In the Tower of Hanoi puzzle , suppose our goal is to transfer all n disks from peg 1 to peg 3, but we cannot move a disk directly between pegs 1 and 3 . ...

I am creating a program which maps an Ellipse to a Circle. However, there is a twist, the center of the Circle is offset inside the Ellipse. See this pict...

I have two ordinary differential equations equations: $$ \dot{x}=1+x^{2}y-(1+A)x $$ $$ \dot{y}=Ax-yx^{2} $$ I need to find the single equilibrium point in...

So I'm told that for a function $f:X\rightarrow Y$ to be surjective then $$\forall y\in Y~,~\exists x\in X~,~f(x)=y,$$ so does this "$\exists$" imply...

A semiring is defined by two operations $+$ and $\times$ on a set $R$, such that: $(R, +)$ is a commutative monoid $(R, \times)$ is a monoid $\times$ left...

I have been able to find several counterexample books in some math areas. For example: $\bullet$ Counterexamples in Analysis, Bernard R. Gelbaum, John M. ...

The questions asks, "Show that the square of any integer is congruent to either $0$, $1$, or $4 \pmod 8$". The answer starts off by stating, &qu...

Task: Solving the PDE $au_x+bu_y+cu=0$. (Source: PDE, 2ndE by Walter A. Strauss, Exercise 1.2.19. Lots of books have it, though.) Solution 1 The PDE can b...

Maybe this is an easy question, but I can't figure it out! What is the inverse mapping of: $f(t) = (\cos(t), \sin(t))$, where $f: [0, 2\pi) \to S^1$ ...

Differentiation has an obvious geometric interpretation, and the Cauchy Riemann equations are closely linked with differentiation. Do the Cauchy Riemann e...