Bernard Pan's user avatar
Bernard Pan's user avatar
Bernard Pan's user avatar
Bernard Pan
  • Member for 3 years, 5 months
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5 votes

Solve the equation $\sqrt{45x^2-30x+1}=7+6x-9x^2$

5 votes
Accepted

Given $X\sim\text{Unif}(0,2\pi)$, find the probability density function of $Y = \sin(X)$

4 votes

Any group of order $5^2q^m$ is not simple if both $q$ is a prime and $m$ a positive integer such that $5^2\nmid q^m!$

4 votes
Accepted

Let $a,b,c$ be integers such that $\gcd(a,6)=3=\gcd(b,6)$. Show that $\gcd(a+b,6)=6$.

3 votes
Accepted

The $2$nd, the $1$st and the $3$rd term of an arithmetic progression form a geometric progression

3 votes
Accepted

Can I compare the cardinality of two uncountable sets

3 votes
Accepted

commutative ring to boolean algebra

3 votes
Accepted

Fourier coefficients - can I see them?

3 votes
Accepted

Proving $ax^2+bx+c=a(x-r_1)(x-r_2)$, where the $r_i$ are the roots

2 votes
Accepted

Show $K=\{g\in S_4\mid\forall x\in G, (gx)H=xH\}$ is isomorphic to Klein four group

2 votes

Show that $\text{ker}(\alpha) \subseteq \text{ker}(\beta\alpha)$. If $\beta$ is one-to-one, show that $\text{ker}(\beta\alpha) =\text{ker}(\alpha) $

2 votes

Simplification of of Boolean expressions

2 votes

Determine if $\prod\limits_{i=0}^\infty A_i$ countable or uncountable

2 votes
Accepted

Showing that X and Y are not Independent

2 votes

Proof for the nature of an eigenvector given a small eigenvalue

2 votes

Is the positive operator $TT^*-T^*T$ on a finite complex inner product space is a zero operator?

2 votes

Given $a_{1} = \frac{1}{2},\;\;a_{n+1} = \frac{a_{n} +3}{4},\;\;n ≥ 1$, find $L = \lim_{n\to \infty} a_{n+1}$.

2 votes
Accepted

How to know when and where to transpose?

2 votes
Accepted

Monotonically increasing function and supremes

2 votes
Accepted

simple summation example and simplyfing it

2 votes
Accepted

$C$ is a closed set in $X$, $X$ is $T_4$, show that $C$ is $T_4$

2 votes
Accepted

Is $B$ countable or uncountable?

2 votes
Accepted

Distributing 10 books to 5 schools

2 votes
Accepted

Let $G$ be a $p$-group : $|G| = p^r$. Prove that $G$ contains a normal subgroup of order $p^k$ for every $k \leq r$.

2 votes

Is there any self complementary graph of order 5 other than C5

2 votes
Accepted

Calculate Probability Using Random Variable?

2 votes

Compact convergence topology coincide with compact-open topology if $Y$ is a metric space.

2 votes

Uniform continuous proof.

2 votes

Proving an inequality from a given condition

2 votes

Prove a function is continuous on the union of closed sets if it is continuous on each set.