Mathematics

Suppose I have f(x)=e^x, how can it be proven that it is smooth?

when we want to tell the computer "for example" to do calculation like calculating the circle's area, we may give the following instruction in different versions, A: Result = [math]r^2{}[/math] * 3.14 B: Result = [math]r^2{}[/math] * 3.1416 C: Result = [math]r^2{}[/math] * 3.14159265 example, input: r = 100000 A: Result = 31400000000 B: Result = 31416000000 C: Result = 31415926500 but yet when we go with real numbers, it start to be worse ... so the best solution would to be, let the machine shows you the best it can do ! this means, let the computer do the division ... and this would be my version of Circle Area Calc .. in C, long d…

So awhile back I found some interesting problems from older versions of the Michigan Autumn Take Home Challenge, but sadly they do not post answers to the past exams. While going through a few of them I ran into some that stumped me: 1. Which is greater [math]10!!!!!! [/math] or [math] 10^{10^{10^{10^{10^{10^{10}}}}}}[/math] (Note: In evaluating towers of exponents, precedence rules state that evaluation should be from the top down rather than from the bottom up. For example [math]2^{3^{2}}[/math] should be interpreted as [math]2^{9}[/math] ) I know that factorial growth generally outstrips exponential growth, so I would guess 10!!!!!! is greater, but I really a…

Can anybody help , with a basic tutorial for the introduction to tensors - with a workable example , perhaps. My algebra and calculus , is ok but slightly rusty.

This is for a coding project I'm working on. It's not to do with men walking on spheres but it's a good way of describing the problem. Can anyone produce equations, code or similar to calculate outputs for given inputs. Inputs are: x, y & z coordinates of the spheres center radius of the sphere start latitude coordinate of the man start longitude coordinate of the man start angle of the man distance for the man to travel For the following scenario: Imagine the sphere centered at given coordinates where the north pole is at the topmost point. A man stands on the sphere at the latitude and longitude specified where 0 latitude is the north pole, …

To my knowledge: [math] 3 \cdot 5 = 5 + 5 + 5 [/math] However [math] 3 \, \mathrm{m} \cdot 5 \,\mathrm{m} = 15 \, \mathrm{m}^2 \neq 5 \,\mathrm{m} + 5 \,\mathrm{m} + 5 \,\mathrm{m} [/math] What is wrong?

Hi! I'm looking for Runge–Kutta's 11th order method. Maybe somebody knows where I can find it? I’m tired to search Google for hours... %)

The book I'm reading (Probability and the Logic of Science by Jaynes) has an example in it that I'm just not following. [math] If [/math] [math] \bar{A}=AD[/math] [math] then[/math] [math] A\bar{B}=\bar{B}[/math] Which I get, but then continues to: [math] and[/math] [math] B\bar{A} = \bar{A}[/math] which I don't get, considering the boolean identities he provides. Anyone know how to do this?

Let h be a hyperbole given by the equation: [math]h : \frac{(x-m)^2}{a^2} - \frac{(y-n)^2}{b^2} = 1[/math] Its asymptotes are then: [math] a_{1, 2}: y-n= \pm \frac{b}{a} (x-m)[/math] We were told in our math class that every line parallel to the asymptotes of a hyperbola intersects the hyperbola in only one point. So let us define a line l which is parallel to one of the asymptotes: [math]l: y=\frac{b}{a}x + c[/math] From what I've been told, this line should intersect the hyperbola only once for every real value of c excluding the ones for which [math] l = a_{1, 2}[/math]. Let's pretend we don't know that, and try to calculate c so that the result…

What do the underbraces in the following equations mean?

This is a good collection of links to audio/video courses and lectures on mathematics from colleges/universities. http://www.infocobuild.com/education/audio-video-courses/mathematics/mathematics.html This contains many courses and lectures on math: linear algebra, calculus, differential equations, statistics, probability, and more.

Hi, Wondering if anyone could tell me how the cosine rule can be the way it is - how it works the way/like it does... Or give me a link to a good explaination for the nature of the rule.. Cheers

Take the binary numbers of a cirtain length, for example. 00 01 10 11 Sort them into how many 1's they have. 00 01, 10 11 Write them in a more familiar form. 0 1, 2 3 And you have a pattern of numbers, which is more interesting with larger examples. 0 1 0 1, 2 3 0 1, 2, 4 3, 5, 6 7 0 1, 2, 4, 8 3, 5, 6, 9, 10, 12 7, 11, 13, 14 15 The first and last rows contain one element. The 2nd row shows powers of 2. More interestingly in all cases all but the last element of the 2nd to last row are prime.

How were numbers like e and pie found? I use them so much in school and have yet to discover how they were discovered.

In the real world a full self-reference is impossible (I can give my name but not my quantum state), if this were somehow incorporated into mathematics, would Godel's Incompleteness proof fail? It's based solely on self-reference, right? Merged post follows: Consecutive posts mergedIf you aren't able to answer, do you know of somewhere or someone else I can ask?

anything by zero is infinity.but is anything by infinity zero?

Hi, if I have a sequence of 1000 random numbers generated by a linear congruential generator of the form: Xn+1=Xn*a+c mod 32 And i know that the 1000 numbers are extracted from the bits 30-16 (15 bits) of the numbers generated with the formula above. (i.e, they range from 0 to 32767). How can i predict the 10 next numbers, i.e, how can i calculate the a, c and seed(Xo) values? I know that it is possible, but i don't have access to the next paper, which i think could be very useful: http://portal.acm.org/citation.cfm?id=66886 Thanks a lot for your help

What is the difference between a statement and a hypothesis?

Hey guys, long time no post! In the past few years I wound up getting a BA in math and then accidently wound up going to grad school. I'm giving an informal presentation in a few days where I will introduce Brownian motion to some colleagues (no laxitive jokes, please!). Anyway, for the presentation I want to pass from discrete Brownian motion to continuous Brownian motion, but I need some help connecting the dots! I'll put what I have so far here and then maybe you can point the way. Thanks! Here we go: Here is a diagram of the simplest Brownian motion: 1 / 0 \ -1 Where each possible outcome (either 1 or -1) has a probability of 1/2. L…

there is correct the expresion [math]\int^{-\pi+\epsilon}_{\pi-\epsilon} d\theta[/math]....where [math]\theta[/math] is a angular coordinate between [math](-\pi,\pi)[/math]....¿what means this?... i believe that this mean that the angular coordinate theta runs from [math]\pi-\epsilon[/math] to [math]-\pi+\epsilon[/math] in the sense anti clock (figure)

The integral is supposed to be the interconnecting thing between the two components. Seeing as how there is a problem, there must be a reltionship, or break down between the two, or three, and so forth, things. The relationship is based on them being related to the problem. The problem is of coure that they need to be 'defined', first as wha they are, and then what they do together. So, if you have two thingies that go together, and they react, te equation will show how they interact. If there was a reaction you will find it by using your 'mytical mathematics' on it. I cannot understand the 'tech', but common sense says that they need to mathematically react, lead…

Here is a strange equation I found: a=b a^2 = ab a^2 - b^2 = ab - b^2 (a + b)(a - b) = b(a - b) a + b = b (a = b) a + a = a 2a = a 2 = 1 This still works, even if you substitute "a" and "b". 2 = 2 2^2 = 2(2) 2^2 - 2^2 = 2(2) - 2^2 (2 + 2)(2 - 2) = 2(2 - 2) 2 + 2 = 2 4 = 2

Can you explain how? how can 0!=1 and 1!=1 Thanx

Many years ago I was shown a simple check for multiplication. The check can indicate a definite mistake; but cannot indicate definite accuracy. The check is performed by adding the individual digits of each part of the calculation. If this results in a number with more than one digit then add the digits of the new number and repeat as necessary until you have a single digit representing each part of the calculation. Example:- 39 leads to 3+9=12, and 1+2=3 58 leads to 5+8=13, and 1+3=4 39 x 58=2262 leads to 2+2+6+2=12, and 1+2=3 If the single digit representing 39 (i.e.3) is multiplied by the single digit representing 58 (i.e.4) we get 12 which leads to 1+…

hi, I was wondering why, in simpsons rule - for calculating the area of irregular shapes, there is a 4 in the formula. like so- A = h/3 (df + 4 * dm + dl)