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network profile
| bio | website | |
|---|---|---|
| location | Stanford, CA | |
| age | 22 | |
| visits | member for | 2 years, 5 months |
| seen | May 6 at 6:13 | |
| stats | profile views | 400 |
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May 30 |
comment |
Obtaining irrational probabilities from fair coins? I'm not looking forward to working out the exact probability, but I definitely believe that it's irrational! |
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May 30 |
accepted | Obtaining irrational probabilities from fair coins? |
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May 30 |
comment |
Obtaining irrational probabilities from fair coins? Thanks guys! It looks like the general idea is to set up an infinite sample space (this can't be done if we declare the maximum number of flips ahead of time, but it can be done so that the procedure terminates with probability 1). |
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May 30 |
revised |
Obtaining irrational probabilities from fair coins? added 112 characters in body |
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May 30 |
accepted | Flip a coin until a head comes up. Why is “infinitely many tails” an event we need to consider? |
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May 30 |
accepted | Qualms about the axioms of probability |
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May 30 |
asked | Obtaining irrational probabilities from fair coins? |
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May 25 |
accepted | Representations of a cyclic group of order p over a field of characteristic p? |
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May 25 |
comment |
Qualms about the axioms of probability When I saw, for example, the "group axioms", I didn't really think of them as "axioms", but more as the definition of a group. I guess in this case, it makes sense to think of the "probability axioms" more as the definition of a probability. |
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May 24 |
comment |
Qualms about the axioms of probability Pete, that's a great question. Maybe "discrete-ly"? I'm taking an intro probability course intended for computer science undergrads, and I got the axioms from Ross's text, "A First Course in Probability". |
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May 24 |
asked | Qualms about the axioms of probability |
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May 24 |
asked | Flip a coin until a head comes up. Why is “infinitely many tails” an event we need to consider? |
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Apr 20 |
comment |
Representations of a cyclic group of order p over a field of characteristic p? This is really cool! I think I see how to make this work when $K = \mathbb{F}_p$, but what if $K$ is not a finite field (so that $V$ contains infinitely many vectors)? |
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Apr 19 |
asked | Representations of a cyclic group of order p over a field of characteristic p? |
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Mar 2 |
accepted | Why can we think of the second fundamental form as a Hessian matrix? |
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Feb 28 |
answered | Why can we think of the second fundamental form as a Hessian matrix? |
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Feb 28 |
comment |
Why can we think of the second fundamental form as a Hessian matrix? Oh thanks, that makes sense: when we have a parametrization of the form $f(u, v) = (u, v, h(u, v))$, the Hessian evaluated at h(0, 0) is precisely the second fundamental form at f(0, 0). I'm not sure how to generalize this to an arbitrary point of an arbitrary parametrization, but that's my own fault for not knowing the Implicit Function Theorem... |
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Feb 27 |
comment |
Why can we think of the second fundamental form as a Hessian matrix? I think the interpretation is that their matrices are the same, i.e. we think of the matrix element $(h_{ij})$ of the fundamental form as the second derivative $\partial^2 h / \partial u_i \partial u_j$ of some function $h$. Also, I'm not sure if there are different ways to define the second fundamental form, but in Kuhnel's text, it's defined as a bilinear form on the tangent space: $II(X, Y) = \langle LX, Y\rangle$ where $L: T_pM \rightarrow T_pM$ is the shape operator. |
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Feb 27 |
asked | Why can we think of the second fundamental form as a Hessian matrix? |
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Feb 26 |
comment |
Smooth curve with no Frenet frame Are you sure that this can be done with a smooth curve? Also, I think it might be important to mention that $X_1, \ldots, X_n$ are smooth vector fields along $\gamma$... |
