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Linking circles inside an immersed surface

A smooth embedding $f : D \to \mathbb{R}^3$ can be isotoped to a canonical inclusion $D \hookrightarrow \mathbb{R}^3$. (This is part of a proof that only the unknot has the disk as a Seifert surface.) ...
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Understanding tensor products and $R$-algebras

Sorry if this question isn't quite precise. Anyways, I'm reviewing for my algebra final right now and two things I don't think I quite grasp as well as I'd like are tensor products and $R$-algebras. I ...
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How to see that the prime gaps functions isn't monotonic?

Let $g(n)$ be the distance between the $n$th prime and the next. By elementary means we can see that $g(n)$ is not eventually constant and that $g(n)$ is not strictly monotonic. Further we know that ...