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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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
74 views
Is there a bijection between an infinite set $E$ and $\big\{f:E\to\mathbb{Z}\,\big|\,|\text{supp}f|<\infty\big\}$? [closed]
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
27 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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67 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
66 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
65 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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0answers
17 views
Recommendation for source for recognizing differential equations
Given a differential equation, I'd like to find a way to recognize what type it is, without much knowledge in the field.
For example, I have the differential equation
$u_{tt}+c_1u_t = c_2u_{xx}$
...
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22 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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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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0answers
26 views
Math cookbooks beside matrix cookbook
Are there cookbook style references for other branches of mathematics such as topology, functional analysis, diff calculus, and so on...
https://www.math.uwaterloo.ca/~hwolkowi/matrixcookbook.pdf
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2answers
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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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Reference request on the Schwartz class on integers
It's a well known fact that the Schwartz class over integers defined by
$$S(\mathbb{Z}^n)=\{\{a_m\}_{m\in\mathbb{Z^n}}\mid \sup_{m\in\mathbb{Z}^n}|m^\alpha a_m|<\infty, \forall \alpha\in\mathbb{N}^...
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3answers
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Books about synthetic projective geometry
Are there books in English about synthetic projective geometry? More specifically, results of Karl von Staudt (imaginary elements theory through elliptical involutions, imaginary circle, infinity's ...
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0answers
33 views
The distribution of Projection, Uniformly Ergodic and Mean Ergodic operators in $\mathbb{B}(\mathbb{E})$
Let $\mathbb{E}$ be a (real or complex) Banach space.
Let $\mathbb{B}(\mathbb{E})$ be the Banach Space of all continuous (bounded) linear operators from $\mathbb{E}$ into $\mathbb{E}$, with the ...
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1answer
22 views
Question about notation on the NIST DLMF
Many relations on the NIST DLMF have certain restriction on parameters that must be satisfied in order for the relation to hold. Take for example equation $15.8.5$ which lists multiple constraints on ...
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Perturbation of Jacobi polynomials
Let us consider the inner product satisfied by Jacobi polynomials
$$\int _{a}^{b}(b-x)^{\alpha }(a+x)^{\beta }P_{m}^{(\alpha ,\beta )}(x)P_{n}^{(\alpha ,\beta )}(x)\,dx$$
where $a=0$, $b=1$ and $\...
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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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1answer
186 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
108 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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32 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
172 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-...
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0answers
26 views
Sets with a time dynamic?
I am looking for advice regarding if there is any literature wrt set theory that also has a inter temporal aspect to the set theory notation. E.g. an element can exist in one set at t=1, but move to ...
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1answer
189 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
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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 ...
6
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1answer
209 views
$q$-series and modular forms
Is there a way/database such that given a modular form
$$f(q) = \sum_{n}a_nq^n$$
with $q=\exp(2\pi i \tau)$, $\tau = \{ z \in \mathbb{C} | \Im(z)>0 \}$ the upper half plane, to find if it can be ...
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1answer
73 views
Is there a version of mean value property for $p$-harmonic funcions?
We know by mean value property that harmonic functions satisfies the equalities
\begin{equation}
u(x) = \dfrac{1}{|B_r|}\int_{B_r}f dx = \dfrac{1}{|\partial B_r|}\int_{ \partial B_r}udS.
\end{equation}...
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1answer
47 views
Regularity of a function by approximation by polynomials.
A standard argument says that a continous function is $ C^{k,\alpha} $ at zero if there exists a polinomial of degree k such that
$$
| (u - P)(x)| \le C | x|^{k+\alpha}.
$$
This is the way for ...
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1answer
34 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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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
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“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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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 ...
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33 views
Research in the Discrete Logarithm Problem
I have already taken a course on Abstract algebra and tis implementation in the criprography, among other topics the course focused on the discrete logarithm problem in finite fields.
Now, I would ...
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Causality Theory of Space-Time.
I'm looking for some books about causality theory in physics from mathematical point of view. I'm already using Global Lorentzian Geometry by John Beem and Semi-riemannian Geometry by Barret O'Neill. ...
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soft question - differential geometry and topology book recommendations
I just need a few book recommendations for studying on my own.
I know the basics (trig, calc, etc.) and on my free time, I studied multivariable and vector calculus, in addition to differential ...
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What is the proper way to cite a math textbook when writing a paper?
For example, I see this written in a bibliography of a paper:
W. Fulton and J. Harris, Representation Theory, A First Course, GTM-RIM 129, Springer, 1991.
The general case isn't clear to me from ...
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1answer
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Sequence of polygons converging
Let $P$ be a polygon ($P$ doesn't have to be regular, convex... it's just $n$ distinct points of $\mathbb{R}^2$). We construct the sequence $(P^{(n)})_n$ with $P^{(0)}=P$ and $P^{(n+1)}$ is the ...
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Can I skip part III in Dummit and Foote?
I am reading Abstract Algebra by Dummit anfd Foote. I have already taken an introductory course in linear algebra, mostly at the level of Strang's MIT OCW Linear Algebra. My question is: Can I skip '...
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Recommendation topic - Numerical Analysis and computational
I'm having a course about 'Numerical Analysis and computational' in my master's. The course is about :
Systems of Linear Equations: direct methods (LU factorization and Cholesky decomposition), ...
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Book of support for reading the Fulton book.
I would like to know about some support reference that could help me in reading the Fulton (Algebraic Curves). Sometimes, some definitions I find in Fulton's book are not clear to me. So maybe with ...
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653 views
Has Number Fields by D. Marcus ever been typeset using TeX by anyone yet? [closed]
As the title suggests, has anyone yet "latexed" Number Fields by Marcus yet? It's a classic book on number theory and I was thinking of slowly typesetting it in LaTeX during my free time, if no one ...
2
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1answer
143 views
Where are the Optimal Tours of TSPLIB 95 Instances?
I am looking for the optimal tours of the TSPLIB 95 instances as downloadable files. I have checked several places, but all lists I could find contain gaps, despite the fact, that all instances have ...
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250 views
Camille Jordan : Treatise on substitutions and algebraic equations ??
Is there english translation available of the monograph by Camille Jordan, titled: Traité des substitutions et des équations algébriques, which is available easily online in french.
The reason for ...
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1answer
214 views
A curious exercise in Spivak's book on calculus
On chapter 9 of the said book there is an exercise in which Spivak asks the reader to prove that Galileo "got his facts wrong". More specifically, Spivak asks one to to show if a body falls a distance ...
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Equivalence between Brouwer fixed-point theorem and Borsuk-Ulam theorem. Is there a simple proof of equivalence between them?
I wonder if Brouwer's fixed-point theorem and Borsuk-Ulam's theorem are equivalent.
Brouwer's fixed-point theorem (simple form). Let $B_{\mathbb{R}^{n}}[0,1]=\{x\in \mathbb{R}^n: \|x-0\|\leq 1\}$ ...
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Is there a name for this defined element?
If $\Theta \in \mathbb{R}^d$ compact, $\rho(x,\theta): \mathbb{R}^p\times\Theta\rightarrow\mathbb{R}^+$ continuous in $\theta \in \Theta$ for all $x$, then $B=\{\rho(x,\theta), \theta \in \Theta\}=\{\...
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1answer
189 views
A good book on Fractional Sobolev space.
Does someone can give me a good reference for fractional Sobolev spaces ? I looked on the internet but I didn't find any course on this subject. The only reference I found is the book of Adams, but it'...
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1answer
253 views
Book about Lattices, Boolean algebra
I have a subject about Applied Algebra and the first part of it it's about lattices, distributive lattices, hasse diagram, etc..
Next day we are going to start with Boolean Algebra. My professor is ...
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1answer
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Reference books for the study of integral equations.
I've got "Integral equations" as the major subject this semester.I need to know what is most suitable reference book for self-study of integral equations?How to study this subject effectively?
Any ...
