Mathematics

okay i have problem, and i want to know how to solve these kind of questions in general. i think i get it, but its alittle confusing. so the problem goes like this, say f(x)=-2x^2+10x-150, find the domain of f such that its inverse exists. I get the Domain of f(x)=R range f inverse, but maybe someone could clarify the situation here for me. Thank you

Hi, I have two points in 3D space: point A: (1,2,3) point B: (4,7,6) I want to find a third point between the two, where z = 5 So, point C: (x,y,5) How can I calculate x and y for point C. Thanks.

When adding 2 vectors by the parallelogram method, it seem's obvious that the operation is always commutative, although I'm not sure how to go about constructing a proof of this. When adding >2 vectors is the operation always distributive?

I'm computer science researcher, but I'm not really good at math, that I want to improve myself, I studied: Basic Calculus, Basic Geometry, Discrete Mathematics, Basic Linear Algebra, Basic Probability & Statistics I know how to get math courses, but in what order should I go .. I want to know the path where I can then understand Quantum, Super mathematics, ..etc best regards, khaled

A seemingly simple question, do all algebras have at least one non-trivial derivation? Noncommutative algebras (lets say over complex or real numbers) always have at least the inner derivations. That is one can pick an element not in the centre and use the commutator to define a derivation. There may be outer derivations also*. Now for the commutative case the same procedure will produce an operator that annihilates all elements in the algebra. So we need outer derivations. If the algebra is generated by a finite number of generators then one need only state the action on the generators and extend this to the whole algebra. So for polynomial algebras with the s…

So what areas, and/or topics in mathematics are you all interested? Analysis, Algebra, Algebraic Geometry, Number Theory, Applied Maths, etc.. Personally I am not at a point where I am absolutely sure what I am interested in, but from my limited experience analysis, algebraic geometry, and number theory all seem to be towards the top of my interest list.

Who is the world's top mathmatician and why ?

Could someone explain, in as simple and non technical terms as possible, what integrating and differentiating are. Is there a simple everyday example where these two things are used. I've had a look in various places and they all tell you how to do it but not what it is you are actually doing i.e. the penny hasn't dropped for me yet. Your help would be much appreciated.

So there's been talk around the internet for a while now about what is wrong with mathematics education in the USA. Lockhart's Lament, is a good read if you want a good synopsis of some of the ideas that have been floating around. I thought this would evoke some good forum discussion. One problem I see is that much of the necessary mathematics for a good high school science education get introduced way too late, or not at all. Take for example the calculus/physics problem. Many high schools don't introduce calculus until near the senior year so students never get a chance to take a good physics course. Instead they get a primarily algebra based physics course tha…

I was wondering why something like X^2 + 2x doesn't = 2x^3, yet via multiplication would...

Begin with Euler's Identity: [math]e^{i\pi} + 1 = 0 [/math] [math]e^{i\pi} = -1 [/math] [math]e^{i 2\pi } = 1[/math] [math]e^{i 2\pi} = e^0[/math] [math]i 2\pi = 0[/math] [math]i = 0[/math] [math]1 = 0[/math] Euler says so!

Hello, I have some data, (x,y) (2, 0.356) (3, 0.543) (4, 0.724) (5, 0.905) (6, 1.086) (7, 1.267) (8, 1.448) (9, 1.629) (10, 1.810) (11, 1.991) (12, 2.188) (13, 2.364) the x,y plot is linear and the correlation R is 1. The y value is a coefficient and I would like to non-linearize the coefficioent to create the following conditions; when x=2, y=1 when x=13, y=2 when x=7, y=4 If I apply a parabolic transformation y= A*(x^2) + (B*x) + C with, A = -2.42 B = 7.1 C = -1.222 I get close, but the maximum values is at x = 8, y= 3.985 This is the transformed x,y data (x,y) ((2, 1.0) (3, 1.920) (4, 2.650) (5, 3.222) (6, 3.635…

Hi all, I was reading an article in new scientistabout physicists suggestion the universe may be fractal, this kind of makes sinceto me since they’re rather good at describing leaves, trees coastlines ..basically anything well.. ‘natural / organic’. I know complex structures likesocial networks can exhibit fractal geometry as well; these structures can alsoexhibit complex and chaotic behaviours like weather patterns, neurons and othergraph structures. Navigating suchstructures could be considered NP-Hard (e.g. what order and how to manipulate proteinsin to fold them optimally). This got methinking about whether fractals could be used to turn the complexit…

This is a problem I initially solved while I was a patient in the mental hospital. A few years later I was testing it to see if it actually worked, which it didn't, so I got into it again with a vengeance, solved every possibility and tested all calculations for any situation on an Excel spreadsheet. This is the result of my work. It's already been solved before but I had to find out for myself. http://jons-math.bravehost.com/triangulation.html A necessary requirement for GPS is to determine the distance between the satellite and the receiver. Somebody told me once that they do that with a time stamp on the signal from the satellite. Even so I s…

I am in the middle of writing a short popular review of the theory of supermanifolds. The account is non-technical but does assume some prior knowledge: functions in many variables, plane geometry and coordinates, and a little elementary algebra. I await to see just how accessible the account really is. The ideals I have tried to follow are: Limit technical language: explain as best as possible any terms that are not "general knowledge". No proofs of theorems or even calculations of anything. Just overall ideas. Give simple examples (if possible!). Use analogy rather than details. Suggest applications, but again present no details at all. Ha…

stability of numerical solutions of an ODE, numerical stability of ODE, and stability of numerical scheme are we talking about same thing or not? I am really very confused. Thanks

Hello to All You Great Mathematicians Out There! I am in desperate need to try and validate what would seem to be a simple mathematical procedure to determine the angle with which a Police Officer acquired a lock on my vehicle during a speed trap. I have already been to court and convicted and am now in my 11th hour of writing my appeal brief. The Laser Technologies (LTI) 20-20 UltraLyte users manual indicates that based on the feet with which the Police Officer locked my vehicle (573 feet) and the fact that he was 72 feet off the direct line of site of my vehicle (6 lanes at 12 feet per lane) that the reading would be considered "Unacceptable" by LTI. This is …

It has been proposed that Pi should be replaced with the Tau for mathematical purposes. The Tau has twice the value of Pi. The reasoning behind this change seems to be that it would simplify many formulae since"2*Pi" is much more common in formulae than Pi on its own. This certainly seems to be the case in electronics and it seems some eminent scholars are convinced. What do you think?

Don't all jump down my neck at once; I'm not a scientist. I appreciate how this kind of stuff, rightly or wrongly, might appear basic, all the same it's raised my curiosity. I was surprised to find a pattern created by the digital root of the platonic solid numbers. Example; Tetrahedral Number - 4, 10, 20, 35, 56, 84, 120, 165, 220, 286, etc The digital root of the above sequence expressed in rows of nine. 4 1 2 8 2 3 3 3 4 7 4 5 2 5 6 6 6 7 1 7 8 5 8 9 9 9 1 Now taking the digital root of the first three numbers, i.e., (412 = 7) and by doing the same with each consecutive three grouping, a repetitive pattern of, - 741 -…

OK, This is what I did: 1. Built a vector with ones in its prime indices, and zeros for the rest. 2. Applied the Discrete Fourier Transform to the vector with a sliding (rectangular) window of 200 samples. 3. Plotted the results (see attached). The x-axis represents the numbers axis. The y-axis is the frequency components axis. The z-axis (color) is the intensity of the specific frequency components in the vicinity of the x number. You can definitely see the frequencies 0.16666Hz and 0.3333Hz going across the entire graph. Now it seems the real avg frequency is 1/0.1666Hz = every 6 numbers, and the 0.3333Hz is just a harmonic of that base frequency. My question is…

If k is a positive integer and if the numeral in the decimal system that represents the product 60k contains only the digits 0 and 2, what is the least possible value of 60k ? If this question was asked in a multiple choice exam, one would simply take an answer and find if it is a multiple of 60. What if there were no answers given? For instance what if the question asked to find the first 5 multiples of 60k, that which 60k contains only the digits 0 and 2? The possibilities are not endless, but wouldn't it be rather difficult to pinpoint them? Thanks in advance.

I've been meaning to ask this for a while. From a layman's point of view (me being the layman), Perelman's solution breaks the most basic rules of topology. - wiki - wiki So...what's the deal?

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Just like any other construction the Neolithic architects and engineers who built Stonehenge knew exactly what they wanted long before the foundations were dug. The stones were positioned in respect of a vision of their vision - a superb premeditated geometric structure. It was also largely prefabricated, just look for example at the complex jointing in the lintels, they can only have been created off-site and must have been trial fitted on the ground (which also indicates just how much thought and planning went into the design). As for all the so called alignments, it has only one, an axis of symmetry; that of the midwinter sunset and midsummer sunrise. Now where does t…

Hey all, I read this article on the Riemann hypothesis: http://plus.maths.org/content/music-primes It's the first article I've read so far that actually showed me the implications the Riemann hypothesis has on prime's. Unfortunately, after reading the article I googled "Riemann harmonics" and didn't find anything. I'm not that surprised that they made the name up and I would like to read more about them; what are they called? Thanks.