Suppose you have an alphabet of $5$ letters: $\left \{ a,b,c,d,e \right \}$. Let's consider a set of words of length 25. What is the number of words ...

I'm currently trying to get clear about some terms that are often used in computer science (I'm a computer science student), but were never form...

From what I understand, a covector is an object that takes a vector and returns a number. So given a vector $v \in V$ and a covector $\phi \in V^*$, you c...

Why should we use six trigonometric ratios when all the three sides of a right angled triangle (opposite, adjacent and hypotenuse) are connected with the ...

This may be a very simple question, but I can't figure out the correct reason behind it. If $x^2 - 16 >0$, which of the following must be true? a....

I'm confused how to find solutions to questions like $11^{-1}\mod 26$ and others like these. The solution is $19$ but I don't understand how. $1...

If we want to have the Fourier transform of a complex exponential $x(t) = e^{i\omega_0t}$ we could "guess" that it's $X(\omega)=2\pi\delta(\omega-\om...

I am having trouble internalizing the geometric significance of Green's Theorem and Line Integrals in general. Why is it that a normal line integral ...

I'm having a hard time understanding what exact processes I have to take to represent a function as a power-series. I understand that $\frac{1}{1-x} ...

I might be having a brain fart here but from these two definitions, I actually can't tell the difference between a complete graph and a simple graph.