Mathematics

I wont pretent to fully understand the hpothesis itself because of lack of knowledge of complex numbers (though i have basic understanding of imaginary numbers i dont understand the "critical line" or why infinite 0's sit on it). However i grasp the concept of the zeta function and how generally exponents create a convergence. I specifically want to know how using the pattern 1-(1/2^s) + 1-(1/3^s) + 1-(1/5^s) + 1-(1/7^s) etc relates to the zeta function. The example i have doesnt clarify how the zeta function and this prime pattern relate exactly so any information would be gladly accepted. (Also any examples of complex numbers that sit on this critical line). …

On Fermat’s last theorem This theorem states that for any n except 2, the equation X^n+Y^n=Z^n is not true for any positive integer triplet X, Y and Z. Fermat’s “I have discovered a truly marvelous proof of this, which this margin is too narrow to contain.” has fascinated mathematicians from 1637 but no one has found what his proof was. Let us try to understand this theorem better. Please read the article at On Fermat’s last theorem http://pengkuanonmaths.blogspot.com/2015/07/on-fermats-last-theorem.html or On Fermat’s last theorem https://www.academia.edu/13665056/On_Fermat_s_last_theorem

Hi, Hope this is in the right place, apologies if not. I've recently started a Maths & Physics Degree and am just about to embark on my first Maths module. I've been toying with the idea of getting myself a graphics tablet to use on my assignments alongside the Windows Maths Input Panel. I'm not planning on using it day to day as i find it easier to scribble with a pen and paper but thought it would save me quite a bit of time when writing up assessments etc. I just wondered if this is something any of you guys have experience of and if it was a viable idea. Additionally if you have used these before do you have any recommendations? Thanks in advance, …

I'm not sure I understand exactly the product in category theoretic terms. The book I'm using gives a very concrete example that is easy to understand. However, I'm not sure I get it generally. How does it work for the product of the reals? What's X in that case? What are f1 and f2?

Now and then I play around with Maths and Scientific thinking. Only later on I check on the available knowledge store. Two days back I thought of testing out the following equation : x y = y x where both x and y are Positive Integers and x is not equal to y. I guessed that there won't be a solution to this equation then I realized that 2 4 = 4 2 and perhaps this is the only solution possible. Are there any other solutions ?

Just what the title says. Say for instance I have [math]ln(x^2/3)[/math]. I want to be able to turn that into [math]2ln(x...[/math]But, I'm not sure exactly what's happening to a number or what the exact operation is when you take an exponent out of the argument of [math]log(x)[/math]. So, I'm not sure exactly what the result is if I assume [math]ln(x^2/3)=2ln(x/sqrt(3))[/math] because every time I try to do something like that, I get some complex constant left over. It "seems" like when you move exponents out of the argument of a logarithm, you're exponentiation everything in the argument by 1/exponent-you-want-to-get-rid-of and for some random reason that exponent then …

I'm not solving a differential equation with an unknown function but it seems it should be similar. What I mean is I want to solve for an unknown operator that has some arbitrary transformation of terms and variables. If for instance I had x^5 and I wanted to find some operator that made x^5 turn into x^4, I should get ^4/5. But let's say I didn't know that property of exponents as a given, how would I mathematically investigate the apparent transformation of variables to find that operation that has the properties of turning x^5 into x^4?

That is is this function oscillatory?

Just what the title says. Say I have some random equation like 2^x, then I have some random equation that I tested and it gives me the points (1,2), (2,4), (3,8), (4,16), (5,32), (6,64), (7,128) but there's no proof it works for (8, 256) other than by testing it to see it works for x=8, if I assume the curve is continuous, is there any sort of weak proof that says it's the equation 2^x? Every taylor series should be unique, yet for any given equation that was derived purely from integers, I could use some kind of a*cos(bx)+c that generates a coefficient of "1" for any given integer. For instance, the equation y=2^x generates (1,2), (2,4), (3,8), (4,16), (5,32), (6,64), (7…

I have been doing research on entropy encoding for some time.. I found some interesting relationships between Arithmetic coding and other methods such as Huffman Coding. I made an article to explain them and am presenting here for review: http://siara.cc/arithmetic_coding_new_approach/ I have also attached a PDF version for convenience Arithmetic_Coding_Formula_based_approach.pdf. Please let me know your ideas.

Having a hard time quantifying certain equations because most the values are below 1. One issue is standard deviation, simple enough but when squaring these numbers they get smaller etc...Also working with angles below 1 degree. For some reason doing opp/sin(x) gives a hypotenuse barely 4^-10 over the adjacent. I've tried a few basic things..multiply by say 100000 then divide by a multiplier that counts the resulting exponent (with standard deviation). Is there a particular trick to working with values below 1? As a side note 3162 is my new favourite number. Regards.

I am looking for reason why anything raised to the power of zero is 1. On a side note any reason why log's of zero are undefined.

Suppose I have a number, any random number like .3252389472395872394729..., is there software that will test possible exact formulas containing certain parameters, like if I want it to test if that number could be some coefficient of pi or e or e*pi or sin(tan(cos(sin(tan(cos(42424244424)?

What exactly is mathematical physics in contrast to non-mathematical physics? I would imagine it is physics done in the way of pure maths, as in designating axioms, definitions, some inference rules implied by the context, and then deriving theorems about the subject matter, or similarly constructing structures that correspond to physical phenomena. But then what is the difference between that and, say, solving some equation and deriving the result using the informal tools of calculus/algebra. Each step in the derivation might not be given a justification like a proof step, and there may be differences in formatting and fullness, but wouldn't it be the same applicatio…

Hi, Math is far from being one of my best subjects, so im looking for some help in this area. How can I measure the bulk density of a dry powder into cubic feet using a 1 cup measurement? Thanks for any help!

I want the geometrical interpretation of the following: > If fxx * fyy} < fxy^2 and fxx has the same sign as fyy at a point, then why is that point a saddle point? Because,in the case that they have the same sign,one would expect that point to be a minimum or maximum point,not a saddle point. Bear in mind,that i have checked the intuitive explanation that is available in wikipedia,but did not understand it. Also, i am studying physics and not math,so please don't complicate things with symbolisms that i might not understand. Also, i want an intuitive answer,because i know the maths behind categorizing critical points.

Can someone help me on the problem: Assume the probability of each relay being closed is 'p' and that each relay is open or closed independently of other relay. What is the probability that current flows from L to R? See the circuit diagram below. The relays are just like switches. If closed current flows else if open current does not flow. This problem is from the book of Meyer : introduction to probability and stastical applications.

This guy is trolling me at school, he keeps saying that "You're a Senior, you should know that", but I find this kind of statement to be invalid. Because if Advancing to the level of Senior = Knowing a specific piece of information was indeed true, then why didn't I know that? So now, I want a to put it into a mathematical equation to shove in his face. Any ideas how to write it?

Why is it that a negative * by a negative equals a positive. Especially given that if I add to negatives I get a negative. Multiplication being addition and all.....

Why is it that 1 is not considered a prime?

I am looking for in depth reasons for why division by zero must remain undefined.

The Not Integer Line ~-5 ~-4 ~-3 ~-2 ~-1 ~0 ~1 ~2 ~3 ~4 ~5 Author: David Elkins

Give an explicit form each of the terms: a(1) = 1 a(2) = 3 a(n+1) = [a(n) + a(n+1)]/2 I just started with this topic. How can I calculate what a(n) is? Should I replace a(n) by 1 and a(n+1) by 3 and divide the result by 2? Would that give me de?

I have little math, But i came across this fact about prime numbers which i thought was interesting and worth a share, Most properly old to those with math, 23X23=529 =(24X22)+1 29X29=841=(24X35)+1 31X31=961=(24X40)+1 37X37=1369=(24X57)+1 41X41=1681=(24X70)+1 I was wondering if there is any sequence to this? Between the multiples of 24? A little find like this to me, brings a new interest and lets me explore where i would otherwise perhaps never go. So my first thought was 3x24 -1=73, So i googled 73 , 73 is an emirp, m…

Hi all, My brother is getting married next week and he and his wife to be are school teachers. They had a bit of a theme going on the wedding invites etc that was the square root of R + V = "heart shape" and I would like to turn this around in a clever maths way of taking the piss. Not to clever though as many guest including myself wouldn't understand!! Can anyone help?