Sometimes it arrives to me that I try to solve a linear differential equation for a long time and in the end it turn out that it is not homogeneous in the...

In page 122 of the book Topics in Number Theory (1956) by William J. LeVeque, there is an exercise for evaluating the following integral in two ways. $$\i...

What is the relationship between cubic B-splines and cubic splines?

Write out the Cayley table for $D_4/\langle r^2\rangle$. I know that $D_4$ is the dihedral group with 4 sides (square) and $\langle r^2\rangle$ is the alg...

A six faced fair die is tossed a large number of times (tending to infinity). What is the mean of outcomes of the die? My try: let the die be tossed $n$ t...

Given a number, there is an algorithm described here to find it's sum and number of factors. For example, let us take the number $1225$ : It's f...

Let $X$ be a compact Hausdorff space and let $\{U_n\}$ be a countable collection of subsets that are open and dense in $X$. Show that the intersection $$\...

Let $L$ be a linear form, goes from $E$ normed vectorial space, in $K=\mathbb R$ or $\mathbb C$. Is it continuous? My idea, is that $K$ is a banach space,...

Let's say you have a $30$ by $16$ grid and $99$ mines. What is the probability of having at least one empty block surrounded by exactly $7$ mines? Fo...

I have to give a presentation on the theorem in Real Analysis with a fellow student. While I've looked over the proof and verified that, yes, step B ...