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Imagining linear maps between finite fields

I can't imagine a right picture of a linear transformation $\mathbb{F}_{p} \mapsto \mathbb{F}_p$ or $\mathbb{F}_{p^2} \rightarrow \mathbb{F}_{p^2}$ etc (over the field $\mathbb{F}_p$) although they ...
katana_0's user avatar
  • 353
17 votes
1 answer
1k views

How to visualize a Witt vector?

As the question title asks for, how do others "visualize" Witt vectors? I just think of them as algebraic creatures. Bonus points for pictures.
Squid with Black Bean Sauce's user avatar
1 vote
2 answers
1k views

Understanding reduced suspension of $S^1$ [closed]

I know this is just $S^2$. To see it, I use the CW structure of $S^1$ x $S^1$ , consisting of one 0-cell, two 1-cells and a 2-cell. Then since the reduced suspension is the cartesian product ...
vanmeri's user avatar
  • 71
5 votes
2 answers
4k views

Visualization of the real projective plane [closed]

Consider a closed (compact and without boundary) and non-orientable 2-manifold $M$. By Whitney embedding theorem, one can embed $M$ in $\mathbb{R}^4$. $M$ cannot be embeded in $\mathbb{R}^3$ and just ...
Sepideh Bakhoda's user avatar
19 votes
5 answers
18k views

Visualization of Riemann–Stieltjes Integrals

The Riemann–Stieltjes integral $\int_a^b f(x)\,dg(x)$ is a generalization of the Riemann integral. It is e.g. heavily used as a starting point for stochastic integration. The approximating Riemann–...
vonjd's user avatar
  • 5,935