Questions tagged [reference-works]

Reference works include encyclopedias, dictionaries, books of tables (which may include numerical tables, tables of integrals, series, and products, tables of Fourier transforms, tables of finite groups, tables of combinatorial designs, etc.).

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Explicit equations describing complex spin groups as affine algebraic groups

Although there are tons of questions about spin groups here on math.SE, I could not find there what I want. What I want is this. Take the complex spin group $\operatorname{Spin}(2n,\mathbb C)$. It has ...
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Anyone recommend a fairly modern/new textbook on functional analysis/PDE's to be used as a reference for a graduate level course? [closed]

See question in title porfavor, just adding words to fill required number of characters
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Need help finding G. Pick's 1917 article "Über affine Geometrie iv: Differentialinvarianten der Flächen gegenüber affinen Transformationen"

I'm studying affine geometry and I need help finding this article "Über affine Geometrie iv: Differentialinvarianten der Flächen gegenüber affinen Transformationen" written by G. Pick in ...
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1 answer
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Is there a comprehensive list of complexity theoretic reductions from and to prime number factorization?

I am interested in the complexity theoretic equivalences of prime number factorization. I am especially interested to learn wether there are some not initially obvious reductions. Im sure there is a ...
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Can someone provide a brief list of when, and when not to, use each finite difference approximation for derivative?

So far, I've received one possible scenario, and may be the only one, for using the forward difference in approximating the derivative rather than its central difference counterpart. And that is when ...
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English translation of Opera Omnia, Euler

I want to read Euler’s works, and yes, I am aware that I can read them online, on Euler Archive. But, I was looking for physical books in which Euler’s works are compiled. When searching for the ...
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3 votes
1 answer
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What computer methods are used to quickly calculate the $\zeta$-function (if any)?

So I can think of how I could compute $\zeta(\sigma + it)$ in principle. We can take $\zeta(\sigma + it)$ for $\sigma>1$ by the usual $\sum_{n} n^{-(\sigma + it)}$ summation. We can use the ...
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1 answer
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Generalized mean value property for the Poisson equation

It is well known that solutions to the Laplace equation in a region $\Omega\subseteq\mathbb{R}^n$, $\nabla^2u=0$ satisfy the mean value property, namely for all $x\in\Omega$, and for all $r>0$, $$ ...
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Mathematical Journal on Logic and Set Theory

I'm looking for free to access mathematical journal about logic and set theory. I found some earlier but all of them need payment/subscription. Is there anyone that know some reference? I'm a little ...
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sharp optmal regularity of p-harmonic functions

It is well konw that solutions of $div(|Du|^{p-2}Du)=0$ in $B_1,1<p< \infty$ are $C^{1,\alpha(p)}(B_{1/2}$. This means that there exists a affine function $l_p(x) : = a x+b$ such that for any $x ...
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Work of Omar Khayyam on cubic equations

I am trying to see the work of Omar Khayyam on cubic equations. It seems that he solved some types of cubic equations. However, I am not getting proper references for it. Can anybody suggest a ...
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Missing a page in a journal paper, is it normal?

My question comes from the paper Propagation of chaos for Burgers' equation published at Annals of the IHP Theoretical Physics, Tome 39 (1983) no. 1, pp. 85-97. However, the page 95 is clearly missing....
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Pseudonyms in mathematics and groups of mathematicians similar to the Bourbaki group.

In the thread at the end of the post the asker asks for pseudonyms for famous mathematicians or (secretive) groups of famous mathematicians. The famous "Bourbaki book series" is an example ...
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Need references to learn about ideals of Hilbert $C^*-$ modules

I'm interested in learning about ideals of Hilbert $C^*-$modules and their relationship with ideals of linking algebra. Can someone please tell me some standard references(books/papers) for the same? ...
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Are there applications of $\mathrm{\int \frac {dx}{tan^{-1}(x)}}$?

This will be a follow up question to my unexpectedly popular question: Is there an exact solution for $\large\int \frac{dx}{\tan^{-1}(x)}$? which is also nicely related to: Indefinite Integral $\...
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Proof that there's only one function that satisifes the properties of a trace. [duplicate]

I've been reading Mathematics for Machine Learning, by Deisenroth, Aldo Faisal and Cheng Soon Ong, and it contains the following lines about the trace of square matrices that I need help with: The ...
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1 answer
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Is there any English translation of the Gergonne paper "Variétés. Essai de dialectique rationnelle" ("Varieties. Essay about rational dialectic")?

Is there any English translation of this Gergonne paper? "Variétés. Essai de dialectique rationnelle", Annales de Mathématiques pures et appliquées, tome 7 (1816-1817), p. 189-228. ("...
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English translation of Riemann's complete works

Browsing in the library I came across with the mathematical (and some philosophical) papers of Riemann, collected by Weber and Dedekind in the original German (although published by Dover). But ...
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Where to find known bounds on expressions?

Example. In a problem I was working on, I had an expression of the form $(1-e^{-\alpha n})^{e^{\beta n }}$. I wanted to find an upper bound $f(\alpha, \beta, n)$ on this that makes it easier to see ...
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"NONCOMMUTATIVE Algebra with a view towards Algebraic Geometry"?

Is there a noncommutative algebra book that is similar to Eisenbud's "Commutative Algebra with a view towards Algebraic Geometry" in the sense that fundamental and geometrically motivated ...
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2 answers
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How To Learn Mathematics Basics [closed]

I wanna learn mathematics from zero to advanced which books should I read and which websites should I visit?
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1 answer
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Lecture notes of complex analysis

I just want to go through the topics of complex analysis, in order to get an overview of the subject. Does there exists any good lecture notes for complex analysis which covers all the topics quickly? ...
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6 votes
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Is there an equivalent of differential geometry for infinite dimensional spaces?

Differential and (Semi/Pseudo-)Riemannian geometry provide a framework for doing calculus on finite dimensional manifolds and have applications in physics (general relativity) and dynamical systems ...
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2 votes
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Is there a bibliography of Lebesgue’s publications (with translations)?

I’m reading in the history of measure and integration and can’t find a complete list of Lebesgue’s publications, which I understand comprise his PhD thesis, some 50 papers, and two monographs. (...
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Mathematical analysis book with a specific result of continuity.

Let $I^{n}\overset{_\mathrm{def}}{=}\left\{x=\left(x_{1}, \ldots, x_{n}\right) \in \mathbb{R}^{n}|\;\;a_i\leq x_{i} \leq b_{i}\,;\; i=1, \ldots, n\right\}$ be an $n$-dimensional closed interval and $I$...
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Reference to an elementary result of mathematical analysis.

Can anyone suggest a mathematical analysis textbook that contains proof of this Proposition below? I have already sought proof of this result in classic textbooks of mathematical analysis such as ...
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Request for list of fields of research (or fields already well-known) not in the MSC [closed]

So I was browsing the Mathematics Subject Classification and various other classification schemes related to it when I read from multiple sources that there are certain fields of study or research not ...
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1 answer
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Summing the first $n$-terms of the series whose general term is $nx^{n-1}$

I suppose several of you know some fancy ways to establish the formula for the sum of the first $n$ terms of the geometric series $$1+x+x^{2}+x^{3}+ \ldots $$ Can you share below some of your fave ...
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Reference request for a resolution

Let $S:=k[t_0,t_1,\dots,t_n]$ and $f\in S$ be an irreducible, homogeneous polynomial of degree $d$. Denote by $R:=S/(f)$. Recall that the Kähler differential of $R$ is the $R$-module $\Omega^1_{R/k}$ ...
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Database of FOL statements and proofs

Is there a database somewhere of simple FOL statements, with their proofs written out in a Hilbert-style deduction system, or perhaps a tool to take such statements and produce proofs? While I see ...
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Question about poles of the Lerch Transcendent

The Lerch Transcendent is defined as the analytic continutation of the sum $$ \Phi(z,s,a)=\sum_{k=0}^\infty(k+a)^{-s}z^k. $$ According to Wolfram functions, for fixed $s$, $a$, the function $\Phi(z,s,...
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Are there pre-computed tables for values of the "sum-of-divisors" function?

Let $\sigma$ denote the "sum-of-divisors" function, i.e., $${\displaystyle \sigma _{}(n)=\sum _{d\mid n}d^{}\,\!.}$$ Note that the sequence $\sigma(n)$, for $n\geq1$ is in the OEIS as entry ...
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References on (more or less) explicit calculations of probability distributions of nonlinear transformations of random variables

Premise. After a former question and related answer, I searched for references on the calculation of the probability distributions of nonlinear functions of (one or more) random variables, in order to ...
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1 answer
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Is there a bijection between an infinite set $E$ and $\big\{f:E\to\mathbb{Z}\,\big|\,|\text{supp}f|<\infty\big\}$?

Let $E$ be an infinite set and let $G$ the set of maps from $E$ to $\mathbb{Z}$ that have finite support. Is there a case where we can prove that there is a bijection between $G$ and $E$? I need a ...
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2 votes
1 answer
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Minimizing a composite non-differentiable convex function over a $2$-norm ball

I am searching for (works on) methods for solving the composite differentiable and non-differentiable convex problem: $$ \min_{x \in B} f(x) + g(x),$$ where $B$ is a $2$-norm ball, ie: $x \in B \iff ...
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Catalog of Categories

Could someone please indicate a website, book or PDF that contains a catalog of categories? I am looking for a place that contains descriptions and properties of the best known categories. I am ...
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What is this symbol: $\mapsto$? [closed]

Back in the old days, I had a book that listed many things about math tables and symbols. What is the modern equivalent book? My question was unclear. I think it was because I used one question in ...
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Reference for idempotent rings

In the wiki page of algebraic ring without multiplicative identity appears the definition of idempotent ring as a weakening of unital ring. Does any have a reference of where or why this concept ...
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Hermite interpolation and basis functions.

I am using piecewise quintic Hermite interpolation at the joint level for a robot (1000 Hz) from a more time-sparse, but smooth trajectory (100 Hz). I have tested this according to the elegant ...
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3 votes
2 answers
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Non-number theoretic formulation of Fermat's last theorem?

We have dozens of non-number theoretic formulations of Riemann hypothesis. I was wondering if there are any non-number theoretic formulations of Fermat's last theorem? I am in particular curious about ...
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1 vote
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Reference request on the Schwartz class on integers

It's a well known fact that the Schwartz class over integers defined by $$S(\mathbb{Z}^n)=\{\{a_m\}_{m\in\mathbb{Z^n}}\mid \sup_{m\in\mathbb{Z}^n}|m^\alpha a_m|<\infty, \forall \alpha\in\mathbb{N}^...
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2 votes
3 answers
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Books about synthetic projective geometry

Are there books in English about synthetic projective geometry? More specifically, results of Karl von Staudt (imaginary elements theory through elliptical involutions, imaginary circle, infinity's ...
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Question about notation on the NIST DLMF

Many relations on the NIST DLMF have certain restriction on parameters that must be satisfied in order for the relation to hold. Take for example equation $15.8.5$ which lists multiple constraints on ...
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How to get a math textbook that's out of publication?

I recently decided I wanted to learn more about the Dehn invariant, so I did what I always do and went on MSE and MO to get recommendations. I found this link, which suggested a book called "Theory ...
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Errata in Convex Analysis and Minimization Algorithms by Hiriart-Urruty and Lemaréchal.

Hiriart-Urruty and Lemaréchal have written Convex Analysis and Minimization Algorithms I and II. Is there an errata list for these books?
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reference request: visualizing ideal structures in CRing

In a basic algebra course last year, I learned some of how rings are taxonomized by properties such as "all the elements have unique factorization", or "all the ideals are principal ideals". Studying ...
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Forward-backward induction

I've seen the famous proof presented by Cauchy for the AM-GM inequality but what other neat proofs use forward-backward induction? Is it fundamentally inextricable from ordinary induction (are there ...
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1 answer
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When authors takes maths with a pinch of a salt [closed]

This thread aims to collect mathematical books where authors deal with serious topics and offbeat humour.
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Sinusoidal decomposition of signal

I have some data of periodic nature. The curve seems to be slightly irregular, and it makes sense to consider it as the sum of two or more different sinusoidals. I'm asking for a source or tools ...
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4 votes
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Editions of Niven-Zuckerman book on number theory

There are several editions of this popular introduction to the theory of numbers. Are they substantially different from one another? Do you think the edition in which Hugh Montgomery appears as co-...
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