# Tagged Questions

The utilization of advanced computing technology in mathematical research: new mathematical results discovered partly or entirely with the aid of computer-based tools.

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### Complicated probability question [closed]

There are 20 empty present boxes numbered from 1 to 20 are placed on a shelf, there are 4 men standing in front of the shelf. Each one asked to pick in his mind 3 numbers without telling any one then ...
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### Can we prove that plumb line is vertical to ground?

Using a plumb line to make sure a wall is vertical for instance, is as far as I know one of the most primary tools in the sense that the very-very ancient builders used it as an instrument. I was ...
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### stochastic experiments like galton board?

do you know some other stochastic/statistic experiments like galton board? I'm looking for something that could be build for learners or people who are interested in mathematics; some sort of "...
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### Assigning levels in factorial design.

I am sorry if the question is too basic. Actually while doing some experiment on 2-level factorial design, I assigned +1 to a low level and -1 to high level. I just need the sign of the regression ...
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### A computational experiment about identities involving the sum of remainders function

Let $\sigma(m)$ the sum of divisors function and $$S(m)=\sum_{k=1}^m\text{m mod k}$$ the sum of remainders function, then it is know that for integers $m>1$ $$\sigma(m)+S(m)=S(m-1)+2m-1.$$ On the ...
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### Hypothesis testing: 2 groups with 2 subgroup each. Which test to use?

I recorded the pumping rate (measurement variable) of two types of worm: normal and mutant, with n=6 the number of worms per type. Then, I exposed these types of worms to a drug. BUT I used a ...
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### Method to study obvious properties

Most of the time studying mathematics we come across various properties like associative, commutative,...etc. These properties are obvious and sometimes I feel why at all they are given in the text. ...
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### how to logically modify a variable so that it accurately fits a given curve

I have 2 sets of experimental data. Each set has 2 variables (A,B) and response data (C). A1 100 100 100 100 100 100 100 B1 11.3 10.1 8.9 8.1 7.7 6.5 5.3 A1/B1 8.8 9.9 11.2 12.3 13.0 ...
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### What subfields use computers the most and least? (soft question)

What areas within research mathematics use computer programming (not including $\LaTeX$) the most and least? What programming languages are most commonly used in those fields?
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### How to calculate these particular values in this experiment?

I am running a statistics experiment where I need to calculate certain values. However, this is where I am having difficulty. Here is how the experiment works: Two Individuals Participate There is ...
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### Most wanted reproducible results in computational algebra

I am interested in suggestions for major computational results obtained with the help of mathematical software but not easily verifiable using computers. "Most wanted" could refer, for example, to ...
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### Conjecture $\int_0^1\ln\ln\left(\frac{1+x}{1-x}\right)\frac{\ln x}{1-x^2}\,dx\stackrel?=\frac{\pi^2}{24}\,\ln\left(\frac{A^{36}}{16\,\pi^3}\right)$

I did some numeric experiments with integrals involving double logarithms (because they received much interest both on this site and in published papers, sometimes under names of Malmsten—Vardi&...
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### For $n\geq 1$, $\sum_{k=0}^{\infty}\frac{(-1)^{k}(nk+1)^{3}}{(k+1)^6}$ in terms of $\zeta(3)$ and $\zeta(5)$ from a series calculator. Is possible?

I am doing experiments with this widget (Wolfram Alpha, a Series calculator, by HIghOPS) http://www.wolframalpha.com/widgets/view.jsp?id=86ceba9f35c96ebae137e44a36c7261a and take for Example. ...
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### Limit superior, limit inferior and a series involging $\sum_{k\nmid n}$k, where $1\leq k\leq n$

The purpose of this post is state assertions by the use of statements and hypothesis in an expository way and after I am asking for reasonable unconditionally results that you can provide us. Using ...
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### Conjectured closed form for $\operatorname{Li}_2\!\left(\sqrt{2-\sqrt3}\cdot e^{i\pi/12}\right)$

There are few known closed form for values of the dilogarithm at specific points. Sometimes only the real part or only the imaginary part of the value is known, or a relation between several different ...
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### Is this infinite product for zeta(2) trivial?

I have crafted an infinite product for zeta(2) shown here. Euler's prime product is the only one I'm aware of. In checking Math World, I don't see any products. Is that because they are trivial?
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### Fibonacci numbers and the nontrivial zeros of the Riemann zeta function

Is this a mathematical coincidence? For $n=1,\dots,7$: $$\left\lfloor \prod_{k=1}^n \arg\left(\rho_k\right)\right\rfloor = F_{n+1},$$ where $\arg$ is the complex argument, $\rho_n$ is the $n$th ...
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### Any correlation to Merten's function?

Here is a plot of partial sums of Liouville Lambda and Moebius Mu: Notice the differences (in green) are tantalizingly close to $-n^{\frac{1}{2}}$. Does this have any correlation to Merten's ...
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### Can these steps be converted to a mathematical expression using equations/graph theory/Calculus/Set theory/functions/?

Want to convert below algorithm into a mathematical model:- General points 1. Let there be a Connected Directed Graph. G = (V, E) V vertices or nodes E edges. This graph can be seen as a network ...
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### On a 50 question multiple choice exam with 5 choices per questions, What are the odds that I get 100% if I were to Guess every answer? [closed]

What would the odds be to get 100% on a multiple choice exam where I guessed the answer to all 50 of the multiple choice questions (5 choices per questions)? A 1 in how many chance?
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### If I flip a coin 1000 times in a row and it lands on heads all 1000 times, what is the probability that it's an unfair coin?

Consider a two-sided coin. If I flip it $1000$ times and it lands heads up for each flip, what is the probability that the coin is unfair, and how do we quantify that if it is unfair? Furthermore, ...
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### Estimate number of songs a radio station has [duplicate]

Imagine the following problem: You listen to a radio station and take notes how often was each song played. How can you estimate based on your notes (e.g. 30 songs played once, 2 played twice, one ...