Vahid Shirbisheh
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 Sep30 awarded Explainer Sep24 awarded Autobiographer Jul22 comment Irreducible action of a group on a set $\mathbb{F}^2_p$ is not just a set. it is a vector space. In this case, it usually means it must not have nontrivial invariant subspace. Jul21 revised Problem with finding a suitable partition of unity added 533 characters in body Jul21 comment Tensor product of duals $V$ is finite dimensional, isn't it? Jul21 comment Tensor product of duals If $V,W$ are vector spaces on some field $F$, it is easy. Assume $V\simeq F^n$. Use the notation $Hom(V\otimes W, F)$ for $(V\otimes W)^\ast$. Then $Hom(V\otimes W, F) \simeq Hom(V, Hom(W,F)) \simeq V\otimes Hom(W,F) \simeq V^*\otimes W^*$. Jul21 comment Problem with finding a suitable partition of unity It follows from your assumption that $x\in U_s$ implies that $x+1, x-1\in U_s$, and more generally $x+n, x-n\in U_s$ for all $n\in \mathbb{N}$. Jul21 comment Tensor product of duals Since they are finite dimensional and they have the same dimension, as soon as you find an injection, it is clear that it is surjective as well. Jul21 comment Problem with finding a suitable partition of unity At first, I didn't pay attention to the requirement that $\phi_i$ should be periodic. But I think the current version is fine. Jul21 revised Problem with finding a suitable partition of unity corrected Jul21 answered Problem with finding a suitable partition of unity Jul20 answered Should I read about Manifolds or Algebraic Topology? Jul20 comment Finding a lie group structure on $\mathbb R^n\setminus\{0\}$ The title of your question is misleading. Jul11 comment Understanding mathematical texts As a practical and yet general suggestion, I think you should consult with the instructor of the course or you can ask questions about any specific subject here in math SE. Jul11 comment Understanding mathematical texts I have never heard of a personal subjective motivation for a mathematical work. In fact, when a mathematicians tries to present his/her work to the public, the first step is to justify the importance of the idea and the work has been done. I call this justification the motivation of a mathematical piece which certainly should be objective. Also I should say that my answer is a very brief suggestion for starting to understand a subject (through understanding the basic ideas of the subject) and it is very different than mastering a subject. Jul11 comment Understanding mathematical texts Also I think if a mathematical idea is relatively new, say born in the last 50 years, then the history of the problem is way more important. Because sometimes old ideas evolve into a very different creature than what they have been at the beginning and if you want to understand the current status of an idea considering only the history of the problem might be misleading. Jul11 comment Understanding mathematical texts Historical considerations are important and reveal some aspects of a mathematical idea. But more generally I'd like to emphasis on the context in which a mathematical idea is introduced and in which it develops and how the idea is related to other ideas. Jul11 answered Understanding mathematical texts May25 awarded Yearling May13 answered Covolution (space) over compact Lie groups