Let $A, B$ be commutative rings with multiplicative identity, let $f: A \rightarrow B$ be a ring homomorphism, let $\mathfrak{a}$ be an ideal in $A$. The ...

A question says: Using the isomorphism theorems or otherwise, prove that a subgroup of a finitely generated abelian group is finitely generated. I would s...

How many strings are there of seven lowercase letters that have the substring tr in them? So I am having a little problem with this question, I know that ...

If I want to find how many possible ways there are to choose k out of n elements I know you can use the simple formula below: $$ \binom{n}{k} = \frac{n! }...

I'm beginner with proofs and I got the follow exercise: Prove the inequality $$(a + b)\Bigl(\frac{1}{a} + \frac{4}{b}\Bigr) \ge 9$$ when $a > 0$ a...

I am in the midst of confusion in regards of this question: I have to find an expression for the differential dV, and hence ${\frac{dV}{dt}}$. The ${\frac...

If infinity is not a number, how can it be larger than any number? A number is a position on the number line. A larger number is the position further on t...

I had a question about how to do one of these problems. So here's the question: Given this equation $y'=\frac{-\cos(t)y(t)}{(t+2)(t-1)}+t$, find...

I think I could have found a prime number generator algorithm, but still I am not very sure, maybe this is an already known property of perfect square num...

How do I solve the following equation? $$\cos(x) - \sin(x) = 0$$ I need to find the minimum and maximum of this function: $$f(x) = \frac{\tan(x)}{(1+\tan(...