So i'm told that a radioactive substance has a half life of 10 years and is modelled by the following equation: A=A_0 * e^(-kt) where A_0 is the orig...

I am just starting dynamical systems and came across the following problem in my textbook. Considering the discrete time logistic growth model, $$N_{t+1} ...

Recently, I stumbled over a few things in very basic Lie group / Lie algebra theory concerning matrix groups. Basically, my question is: Is there a way to...

$$\sinh(x) = \frac{1}{2(e^x - e^{-x})}$$ $$\cosh(x) = \frac{1}{2(e^x + e^{-x}}$$ $$\tanh(x) = \frac{\sinh (x)}{\cosh (x)}$$ Prove: $$\frac{d(\tanh(x))}{dx...

I tried looking it up but many websites just state it without proof and without intuition. I'm hoping to learn it a little bit better so that I don&#...

Let $f : [a, b] \rightarrow R $ of bounded variation. Let $$p_{f}(x) =\frac{1}{2}[V_{f}(x) + f(x)-f(a)]$$ and $$q_{f }(x) =\frac{1}{2}[V_{f}(x) - f(x) + f...

Binomial problems: Mean and standard deviation Suppose that the New England Colonials baseball team is equally likely to win any particular game as not to...

According to wikipedia, "The chamfered dodecahedron is a convex polyhedron with 80 vertices, 120 edges, and 42 faces: 30 hexagons and 12 pentagons. I...

$\mathbb Z$ (Our usual notation for the integers) with a little subscript at the bottom. This is the question being asked: what are the subgroups of order...

How can I prove that: A and ( not A or B) is equivalent to A and B It is easy to show with a truth table how can I do only using the properties of the log...