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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Principal value methods for fourier laplace etc.

I recently saw this here: $$\int_{-\infty}^{\infty} \frac{1}{\omega^2} e^{j\omega t} d\omega$$ and I was unable to understand how such an integral could be computed. I want to learn about this ...
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0answers
10 views

The Weierstrass-Enneper representation, the Gauss map

Lemma: Let $x:S\to\mathbb{R}^3$ be a conformal minimal immersion of a Riemann surface. The 1-forms $f_k=(x_{k,u}-ix_{k,v})dz$ satisfy: $$ \sum_kf_k^2=0\qquad (1)\qquad \&\qquad ...
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1answer
31 views

Need visualization advice for learning partial derivatives and calculus with more than one variable.

Okay so I just recently started learning calculus with more than one variable and whilst I'm coming to grips with many of the ideas and stuff I'm finding it difficult to visualize certain things for ...
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0answers
12 views

Inflation-restriction exact sequence

What are classical or basic applications of the inflation-restriction exact sequence in group cohomology? (I assume that it is more than an abstract result.)
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0answers
31 views

Suggestion for modern reference on calculus

I need a book for reference in conference paper. Actually, i use Green's theorem: If functions $P(x,y)$ and $Q(x,y)$ satisfy $$\frac{\partial P}{\partial x} = \frac{\partial Q}{\partial y}$$ in ...
2
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1answer
62 views

How to learn commutative algebra?

I want to learn commutative algebra from scratch. I was wondering, as you guys are experts in mathematics, what you think is the best way to learn commutative algebra? Is there any video course ...
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0answers
8 views

Prerequisites for reading book on deformation theory

I just finished to read the last chapter of Miranda's book about Riemann surfaces and algebraic curves. In the last chapter, there is a few things about deformation theory, and I'll very interested by ...
2
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1answer
29 views

Reference for amazing generalized version of Morera's Theorem

I recently came to know about following amazing generalized version of Morera's Theorem: Theorem:Let $f$ be a continuous function on the complex plane and suppose that there exist numbers $ r_1,r_2 ...
3
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1answer
12 views

Multivariable Calculus with Tensors

I'm looking for a book at the undergraduate level on multivariable calculus (for a 2nd course of multivariable calculus) that introduces and makes use of tensors to describe higher order derivatives ...
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1answer
28 views

Spectral theory for $f\mapsto f\circ g$

Consider the Banach space $B = C([0,1] \to \mathbb R)$ of continuous functions from $[0,1] \to \mathbb R$ with the supremum norm. Let $g$ be a continuous function $g:[0,1] \to [0,1]$. Then one can ...
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1answer
25 views

Book on probability theory with sigma algebra

Please suggest or recommend a book on Probability theory emphasising on sigma algebra and with Kolmogorov’s axiomatic development.
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1answer
25 views

What delimits the mathematical framework within which information compression limits (from entropy) are valid.

Lets suppose for absurd that I eliminate one number from the naturals. If I were supersticious I would eliminate number 13. Now imagine that to keep normal mathematics possible within such system ...
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0answers
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Mixing time of three particle systems

Is there anything known about mixing time of Markov chains for three particle systems? It is proved here that the mixing time of an exclusion process is $\operatorname{O}(n)$. We can think if a ...
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0answers
36 views

What is known about this well-ordering of the rationals in a finite interval?

Given any interval $I=(a,b) \subset \mathbb R^+$, we may order the rationals in $I$ with a denominator-first lexicographic order, as follows: First, we list, in increasing order of numerator, all $q ...
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1answer
31 views

Where can I find a proof of this result?

Does anyone know where I can find a proof of the underlined statement? Newman states it without a proof, and I could see how he gets $\dfrac {\sigma}{n} + O\left(\dfrac{1}{n^{3/2}}\right)$. Any ...
3
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1answer
31 views

Generalizations of pregeometries

Combinatorial geometries and pregeometries are important in classifying strongly minimal (as well as O-minimal) theories. More formally, a model of a strongly minimal (or an O-minimal) theory with the ...
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0answers
17 views

On Diophantine approximation and irrationality proofs

This question is an offshoot from this previous MSE post. I have a ratio of two numbers $a$ and $b$ (presumably both positive integers), where $a$ and $b$ are determined by some arithmetic / ...
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1answer
14 views

Voronoi Diagrams (Reference request)

I'm studying some solid state physics and I saw the definition of Wigner-Seitz cell (or Voronoi). I'd like to see some examples of this with rigorous mathematics. I mean just some simple cases like ...
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0answers
38 views

Reference Request : Quotients of nilpotent groups which are torsion free

I am currently writing my thesis and looking for a reference (or a short proof) to the following fact: Let $N$ be a finitely generated nilpotent group, and denote its central series by ...
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0answers
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Trace theorems for arbitrary differentiability $k$, with embedding constants under control as $k\to\infty$

The usual trace theorem (with non-optimal exponents, but I don't care for those at the moment) says that $$ W^{1,p}(\Omega)\hookrightarrow L^p(\partial\Omega) $$ for Lipschitz domains. When ...
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0answers
36 views

A Good book for Combinatorial Theory

I am looking for a good book on Elementary Combinatorics (Olympiad level). For some reason I do not like Lint. I am currently reading "A Walk Through Combinatorics" by Miklos Bona and I find it really ...
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0answers
23 views

If $q^k n^2$ is an odd perfect number with Euler prime $q$, are the following statements known to hold in general?

(Note: This question has been cross-posted from MO.) Let $\sigma$ be the classical sum-of-divisors function. A number is said to be perfect if $\sigma(N)=2N$. If $q^k n^2$ is an odd perfect number ...
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0answers
10 views

Proof of Kolmogorov zero-one law in measure-theoretic setting

I have met, in some paper, the following form of the Kolmogorov zero-one law used: If $A\subseteq 2^\Bbb N$ is a subset of Cantor space such that when $x,y\in 2^\Bbb N$ are such that $x,y$ differ ...
2
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1answer
24 views

Total variation distance is complete

For a given measurable space $X$, $\mathcal{P}(X)$ denotes the space of all the probability measures on $X$. The total variation distance $\rho$ on $\mathcal{P}(X)$ is defined by: for $\mu, \nu \in ...
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1answer
44 views

The set of infinite sequences with finitely many nonzero values is dense.

Could I get a proof to this lemma or a reference if a proof is too time consuming?
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1answer
99 views
+100

Textbooks for visual learners

Perhaps this question has already been asked (if so, please let me know) but I am looking for books that appeal to visual learners. I discovered that I am able to understand concepts much quicker ...
2
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1answer
28 views

Models of Linear Logic

I am looking for an introduction to the model theory of Linear Logic. Can you recommend any clear introductions? I am particularly interested in those models that regard coherence spaces.
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0answers
85 views

Review on Riemannian Geometry

I'm currently reading through Griffiths and Harris Principles of Algebraic Geometry, and the only subject in the foundational material section that I am not completely comfortable with is riemannian ...
0
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1answer
32 views

$L^1([0, 1]) \subset C([0, 1])^*$

Basically my question is: how can I prove that $L^1([0, 1]) \subset C([0, 1])^*$, where $C([0, 1])$ represents all continuous functions on $[0, 1]$, and the superscript $^*$ means the dual space. ...
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0answers
30 views

Roadmap to $p$-adic numbers: where a self-learner should look for references

TL;DR at the end of the question. I’m currently trying to learn as much as possible about p-adic numbers. I’m not sure what is the most fascinating part of the theory, but the use of the adjective ...
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2answers
42 views

where to begin with mathematical logic- text suggestions

My name is battlefrisk and I intend to pursue a career in either operations research or artificial intelligence. I have only taken a single class on logic, and I am considering buying a text on the ...
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0answers
92 views

Comprehensive Linear Algebra Text

Occasionally I come across a fact from linear algebra that I have not seen before. These facts are often obscured in search engines by either introductory texts or unrelated papers, and it is ...
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0answers
30 views

a question in De koninck and luca's analytic number theory [on hold]

what is your idea,can you introduce a book for these kind of problems?
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0answers
20 views

Reference on Gibbs phenomenon

I need a reference that explains the following result (also known as the Gibbs phenomenon) Let $g$ be a $2\pi$-periodic function, $C^1$ per pieces (i.e., there exists a partition $x_1 < \cdots ...
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0answers
54 views

Source for (somewhat) Informal Mathematics of All Levels [on hold]

I've been around this site for a couple years now, but never formally made an account until now. I recently stumbled upon a new mathematics blog, and I wanted to know if it is a legitimate resource. ...
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0answers
67 views

Applications of math [on hold]

I am a soon-to-be math teacher (high school level). I know my request is broad and vague, but I still feel the need to ask you all. I want to be able to answer my students´ somewhat feared question, ...
2
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1answer
22 views

References for loop rings

I recently saw a paper on alternative loop rings, as always, I am interested in all kinds of rings, and new kind of ring looked attractive. I would like to read loop and then loop rings in detail from ...
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1answer
46 views

Looking for a “Guide for the Perplexed by Low-dimensional Topology”

The following excerpt is from pp. 56-57 of Loring Tu's (so far very enjoyable) textbook An Introduction to Manifolds (2nd ed.): One of the most surprising achievements in topology was John ...
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0answers
50 views

How I can make a proof to this conjecture if it is possible?

Is there someone who can show me the way helping me to proof this conjecture. If it's not open, at a least show me links or papers which to be helpful. Conjecture: Assume $c > 0$ and that an ...
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0answers
31 views

Algebraic approach to Local Analytic Complex Geometry

I'm attending a second course in Complex Analysis from a geometrical point of view. In the final part of the course we have discussed about germs of complex analytic sets and their algebraic ...
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1answer
35 views

Multiplicative spectral sequence

I have a simple question regarding the definition of a multiplicative spectral sequence, which I couldn't answer myself by looking at the definitions in various texts: Is the product assumed to be ...
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0answers
23 views

How to find a set of integer vectors (of length L) such that all its subsets with size L are linearly independent?

Given a number $M\geq L$, how to find a set of $M$ vectors in $\mathbb{Z}_{\geq0}^{L}$, say $S=\{\mathbf{a}_1,\cdots,\mathbf{a}_L\}$, such that: 1-All subsets of $S$ with size $L$ are linearly ...
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4answers
279 views

An introduction to algebraic topology from the categorical point of view

I'm looking for a modern algebraic topology textbook from a categorical point of view. Basically, I'd like a textbook that uses the language of functors, natural transformations, adjunctions, etc. ...
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0answers
22 views

Isometry of covering space [on hold]

Let $M$ be a compact Riemannian manifold. Consider a covering space $N$ of $M$, with the pull-back metric from $\pi : N \to M$. Given a point $x \in M$, and a couple of points $y, z \in \pi^{-1}(x) ...
2
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0answers
26 views

Reference Request: Replacement for Anderson and Fuller

I'm working through Rings and Categories of Modules by Anderson and Fuller. It's a great text, but I would like a more modern replacement. The text focuses too much on the language of generation and ...
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0answers
24 views

Help in finding a paper on nonlinear Schrodinger equations [on hold]

I'm looking for the following paper: Authors: Baillon, Jean-Bernard; Cazenave, Thierry; Figueira, Mario Title : Equation de Schrodinger non linéaire. (C. R. Acad. Sci. Paris Ser. A-B 284 ...
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0answers
15 views

Help in identifying the one dimensional map

In the paper: http://inds08.uni-klu.ac.at/INDS2008/INDS08_System_Identification_using_Symbolic_Chaotic_Sequence.pdf there is a chaotic map in Eq(11) $$c_{n+1} = \frac{\gamma c_n(1-c_n^2)}{1+\rho ...
2
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1answer
37 views

Equation with mean of random variables

In a proof I found the following conversion $$E\left[|X|\mathbf{1}_{[a,b]}(Y)\right] = E\left[|X|P(a \le Y \le b)\right]$$ I understand, why $E\left[\mathbf{1}_{[a,b]}(Y)\right] = P(a \le Y \le b)$, ...
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0answers
8 views

If $U(\mathbb{Z}G)$ is nilpotent/ FC group than $TU(\mathbb{Z}G)$ is a subgroup.

I am doing a short paper by Miles and Parmenter "GROUP RINGS WHOSE UNITS FORM A NILPOTENT OR FC GROUP" and the main theorem in that is the following- Now for (i) or (ii) implies (iii) he writes ...
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0answers
7 views

Reference for S.D. Berman Paper on integral group ring

Can somebody tell me where I can find this paper "S. D. Berman, On the equation $x^m = 1$ in an integral group ring, Ukrain. Math. Z., 7 (1955), pp. 253-261." I looked it up in springer Here only ...