Questions tagged [problem-solving]

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How this second ODE is solved by Bessel’s function

Any help how this equation ( Eq. B3 in paper ) : $$\phi’’(\eta) + \frac{6(1+\omega)}{1+3\omega)} \frac{1}{\eta} \phi’(\eta) + \omega k^2 \phi(\eta) =0$$ Has been solved by Bessel’s function with a ...
• 99
232 views

Where can I access American Mathematical Monthly problems given an index?

I don't know if this is the appropriate website to ask, so I understand if this post gets closed. I want to explore (and maybe solve) some of the currently-unsolved problems submitted by readers on ...
• 151
1 vote
246 views

Method to solve system of exponential sums of the form $a^x+b^x=c$ given more equations than variables [closed]

Cross post with mse For example, let's say I have the following equations. \begin{gather*} a^{x-1}+b^{x-1}=337 \\ a^{x}+b^{x}=1267 \\ a^{x+1}+b^{x+1}=4825 \\ a^{x+2}+b^{x+2}=18751. \end{gather*} What ...
• 13
1 vote
150 views

Is it possible to find UNSATisfiable solutions to a SAT problem with a SAT problem?

I'm working with several problems, which can have special unsatisfiable configurations. For example, consider the simple function $f(x,y)=x+y+2$ with $n$-bit unsigned inputs and $(n+2)$-bit unsigned ...
275 views

How does one build and refine strong technical skills relevant to research?

I am an early career researcher working in an area of "hard" analysis but this is a fairly broad question. My technical skills are likely below par and my greatest hindrance to my research ...
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• 2,071
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Why are there so few zero-dimensional polynomial system solvers and is this because there is no real market for them?

My questions involve the quotes below from wikipedia regarding solving polynomial systems, which given the size of the market for Big Data & Predictive Analysis applications I find puzzling: "...
• 149
1 vote
211 views

Problem on the digits of $n!$

let $m$ be a natural number, does always exist a $N\in \mathbb{N}$ such that $m$ or more "$0$" digits (excluding the terminal ones) appears amongs the decimal digits of $n!$ if $n\ge N$?
• 111
1k views

Expected value of swaps

Suppose you have a list of non negative numbers of size N. Now you calculate the maximum element in the list by scanning the list linearly and constantly updating a variable which has initial value of ...
• 123
514 views

How to simplify conditional probability of union of several events

I have an output binary scalar, $y∈B=\{0,1\}$, and an input binary vector $x=[x_1, x_2,…x_M]$ where $x_i∈B=\{0,1\}$. I know that the output $P(y)=1$ depends entirely on the input x. Thus, I want to ...
183 views

A challenging non homogenous fractional inequality

I have posted this question on Stackexchange but it has received no answer so far. It is a challenging generalization of several difficult inequalities, where none of the usual methods used in ...
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860 views

Topological Problems Solved by Lattice Duality

It is well known the success of lattice dualities (as Pontryagin duality for abelian groups, Stone duality for Boolean algebras and Priestley duality for distributive lattices) to solve algebraic ...
2k views

When did you "meet Polya"? [closed]

I guess most of us didn't meet Polya in person (this is the answer to the title)! Perhaps, it is much easier to guess that most of us have met one of his writings (or alike) on problem solving, and ...
3k views

Is “problem solving” a subject to be taught?

I am witnessing a new curriculum change in my country (Iran). It includes the change of all the mathematics textbooks at all grades. The peoples involved has sent me the textbook for seven graders (13 ...
1 vote
275 views

Reducing system of polynomials with symbolic factors

Getting nowhere with maple using its triangularize and groebner decompositions for even moderate size systems with any symbolic factors. Any suggestions on how better to approach this would be ...
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number of non-negative integer solutions for a set of equations [closed]

How to find the exact number of non-negative integer solutions of the following set of equations : $$x_1 + x_2 + x_3 + x_4 + x_5 + x_6=6$$ $$2x_1 + x_2 + x_3 = 4$$ $$x_2 + 2x_4 + x_5 = 4$$  x_3 +...
• 209
241 views

Problem solving equation of type x=a*b^x [closed]

I have the equation x = a*b^x and want to solve it for x. But every online solver I tried says that it is not possible. But when I choose a==8 and b==0.5 there is a solution for x==2 Is it not ...
• 3
1 vote
238 views

First moment of a function of a normally distributed random variable

I'm trying to find the first moment of the following function: $f(x) = \frac{(-ax+\sqrt{1-a^2})(-bx+\sqrt{1-b^2})}{\sqrt{x^2+1}}H(-ax+\sqrt{1-a^2})H(-bx+\sqrt{1-b^2})$ where $H(x)$ denotes the ...
184 views

Transformation problem involving 2 random variables

Any help in this problem? Suppose U and V are independent random variables with density f(u) and g(v) respectively. The domain of U is the interval (0, 1) and the domain of V is v > 0. After the ...
• 103
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Help me find good math questions for my students [closed]

I am a teacher at 西铁一中。 I teach mathematics in English for students going abroad. Now this is my problem, there are few mathematics books written in English that are at the level of high school, ...
3k views

Truncated Exponential Series Modulo $p$: Deeper meaning for a Putnam Question.

Apparently B6 of the Putnam this year asked: Suppose $p$ is an odd prime. Prove that for $n\in \{0,1,2...p-1\}$, at least $\frac{p+1}{2}$ of the numbers $\sum^{p-1}_{k=0} k! n^{k}$ are not divisble ...
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Contest problems with connections to deeper mathematics

I already posted this on math.stackexchange, but I'm also posting it here because I think that it might get more and better answers here! Hope this is okay. We all know that problems from, for ...