January 19th, 2011, 10:28 AM
In my country's level of grade 10, there is no calculus but there is every thing algebra I, II, Geometry (euclidean and solid), and Trigonometry.
I wanted to learn calculus. SO if you guys who are familiar, could direct me where to start.
Any books, websites or other resource.
Thx
Are you ready for calculus?
January 19th, 2011, 04:23 PM
Learn algebra, geometry and trigonometry well, then you are ready for calculus. You are better off learning calculus at a university with a competent mathematician than simply learning symbol manipulation in a high school.Originally Posted by yeinstein
In my country's level of grade 10, there is no calculus but there is every thing algebra I, II, Geometry (euclidean and solid), and Trigonometry.
I wanted to learn calculus. SO if you guys who are familiar, could direct me where to start
Any books, websites or other resource.
Thx
http://www.gutenberg.org/ebooks/33283
The best Calculus text ever for beginners.
Such titles as "Calculus Made Easy" seem overly pathetic to me; the human race will go to any measure to ensure that their tasks are as simple as possible. The truth is that understanding calculus requires time and effort that is rewarded by knowledge and problem-solving ability, and there is no available shortcut. It is true that the world is not fair and some learn more rapidly than others, but there is no difference too great such that it can not be made up for via hard work.
The book was written in 1914.
Any particular implication related to this?
Hey, Troll! Did you bother reading past the title? Of course there is no royal road to geometry, or calculus for that matter. The "Easy" part relates to a gentle introduction to the main concepts involved, as opposed to a deluge of "symbol pushing" techniques.
Are you ready to make a contribution yet? Or, for that matter, to integrate with polite society on a level at least slightly superior to a turd in a punchbowl?
Nope.
Any particular implication related to this?
????
Look at the book.
It would not be suitable for the usual university calculus class today.
It's a piece of garbage in 1914 anyway. It's introductory quote "What one fool can do, another can." A good way to build up a student's self-confidence (I'm being sarcastic). The book skips the difference quotient (which was around for far longer than 1914) and is essential to understanding the derivative. I could write a better introductory calculus book (with proofs).Any particular implication related to this?
????
Look at the book.
It would not be suitable for the usual university calculus class today.
It is an old well-known book. It served a purpose in its day. I wouldn't use it today. But the majority of even modern calculus texts are pretty bad. Spivak is OK but not widely used.
The culture in 1914 was a bit different than that of today, and I suspect that the quote was better received.
You don't necessarily need "difference quotients", particularly when dealing with polynomials. To really do things properly you need to know about the completeness of the real numbers, in the form of the "least upper bound property -- and most calculus books do not go into this. This book actually does a better job of handling the exponential function and logarithms than do most modern books -- and that comes from building on the study of polynomials rather than emphasizing "difference quotients". The necessary ingredients to do rigorous proofs are not typically seen until you have a course in "Real Analysis".
No, you couldn't.
Don't take it personally if all my posts relate to how outdated your knowledge is once I attain my Ph.D.
Okay, I forgot a qualifier. Free!
I didn't necessarily mean that the book was bad simply by viewing the title (although after reading a few pages on differentiation I disliked it due to the lack of any mention of the interpretation of the derivative as a limit of secant lines); my statement was more directed towards the trivial titles often given to such books. The fact that it is free is certainly a plus.Okay, I forgot a qualifier. Free!
Go for it.
Will do.Go for it.
If you get to that point one thing you will find out is that in mathematics, unlike other disciplines, knowledge never becomes outdated. What changes are fashionable areas, approaches, perspectives and the extent of what is known, but theorems are eternal.Will do.Go for it.
Just kidding, of course.
By the way Dr. Rocket, would an achievement of solving two millennium problems qualify one as being a better mathematician than Newton? If not, than is there anything left to be accomplished that would?
Comparisons like that are meaningless.Just kidding, of course.
By the way Dr. Rocket, would an achievement of solving two millennium problems qualify one as being a better mathematician than Newton? If not, than is there anything left to be accomplished that would?
Solving even one of those problems would make one a senior mathematician. Those problems are so specialized and so difficult that it is unlikely that anyone wiil solve two of them.
Only one has been solved so far -- the Poincare conjecture in dimension 3. While Pereleman gets the credit for that (and a Fields medal as well) one must remember that it was Hamilton's work on the Ricci flow that enabled Perrelemans work.
I can guarantee many awards to anyone who cracks the Riemann hypothesis. That one is not only a Millenium Problem, it was a Hilbert Problem in 1900. It is widely regarded as the most important and difficult open problem in mathematics.
But Newton is the source of science as a predictive discipline, classical mechanics, classical gravity, calculus, differential equations, and orbital mechanics. That is a tough act to follow for lots of reasons, some historical.
There is one question in the millenium prize problems that seems to be out o place. I thought the yang-mills existence and the existence of the mass gap problem was more of a physics problem, despite its heavy mathematical background and implications involved.
Ph.D in what, exactly? sure as hell not mathematics any time soon.Don't take it personally if all my posts relate to how outdated your knowledge is once I attain my Ph.D.
I was just joking (as you would have noticed if you saw my succeeding post). Even with the question related to Newton I was being more or less sarcastic (otherwise I would usually message Dr. Rocket if I have anything serious to ask him).
You need to read the official problem description by Jaffe and Witten. It is an excellent survey as well as a formal description of this particular Millenium Problem. http://www.claymath.org/millennium/Y.../yangmills.pdf
From that description:
4. The Problem
To establish existence of four-dimensional quantum gauge theory with gauge
group G, one should define a quantum field theory (in the above sense) with local
quantum field operators in correspondence with the gauge-invariant local polynomialsin the curvature F and its covariant derivatives, such as Tr FijFkl(x).1 Correlation functions of the quantum field operators should agree at short distances with the predictions of asymptotic freedom and perturbative renormalization theory,as described in textbooks. Those predictions include among other things theexistence of a stress tensor and an operator product expansion, having prescribed local singularities predicted by asymptotic freedom.
Since the vacuum vector is Poincar´e invariant, it is an eigenstate with zero
energy, namely H = 0. The positive energy axiom asserts that in any quantum
field theory, the spectrum of H is supported in the region [0,1). A quantum field
theory has a mass gap if H has no spectrum in the interval (0, ) for some > 0. The supremum of such is the mass m, and we require m < 1.
Yang–Mills Existence and Mass Gap. Prove that for any compact simple gaugegroup G, a non-trivial quantum Yang–Mills theory exists on R4 and has a mass gap > 0. Existence includes establishing axiomatic properties at least as strong asthose cited in [45, 35].
The mass gap is an essential feature of a solution, but the fundamental problem is the demonstration of a rigorous mathematically well-defined and consistent quantum field theory on a four-dimensional spacetime. It might interest you to know that mathematicians studied gauge fields under the name "principal fiber bundles" long before physicists re-discovered them as "gauge fields".
The level of rigor needed to claim this prize is higher than what you would find in physics texton quantum field theory.
This surely does interest me indeed to find out that rigorous topology has set the fundamental background of one of the leading ideas in quantum mechanics today.It might interest you to know that mathematicians studied gauge fields under the name "principal fiber bundles" long before physicists re-discovered them as "gauge fields".
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