On P. Starni's "Some Extensions to Touchard's Theorem on Odd Perfect Numbers"...
I am currently skimming through Paolo Starni's Some Extensions to Touchard’s Theorem onOdd Perfect Numbers.I shall start citing from Statement $1$ in page $1$:Statement $1$ (Euler). If $n$ is an odd...
View ArticleIntuition behind picking group actions and Sylow
A common strategy in group theory for proving results/solving problems is to find a clever group action. You take the group you are interested in (or perhaps a subgroup), and find some special set that...
View ArticleDensity of heads with a biased coin stopped after k heads
If a biased coin (prob of heads=p) is flipped until you get $k$ heads, and $X$ is the number of flips, you can compute that the expected value of $(k-1)/(X-1)$ is p by computing the sum...
View ArticleLearning path of Algebraic Geometry and differential geometry for students in...
I am a student in the direction of numerical PDE, in the past few years, algebraic geometry and differential geometry and conformal geometry has been used in structured grid generation, see papers like...
View ArticleWhat is a set called when it implements a distance function
Sorry, it's been a few years since I've looked into this stuff so my terminology may be off. Please bear with me.When a set is ordered, the < operator is defined for that set. I can't think of an...
View ArticleOn a mathematical expansion of Burrows Wheelers Transform (BWT) given a...
Considering the Burrows Wheelers Transform (BWT) as I have tried to formally describe in an old question of mine.In this question I will try to expand it in yet another direction.Consider the...
View ArticleStructuring/Planning Your First Original Research Project (graph...
thank you for taking the time to read this post.Some Context on My Background: I am an undergraduate student in mathematics, and I recently coauthored my first paper with my summer mentor. While...
View ArticlePutnam Exam Prep Plan [closed]
I'm currently taking a gap year and will enter college in the fall. That means I have basically all of January to August to get ahead and prep for the putnam. For reference, I have taken Calc 3, Linear...
View ArticleDoes exponential cone optimization is more challenging to solve than second...
I am a network engineer engaged in optimizing network functionalities and have observed a certain progression in the development of optimization solvers. Notably, it seems common for developers to...
View ArticleIs there a name for the abelian part of a finitely generated...
Suppose $G$ is a finitely generated Abelian-by-$\mathbb Z^n$ group, i.e. it admits a short exact sequence $1 \to A \to G \to \mathbb{Z}^n \to 1$ where $A$ is (potentially infinitely generated) abelian....
View ArticleGPA, Graduate School, and trying to become a mathematician [closed]
I am currently an undergraduate student with around a year and a half-ish left in my degree progression, I could work to make that go faster or slower depending on need...[removed]
View ArticleCollection of surprising identities and equations.
What are some surprising equations/identities that you have seen, which you would not have expected?This could be complex numbers, trigonometric identities, combinatorial results, algebraic results,...
View ArticleAm I doing it right? Seeking advice as undergrad doing research. [closed]
I am currently a second-year undergraduate working on my second research project, and I’m not sure if I’m doing things right. My first project was over the summer and involved grinding through an...
View ArticleA category equivalent to $\mathbf{Man}$ that doesn't require local models
Question. Is there a category $\mathcal{C}$ that is equivalent (or anti-equivalent) to the category of smooth manifolds $\mathbf{Man}$ such that the definition of the objects of $\mathcal{C}$ does not...
View Articlelocalization over different rings
I guess this is a bit of a soft question. Suppose you have a hom of commutative rings with identity $R\to S$, and a hom of $S$ modules $f: M\to N$. Somehow it shouldn't matter whether you localize $f$...
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Constructing position vector
I am a student from a non-English speaking country. And I recently took a linear algebra class and heard about position vectors. Here, I started to have questions about the process of constructing...
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Circle/ Ellipse geometry problem from Ramanujan
Does someone have detail of the problem and his solution? I saw it in youtube. A rough hand sketch remade seeing YouTube video SR geometry problem (17 min 51 sec). I have no access to the TIFR book...
View ArticleVarious Ways to Prove the Half-Angle Formulae for Sine and Cosine
I was pondering about the different methods by which the half-angle identities for sine and cosine can be proved.$$\left|\sin\left(\frac{x}2\right)\right|=\sqrt{\frac{1-\cos...
View ArticleAre there specific main challenges in extending the inscribed-square theorem...
According to this video https://youtu.be/IQqtsm-bBRU?si=pSXEDQjTugHhhtI9 on Toeplitz' conjecture, if I've understood correctly, it is known that every smooth simple closed curve has an inscribed square...
View ArticleExtrinsics vs Intrinsics geometry, intuitive explanation
I was wondering if anyone can give me an insight of what is meant with "Intrinsics Geometry" and "Extrinsics Geometry". At the beginning I thought this was like a distinction between differentiation...
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