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Online Video Lectures for Graduate Level Mathematics?

I am wondering if there is a nice compilation of good video lectures in graduate level mathematics? I mean a website, or a forum, or maybe something like course-era (which is mostly undergraduate ...
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Proof by induction

I've proved the base case where $n=1$ and made the assumption that $n=k$ is true, but I'm stuck on the $n=k+1$ part. I just cannot seem to get the algebra to work in my favor. Here is the original:...
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B of Eilenberg-MacLane space

Let $K(m, \mathbb{Z})$ be the Eilenberg-MacLane space. I've read that $BK(m, \mathbb{Z}) = K(m+1, \mathbb{Z})$, but I'm trying to understand this. I'm familiar with the bar construction $BG$ for a ...
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Checkers Board Problem

Here we consider a checkerboard expanded to size 12 × 12 instead of the ordinary 8 × 8 checkerboard. a) How many squares on this board contain more than a third of the total number of dark small ...
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Something is wrong with this argument (Lorentz and Rosenthal-Woo sequence spaces)

Fix once and for all $1<p<\infty$. Throughout, $w=(w_n)_{n=1}^\infty$ will denote a sequence of positive real weights satisfying 1=w_1\geq w_2\geq w_3\geq\cdots>0\;\;\;\text{ ...
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Ito's Formula applied to a weird equation…

I was just wondering if someone could explain how to solve this problem. I have an equation $X(t, S_{t}) = s\partial_{s}u - u$ where we have $u(t,S_{t})$. Now, according to the paper, evaluating $dX$ ...
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Feasible Region of QCQP and Semidefinite Programs

I am trying to visualize the feasible region of a Quadratically Constrained Quadratic Program (QCQP) which is expected to be non convex (actually is a set of ellipses in $\mathbb{R}^2$) and the ...
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Limit of a probability vector.

There will be a 200 rep bounty for this question. Let $U_1,...,Un$ be iid uniform on (0,1). Set $L_n=\max_{i\leq n} U_i$. Also $S(n)= \inf\{i\leq n| U_i = L_n \}$ the time were the highest value is ...