Tagged Questions

Mathematical intuition is the instinctive impression regarding mathematical ideas which originate naturally without regard to formal mathematical proofs. It may or may not stem from a cognitive rational process.

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I need an intuitive explanation of eigenvalues and eigenvectors

Been browsing around here for quite a while, and finally took the plunge and signed up. I've started my mathematics major, and am taking a course in Linear Algebra. While I seem to be doing rather ...
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Dirichlet conditions - Explanation of the proof of theorem $4$

I have a few difficulties understanding the first part (Dirichlet conditions) of the proof of theorem $4$ in the book Strauss W.A. Partial differential equations - an introduction (Wiley, $2008$, $2$...
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Bayes' rule application proving my intuition wrong

This is the example I am looking at. Question: Suppose a family has $2$ children and one is a boy, and that the probability of having a child of either sex is equal and independent across ...
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Intuitive explanation of $L^2$-norm

I have to play a lot with the $L^2$-norm defined as $\|w\|=\sqrt{\int_a^b <f,f>}$. However, I don't understand the interpretation of that norm. We know that the euclidean norm measure the length ...
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How do curves consist of points?

According to Euclid, a point is something which has no dimensions. And we know that all curves of any type consists of points. Now this thing bothers me because if a point has no dimensions, i.e. in ...
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Is counting roots with multiplicites at all a geometric concept?

It is well known that a polynomial of degree $n$ admits $n$ roots when the field is algebraically closed. However, this comes with a caveat, in particular that the roots be counted with multiplicity. ...
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Propositional Logic - Can you Derive $C \to A$ from $A$ alone, given the introduction rule?

Apparently, according to the Conditional Introduction rule, this is valid: Prove $C \to A$ Source: http://kpaprzycka.wdfiles.com/local--files/logic/W12R Page 5 So before this, the way I viewed ...
How many complexes modulo a prime $p$ are of multiplicative order $p^2 - 1$?
If $i = \sqrt{(-1)} \bmod p$, $p$ prime, does not exist, then we can form numbers of the form $a+b i \bmod p$ with multiplicative order $p^2 - 1$. How often do these numbers occur modulo $p$? In ...
How quickly can we detect if $\sqrt{(-1)}$ exists modulo a prime $p$?
How quickly can we detect if $\sqrt{(-1)}$ exists modulo a prime $p$? In other words, how quickly can we determine if a natural, $n$ exists where $n^2 \equiv -1 \bmod p$? NOTE This $n$ is ...