# Tagged Questions

This tag is for questions seeking external references (books, articles, etc.) about a particular subject. Please do not use this as the only tag for a question.

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### Ind- and pro-objects, reference request

Can someone point me to a good exposition of ind- and pro-objects, the intuition behind, and how one "in practice" works with them (i.e. prove things)? The nlab page is nice (especially for the ...
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### reference for classifying groups of order $p^2q^2$

In a previous question I asked about the number and structure of groups of order $p^2q^2$ where $p,q$ are primes and with the help of Prof. Derek Holt I understand it now (see here non-abelian groups ...
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### $A^{\frac 32}$ for $A\geq0$ self-adjoint as an integral of the Resolvent

Let $A\geq0$ be a bounded self-adjoint operator on a Hilbert space. I would like to show that $$A^{\frac 32} =c \int_0^\infty A^2 (y+A)^{-1}y^{-\frac 12}\text{d}y,$$ where $c>0$ is an appropriate ...
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### What is the difference between high dimensional and low dimensional chaos?

Often I read of high and low dimensional chaos. But, I don't know what is their difference. I have thought the following answer. Let us consider a time series $\{x_i\}_{i\in\mathbb N}$. According to ...
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### What is a number theory book I can read in bed?

I am looking for a good book that is very easy going but not a "pop science" account i.e. something that goes through theory that would be on a basic undergraduate course for someone who finds the ...
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### Evaluate $\int_0^{\pi/2}(\sin x)^n e^{-(2+\cos x)\log k}dx$ for fixed integers $n,k\geq 1$

My question is the following Question. Can you compute some of the following $$c_{n,k}=\int_0^{\pi/2}(\sin x)^n e^{-(2+\cos x)\log k}dx$$ where $n\geq 1$ is a fixed integer and $k\geq 1$ is ...
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### Input Error estimation

I was wondering what are the methods used to detect the input's error when having the output's error of a model. I thoroughly searched on google, but I failed to find a well explined method, or ...
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### Name of the theorem: If $p^k$ divides $|G|$, then $G$ has a subgroup of order $p^k$?

Note: I am not asking for a proof of this theorem or any other theorem or help with a mathematical problem. This question is a reference request. I use the following well-known and somewhat-easy-to-...
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### Reference about $\sigma$-linked posets and related notions

In this link, the following list appears: Some chain conditions [of posets], listed from easiest to satisfy to hardest to satisfy: ccc powerfully ccc productively ccc $\sigma$-...
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### A topology on the natural numbers

Is there a name of or a reference to the following topology on $X=\mathbb N$: $A\subseteq X$ is closed if and only if $n\in A\wedge m|n\implies m\in A$?
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### Courant-Hilbert's Book: Weyl's asymptotic law for eigenvalues - Planar domains

In the book Strauss W.A. Partial Differential Equations - an Introduction (Wiley, 2008, 1st Ed.) page $311$, there is a comment Now an arbitrary plane domain $D$ can be approximated by unions of ...
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### Curvature of curves on surfaces

Are there ways to know the curvature of a curve $\gamma$ that lives on a surface $\mathcal{S}$starting from the gaussian curvature of $\mathcal{S}$? In general, is it possible bound the curvature of ...
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### Applications of PDEs in many variables

One reason that solving systems of partial differential equations is so important is the many applications of PDEs in science and engineering (eg. the heat equation, the wave equation, etc.). Often ...
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### In which quadrant of the circle does the angle of $90^\circ$ lie?

By definition and with an authoritative reference, in which quadrant or quadrants does $90^\circ$ lie? (There are non-authoritative references which answer the question, and a related question which ...
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### Decidability of quantifier-free formulae in Peano- and True Arithmetic

It is well-known that validity in Peano Arithmetic is undecidable. It is less well-known that validity is already undecidable in True Arithmetic (the theory of the standard model of Peano Arithmetic). ...
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### Differential forms vector space over function field?

Let $V$ be a vector space and $V^*$ be its dual space. Then I know that $V^*$ is considered a vector space because we can scale the basis covectors by real numbers and add them together and all of ...
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This is a continuation of this question. My main question is that, in the previous question we were mainly concerned about the sign of, $$f_{2}(n)=\pi\left((n+1)^2\right)+\pi\left(n^2\right)-2\pi\left(... 1answer 20 views ### On terms “Orientation” & “Oriented” in different mathematical areas? The goal of this question is to help to deal with different meanings of the words such as "orientation" and "oriented" in different mathematical areas. Are different oriented concepts somehow ... 0answers 8 views ### Are Oriented Graphs Related to Oriented Matroids? My professor said that oriented matroids make it easier to investigate things such as connectivity. Recall that an oriented graph is a digraph without multiple edges or loops. Now Are oriented graphs ... 12answers 405 views ### The Big List of the Mathematical Songs [closed] I recently watched a music video in Youtube about a finite simple group of order two! (See also this link). What are other examples of songs about mathematicians and mathematical objects? Please ... 2answers 39 views ### Special Relativity-Book I would a good book to study the Special Relativity. In my course the professor has treated the following topics: (1) Lagrangian and hamiltonian dynamic of a charged particle; (2) Relaticistic ... 2answers 242 views ### modern calculus or analysis text that emphasizes Landau notation? Is there a comprehensive calculus or analysis textbook or problem book, written in the last twenty years, that emphasizes the use of Landau notation (big and little oh), especially for making ... 0answers 13 views ### Area of Operations Research on graph theory and reliability engineering? [closed] I am confused by the jargon in Operations Research (OR) when it is the same as in Graph theory such as component but it can mean just a vertex. So I am confused to the extent that reliability ... 0answers 64 views ### Legendre's Conjecture Theme (Part I) Main Question Recently I have been thinking about the Legendre's Conjecture. I noticed that a proof of the conjecture can be obtained if we can prove any one of the following, Conjecture 1. For ... 0answers 36 views ### Introduction to p-adic vector spaces I'm interested in learning about vector spaces over \mathbb{C}_p and \mathbb{Q}_p. Most textbooks on p-adic numbers (Koblitz, Schikhof) focus on analysis and number theory. Is there any ... 0answers 37 views ### Image of the norm map in imaginary quadratic fields Let K=\mathbb{Q}(\sqrt{D}) be an imaginary quadratic field of discriminant D<0. I want to know the image of the norm map$$ N^K_{\mathbb{Q}}:\mathcal{O}_K\to\mathbb{Z}  and the values of $N^... 1answer 31 views ### Ultrafilter on$[0,1]\$ consisting of closed sets

Today we learned about filters and ultrafilters in the General Topology course. I am trying to play around with these definitions. I wish to ask a question that I am unsure about. Let us say, we have ...
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### Books on inference for stochastic analysts

I realize that book recommendations to learn statistical inference is a hackneyed topic but I have something more specific in mind. I work on diffusions and would like to quickly and effectively learn ...
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### Maclane/Birkhoff's “Algebra” as a first book on the subject?

Would the more knowledgeable and well-versed members of this community be so helpful as to give their opinion on using Birkhoff & MacLane's famous "Algebra" for a first course in Abstract Algebra? ...
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### Spivak's Calculus?

I have seen many users here asking questions about problems in what they call "Spivak's Calculus Book". I have never seen the book, and information online is scarce. From what I've gathered, it is ...