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4h
answered From the perspective of the multiverse theory, would maths “work the same” in every possible Universe?
5h
comment Factoring bivariate quadratics with real coefficients (for high school students).
Cool thanks. Good to know that the terminology is a bit screwy ahead of time :)
5h
comment Factoring bivariate quadratics with real coefficients (for high school students).
What do we call the expression $4ac-b^2$ or its negative? I suppose this isn't simply called "the discriminant"...
5h
comment Factoring bivariate quadratics with real coefficients (for high school students).
I understand half the answer. I think you replace dependence on $x$ with dependence on $z$ in such a way that the coefficient of the "mixed term" $yz$ in the resulting polynomial becomes $0$. The next step makes little sense to me. If you could elaborate on how it is obtained, that would be nice. Also, note that what I really want is a factorization of $P$, not a formula for the solutions to $P=0$. I'm sure its possible to reverse-engineer the factorization given the solutions, but it would be better to answer the question as-posed rather than answering a closely-related but distinct question.
6h
comment Factoring bivariate quadratics with real coefficients (for high school students).
@MichaelGaluza, all I mean by "systematic" is that there's a deterministic process you can follow that always gets you the right answer eventually. For example, Gaussian elimination counts as a "systematic procedure." It sounds like I'll have to read up about conic sections.
6h
comment Factoring bivariate quadratics with real coefficients (for high school students).
@MichaelGaluza, please elaborate. How do you propose to solve equations obtained in this way systematically, and where did you learn this technique?
7h
comment Factoring bivariate quadratics with real coefficients (for high school students).
@MichaelGaluza, that's just guess-and-check though. The idea is to be systematic.
8h
comment Factoring bivariate quadratics with real coefficients (for high school students).
@MichaelGaluza, where does one learn this stuff? I'm not sure what to search for, or which books to look in, or which articles to read. Note also that $P$ isn't an equation, its a polynomial.
8h
revised Factoring bivariate quadratics with real coefficients (for high school students).
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8h
asked Factoring bivariate quadratics with real coefficients (for high school students).
2d
comment Is $i^i$a real number or not?
Can I somehow downvote the aforementioned introductory calculus course?
2d
revised How to conceptualize “dividing out” a number (e.g. in permutations, Bayes' Theorem)?
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Jul
31
revised How to conceptualize “dividing out” a number (e.g. in permutations, Bayes' Theorem)?
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Jul
31
answered How to conceptualize “dividing out” a number (e.g. in permutations, Bayes' Theorem)?
Jul
31
comment How to conceptualize “dividing out” a number (e.g. in permutations, Bayes' Theorem)?
Perhaps this can be done with the orbit-stabilizer theorem.
Jul
31
comment Is there a deep reason why replacing $\cos(x)$ with $e^{ix}$ and taking the real part often makes a contour integral work out?
@DanielMcLaury, perhaps that is the question you should be asking (as explicitly as possible.)
Jul
28
revised Is $1 : 7 = 1 / 8$ or is it $1/7$?
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Jul
28
comment Is there accepted notation for the pushforward measure that doesn't mention $\mathbf{P}$?
@Potato, I've standardized it a bit, in light of Nate's comments.
Jul
28
revised Is there accepted notation for the pushforward measure that doesn't mention $\mathbf{P}$?
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Jul
28
comment Is there accepted notation for the pushforward measure that doesn't mention $\mathbf{P}$?
@NateEldredge, well, thanks for your honesty.