# Tagged Questions

The process of studying mathematics without formal instruction. _Don't_ use this tag just because you were self-studying when you came across the mathematical question you're asking; it is only for when the fact that you're self-studying is what your question is _about_.

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### Learning higher-mathematics on your own

I was hoping someone had an opinion on how to learn higher-mathematics (specific fields that could be of use to me) outside of a classroom setting. I graduated with an M.S. in Computer science about ...
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### Derivation of an integration

Can someone explain to me the difference between the results of $A$ and $B$, where $$A=\frac{d}{dc} \int_{-\infty}^c xf(x) dx$$ $$B= \frac{d}{dc} \int_c^{+\infty} xf(x) dx$$ You can image $f(x)$ ...
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### Concrete examples and computations in differential geometry

I've been studying differential geometry by myself for some time now. I studied a fair amount of the basic general theory and gone through a lot of the exercises from several textbooks. Lately I ...
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### Self-learning SAT

I want to take SAT, but I don't know which textbook is good to learn on Mathematics II. At least more than 1 textbook, or just textbook for each curriculum. I really need suggestion.
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### Efficient way to rigorously learn AI prerequisites

Question: My formal goal is to be able to rigorously understand the mathematical basis for modern statistical learning methods (ML, deep learning). I am told by math people that this involves: linear ...
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### Is there a way to maximize this probability by taking the derivative of the cumulative normal distribution function?

I'm self-studying Brownian motion and encountered the following problem. I understand the author's solution, and it is clear why maximizing the right-hand side of the inequality provides such $t$ ...
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### Derivative of a determinant whose entries are functions

Happy New Year, everyone! I do not understand a remark in Adams' Calculus (page 628 $7^{th}$ edition). This remark is about the derivative of a determinant whose entries are functions as quoted below. ...
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### How to decide whether PDE is Homogeneous or non-homogeneous.

I am studying second order PDE. And I have seen homogeneous and non-homogeneous PDE. But I cannot decide which one is homogeneous or non-homogeneous. For examples; (1) $(D^3-3D^2D'+4D'^3)u=0$ ...
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### Complex form of Fourier Series

So, the last part of the university syllabus in the chapter of Fourier Series is: ...
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### Expected value of division

Let $X,Y$ and $Z$ be three indenependent real valued random variables. Al with finite second momennt and all with mean $0$ and variance $1$. Define $$W= \frac{X+YZ}{\sqrt{1+Z^2}}$$ Show that ...
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### Cholesky decomposition: No uniqueness when A is positive semidefinite

I can get as corolary of the following theorem, that Cholesky decomposition is not unique for positive semidefinite matrices? Thank's in advance If $A\in \mathbb{M}_{n\times n}$ is a positive ...
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### Meaning of $E(u|v) = p\,v$

I am having problem understanding the intuition behind this: if $u$ and $v$ are jointly normal (with zero mean), then $E(u|v) = p\,v$, for some parameter $p$ ?
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### Poisson and conditional distribution

Given a source that emits photons let be $X$ the number of photons emitted in $s$ seconds. Let be $p$ the probability that photons reach a detector and let be $Y$ the number of photos that reached the ...