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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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the probability distribution of Y is P{Y=-1}=p P{Y=1}=1-p,(0<p<1),set Z=XY. [on hold]

Let the random variables $X$ and $Y$ be independent,$X$ follows the exponential distribution with parameter $1$, and the probability distribution of $Y$ is $P${Y=$-1$}=$p$ $P${Y=$1$}=$1$-$p$,set$ Z=XY$...
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*Reference Request* - Monograph on Triangular Numbers

Does anybody here know of a good monograph on triangular numbers, which preferably covers the basic number theory stuff and connections with other number-theoretic concepts? I tried searching MSE to ...
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Search for a paper?

I'm going to work on this paper: An existence theorem for weak solutions of differential equations in Banach spaces..I searched for it by internet, but I found it nowhere Can you help me find it? I ...
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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
58 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
91 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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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
96 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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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
73 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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342 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
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$q$-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
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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
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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
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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
89 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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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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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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1answer
108 views

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
83 views

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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502 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 ...
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1answer
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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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175 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
196 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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324 views

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
127 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
194 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 ...
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3answers
658 views

Pentagon properties [closed]

I am looking for some beautiful properties of pentagon. Can you guide me to a reference which had the properties or hint me here about them . thanks in advanced . I lookup wikipedia ...but I can't ...
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1answer
315 views

How does one do research in any field? [closed]

I have started my PhD in this academic year.The topic which I have been given to work on is Spectral Graph Theory. As I have just completed my Master's Course which was very straight forward for me ...
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4answers
563 views

More comprehensive General Topology's book than Engelking

Other than Engelking General Topology, I also come across other graduate general topology text such as Dugundji and Kelley, which I also find them interesting. However, I find Engelking's book more ...
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1answer
99 views

What's a good intro to pure math/proofs book that focuses on knowing/learning definitions, corollaries, theorems, basic concepts?

I looked at rudin and some others and I feel like Rudin's real analysis tests you on your ability to pull magic tricks out of a black hat rather than on your ability to know key definitions,...
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114 views

Nets with no convergent subnets in Banach spaces

Is there a characterization of nets with no convergent subnets in a Banach space? Does someone know some survey or book's chapter that deals with this kind of stuff?
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1answer
66 views

Must proofs be self-contained or can you cite references?

In a proof (in general, not just for school work), must the proof be self-contained or could you cite references within the proof? For instance, if I want to show that the Cantor set is uncountable, ...
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1answer
49 views

bialgebras and hopf algebras over a category

I am currently looking for a reference on how to define a bialgebra over a category or a Hopf algebra over a category, I have consulted in several texts of Hopf algebras but only define these ...
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List of 2D definite integrals not reducible to products of 1D integrals

I'm writing numerical integration routines for 2D surface integrals. To test it, I'm looking for a list of definite integrals which have analytic forms. I need Integrals in polar coordinates over the ...
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Practice questions

I would like to know if there are any good textbooks/online resources that include plenty of practice problems with solutions for the following topics: Triple integrals in cylindrical coordinates, ...
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1answer
25 views

Journal Volume or Number? [closed]

In the citation Proc. Amer. Math. Soc. 2 (1951), 839-848 originally found here: http://www.ams.org/journals/proc/1951-002-06/S0002-9939-1951-0045941-1/ How should I interpret the 2?
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339 views

Reference book of complex analysis [duplicate]

Please tell me a good reference book of complex analysis. I am a postgraduate student. I really need this. I want to strong my basic concepts from starting. So please help me ..... Now I am reading ...
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1answer
110 views

First use of little $o$ notation?

I am reading some material which makes use of Landau(-Bachmann) notation for the asymptotic behavior of some error. I started to wonder when this notation (especially the little $o$ on) has been ...
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1answer
76 views

Translation suggestion of an operation - adding and subtracting the same term - German: Nullergänzung

How would one call this operation in English where we add a term $a$ and subtract the additive inverse $-a$ right away again, so $$ f(x)-g(x)=f(x)-a+a-g(x) $$ for example here where we also use the ...