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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3
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0answers
43 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
28 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. ...
0
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0answers
17 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 ...
1
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2answers
30 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 ...
2
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0answers
76 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 ...
-2
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0answers
26 views

a question in De koninck and luca's analytic number theory

what is your idea,can you introduce a book for these kind of problems?
1
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0answers
17 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 ...
1
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0answers
50 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. ...
0
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0answers
59 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
votes
1answer
21 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 ...
0
votes
0answers
5 views

Space complexity of the GNFS

The time complexity of the general number field sieve is generally quoted as $L_n\left[\frac{1}{3}, \sqrt[3]{\frac{64}{9}}\right]$. I'm looking for a credible reference (something that can be quoted ...
2
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0answers
24 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 ...
1
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0answers
48 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 ...
1
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0answers
28 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 ...
1
vote
1answer
30 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 ...
1
vote
0answers
17 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 ...
6
votes
4answers
246 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. ...
0
votes
0answers
20 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
20 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 ...
0
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0answers
23 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 ...
0
votes
0answers
14 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 ...
1
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0answers
26 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 $E\left[\mathbf{1}_{[a,b]}(Y)\right] = P(a \le Y \le b)$, ...
1
vote
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 ...
0
votes
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 ...
6
votes
2answers
55 views

Homotopical perspective on the long exact sequence in homology and Mayer-Vietoris

For a while I have been wondering whether the long exact sequence in homology and the Mayer-Vietoris sequence can be phrased in homotopical terms. Recently, I heard that both may be reformulated via ...
0
votes
0answers
6 views

Minimizing constrained functions on $l^p$

Suppose we have some functionals $H,G:l^p(\mathbb{N}^+)\to\mathbb{R}$, and we want to find some $p \in l^p(\mathbb{N^+})$ which minimize $H$, subject to the constraint that $G(p)=0$ is constant. As ...
-1
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0answers
34 views

Suggest good book for understanding Fourier transform

I am beginner and want to learn Fourier transform. I want to understand Fourier transform in detail . So can anybody suggest good book or resource to learn Fourier transform which have Simple ...
4
votes
0answers
56 views

Are there differences between the International and U.S. Editions of Dummit and Foote?

I'm taking an abstract algebra course this fall and want the textbook over the summer. I found an international copy of Dummit and Foote Abstract Algebra 3rd ed. for much cheaper than the U.S. ...
3
votes
1answer
54 views

The limit is that which is neither too big nor too small to be the limit.

Proposed definition: $$ \lim_{x\to a} f(x) = L $$ means $L$ is the only number that is neither too big nor too small to be the limit. This can make sense only if one says precisely what "too big" and ...
3
votes
1answer
61 views

Has this approximation $0.41468250985111166$ a name?

William Hughes calculated on WolframAlpha the expression $$ \sum_{n=1}^{\infty} \frac{1}{2^{\operatorname{prime}(n)}} $$ and got the approximate value $0.41468250985111166$. If one enters this value ...
3
votes
1answer
28 views

Reducing a double ultrapower to a single ultrapower

I hate having to ask this question, as I know for a fact I have seen the answer before but cannot seem to find it. So I'm breaking down and asking for a reference. Given a structure, let's say a ...
10
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0answers
93 views

Is there a “ping-pong lemma proof” that $\langle x \mapsto x+1,x \mapsto x^3 \rangle$ is a free group of rank 2?

Let $f,g: \mathbb R \to \mathbb R$ be the permutations defined by $f: x \mapsto x+1$ and $g: x \mapsto x^3$, or maybe even have $g:x \mapsto x^p$, $p$ an odd prime. In the book, by Pierre de la ...
0
votes
0answers
23 views

Seminar concearning Spectral Theory of Differential Operators?

I must prepare a seminar about spectral theory of linear partial differential operators. However, I'm at a loss as to a nice reference. I'm looking for something that fits in a graduate spectral ...
0
votes
0answers
13 views

The difference between weakly ordered set and partially ordered set?

I need a reference that discusses the difference between a weakly ordered set and a partially ordered set. My understanding is that a weakly ordered set $<X, \succsim>$ is one where the ...
0
votes
2answers
51 views
+50

Point-set topology

I am about to begin a self-study project in point-set topology. I am a final year undergraduate. I am looking for suitable resources, I have so far come across Munkres' textbook and would like to find ...
3
votes
1answer
27 views

Book recommendation for network theory

I'm looking for a mathematically rigorous book on Network theory covering topics like entropy, degree distribution, centrality, and regular, random, small-world and scale-free networks. I'm familiar ...
1
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0answers
13 views

solving non-linear systems inequalities

I am trying to solve a non-linear systems of 14 inequalities with 12 variables, involving exponential and polynomial functions. I have been searching over the web for leads,but without any success.I ...
4
votes
2answers
70 views

Non-compactness of the resolvent

Consider a complete non-compact Riemannian manifold $M$ and the resolvent of the Laplacian $(-\Delta + \lambda I)^{-1}$. It is known that the resolvent is in general not a compact operator. I am ...
6
votes
1answer
44 views

Group cohomology of dihedral groups

If $m$ is odd, the group cohomology of the dihedral group $D_m$ of order $2m$ is given by $$H^n(D_m;\mathbb{Z}) = \begin{cases} \mathbb{Z} & n = 0 \\ \mathbb{Z}/(2m) & n \equiv 0 \bmod 4, ~ n ...
-3
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0answers
59 views

Does anyone know of a book that explains factoring well?

Can anyone recommend me a book comes well explained the process to factor a polynomial of two variables with complex coefficients, as the multiplication of convergent power series in two variables ...
2
votes
1answer
57 views

Example of function not Fourier Invertible in $L^1$

It is well known that, if $1 < p \le 2$, then, for every $f \in L^p$, $$ \int_{[-R,R]^n} e^{-2\pi i x \cdot y} \hat{f}(y) dy \rightarrow f(x) $$ As $R \rightarrow \infty$, in the $L^p$ sense. ...
2
votes
0answers
20 views

graded Hopf algebra and its dual

I am learning Hopf algebras, and there are two questions as follows: Is the tensor product of two Hopf algebras still a Hopf algebra? Let $A$ be an infinite dimensional algebra. Is the dual ...
4
votes
0answers
36 views

Number of squarefree numbers and the Basel problem

Who discovered/proved that there are about $$ \frac{x}{\zeta(2)} $$ squarefree numbers up to $x$, or (roughly) when was this first known? Today I think this is considered 'obvious', but I don't know ...
2
votes
1answer
24 views

Runge's Theorem for meromrophic functions

Is there a name for this extension of Runge's theorem? Theorem: Let $K\subset\mathbb{C}$ be compact, and let $A\subset K^c$ be a set which intersects each component of $K^c$. Let $f$ be meromorphic ...
4
votes
2answers
40 views

A Mertens-like product over primes

MathWorld's page Prime Products gives the 'related result' (7) to Mertens' theorem: $$ \lim_{n\to\infty}\log p_n\prod_{k=1}^n\frac{1}{1+1/p_k}=\frac{\pi^2}{6e^\gamma}. $$ Does this identity have a ...
6
votes
0answers
56 views

Multivalued Functions for Dummies

I have been studying complex analysis for a while, but I still cannot "get" how multivalued functions work. Despite having it explained to me many times, my brain cannot process it. For example, I ...
1
vote
1answer
47 views

Does a $K_n$ with $n$ pendants have a name?

Consider the graph we get by taking the complete graph on $n$ vertices, and then attaching a pendant vertex to each of the $n$ vertices by an edge. Does such a graph have a name, i.e. do such graphs ...
0
votes
0answers
15 views

Reducing uncertainty of a mathematical model with data (Process control)

I know this is a very broad question, but need suggestions, link to good reference papers etc. So here is the question: I have an uncertain model whose parameters are static (not changing with time) ...
2
votes
0answers
56 views

Real form and real structure on a complex Lie group

E.B.Vinberg and A.L.Onishchik in their book give the following two definitions. For a complex Lie group $G$ its real Lie subgroup $H$ is called a real form of $G$, if a) the Lie algebra $L(H)$ of ...
0
votes
1answer
23 views

Ratio of degrees of nodes in Graph

I have a question regarding to graph and ratio of degrees of nodes in graphs. See the following image: I'm going to find a relation between $A$ and $C$. So, I count all links from $C$ to $B$s $= ...