a personal friend of Charles Darwin): http://aleph0.clarku.edu/huxley/CE2/OrS.html It is from the Huxley Files: http://aleph0.clarku.edu/huxley/

A hallmark of religion is circular logic and circular myths. A good example of evolution in rapid action is the constant changes in influenza viruses. It only takes a few weeks for a flu virus to mutate sufficiently to become infectious again in a previously immune host. You should read this essay by Prof. Thomas Huxley (a personal friend of Charles Darwin): http://aleph0.clarku.edu/huxley/CE2/OrS.html It is from the Huxley Files: http://aleph0.clarku.edu/huxley/

Actually, beleive it or not, I'm studying exactly that this semester (among other things). If your means of representing the language is limited to single characters of an infinite alphabet "sigma" and your language consists of all string over the alphabet "sigma" (also known as the "Kleene Star" of sigma), then there are still an infinite number of infinite languages that can not be represented by your representation scheme. In other words, sigma is referred to as being "countably infinite" under set theory, but "sigma-star" is uncountably infinite (being the "power set" of sigma). So, even with an infinite choice of characters, you still miss an infinite number of languages. Thus, one infinity is actually greater than another. David Hilbert's first problem discusses this in more depth.

And people say advanced degrees in computer science don't have any real-world applicability...

The other way would be the set of values for which the Julia set is unconnected.

WPI, which is down the road, also uses Java so far as I know.

Students mostly use XP, but a sizable percentage use Macs.

The diverse environment means Windows malware infects a smaller percentage of the total computers.

Depending on where you go, the college administration won't care about what happens. At my university, unless you're selling drugs from your dorm room, the administration doesn't give a damn. I've never had anyone enter my room without permission, and I've never been trouble despite not following every housing rule.

Also, you're very unlikely to meet as many people off campus as you are on; this varies from school to school, but the fact remains that dorms offer benefits that I(rispee_I(reme may not appreciate. That doesn't mean dorms are for everybody, but they're worth at least trying.

Also, consider downloading scans of textbooks and auditing classes

That's fine advice for the unethical, but the rest of us simply buy used. Still, you should consider auditing classes, attending lectures and finding other ways to immerse yourself in the intellectual life of the university.

At my high school, which I attended not so long ago, the majority of teachers seemed to be in it for a paycheck, or for something to do. At the University I attend, a fair number of students are interested in teaching or working towards their teaching certificates. Sadly, these tend not to be the brighter ones, or the hard-working ones; many seem like the sort that would be scared to stand up for their beliefs.

Anyway, I agree with your basic assertion that teachers should stand up for what they believe in. Still, Perhaps the teacher in question does fight for some things, but no man can fight for all things all the time.

Note: Of course, there are some great teachers, but in my experience they had to struggle against much, including the mediocrity around them.

It's hard talking about computers with those who support their platform with the vehemence of a holy warrior -- and that can apply to Windows, Apple and Linux users, although the latter two make a lot of noise -- and it's just as hard trying to explain why an IT policy like the one you describe is just.

But I say: good for your school.

I attend a small liberals arts college that will remove net access for abuses like Kazaa and worm-spewing computers. Last year, they banned any Windows machine from coming on the network until the user installed McAfee and removed Blaster and other worms on their system. I spent numerous hours trying to explain to people why their "IE" wouldn't work. (The Apple and Linux users could log on without having to go through the hoopla.)

As for me, I'm delighted. The network runs faster without p2p clients, and downloads of important files (like the multiple-MB database files I need for work) goes much faster better. The only way to make people understand that they need to change their behavior is to create consequences for actions, or their negligent inaction. Example: unpatched XP machine. Result: viruses. Consequence: you don't play nice in the sandbox and you get kicked out. Result: student learns to patch Windows box, or gets a CS major to do it for him/her.

If you look at large public schools, graduation rates aren't nearly as high, even over six years compared to five. The US News and World Report College issue shows a wide discrepency between public and private schools. The online version requires a premium description, so I can't provide a link. The fact remains that, to rephrase the post of the grandparent post: "Hell, most public universities overbook themselves at the undergraduate level on the basis that only 65% of students stay past their first year."

The Elements is a brilliantly organized treatment of the science of geometry as a whole. While reading it, ask yourself what the subject of each book is (there are 13 books). Ask why they're in the order they're in. Ask why the propositions within each book are done in this order. When he gives a definition (like the definition of a circle) ask yourself whether that's the best definition, and why. Read each of the propositions (proofs) carefully, and try to re-present them in writing without looking at the book.

I know the OP is suggesting algebra, and I'm suggesting geometry, but high-school algebra is really no different than geometry represented symbolically. Book II of the Elements is devoted to geometrical representations of the same truths that high schools teach algebraically.

Even Abe Lincoln read Euclid every night before he fell asleep because it helped him to think logically and even philosophically.

The worst travesty done to ancient mathematical thought has been to try to introduce it to children in modern math textbooks.

Belloc

This curious mathematical relationship, widely known as the "Golden Ratio," was defined by Euclid more than two thousand years ago because of its crucial role in the construction of the pentagram, to which magical properties had been attributed.

Funny, because there's not a single pentagram anywhere in Euclid's Elements. Care to research your plagiarees a bit further?

Belloc

I know that this is Slashdot and that around here the looks of a mathematician are more important than her work, but if anyone is interested, here are a few pointers to get to know more.

First, a short description of Hilbert's problems at Wolfram: Hilbert's Problems -- from MathWorld.

Then, a link to a text of Hilbert's original lecture in Paris in 1900.

Next, a quote of the 16-th problem as laid out by Hilbert. (Sorry, no fancy LaTeX here.)

16. Problem of the topology of algebraic curves and surfaces

The maximum number of closed and separate branches which a plane algebraic curve of the n-th order can have has been determined by Harnack. There arises the further question as to the relative position of the branches in the plane. As to curves of the 6-th order, I have satisfied myself--by a complicated process, it is true--that of the eleven branches which they can have according to Harnack, by no means all can lie external to one another, but that one branch must exist in whose interior one branch and in whose exterior nine branches lie, or inversely. A thorough investigation of the relative position of the separate branches when their number is the maximum seems to me to be of very great interest, and not less so the corresponding investigation as to the number, form, and position of the sheets of an algebraic surface in space. Till now, indeed, it is not even known what is the maxi mum number of sheets which a surface of the 4-th order in three dimensional space can really have.

In connection with this purely algebraic problem, I wish to bring forward a question which, it seems to me, may be attacked by the same method of continuous variation of coefficients, and whose answer is of corresponding value for the topology of families of curves defined by differential equations. This is the question as to the maximum number and position of Poincare's boundary cycles (cycles limites) for a differential equation of the first order and degree of the form dy/dx = Y/X where X and Y are rational integral functions of the n-th degree in x and y. Written homogeneously, this is X(y dz/dt - z dy/dt) + Y(z dx/dt - x dz/dt) + Z(x dy/dt - y dx/dt) = 0, where X, Y, and Z are rational integral homogeneous functions of the n-th degree in x, y, z, and the latter are to be determined as functions of the parameter t.

Finally, I'll quote the abstract from Miss Elin Oxenhielm's article On the second part of Hilbert's 16th problem :

Let k be an integer such that k is larger than or equal to zero, and let H be the Hilbert number. In this paper, we use the method of describing functions to prove that in the Lienard equation, the upper bound for H(2k+1) is k. By applying this method to any planar polynomial vector field, it is possible to completely solve the second part of Hilbert's 16th problem.

Author Keywords: Second part of Hilbert's 16th problem; Hilbert number; Lienard equation; Describing function; Limit cycle; Polynomial vector field

To get the full text of the article you must apparently have a subscription of pay a $30 fee. It is easily available if you follow the directions from the author's page as I did.

Hope this helps

Now allow me for a few comments: solving one of Hilbert's problem is a huge achievement, even it's only part of one. What is even more stricking is that it's coming from a woman. Don't get me wrong, I'm no sexist, quite the contrary. What I mean is that only very few women made it to be recorded in the history of the mathematical science at large: other than Hypatia of Alexandria; Maria Gaetana Agnesi; Sophie Germain; Ada Byron, Lady Lovelace; Sofia Kovalevskaya; Emmy Noether, not many names come to mind. It would be really nice to add another one, to begin, and then work up from there.

Xavier

But in brief, it appears to be a problem about the "topology of real algebraic curves"

"Topology" is all about the shape of things. e.g a donut and coffee cup are the same from a topological viewpoint because you can transform one to the other without tearing the donut or coffee cup. There is probably lots of good introductions on the web.

As to "real algebraic curves", here is a link:

I quote:

Curves that can be given in implicit form as f(x,y)=0, where f is a polynomial, are called algebraic. The degree of f is called the degree or order of the curve. Thus conics (Section 7) are algebraic curves of degree two. Curves of degree three already have a great variety of shapes, and only a few common ones will be given here.

Basically polynomials of several variables is what they are, as far as I can tell. y = x^2 (which is a parabola) is a simple example.

So Hilbert was asking about the "shape" of algebraic curves (I think).

Now that was just the first part! I am not really sure the second part is about ...

The link again is

here

I welcome corrections from anyone with more math knowledge.

it is believed (but not quite proven) that there is no highest prime

I'm puzzled that you've not seen the proof of this, since it's been around since 300 BC or so.

Exactly right. The Mandelbrot set is the perfect example: http://aleph0.clarku.edu/~djoyce/julia/explorer.ht ml
The only thing these methods do is increase the improbability of getting 2 numbers the same. Most of the methods used create numbers with probabilities of .000000001% of being reproduced.

I beg do differ :) Although math has exploded during the last century, important Mathematicians are known from as early as 1700BC.

Math is a pre-requisite to technology, and it has the advantage of being the only science that needs *no* apparatus to study. This is why there are *significant achievements* in math were possible even during periods of human history which are pretty desolate otherwise.

If you'd like to know more, check out the Chronological List of Mathematicians.

Actually, it is not so bad. Incredible jazz scene and the best bluegrass night (Behind the Barn at Barley's) you'll ever see for free. Clarence Brown Theatre is great at the University and you haven't lived until you've seen a Kubrick triple feature at the Tennessee Theatre for 5 bucks with Bill Snyder firing up the Mighty Wurlitzer. Then there is great backpacking, mountain biking and kayaking too. But you also have to put up the the Orange and White Nuremburg Rallies called UT Football games, people who use the word 'coon' in polite conversation to refer to African-Americans and a state government run like the Ottoman Empire on acid.

Doctorate here I come. Damn, Worcester isn't much better ...

Evolution underlies most of molecular level biology these days.

"From the earliest times of which we have any knowledge, Naturalism and Supernaturalism have consciously, or unconsciously, competed and struggled with one another; and the varying fortunes of the contest are written in the records of the course of civilisation, from those of Egypt and Babylonia, six thousand years ago, down to those of our own time and people.

These records inform us that, so far as men have paid attention to Nature, they have been rewarded for their pains. They have developed the Arts which have furnished the conditions of civilised existence; and the Sciences, which have been a progressive revelation of reality and have afforded the best discipline of the mind in the methods of discovering truth. They have accumulated a vast body of universally accepted knowledge; and the conceptions of man and of society, of morals and of law, based upon that knowledge, are every day more and more, either openly or tacitly, acknowledged to be the foundations of right action.

History also tells us that the field of the supernatural has rewarded its cultivators with a harvest, perhaps not less luxuriant, but of a different character. It has produced an almost infinite diversity of Religions. These, if we set aside the ethical concomitants upon which natural knowledge also has a claim, are composed of information about Supernature; they tell us of the attributes of supernatural beings, of their relations with Nature, and of the operations by which their interference with the ordinary course of events can be secured or averted. It does not appear, however, that supernaturalists have attained to any agreement about these matters..."

T H Huxley, Essays upon Some Controverted Questions (1892)

Well, it's only to be expected since we have the cube (purist link) and the sphere.

Look at this this one for instance.

Am I the only one spotting mandelbrots here?

-skurk

Most students here leave KaZaA running 24/7. This means that even if they only download, say, 30 megs per day, they're trying to upload hundreds of megs. To make things worse, they don't even use KaZaA Lite - so they get plenty of spyware with their p2p apps. (Yesterday I brought KaZaA Lite with Speedup to a neighboring dorm room. For kicks, on the same CD I tossed Mozilla and Exact Audio Copy. The latter was a pain to set up, as usual, but they loved the combination of new software.) Schools have no choice because most students don't understand the issues ITS faces. I hear plenty of them complaining about how slow the "internet" is, because they use the net almost exclusively for p2p apps. And I've stopped trying to explain the reasons WHY p2p is so slow, because they never want to hear them.

But the connection is plenty fast to download the occsional mp3. It just means that people become extremely happy when I bring Exact Audio Copy over; yesterday I also installed CDex on my computer because EAC has issues on some CD drives. The article a few days ago about a CD with open source Windows software was of great interest to me, since I've already given out half a dozen CDs with various programs.

Here is a 700+ page book similar in content to a freshman college text MotionMountain

This is a Classical Electrodynamic book at a graduate level Classical Electrodynamics-Bo Thide

A site for Statistical and Thermal Physics with some good notes by Harvey Gould Statistical and Thermal Physics (STP) Curriculum Development Project

Quantum Mechanics--Niels Walet-- see the "Big .ps file

Lecture Notes on General Relativity-- Sean M. Carroll

A list of books to look into Cease's Book List

A few authors I like are A.P. French, Halliday Resnick for intro, Griffiths

A very respectable Oxford Physics booklist can be found in their handbook here

Many college professors put courses online. The lower level/remedial college courses would be excellent for junior high and high school aged children.

Here's link to an annotated, java-illustrated Eudlid's Geometry, since it's way cool, and geometry is taught as early as 8th grade in schools.

K-6 material is more difficult to find for free, I agree. Schoolhouse Technologies has a math worksheet factory that we like, available in pay, trial, and free(lite) versions. Another tool we use is StartWrite which also has a trial version. (Google can't find any pages which link to both of those sites. bummer.)

There is probably a lot of print material for the basics which has expired copyright, but is hard to find since it is so old. The historical fiction by G.A.Henty is excellent. Gutenburg has a few, and the rest are being republished at Prestonspeed Publications.

Here's one that isn't 4 megabytes in size. 190k animated gif. Hopefully the server can handle it ;). It moves slower than the original, but other than that it's the same
-Aaron

• Gain insight into the minds of the ancients (Plato would not let anyone into his school who hadn't mastered the geometry of the Elements),
• Improve your reasoning skills (Abraham Lincoln read Euclid when he decided to supplement his education later in life), and
• Be exposed to some of the most beautiful things that mathematics - or any academic pursuit - has to offer ("Euclid alone has looked on beauty bare." --Edna St. Vincent Millay)