1. S

    Could someone please explain how a specific part of the expression for the Riemann su

    I'm really sorry if this post is not appropriate for this forum. My math level is quite low and it might have been because of that I could not understand this concept. So, the problem that I have is that I don't understand how a part of this expression is generated: 1. $$S =\sum_{i=1}^n 2...
  2. S

    Note on the Riemann hypothesis

    It is well known that there is some freedom, at times, to do order of operations in algebra is different orders. We might choose to do a distributive operation before an additive one, for instance. Suppose we we use that freedom not to do the additive absorptive operation of infinity until it...
  3. M

    Proof of Riemann Hypothesis

    Sir Michael Atiyah is a huge name in mathematics. He's one of the best mathematicians alive today. He has proven the famous Atiyah-Singer index theorem, and has won a Fields medal. What's more, at 90(!!) years of age, he will present this monday a proof of the Riemann hypothesis, arguably the...
  4. A

    Self-studying multiple Riemann integrals

    As the title says, I would like to self-study multivariable real analysis (integration, specifically; the Riemann integral) and I need some recommendations (resources, books, videos, ...). I'm from Croatia and got my hands on some Croatian notes about multivariable real analysis so if some of...
  5. G

    Riemann sums problem

    Hello! I am struggling with approaching the following problem: \lim_{n\to\infty} \sum_{k=1}^{n} \frac{n}{\sqrt{n^4 + k^2}} I know that I probably have to use something like the following: \lim_{n\to\infty}\frac{b-a}{n} \sum_{k=1}^{n}f(x_k) = \int_a^b f(x) dx ... but currently I'm in a block...
  6. S

    Lebesgue integration - Riemann integration

    What the differences between Lebesgue integration and Riemann integration?
  7. M

    Riemann's Sum Problem

    Brief Overview What I've done so far: The Question If the safety capacity for the benign use of a camping gas lamp inside a confined space is (104÷5) m^3, calculate whether it would be safe to use the lamp within the lightweight ‘pop-up’ tent. I know the height of my tent is...
  8. S

    Riemann Sphere

    What is the connection between Riemann Sphere to Trigonometric Functions?
  9. R

    Riemann hypothesis

    how to solve Riemann hypothesis
  10. J

    My elegant formula for the Harmonic Numbers of order k

    I'm looking for someone who can "introduce" me to the arXiv.org site, so I can upload a paper that demonstrates my elegant formula for the Harmonic Numbers of order k. Because I no longer have a university email, and haven't published in my undergrad years, there's this little obstacle that you...
  11. 7

    Riemann Hypothesis

    P: ζ(sᵢ)=0 Q: sᵢ=σ+it R: t≠0 S: σ=1/2 A: P≡[Q≡(R≡S)] It is that ζ(1/2)=0 if the Proposition A doesn't hold, but actually, ζ(1/2)≈-1.4603545; therefore RH does hold.
  12. N

    Use the definition of the integral as a limit of a Riemann sum

    Equation: "integral from 0 to 6 of -(x^2)+36" I know how to find it the easy way... Ex.) I know to take the integral -(x^3)/3+36x and evaluate it from 0 to 6 which = (-216/3) + 216 == [144] So I know the answer, I just don't understand what my teacher wants. I know there's an...
  13. T

    Riemann hypothesis

    Hello, I am looking for a good read or video about the Riemann zeta function and its distribution of prime numbers, if anyone knows of any.
  14. V

    Solving Riemann Lower sum

    I'm trying to find the integral of f(x)=x^{2},f:[0,1]\rightarrow \mathbb{R} using Riemann's criterion. I created a partition with equal intervals like this P_{n}=\{0<\frac{1}{n}<\frac{2}{n}<...<\frac{n-1}{n}=1\} and then I started cxalculating the lower sum...
  15. Z

    Riemann Sums

    $\lim_{n \to \infty} \sum_{i=0}^n sin \left[ \left( 2 + \frac{3}{2n} \right) + \frac{3}{n}i \right] \cdot \frac{3}{n} ~=~ \int_a^b \sin(x)$ dx What will be the value of b and a?
  16. N

    Riemann Sums and Definite Integrals

    Use Example 1 as a model to evaluate the limit \lim _{n\to \infty }\left(\sum _{i=1}^n\left(f\left(ci\right)Δxi\right)\right) over the region bounded by the graphs of the equations. (Round your answer to three decimal places.) f(x) = sqrt(x), y = 0, x = 0, x = 3 HINT: Let...
  17. N

    Find the Riemann Sum

    Find the Riemann sum for f(x) = x2 + 3x over the interval [0, 8], where x0 = 0, x1 = 1, x2 = 2, x3 = 7, and x4 = 8, and where c1 = 1, c2 = 2, c3 = 5, and c4 = 8. I'm confused. What do the c's and x's mean again? I know, I'm dumb and have no clue on where to begin.
  18. M

    Riemann Hypothesis proven by physicists

    Read this : https://phys.org/news/2017-04-insight-math-million-dollar-problem-riemann.html
  19. F

    Riemann Hypothesis does not exist, himself has proved it

    In fact, Riemann himself has proved the problem. Please look at https://arxiv.org/pdf/1508.02932v5.pdf
  20. J

    looking for an equation of a curve

    While reading about Riemann, I came across a relation between random numbers and e. I am not sure if Riemann discovered the relation. This led to an empirically calculated curve that connects the points 0,1 and 1,e, in which the slope at x=0 is 1 and the slope at x=1 is 2. Has anyone seen such...