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1500 questions
57
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3 answers

How to think of the group ring as a Hopf algebra?

Given a finite group $G$ and a field $K$, one can form the group ring $K[G]$ as the free vector space on $G$ with the obvious multiplication. This is very useful when studying the representation theory of $G$ over $K$, as for instance if…
Will
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Probability that a quadratic equation has real roots

Problem The premise is almost the same as in this question. I'll restate for convenience. Let $A$, $B$, $C$ be independent random variables uniformly distributed between $(-1,+1)$. What is the probability that the polynomial $Ax^2+Bx+C$ has real…
Hungry Blue Dev
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6 answers

Does $\zeta(3)$ have a connection with $\pi$?

The problem Can be $\zeta(3)$ written as $\alpha\pi^\beta$, where ($\alpha,\beta \in \mathbb{C}$), $\beta \ne 0$ and $\alpha$ doesn't depend of $\pi$ (like $\sqrt2$, for example)? Details Several $\zeta$ values are connected with $\pi$,…
GarouDan
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2 answers

Why doesn't Cantor's diagonal argument also apply to natural numbers?

In my understanding of Cantor's diagonal argument, we start by representing each of a set of real numbers as an infinite bit string. My question is: why can't we begin by representing each natural number as an infinite bit string? So that 0 =…
usul
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2 answers

Order of general- and special linear groups over finite fields.

Let $\mathbb{F}_3$ be the field with three elements. Let $n\geq 1$. How many elements do the following groups have? $\text{GL}_n(\mathbb{F}_3)$ $\text{SL}_n(\mathbb{F}_3)$ Here GL is the general linear group, the group of invertible n×n matrices,…
user9656
57
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14 answers

Is there a math expression equivalent to the conditional ternary operator?

Is there a math equivalent of the ternary conditional operator as used in programming? a = b + (c > 0 ? 1 : 2) The above means that if $c$ is greater than $0$ then $a = b + 1$, otherwise $a = b + 2$.
dataphile
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57
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1 answer

How does TREE(3) grow to get so big? (Laymen explanation)

I am not a mathematician but I am interested in big numbers. I find them to be really interesting, almost god-like. I am watching a series of videos from David Metzler on YouTube. I have a basic understanding of some fast growing functions. David…
Josh Kerr
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10 answers

A really complicated calculus book

I've been studying math as a hobby, just for fun for years, and I had my goal to understand nearly every good undergraduate textbook and I think, I finally reached it. So now I need an another goal. I've just found a very nice book /S. Ramanan –…
Thomas
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3 answers

What is the formula for pi used in the Python decimal library?

(Don't be alarmed by the title; this is a question about mathematics, not programming.) In the documentation for the decimal module in the Python Standard Library, an example is given for computing the digits of $\pi$ to a given precision: def…
ShreevatsaR
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57
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2 answers

Books about the Riemann Hypothesis

I hope this question is appropriate for this forum. I am compiling a list of all books about the Riemann Hypothesis and Riemann's Zeta Function. The following are excluded: Books by mathematical cranks (especially books by amateurs who claim to…
Marko Amnell
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Evaluate $\int_0^1\left(\frac{1}{\ln x} + \frac{1}{1-x}\right)^2 \mathrm dx$

Evaluate $$\int_0^1\left(\frac{1}{\ln x} + \frac{1}{1-x}\right)^2 \mathrm dx$$
user 1591719
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57
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6 answers

What is the difference between homotopy and homeomorphism?

What is the difference between homotopy and homeomorphism? Let X and Y be two spaces, Supposed X and Y are homotopy equivalent and have the same dimension, can it be proved that they are homeomorphic? Otherwise, is there any counterexample?…
liufu
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2 answers

Is it possible to prove a mathematical statement by proving that a proof exists?

I'm sure there are easy ways of proving things using, well... any other method besides this! But still, I'm curious to know whether it would be acceptable/if it has been done before?
chubbycantorset
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9 answers

A linear operator commuting with all such operators is a scalar multiple of the identity.

The question is from Axler's "Linear Algebra Done Right", which I'm using for self-study. We are given a linear operator $T$ over a finite dimensional vector space $V$. We have to show that $T$ is a scalar multiple of the identity iff $\forall S \in…
abeln
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18 answers

Is it possible to determine if you were on a Möbius strip?

I understand that if you were to walk on the surface of a Möbius strip you would have the same perspective as if you walked on the outer surface of a cylinder. However, would it be possible for someone to determine whether they were on a Möbius…
Steven Wallace
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