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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1answer
35 views

Metrics on integers

I am looking for a list of distances that are defined on the set of the positive integers. I am mostly interested in metrics that make the set complete, but I also consider other metrics. Any ...
0
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1answer
24 views

Linear/Integer programming reference request

There are a few other similar questions out there, but I think mine is not a duplicate because I am looking for a different kind of references than most people. I am primarily a discrete ...
0
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1answer
42 views

Curvatures in differential geometry-interpretation

The are various notions of curvatures in differential geometry: soft such as full curvature tensor for a given connection (which is tensor of type $(1,3)$), Ricci curvature tensor (type $(0,2)$ ...
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0answers
101 views

Are Lang's books reliable?

Serge Lang wrote a lot of textbooks on mathematics. However, Goro Shimura criticized him for writing so many books containing a lot of mathematical errors(he did not mention the name of the author, ...
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2answers
40 views

Finite sums of integers and similar problems: book request

I recently learned about Faulhaber's formula, which says that for each integer $p \geq 1,$ we can simplify the finite sum $\sum_{k \in \mathbb{N}}[k<n]k^p$ so that it becomes an (integer-valued) ...
4
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2answers
90 views

Gluing diagrams: is it possible to glue a surface with itself in the same point? how is the diagram drawn?

I am learning the basic concepts of Topology, and playing now with the gluing diagrams (describing the fundamental domain of a topological space), this is an excerpt of a basic description I took from ...
2
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1answer
35 views

What is the Haar measures on $SL(2, R$ And $SL(2,R) / SL(2, Z)$?

How does one parametrize those spaces in order to do integration over them? What's a good reference for doing integral a with Haar measures over matrix groups?
3
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0answers
55 views

Quick question: Determinant bundle is Cartier?

$X$ is an algebraic surface (i.e. compact complex, which embeds in a projective space). $V$ is a vector bundle of rank 2 over $X$. Why is $\det{V}=\mathcal{O}_X(D)$ for some divisor $D$? Is there a ...
2
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1answer
38 views

Is there a summary of all rules for each type of logic?

I am learning about rules in logic and type systems and am having to piece together fragments of them from different articles and books, which makes it difficult to see the subtle differences in each ...
3
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0answers
21 views

What was Gauss' 2nd Factorization Method?

Reading Jean-Luc Chabert's A History of Algorithms, I learned that Gauss, prompted by the poor state-of-the-art, designed two distinct methods for fast integer factorization. Chabert's book discusses ...
2
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0answers
23 views

Analytic version of Hilbert's XIX problem

The famous Hilbert's nineteenth problem, initially stated in the $C^\omega$ category, was reduced by Bernstein and Petrowsky to the analogous statement in the $C^\infty$ category (and, after ...
2
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1answer
79 views

Intuitive functional analysis book

I want to know a functional analysis book like Terence tao's real analysis and measure theory book, full of intuition. I am aware of linear algebra, real analysis, measure theory, Probability theory.
2
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2answers
56 views

Logical Formulation of the Ending of “Ode on a Grecian Urn” by John Keats [closed]

Thanks very much in advance to anyone who can help me on this problem. Here is the well-known conclusion of "Ode on a Grecian Urn" by John Keats: "Beauty is truth, truth beauty,"—that is all / Ye ...
2
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1answer
61 views

Multilinear Algebra Proof of the Cayley-Hamilton Theorem.

I am trying to understand the proof of the Cayley-Hamilton Theorem given in Section 4 of this document. On pg. 4 of the document, there is a line which reads: From general multilinear algebra, we ...
0
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0answers
27 views

Can anybody refer me a good textbook for Matrix Calculus?

I need a good textbook with mathematical approach on finding e.g. derivative of trace of a matrix, w.r.t. another matrix on which it is dependent. I need it for my study of PG Communication ...
3
votes
1answer
69 views

concept of the classification of $C^\ast$-algebras, introduction/overview

I don't have a specific mathematical problem at the moment but nevertheless I hope, my question is suitable for math.stackexchange. I'm interested in $C^\ast$-algebras and I would like to begin with ...
5
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3answers
114 views

reference for linear algebra books that teach reverse Hermite method for symmetric matrices

The method I mean is useful for symmetric matrices with integer, or at least rational entries. It diagonalizes but does NOT orthogonally diagonalize. The direction I do it, I usually call it Hermite ...
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0answers
21 views

Methodologies for non-continuum inverse problem

I am solving an ill-posed inverse problem and having a difficult time researching related methodologies because I don't know the appropriate jargon/nomenclature. I have a system with several ...
4
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0answers
21 views

terminology for a “forward flow” type of random digraph

I am trying to find a characterization of the probability that vertex $1$ is connected to an arbitrary large vertex $N$ in a random digraph. The difference from typical random digraphs is that if ...
1
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2answers
26 views

Definition of associative algebra over a field

In the definition of an algebra over a field in the wiki entry , it states that an algebra over a field is a vector space equipped with a bilinear product. Question: Does anyone know how a bilinear ...
0
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0answers
14 views

approach for clustering of huge networks

Can you give me some kind of direction on the best approach for clustering huge networks? (so large, that even the list of nodes cannot be stored in RAM) Thanks for anyone who helps.
0
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0answers
19 views

For graphs in a recursive graph class: Does m = O(n) hold?

For recursive k-terminal Graph classes - for example definied in this paper - is it true that |E| = O(|V|)? If so, I would be very grateful for a reference! Thanks!
3
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0answers
83 views

Inner Functions in Annuli: Not Likely!

The other day someone reminded me of something I'd thought about some years ago. As back then it took me a little while to see why there was any problem; this time I got much farther on a solution ...
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0answers
37 views

Transformation laws for tensors on general manifolds

I was interested in tensor products rather from the mathematical, abstract point of view, so topics like various tensor products in the context of, for example, Banach spaces, $C^*$-algebras and so ...
3
votes
1answer
31 views

Diameter of Schreier coset graphs.

I'm looking for a source from which to learn about Schreier coset graphs. Especially, examples in which combinatorial properties (specifically, diameter) of Schreier graphs are calculated. Also, is ...
0
votes
1answer
31 views

Sign patterns in kernel and rowspace of a matrix

I'm looking for the reference of the following fact from oriented matroid theory. This must be known; in fact, I think it is in the book "Oriented Matroids" by Björner et al., but I can't locate it. ...
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0answers
20 views

Why Klein Maskit Combination Theorem is important?

I am learning basics about Kleinian Groups. Recently, I read the proof of Klein Maskit Combination Theorem. I want to know about some good applications of this tool. Please share some references.
3
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0answers
30 views

Convex hull of curve

Let $f_1, \ldots, f_n \in \mathbb{R}[t]$ and let $S = \{(f_1(t), \ldots, f_n(t)) : t \in \mathbb{R}\}$. Is there a method of computing the convex hull of this set? How about if each $f_i$ has the same ...
0
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0answers
26 views

To use topology and Riemann surface in number theory.

I would like to learn some rudiment topology and Riemann surface in order to apply in number theory. I already know some algebraic topology, like covering space and fundamental group, singular ...
1
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1answer
43 views

Good reference on higher dimensional derivatives?

I've spent several months now periodically scouring the internet for a comprehensive overview of an introduction to higher dimensional derivatives. I've already read baby Rudin's section on the ...
0
votes
2answers
48 views

I need a good statistics book [duplicate]

I have an upcoming statistics exam and I'm studying it on my own. I was recommended Hogg's Introduction to Mathematical Statistics, but I didn't find it helpful. I just want a book which covers basic ...
0
votes
1answer
23 views

Reiterating the piecewise-and-uniform-limit operation

Probably a hopeless question, but: Let $C$ be the class of constant functions $f$: $[a, b]\longrightarrow\mathbb{R}$. Let $\mathcal{U}(\mathcal{P}(C))$ denote the class of uniform limits of piecewise ...
0
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0answers
31 views

The boundary integral equation

in which case we use the single layer potential and the double layer potential for the Laplace equation ? \begin{eqnarray}\tag{1} \Delta u = 0 \; \mathbb{R}^2\backslash\omega\\ u \to 0 \; at \; ...
3
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1answer
35 views

Induction and Compact induction of representations

Let $H \leq G$ be a subgroup of a finite group, $G.$ Suppose $(\sigma, W)$ is a representation of $H.$ Then we know that $Ind_H^G \sigma $ and $ind_H^G \sigma $ are isomorphic, where $$Ind_H^G ...
5
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0answers
54 views

Higher-Order Differential Operators as Vector Fields

On a $C^\infty$ manifold $M$, one can produce the tangent space $T_p M$ at a point by equivalence classes of tangents to smooth curves through the point $p$. When realised this way, the tangent ...
4
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0answers
63 views

Normal curvature of geodesic spheres

I would like to ask the community for a reference on the following property of geodesic spheres. Let $(M,g)$ be a compact Riemannian manifold without conjugate points and $\tilde{M}$ its universal ...
3
votes
1answer
125 views

Construction of a Strongly Regular Graph which has regular Neighbourhood graphs in all iteration.

Notation and Definition: $G$ is a Strongly Regular Graph (not complete or a cycle) and is denoted by $\mathrm{SRG}(n,r, \lambda, \mu)$ if it has the following properties: Every two adjacent ...
2
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1answer
46 views

Upper bound for $|\zeta'(s)|$ near the line $\sigma=1$, a detailed proof

In page 285 Apostol leaves as a reader's asigment the proof that $|\zeta'(s)|=O(\log^{2}t)$, this is for every $T>0$ there exists a positive constant $K$ (depending on T) such that ...
2
votes
1answer
86 views

Old calculus books?

this is really a question about math and not books. I am mainly wondering if reading really old calculus books is still beneficial for undrgraduate students today. I was told that the material covered ...
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0answers
42 views

Possible Connections between Harmonic Analysis, Potential Theory and Analytic Capacity for a Fourier Analyst

So, Folks, here's the deal: After looking at this question, posted a little earlier on this site, and getting quite inspired by the beauty of this kind of result, I have got quite interested on this ...
5
votes
1answer
319 views

If a $n$-manifold exists, then is it the boundary of an existing $(n+1)$-manifold?

I am reading some basic context books about topology (i.e. The Poincaré Conjecture, by Donal O'Shea between others) and following this open Topology and Geometry video lectures of the brilliant ...
2
votes
2answers
94 views

$\zeta(2n)$ proof [duplicate]

Can anybody pass me on a good source to see the steps in proving, \begin{equation} \zeta(2n) = \frac{(-1)^{k-1}B_2k (2 \pi)^{2k}}{2(2k)!} \end{equation} I know how we start by looking at the product ...
10
votes
2answers
225 views

Proof of infinitude of prime elements?

All proofs of infinitude of primes which I know of essentially prove that there are infinitely many irreducible elements of $\Bbb Z$, and with this goal in mind we can very easily extend this proof to ...
0
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0answers
18 views

$\liminf_n \min(a_n,b_n)=\min( \liminf_n a_n, \liminf_n b_n)$

Do you have a reference for the following intuitive result? Let $(a_n)_{n\ge 1}$ and $(b_n)_{n\ge 1}$ be two sequence of reals. Then $$\liminf_n \min(a_n,b_n)=\min( \liminf_n a_n, \liminf_n b_n).$$
1
vote
1answer
52 views

Special Properties of Real Matrices With Real Distinct Eigenvalues

Are there any special properties of real matrices (not necessarily symmetric) with "real" distinct eigenvalues, other than the well-known properties like being diagonalizable, which has nothing to do ...
1
vote
1answer
61 views

Number of Automorphisms of a Irregular Graph.

I have been looking for results on number of graph automorphisms of irregular graph(upper and lower bound). I searched , but could not find anything which can be used directly. Say, $G$ is $k$ ...
2
votes
1answer
29 views

Field norm of $F(\sqrt[n]{a})$

Let $F$ be a field of characteristic zero that contains a primitive $n^{th}$ root of unity. Pick $a$ such that $K=F(\sqrt[n]{a})$ is a cyclic extension of $F$ of degree $n$. Let $\sigma$ be a ...
5
votes
1answer
56 views

A good, self-study statistical computing book

I'm looking for a book an introductory statistical computing that has proofs for the methods as well as examples. I'd like proofs that are about the same level as (or lower than) proofs in Statistical ...
2
votes
1answer
150 views

Solution of Graph Isomorphism in current literature.

As of 2008, the best algorithm for graph isomorphism (Babai & Luks 1983) has run time $2^{O(\sqrt(n log n))}$ for graphs with n vertices. Does this algorithm gives a yes / no answer or provide ...
5
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0answers
105 views

Are there papers or books that explain why Bernhard Riemann believed that his hypothesis is true?

I would like to know what are the mathematical reasons for which Bernhard Riemann believed that his hypothesis is true, and I would like to know if those mathematical reasons were cited in his ...