Mathematics

Hello everyone I was wondering if there was a general formula (sum, product, ...) to define the n-th derivative of the m-th power of a function f(x) So far, I've found that for [math]n[/math] up to 3, the following should be right (if I made no mistakes): [math]\frac{d^{n}\left[f(x)\right]^m}{dx^n}=\frac{d^{n}f}{dx^n}m\left[f(x)\right]^{m-1}+\left(\frac{df}{dx}\right)^n\left[f(x)\right]^{m-n}\cdot\prod_{i=0}^{m-1}{(m-i)}+n\left[f(x)\right]^{m-n+1}\cdot\prod_{i=1}^{m-1}{\frac{d^{i}f}{dx^i}}\cdot\prod_{i=0}^{m-2}{(m-i)}[/math] Can anyone tell me if it's even possible to make such formula, and if yes, what that formula is exactly? Thanks. Function

Well, with my fascination of the Collatz conjecture, I might as well test other things with it. When I combined some concepts to make one. So, here is what I am presenting: Pretty much what this notation is presenting is that using the Hailstone sequence, sum the reciprocals of all the numbers of the hailstone sequence, besides 1, to a get a solution. My conjecture here is that the summation will always have a high bound 3(unsure about a lower bound). I have tested with many numbers and haven't found a counter example, though larger numbers may present different results. Another part of the conjecture is if the solution can get close to 3, but never re…

You thought it was difficult? They did it... In a set of p*q elements, which is not a field, and where the prime p and q are chosen big (like 500 bits), computing ax is quick, but the reverse operation called discrete logarithm is long - that is, no quick method was known. So much that some methods for computer security rely on that, for instance some passports. http://en.wikipedia.org/wiki/Discrete_logarithm That was before. On May 12 at Eurocrypt 2014, Razvan Barbulescu and his mates have described a method in quasi-polynomial time: http://ec14.compute.dtu.dk/program.html they claim as an example that number sizes that would have needed 2128 operations to crack go in …

I was thinking about the quote "Nothing is impossible" and it brought up the idea of carrying out a specific task the same, but with a different set of restrictions or rules applied to that task needed to be done. Yes, certain things are impossible because of the rules of physics and the rules of mathematics, but some how we find a way to accomplish that task another way. I find it interesting how this can be done even within a different set of rules and restrictions. So, it got me thinking that these tasks being done in a different set of restrictions can be generalized by a function that if you have found the process of completing a task within one set of restrictio…

Hello everyone I'd just like to known if the formulas below are correct. Normally I wouldn't post such a short/maybe dumb question, but since Wolfram|Alpha won't generate these formulas, which are, according to me, somewhat obvious, I'd just like to know if there are correct. [math]a^n-b^n=(a-b)\cdot \sum_{i=1}^n{\left(a^{n-i}\cdot b^{i-1}\right)}[/math] [math]a^n+b^n=(a+b)\cdot \sum_{i=1}^n{\left((-1)^{i-1}\cdot a^{n-i}\cdot b^{i-1}\right)}[/math] Thanks. Function

Given a function f(x) that is not a regular polynomial equation(x^n +/- x^n-1 +/- x-2...), how would one determine if a function is smooth over a curve or not? For example, let us say there is a given function that has a curve involved. Given the conditions above, how would one determine if all the parts of the curve are smooth in the sense that there are no other irregular curves on that curve even at the most minuscule spot of the curve?

This is a problem faced within another topic and I made this topic separate because I wanted to focus on this specific problem, which would deviate from the other topic. However, if moderators feel otherwise then it will be fine if the topic is moved to the other topic. So the problem(which I still haven't solved) is dealing with finding an equation to predict the amount of matrix solutions for a given Collatz-Matrix equation, which is defined by as the following: [math]C(x)_{k\times d}\begin{Bmatrix} a_{f} &b_{f} \\ u_{f}&v_{f} \end{Bmatrix},s(k_{p},d_{p})[/math] Now, how these work is there could be multiple or just 1 matrix solution for a given Coll…

Hello everyone In a dissertation for maths, I've mentioned once "quadratrix"... Can't really explain what it is, but I think I know what it is, and I've discovered what seems to be a pretty beautiful property of the quadratrix of a circle (commonly known as the quadratrix of Dinostratus) So I thought: what if I 'completed' the quadratrix? (i.e. completing the circle and the quadratrix, resulting in a horizontal flip of the quadratrix over x=0, a vertical one over y=0, and a horizontal one of the vertically flipped one over x=0) The result: an eye-shaped geometrical figure. If you're eager to see this 'completed' quadratrix, you can ask me and I will try to up…

hello everyone Let me get straight to the point: [math]p[/math] is prime, [math]a\in\mathbb{N}[/math], [math]p\nmid a[/math]; [math]A=\{a,2a,3a,\cdots ,(p-1)a\}[/math] Let [math]ra\equiv sa\pmod{p}[/math] Then: [math]ra=mp+R[/math] and [math]sa=np+R[/math] [math](r-s)a=(m-n)p[/math] So [math]p\mid (r-s)[/math] So [math]r\equiv s\pmod{p}[/math] The elements of [math]A[/math] must thus all be different and congruent with the elements of the set [math]B=\{1,2,3,\cdots ,(p-1)\}[/math]. The sequence is not important. I found these steps of the proof (which continues after this) on the internet, and I don't really get the statement I put …

Hello out there, I am a long time lurker of this site, but this is my fist post. When I was in primary school, I never particularly cared for mathematics. I used to think it was boring and was not given any context for the work I was doing. Years later, in college, I would read the work of Rene Descartes and it really revolutionized how I thought about mathematics, geometry, and the world around me. I might be a bit of an eccentric, but I spend a lot of my free time studying maths and get a lot of enjoyment out of it. This enterprise wound up leading me into finding this website and spending a lot of time on it. I started studying from the ground up on all the stuff …

So whats the relationship between an angle and its sine? I typed out all the degrees between 0 and 89 into a spread sheet and wrote out the answer then made a graph. Using the mighty powers of excel I got equations for the graph. I had the option of choosing how many polynomials I wanted in my function. here is the one to the order of two: y = -0.0001x2 + 0.0208x - 0.0227 Here is the one to the order of six: y = 2E-13x6 - 4E-11x5 + 6E-09x4 - 1E-06x3 + 5E-06x2 + 0.0174x + 1E-05 each one of these will allow me to put in lets say 10 degrees and get an answer of 0.1753 or 0.17357 or 58 degrees and get an answer 0.88018 or 0.8473 These are app…

What would you say is the validity of statistics? Also, if you're going to support your argument with definitions please don't, as I think you must ask yourself why you have so much confidence in the definitions in the 1st place I believe the uncertainty just encourages people to not search for the *real* relationship or variables / constants, and it also encourages pointless studies that emphasizes on correlation when the true relationship (if existent at all) is *not* proven. This also goes for probability, however, I heard that probability is quite applicable in quantum physics.

Hello everyone I have a rather odd question for you this evening. Yesterday I posted a topic on the quadratrix (you should read it if you'd like to know more about it) and now I'd like to know if there's something special about the number 6.37, or a number that's really close to it, because, that's the place that the quadratrix of a circle with radius 10 intersects the x-axis... I've tried using square root of pi, pi squared, square root of 10, and much more... I've even used the constant e... But I can't to find an expression, using methematical constants and 10, which results in about 6.37... The closest point I find is 2*pi... Could someone help me…

what is the difference between euclidean and non euclidean geometry-thankyou

I have been busy putting together a guide to the new HP Prime graphing calculator: url deleted Hope you enjoy, Like and subscribe please, Regards MC

Well, this is probably thought of already, but might as well give people the concept. This work is a small fraction of Collatz Theory So, basically, the idea is that it is an "equation" that lies on multiple dimensions(two dimensional). It is an evolving equation matrix, meaning on an infinite scale it involves infinitely. Here is the notation of a Collatz Matrix equation: [math]C(x)_{k\times d}\begin{Bmatrix}a_{f}&b_{f}\\u_{f}&v_{f}\end{Bmatrix},s(k_p,d_p) = A_{k\times d}[/math] In this case, the four variables that end with the subscript f are the formulas used in the equation to calculate the matrix. In each case, if the number were to be moved up the m…

Hi folks, Here's an armchair question... A significant figure (sigfig) is the number of figures (a.k.a. digits) to which a number is meaningful, even if the numbers are zero. For example, 10.000 has 5 sigfigs if indeed one has that much precision. But how about in the instance of degrees of a compass, when measuring it as a full 360 degrees... if the current measure is 5 degrees, how many sigfigs does this have? I would think it effectively has three. Or maybe it's simply a question of semantics. Your thoughts? Mike P.S. My first post here! ScienceForum.net looks like a nice active place.

This is not to say that there were will be times when this happens, but what if it does happen? Would it show Mathematics to have flawed axioms? Or would it simply reveal loop holes within assumed axioms of mathematics? What other consequences would occur?

Let's take a look at the following picture: Of course, a^2+b^2 = c^2 has infinite primitive(I think) Pythogorean triples where a,b, and c are whole numbers, proven by Euclid. However, are there infinite primitive Pythagorean triples where one of the elements, when square rooted, is also a whole number? I am asking this because, for example, let us take the primitive Pythagorean triple (3,4, 5). Notice how the square root of 4 is 2, obviously. Let us apply this to a geometric visual. This means that it takes a real whole number sided square to get two squares that have irrational sides. In interesting phenomena, I say.

Is the summation below true? [latex] \sum_{a}a * Pr[R=a] \leq \sum_{a\leq b}b * Pr[R=a]. [/latex] Where R is a random variable and Pr[R=a] means that the probability that the random variable is equal to some number 'a'. You can ignore that part and replace Pr[R=a] with x: [latex] \sum_{a}a * x \leq \sum_{a\leq b}b * x. [/latex] The first summation provides all 'a' values, so the summation is over larger amount of terms. The right hand side sums only those a<=b, so the right hand sums over less amount of terms. But at the same time the right hand is multiplied by b>=a. So it is not clear which one is bigger. I am not extremely familiar with Riemann sum, so …

Hello, This is a question for the professional mathematicians on this board. I want to become a mathematician. My background is in law. I would most likely be able to begin studies in the spring semester of next year. I am 25 years old. From your perspective, am I coming to mathematics too late in life? Do you have any advice to someone wanting to make the transition to math? A few other questions: In law, we approach problems using "legal reasoning". Legal reasoning is an approach to problem solving taught in legal schools, and learned with practice. Is there an analogous process of approaching mathematical problems along the lines of "mathematical reasoning"…

Hello again folks. Is the following of any interest if it can be proved? P: Relative to any finite set of primes there are infinitely many pairs of consecutive twin primes. Note 1. In case it's the wrong word - by 'relative' I mean that none of the primes in the set are factors of the pair of twin primes. Note 2. This is nothing like a proof of the TPC. Thanks for any replies.

While looking for a modular building block for a sieve of Eratosthenes, for example, an 8-bit block of zeros with composite multiples of 2 and 3 already marked as ones,I noticed something bazaar. If I grouped the digits from the sieve into groups of 8 and marked the composites, it takes the same number of groups of eight to form a repeatable block as the prime who's composites i was marking. For example, here are some primes and the groups of eight digits for the sieve. 2 == 10101010 3 == 10010010 01001001 00100100 5 == 10000100 00100001 00001000 01000010 00010000 7 == 10000001 00000010 00000100 00001000 00010000 00100000 01000000 11 == 10000000 00010000 00000010 00…

Of course it hasn't been solved yet, but it would be significant to consider other properties of Hailstone sequences after it has been solved(or the properties brought in this post will be solved with the solution to the problem). Before introducing these problems, here are things to be defined: A Collatz number is defined by a number in a Hailstone sequence that is represented by [math]c_{x}=6x-2[/math] where x is the index of the number. This is a result of [math]c_{x}=3(2x-1)+1[/math]. A Hailstone sequence is a sequence of numbers resulting from the Collatz conjecture rules. A Hailstone exception is a number that does not follow the pattern of a Collatz number …

So, something I've been doing lately is reviewing driver safety. I got my license in 2008, and I have reviewed driver safety the past few months. I think I'm a much better driver than in 2008, but I've been reviewing skills to prevent myself from ever getting into an accident. One of the mathematical models that I came across lately in driver safety is the Solomon curve. http://en.wikipedia.org/wiki/Solomon_curve It's a mathematical model describing the relationship between speed between drivers and the probability of getting into an accident. What I don't understand about the curve, and perhaps some mathematician here could do research and give me insight, becaus…