Tag Archives: MathOverflow

Can $approx$ be used in rigorous proofs?

The notation $approx$ is often used for calculations but is generally poorly defined, although other notation like $sim$ (asymptotic to) or big-O or little-o notation appears in rigorous proofs and often have a similar interpretation. I’m just wondering if one can use $approx$ in proofs. (I for example am attempting a computation and in an… Read More »

Von Karman equations system, biharmonic operator,

I am studying the Von Karman equations system (A semi-linear elliptic system of two fourth-order partial differential equations with two independent spatial variables) and I want to solve this equation by means of homotopy analysis method (HAM). After applying homotopy in accordance with the articles published by Mr. Liao and a similar paper by Mr.… Read More »

Indirect attempts at showing that Peano Arithmetic proves Fermat’s Last Theorem

So, Peano Arithmetic almost definitely proves Fermat’s Last Theorem (see What is known about the relationship between Fermat’s last theorem and Peano Arithmetic?). That being said, constructing an actual proof of Fermat’s Last Theorem in Peano Arithmetic will likely be extremely difficult? I am wondering if anyone has attempted to show that a proof exists,… Read More »

Advice on proof-writing [on hold]

I am currently writing a proof for the strength of an ordinal notation. I want to analyse it with second order arithmetic subsystems and I would like to get some advice from experts if possible. I understand that to find a proof-theoretic ordinal of a theory, one has to find the set of well-orderings provably… Read More »

How do I approach Optimal Control?

Other than learning basic calculus, I don’t really have an advanced background. I was curious to learn about Optimal Control (the theory that involves, bang-bang, Potryagin’s Maximum Principle etc.) but any article that I start off with, mentions the following: “Consider a control system of the form…” and then goes on to defining partial differential… Read More »

Is the “composition” of two dense subsets of functions dense?

Given $F subseteq C_C(mathbb{R}^d, mathbb{R}^p)$, $F$ is dense in $C_C(mathbb{R}^d, mathbb{R}^p)$ in the supremum norm $|cdot|_infty$. Also given $G subseteq C_C(mathbb{R}^p, mathbb{R}^s)$, $G$ is dense in $C_C(mathbb{R}^p, mathbb{R}^s)$ in $|cdot|_infty$. Is the set $G circ F := {g circ f: g in G, f in F, g circ f in C_C(mathbb{R}^d, mathbb{R}^s)}$ dense in $C_C(mathbb{R}^d,… Read More »

Cohomology of $BE_8$ and $BSU(2)$

What are the cohomology of the classifying space of $E_8$ group and $SU(2)$ group, $H^*(BE_8;mathbb{Z})$ and $H^*(BSU(2);mathbb{Z})$? In the paper http://homepages.math.uic.edu/~bshipley/ConMcohomology1.pdf , it was given that $H^∗[BSU(2); mathbb{Z}_2] = mathbb{Z}_2[u_4]$. But I like to know the result for integer coefficient.