I'm doing a problem in which I have to find the minimum distance between the origin and a point on a parabola. I understand that the minimum of a fun...

Let $t(n)$ denote the n$^{th}$ triangular number. Let $T(n)$ denote the sum of the first $n$ triangular numbers. Is there a formula for $T(n)$?

If I flip a fair coin 100 times, and each time I get a heads immediately followed by tails, I win $5. How much am I expected to win during the game? I kno...

Warning: naïve question ahead! Littlewood proved in 1914 that there exists a number $n\in\mathbb{N}$ (called Skewes' number) such that: $$ \pi(n) >...

I hope this question is appropriate for this site, if not, just leave a comment and I will delete. I am interested in knowing how to derive the electric f...

Recall Theorem 7.25 of Rudin's Principles of Mathematical Analysis: If $K$ is compact and $f_n \in \mathscr{C}(K)$ for $n \in \mathbb{N}$, and if $\{...

Let $f$ be a modular form where $f:H\to \bar{C}$ is any meromorphic modular form. Say I want to study the singularity behaviour at $i\infty$ of $f$. I can...

As a follow up to Average projected area in higher dimension, I started to think about a variation of the original post. Let's visualize a circle wit...

Do transient state and steady state go hand in hand in differential equations? Meaning, if there is a transient state, is there always going to be a stead...

I'm trying to learn, or revise, some topology from James R. Munkres' TOPOLOGY, 2nd edition. I'm working alone; that is, I'm self-learn...