# All Questions

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### What is the definition of a product topology?

I am new to advanced mathematics and I recently started reading a book on topology. I am struggling to understand what it is saying in this paragraph. This is what it says: Let $E_i$ ...
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### What book or (math)course do you recommend? [migrated]

Can anyone recommend me a book or an online math course, that can help me to overcome my fear in math? I'm sick and tired of being afraid of numbers. Thanks in advance!
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### Given a field F and an element c in F, prove a polynomial p(x) is irreducible in F iff p(x+c) is irreducible [on hold]

Given a field F and an element c in F, prove a polynomial p(x) is irreducible in F iff p(x+c) is irreducible. It's a relatively simple question but I'm having a hard time coming up with a good way to ...
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### Proving $d(R(F))=R'(F(X)) \odot dF$

I came across the result from the title while reading this article on Matrix Calculus. The precise formulation is that "R is an “elementwise” function $R : R^{m×n} → R^{m×n}$. (e.g. exp or sin.) The ...
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### integer local ring complete of dim 1 noetherien

If A is complete ,local, noetherien ring of krull dimension 1 and A is domain and A contain $\overline{Q}$ and the A/m is $\overline{Q}$ and m is the maximal ideal of A. I want to ask if A is regular ...
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### equality that should be a consequence of plancherel formula

I am stuck with this line in my reading of a book: By the Plancherel formula we have: $\int \frac{|u(x+y)-u(x)|^2}{|y|^{2s+d}}dx = \int \frac{|e^{i(y|\xi)} -1|^2}{|y|^{2s+d}} |\hat{u}(\xi)|^2 d\xi$ ...
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### Minimum number of variables on which a multivariate polynomial depends?

Let $p:F_2^n\rightarrow F_2$ be a multivariate polynomial, let's say of degree 3. (Both the degree and the order of the field could probably be replaced by other constants without affecting this ...