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Different ways to factor
I'm interested to know some different methods to factor equations of the form $ax^2+bx+c$, where $a \ne 0$, other than pure guess and check.
Apr 15, 2026
Archive: News
news
Linearity of expectations - Why does it hold intuitively even when the r.v.s are correlated?
An experiment - say rolling a die, is performed a large number of times, $n$. Let $X$ and $Y$ be two random variables that summarize this experiment. Intu...
Apr 15, 2026
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Show that 1/x is NOT uniformly continuous
I have to prove that the function $f(x)=\frac{1}{x}$ on $(0,\infty)$ is not uniformly continuous (for the definition of uniform continuity see here). I ne...
Apr 15, 2026
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Proof of the Cayley Transform. Showing that $H=i(I-U)(I+U)^{-1}$ where $U=(I+iH)(I-iH)^{-1}$ for a Hermitian matrix $H$.
I am working on showing that a Hermitian matrix $H=i(I-U)(I+U)^{-1}$ where $U=(I+iH)(I-iH)^{-1}$. I have already shown that $I-iH$ is invertible and that ...
Apr 15, 2026
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Log rule restrictions
I've been working with logarithms of negative numbers and I've realized that most of the common log rules don't hold for $x<0$. While th...
Apr 15, 2026
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Divergence of separation vectors $ \nabla \cdot ( \frac{\hat{q} }{q^2})$
In Griffiths Intro Electrodynamics, it is shown that $$\nabla \cdot( \frac{\hat{r} }{r^2}) = 4 \pi \delta^3 (r) \tag{1}$$ Eqtn discussed in this post and ...
Apr 15, 2026
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Strict monoidal categories, the definition.
I found two definitions of 'strict monoidal category'. First definition: a strict monoidal category is a monoid in $\operatorname{Cat}$. Definit...
Apr 15, 2026
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What's the difference between marginal distribution and conditional probability distribution?
My understanding of both starts with this model: which has two random variables whose individual distributions are shown in red and blue, and their join d...
Apr 15, 2026
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Integrate cos (lnx) dx
Integrating by parts: I'm having a hard time choosing the $u$, $du$, $v$ and $dv$... I gave it a shot. $u = \ln x \implies du = 1/x \ dx$ $v= \ ?$ $d...
Apr 15, 2026
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Why is it useful to find the domain and range of a function graph
I know about domain and range but my professor has asked us why it may be useful to find the domain and range and I cant really think of a reason that wou...
Apr 15, 2026
