# All Questions

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### What is the fewest number of points you must delete from $\mathbb{R}^3$ to make it not simply connected?

This question concerns a set-theoretic aspect that I found interesting in the recent question asked by user Nick R., namely, Is $\mathbb{R}^3\setminus\mathbb{Q}^3$ simply connected? He had asked ...
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### Closed form answer to a naive integral

Let a and b be positive real numbers. How to find a closed form answer to the integral $$\int_0^t \left(-a t + \big(1+ \dfrac{2bt}{3}\big)^{-3/2}\right)^{5/3} dt$$ If it is not possible to find a ...
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### Decomposition of orthogonal matrix into 2 orthogonal matrices [on hold]

Is there anyway to find a decomposition of orthogonal matrix $A$ into 2 orthogonal matrices $P$ and $Q$ such that $A = PQ^T$?
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### Optimisation of betting strategy

Consider integers $r \geq 1$ and $k \geq 1$ and consider the following game: We start with $r$ tokens and at each round we choose $i \in \{1,...,r\}$ tokens to bet (if we have $N<r$ tokens we ...
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### cohomology of iterated loop space on spheres

In the book The homology of iterated loop spaces, the homology Hopf algebra (1) $$H_*(\Omega^n \Sigma^n X;\mathbb{Z}_p)$$ for primes $p\geq 2$ is obtained on p. 226, Thm. 3.2. In particular, the ...
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### Interpolating Product of two Polynomials

Consider we have two non-constant polynomials $A(x)$ and $B(x)$. We define the polynomials over field $\mathbb{Z}_p$, for a large prime number $p$. We define Polynomial $A(x)$ as follows: ...
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I tried this post on StackExchange with no luck. Hopefully the experts at MathOverflow can help. In algebraic topology there are two canonical "advanced" textbooks that go quite far beyond the usual ...
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### Adjunctions of uniformly locally connected spaces

A space $X$ is uniformly locally connected (ULC) if there exists an open neighbourhood $U$ of the diagonal $\vartriangle_X$ in $X \times X$ and a homotopy $H: U \times I \to X$ between $\pi_1|U$ and ...
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### Lower bounding the multiplicative order of 2 modulo p

For $p$ prime denote by $\mathsf{ord}_p(2)$ the multiplicative order of $2$ modulo $p$. Does there exist $N > 0$ such that, for ALL primes $p$, $\mathsf{ord}_p(2)$ is at least $\frac{(p-1)}{N}$? ...
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### Computer algebra system for Weyl algebra computations

Does anyone have a suggestion for the best computer program to perform calculations in the 2nd Weyl algebra?
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