Definitions of direct product and of direct sum
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Definitions of direct product and of direct sum

I was wondering if there are some general definitions for direct product and for direct sum, for example in category theory or in set theory, so that the ...

Published: Aug 22, 2026

Can I factorize $x^4 + 27x$ without using the factor theorem?
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Can I factorize $x^4 + 27x$ without using the factor theorem?

I am doing some self-assigned homework questions. One question asks me to factorize $x^4 + 27x$. I used the factor theorem to solve it. I observed that $f...

Published: Aug 22, 2026

Find General Solution of First Order DE.
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Find General Solution of First Order DE.

Find general solution of $$y'+\frac{2y}{x}=\frac{3}{x^2}$$ and find solution for which $$y(2)=-1$$ I know $$xy'+\frac{r(x)y}{x}=3r(x)x$$ $$(ry&#...

Published: Aug 22, 2026

Endomorphisms of a finite dimensional vector space
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Endomorphisms of a finite dimensional vector space

From Humphreys' Introduction to Lie Algebras and Representation Theory: If $V$ is a finite dimensional vector space over $F$, denote by $\text{End }V...

Published: Aug 22, 2026

Determine the value of N
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Determine the value of N

I'm a complete n00b at math, but I'm wondering how one would go about determining the value of n in the following comparison. n * 1.5 + 12.5 = 1...

Published: Aug 22, 2026

Find the distribution of linear combination of independent random variables
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Find the distribution of linear combination of independent random variables

Given independent and identically distributed random variables $X_1, X_2, \dots, X_n$, each of them has the same p.d.f $f(x) = Pr(X = x)$ on support $(a, ...

Published: Aug 22, 2026

How many algebras are there of finite-sized $\Omega$?
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How many algebras are there of finite-sized $\Omega$?

An algebra of $\Omega$ is a family that contains $\Omega,$ is closed under complement and finite union. If $\Omega=\{\}$, there can only be 1 algebra asso...

Published: Aug 22, 2026

$y = 2+\frac{ 1}{x^2}$ stretched vertically by a factor or $3$.
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$y = 2+\frac{ 1}{x^2}$ stretched vertically by a factor or $3$.

Alright folks, having a little problem with this calculus question. anyone help? The factor and direction of the given function is to be stretched or comp...

Published: Aug 22, 2026

User Matthew H. - Mathematics Stack Exchange
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User Matthew H. - Mathematics Stack Exchange

Q&A for people studying math at any level and professionals in related fields

Published: Aug 22, 2026

Compact sets are closed?
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Compact sets are closed?

I feel really ignorant in asking this question but I am really just don't understand how a compact set can be considered closed. By definition of a c...

Published: Aug 22, 2026

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