I have been looking for information about Frattini subgroup of a finite group. Almost all the books dealing with this topic discuss this subgroup for p-groups. I am actually willing to discuss the following questions : Let G be a finite group, is the Frattini subgroup of G abelian ? Why is the order of […]

Math people: This question is a generalization of the one I posed at https://math.stackexchange.com/questions/348296/find-area-bounded-by-two-chords-and-an-arc-in-a-disc . Below is an image of a unit circle with center $O$. $\theta_1, \theta_2 \in (0, \pi)$ and $\gamma \in (0, \min(\theta_1,\theta_2))$. $\theta_1 = \angle ROS$, $\theta_2 = \angle POQ$, and $\gamma = \angle ROQ$. I want to find the area […]

can anyone help me to inform the name of any book where I can get the following theorem, or give some detailed hint to solve this one: Let $X$ and $Y$ be two random variables, if the moment generating functions of $X$ and $Y$ are equal then the probability distributions of $X$ and $Y$ will […]

Lets say that $X\sim p$, where $p:x\mapsto p(x)$ is either a pmf or a pdf. Does the following random variable possess any unique properties: $$Y:=p(X)$$ It seems like $E[Y]=\int f^2(x)dx$ is similar to the Entropy of $Y$, which is: $$ H(Y):=E[-\log(Y)]$$ It seems like we can always make this transformation due to the way random […]

It is easy to come up with objects that do not satisfy the Peano axioms. For example, let $\Bbb{S} = \Bbb N \cup \{Z\}$, and $SZ = S0$. Then this clearly violates the axiom that says that $Sa=Sb\to a = b$, unless we agree that $Z=0$, in which case what we have is exactly the […]

I’m studying functional analysis and I was wondering if there are some exercise books (that is, books with solved problems and exercises) The books I’m searching for should be: full of hard, non-obvious, non-common, and thought-provoking problems; rich of complete, step by step, rigorous, and enlightening solutions;

I have been scouring the internet for answers for some time and would therefore appreciate a reference or a proof since i’m not able to produce one myself. Let $(\mathcal{X},d)$ be a metric space, and let $$ BL(\mathcal{X})=\{f:\mathcal{X}\to \mathbb{R}\, \, | \, \, f \text{ is Lipschitz and bounded}\} $$ denote the bounded real-valued Lipschitz […]

I’m looking for a Theorem that I can cite which proves that Newton’s method for finding a zero of a function converges globally and quadratically if the function $f : [a, b] \rightarrow \mathbb{R}$ is increasing and convex and has a zero $r \in [a,b]$ with $f(r) = 0$ and $f'(r) \neq 0$, with starting […]

For a compact set $K\subset\mathbb{C}$ the analytic capacity is defined as $$\gamma(K)=\sup\{|f^\prime(\infty)|:f\in M_K\}$$ where $M_K$ is the set of bounded holomorphic functions on $\mathbb{C}\backslash K$ with $\|f\|_\infty\le 1$ and $f(\infty)=0$. I have two questions. What is the intuition behind this definition? What does $f^\prime(\infty)$ mean? It doesn’t seem to be $\lim_{z\rightarrow\infty}f^\prime(z)$ so I’m confused. It […]

I’m a third year student who is mostly interested in commutative algebra. In Algebraic Geometry a lot of example come from Complex Analysis. So to deepen my understanding/intuition, I’ll finally attend an Introduction to Complex Analysis lecture. (Which is actually made for second year students, but let’s say I’ve not been a big fan of […]

Intereting Posts

Radical ideal of $(x,y^2)$
Proving $A: l_2 \to l_2$ is a bounded operator
Indefinite Integral of $\sqrt{\sin x}$
Proving that for each prime number $p$, the number $\sqrt{p}$ is irrational
Independent, Identically Distributed Random Variables
Finitely generated free group is a cogroup object in the category of groups
How is it, that $\sqrt{x^2}$ is not $ x$, but $|x|$?
Prove that 10101…10101 is NOT a prime.
Calculate sums of inverses of binomial coefficients
Why is $l^\infty$ not separable?
Probability of winning in a die rolling game with six players
Tangent bundle : is a manifold
Proving $\sqrt{a+\sqrt{b}}=\sqrt{m}+\sqrt{n}\iff a^{2}-b$ is a square
The logic behind partial fraction decomposition
Proving that isomorphic ideals are in the same ideal class