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Suppose $\sigma\in S_{n}$ is written in cycle notation, with its fixed points included. We say $\sigma$ is written in canonical cycle notation if each cyc...
I know that the probability of getting the 3 dice to be of the specific same number in a 3 dice roll is (1/6)*(1/6)*(1/6) = 1/216. What is the probability...
While reading about random walks, I started thinking about this and got a headache: Given a random process $\{X_n\}_{n\in \mathbb{Z}^+}$ with a real state...
I'm not sure if I'm doing this correctly, it's been a while since I've done any calculus. I drew the graph, and since I'm not con...
Problem: Prove that there are infinitely many primes of the type 5 mod 6. My professor did the problem and the proof was horribly long. Can someone show m...
I am merely looking for the result of the convolution of a function and a delta function. I know there is some sort of identity but I can't seem to f...
The symmetric derivative is always equal to the regular derivative when it exists, and still isn't defined for jump discontinuities. From what I can ...
Consider a concave kite $ABCD$ with $AB = AD$ and $BC = CD$ Want to show that angle $ABC$ = angle $ADC$ Is it sufficient to say that since the triangles h...
Okay, I do know that there are three ways of showing that it equals $-1\over 12$: 1) The Reimann zeta function calculated for $-1$(see picture) 2) The one...
Suppose a quadratic equation has been given where the a value (ax^2 + bx + c) is a positive and it has been said that the graph of the equation lies above...
