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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96 views

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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31 views

Schwarz-Christoffel transformation French references

It might be a weird question but I am looking for a good reference written in French on Schwarz-Christoffel transformation https://en.m.wikipedia.org/wiki/Schwarz%E2%80%93Christoffel_mapping I would ...
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24 views

Looking for references: in PDEs

This is not a technical mathematical question. I came across some PDEs with no references nor their names. $$-\Delta u + \int_\Omega udx = f\qquad \hbox{in $\Omega$} \tag{Eq1}$$ The above equation can ...
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1answer
119 views

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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24 views

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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22 views

Table of potential function for field

I know there is books that has table of common integrals, and I was wonder if there is a book that contain a table of common potential functions of fields.
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1answer
140 views

“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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2answers
56 views

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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77 views

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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93 views

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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0answers
20 views

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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1answer
69 views

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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52 views

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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0answers
56 views

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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16 views

AMS Reference Style - No date

When including a reference in your bibliography, and the source has no date on it, how should this be indicated in the AMS reference style? Is it "n.d." or should the date simply be omitted?
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93 views

Book recommendation : Olympiad Algebra Book

I was searching for a book for olympiad algebra, I coudn't find good books. Can someone please help me with this? It will be much appreciated!
2
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1answer
40 views

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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19 views

Find this reference

I need this reference, but I couldn't find it online as a $\text{PDF}.$ Any help please? J. Sun, X, Zhang, The fixed point theorem of convex-power condensing operator and applications to abstract ...
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1answer
149 views

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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2answers
108 views

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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1answer
28 views

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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13 views

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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1answer
46 views

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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1answer
167 views

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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1answer
69 views

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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76 views

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 ...
3
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0answers
89 views

About the research papers which led to beginning of Sieve Theory

I am an undergraduate and during these uncertain times due to covid -19 i have got a lot of spare time. I have a good background in Analytic number theory, Abstract Algebra, Real/Complex /Functional ...
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1answer
234 views

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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27 views

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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0answers
82 views

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 ...
3
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2answers
104 views

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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0answers
31 views

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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3answers
134 views

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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1answer
25 views

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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61 views

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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23 views

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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42 views

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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1answer
568 views

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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1answer
118 views

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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35 views

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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1answer
195 views

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-...
3
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1answer
314 views

Book on the Lambert W function.

The Lambert W function is the inverse of function $x\mapsto xe^x$. It is traditionally denoted by $W(x)$. The function $W(x)$ is bivalued in interval $(-\frac{1}{e},0)$. See Wikpedia and Wolfram for ...
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2answers
2k views

Need good reference or a proof on regularity of solution to Neumann problem

Let $\Omega\subset \mathbb{R}^d $ be a bounded open subset ($d\in \mathbb{N}$) and denote $\partial\Omega$ its boundary which we assume to be Lipschitz. The classical inhomogeneous Neumann problem ...
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1answer
302 views

$q$-series and modular forms

Is there a way/database such that given a modular form $$f(q) = \sum_{n}a_nq^n$$ with $q=\exp(2\pi i \tau)$, $\tau = \{ z \in \mathbb{C} | \Im(z)>0 \}$ the upper half plane, to find if it can be ...
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1answer
117 views

Is there a version of mean value property for $p$-harmonic funcions?

We know by mean value property that harmonic functions satisfies the equalities \begin{equation} u(x) = \dfrac{1}{|B_r|}\int_{B_r}f dx = \dfrac{1}{|\partial B_r|}\int_{ \partial B_r}udS. \end{equation}...
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1answer
57 views

Regularity of a function by approximation by polynomials.

A standard argument says that a continous function is $ C^{k,\alpha} $ at zero if there exists a polinomial of degree k such that $$ | (u - P)(x)| \le C | x|^{k+\alpha}. $$ This is the way for ...
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1answer
37 views

About a confidence interval Theorem

Does someone know where this theorem is from? From which statistic book? I've searched on two books already: Wackerly and Canavos statistic books. Theorem. Let $x_i$ and $y_i$ two independent ...
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0answers
75 views

The leatest research regarding ergodic operators

I always ask myself the following question which states: Where might the leatest research regarding ergodic operators be found ? It is undoubtedly I am not asking for the books that illustrate the ...
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1answer
207 views

“Theorems on factorization and primality testing” Reference request

I would like to ask two questions : Is John M. Pollard's 1974 paper Theorems of factorization and primality testing available online for free ? Independently of that : where can I find the material ...
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0answers
91 views

Is it possible to study Differential Geometry from Spivak's books starting with the second volume without reading the first one?

Is it possible to study Differential Geometry from Spivak's books starting with the second volume without reading the first one ? The content of Differential Geometry course that is taught in the ...