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 Oct 29 accepted Prove that a random walk on $\mathbb{Z}_+\cup \{0\}$ is transient Oct 29 accepted Prove that if the Hessian of $f$ is positive definite at $a$, then the function attains a minimum at $a$ Oct 29 accepted Why are call options necessary? Oct 28 comment Motivation on how does complex analysis come to play in number theory? I think a lot of the connection comes from the fact that a number of very important infinite series which encode 'statistical' information about the arithmetic structure of rings can be analytically continued to open sets in the complex plane. Examples: zeta functions, l-functions, etc. Oct 26 comment Show that a real-valued function with non-empty subdifferential is convex if $\partial f(x)$ is non empty for all $x\in X$, then $\forall x\in X$ $\exists g\in\mathbb{R}^n$ s.t. $\forall z\in X$, $f(z) \geq f(x) + g^T(z-x)$. Play around with this expression and the definition of a convex function. Oct 26 comment Sample Geometric Mean as an estimator for a Gamma Distribution so you need to find the the distribution of $X_i^{1/n}$ correct? and then evaluate the associated expected value integral, it should be fairly straight forward. Oct 26 comment Sample Geometric Mean as an estimator for a Gamma Distribution who cares, life is too short to do statistics, go outside, have fun, enjoy life Oct 26 comment Is the set of functions $f$ in $C[-1,1]$ with $f(-1)=f(1)$ a subspace of $C[-1,1]$? what do you mean 'one value in the domain'? The domain is $[-1,1]$. Oct 26 comment Terminology for function that has only one peak unimodal??????? Oct 26 revised Probability of randomly selecting a random real number added 16 characters in body Oct 26 answered Probability of randomly selecting a random real number Oct 25 comment Maximizing Expected Profit (in the Abstract) you need to assume that $c$ and $f$ are differentiable with respect to $\alpha$, and also some other assumptions to pass the derivative under the integral sign, but other than that it looks ok to me. Although you may have some problems actually solving for $\alpha$ in practice. Oct 25 comment Mobius function vanishes over sum of totient numbers I don't see how this could be true unless there are only finitely many non-zero terms in the series, but I don't think that's the case here. Oct 25 comment Find infinitely many n such that $\sigma (n) \le \sigma (n+1)$. Think about primes. In fact, that inequality can be made strict. Oct 24 comment What is $X$? ${}{}$ $X$ is a transcendental over the ring that your polynomial takes its coefficients from, simple as that. This insures that two polynomials are unique exactly when they don't have the same coefficients. Oct 23 comment Simplest vector parametric expression? show your work. Oct 23 comment General formula for the exponential of a block matrix I doubt you can say much about $A,B,C,D$, but if $M$ is symmetric then it has an eigen-decomp as $M=P^TDP$ and so I think you have $e^M=P^Te^DP$. I don't know if that helps any. $D$ contains the (possibly absolute value or squared can't remember) eigenvalues of $M$, but unless the top right or bottom left block is the zero block, there is no relationship known between the eigenvalues of the blocks and the eigenvalues of $M$. Oct 23 comment General formula for the exponential of a block matrix the case where $M$ is a real symmetric matrix, or where the sub-matrices are? Oct 22 comment Questions about the quotient ring $(\mathbb{Z}/2\mathbb{Z})[x]/\langle x^2+x+1\rangle$ your quotient ring is $\mathbb{F}_4$ I think since $x^2+x+1$ has no roots over $\mathbb{Z}_2$. As for why $x^2=x+1$ this is because a quotient ring is basically a ring formed by taking your original ring and breaking it up into equivalence classes with the ideal you're quotienting out by being the $0$ class. Thus $x^2+x+1=0$. As for intuition you're unlikely to find much in isolation, but as you study more algebra and see how this piece fits into larger and more general frameworks your intuition about it will increase. Oct 21 comment Property of positive definite matrix $||Px||_2=\sqrt{x^TP^TPx}$, then use the eigen-decomposition of $P$ and simplify.