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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14 views

Reference for Inverse Scatering Transform

I am looking for a good introductory text to learn inverse scatering transformation and related topics (Lax pairs, nonlinear FT). Any pointer is much appreciated.
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1answer
59 views

Rigorous numerical analysis textbook

I'm currently taking a numerical analysis course. We are covering linear algebra topics, the gist of the first chapter of the course being solving systems of linear equations. The lecturer has ...
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1answer
11 views

Invariants of a finite abelian group written as a central extension of a cyclic group by a finite abelian group.

Notation : If $A$ is a finite abelian group then $(d_r,...,d_1)$ are the invariants of $A$ if $d_r>1$ : $$A\text{ is isomorphic to } \mathbb{Z}/d_r\times...\times \mathbb{Z}/d_1 \text{ and } ...
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0answers
85 views

Good text to start studying topological games?

Topological games and some similar infinite games seem to be often used used as a tool in some areas of general topology, but also some other areas, such as Ramsey theory, filters, etc. Probably the ...
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0answers
40 views

Comprehensive Mathematics References/Textbooks (Like Bourbaki's Elements, or the Stacks Project)

Are there any comprehensive mathematics reference/textbooks that could be considered somewhat like a modern version of Bourbaki's Elements? "Comprehensive" here could refer to a single area of ...
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0answers
42 views

What's the name of this problem? Interesting minimisation of a length.

There is a problem which has to do with minimising the length of a (possibly disjoint) barrier in a region of space (often a 2D circle) such that no straight line can pass through the particular ...
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3answers
74 views

Textbook on group theory for physics student

I'm an undergraduate physics student and realize I should learn some group theory for physics. Does anyone know any good textbooks that would be good for this? I've found the following but am not sure ...
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0answers
35 views

Plane curves admitting several ways to seal it up by the disc

Let $\gamma:S^1\to\mathbb R^2$ be an immersed closed curve with only isolated transversal self-intersections. Say that $\gamma$ is sealed by the disc if there is an immersion $f:D^2\to\mathbb R^2$ ...
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0answers
18 views

What is a good book/online source about the subject of reliability? [closed]

I am particularly interested about Reliability function $R(t)$ Failure function $h(t)$ Renewal process Maintained systems Nonhomogenius Poisson process and reliability growth Thank you.
3
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0answers
30 views

Reference request on non-Hausdorff topology

I am looking for a introductory textbook dedicated to non-Hausdorff topology, covering how standard definitions and concepts can be adapted to that case. That would be great if the book could include ...
1
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1answer
20 views

1-model complete

For $L$ structures $A$ and $B$ we write $A\preceq_{1}B$ if $A\subseteq{B}$ and $A\models{\varphi(a)}$ iff $B\models{\varphi(a)}$ for any finite tuple (of the correct length) $a$ from $A$ and for any ...
3
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1answer
34 views

Literature on the differential operator $-\frac{d^2}{dx^2}-\frac{2\nu+1}{x}\frac{d}{dx} + x^2$

I'm trying to find any possible literature on the differential operator $-\frac{d^2}{dx^2}-\frac{2\nu+1}{x}\frac{d}{dx} + x^2$. This is constructed out of the Fourier-Bessel differential operator and ...
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2answers
23 views

Reference for stochastic calculus with jumps

All the standard books I know on stochastic calculus work almost exclusively with continuous martingales. What are the standard references for the general theory (with jumps)?
3
votes
1answer
102 views

Equivalent bimodule categories

Let $A,B$ be two rings such that their categories of bimodules are equivalent: $$A\mathsf{-Bimod} \simeq B\mathsf{-Bimod}$$ What can we say about $A$ and $B$? Are they isomorphic? Are they ...
2
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1answer
50 views

Complex Elliptic Surfaces without sections

Is there a description of smooth complex projective surfaces without sections? While working on a problem a surface $X$ showed up with the following property: it is a non-ruled surface that has an ...
0
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0answers
13 views

Haar System on the Unit Intervall

Where can I find a proof that the Haar functions form on orthonormal basis of $L^2[0,1]$? Here the Haar functions are defined as $$h_m:[0,1]\to \Bbb R,\quad t\mapsto 2^{n/2}\,f(2^nt-k)$$ with ...
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0answers
36 views

Which book to use in conjunction with Munkres' TOPOLOGY, 2nd edition?

Although Topology by James R. Munkres, 2nd edition, is a fairly easy read in itself, I would still like to know if there's any text (or set of notes available online) that is a particularly good ...
5
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2answers
173 views

Book on applied mathematics/analysis

My Applied Mathematics course covers these subjects: -Calculus of Variations -Laplace Transform -Fourier Analysis -Special Functions -Integral Equations And as an introduction to the subject it has ...
0
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1answer
27 views

operator theory background

Mathematics is often divided into Analysis and Algebra. I want to know under which area Operator Theory lies. I have studied functional analysis where we studied operators on infinite dimensional ...
3
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1answer
22 views

Congruences and solution repeat intervals

I'm teaching myself about congruences, and I've done quite a few examples, but the answers to two problems have me confused. I understand $$3x \equiv 5 \pmod{7}\quad \Rightarrow\quad x \equiv 4 ...
0
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1answer
41 views

Reference request: Proof that every product of vector space is isomorphic to the tangent bundle

On Wikipedia, it says On every tangent bundle $TM$, considered as a manifold itself, one can define a canonical vector field $V : TM → TTM$ as the diagonal map on the tangent space at each ...
2
votes
1answer
56 views

Proof of general Poincaré Conjecture $\dim > 5$

Given $M$ is simply connected, $\dim(M) > 5$ and homotopy equivalent to a sphere. Let $W := M - D_1 \cup D_2$ for two smoothly embedded disjoint disks. How does one see that $W$ is simply ...
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0answers
9 views

Reference requests on SP -graphs to outline its research areas

I want to understand SP graphs (series-parallel graphs) deeper for more elegant computation. I want to understand which area to research to understand sp-graph deeper: logical formalism? ...
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0answers
49 views

what is the origin of the proof via peaks?

What is the history of the proof of the existence of a monotone subsequence via peaks as found for example here as well as in problem 6, page 4 here (where they are called "giants" instead of ...
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2answers
43 views

Finance mathematics for high schools - book recommendation

I am looking for books of Finance mathematics for high schools with exercises and problems. Please, could you recommend me some books? Thanks.
5
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1answer
48 views

Components of the space of immersions 2-manifold into $\mathbb R^3$

Let $M$ be a $2$-sphere with $g$ handles. Consider the space of maps $M\to \mathbb R^3$, which are immersions [i.e. smooth maps with nondegenerate differential in each point $x\in M$], with ...
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0answers
27 views

Mathematics of finance - reference - Exercise, Problem books for High schools [duplicate]

Please, could you give me any examples of books (Problem books with exercises) of Mathematics of finance for High schools? Thanks for any advice.
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1answer
87 views

Diophantine equations for polynomials

I know that there has been work on diophanitine equations with solutions in poynomials ( rather than integers ) of the Fermat and Catalan type $x(t)^n+y(t)^n=z(t)^n$ ; $x(t)^m-y(t)^n=1$ and these have ...
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0answers
56 views

Books with similar coverage to Linear Algebra Done Wrong

Axler's book is great, but for my immediate purposes, it isn't suitable. I've been looking at the Table of Contents of Linear Algebra Done Wrong by Treil starting at p. 5 of this document but there's ...
2
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1answer
42 views

Question on syzygies

It is hard to formulate a question, but I want to ask about a reference/recipe for computing syzygies in general. For example, on $\mathbb{P}^1_{(x:y)}$ there is an exact sequence $0\longrightarrow ...
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2answers
43 views

Line in projective space is an example of a curve of genus $0$?

Let $L$ be a line in the projective space $\mathbb{P}^n$ over a field $k$. Is a line $L$ an example of a curve of genus $0$ in $\mathbb{P}^n$. I was wondering if I could verify this with someone, ...
2
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2answers
43 views

Reference/Literature on Cantor Sets

I recently came across Cantor sets in my analysis course while doing a hw problem and find them extremely fascinating. I am trying to find other notes/literature on cantor sets with no success. I only ...
2
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0answers
21 views

Website for sharing solutions/proof verification?

Is there a website for sharing solutions to exercises in math books? I'm self-studying math and I find solution manuals like this very helpful. When I do an exercise, I usually scribble down a few ...
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2answers
52 views

Is $x_1^d + x_2^d + x_3^d + x_4^d + x_5^d= 0$ a geometrically integral hypersurface in $\mathbb{P}^4$?

Let $d>2. $Let $X$ be a surface defined by $x_1^d + x_2^d + x_3^d + x_4^d + x_5^d= 0$ in $\mathbb{P}^4_{\mathbb{Q}}$? I am interested in finding out if this is a geometrically integral hypersurface ...
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0answers
26 views

Hilbert's inequality for $\left|\sum_{n\neq m}\frac{a_n \bar{a}_m}{\left(n-m\right)^\lambda}\right|$.

We know that, the Hilbert's inequality for double series states $$\left|\sum_{n\neq m}\frac{a_n \bar{a}_m}{n-m}\right|\leq\pi \sum_n |a_n|^2$$ for $a_n\in\mathbb C$. I'd like to know if inequalities ...
2
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0answers
39 views

Construction of Tate curve and formal schemes

In the notes websites.math.leidenuniv.nl/geom/tate.ps (and probably in other places), there is a construction of the Tate curve, where the steps are summarized below. 1) Take ...
3
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0answers
49 views

Short exact sequence on $\mathbb{P}^1$

Let F be a torsion free sheaf of rank $n+4$ over $\mathbb{P}^1$ which fits in the SES $0\longrightarrow\mathcal{O}_\mathbb{P^1}(-3)^{n+2}\longrightarrow ...
3
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0answers
81 views

Symmetry and trivial solutions to Pell equations

Below is a representation of the solutions to the equation $x^2-Dy^2=1$ for $6(6-1)\leq D \leq 6(6+1)$: \begin{array}{c} & 30 & 31 & 32 & 33 & 34 & 35 & 36 & 37 & ...
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0answers
24 views

Reference request: correlation and spectral analysis of stochastic processes

I'm wondering if anyone knows of a reasonably rigorous text on stochastic processes that discusses specifically things like the autocorrelation, spectral density, and other "correlation and spectral" ...
0
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0answers
43 views

Text book on solid geometry/stereometry, without involving analytic geometry

As the title says I'm searching for a textbook, about solid geometry, without involving analytic geometry. The material which the book should cover is the stereometry learned in the eastern bloc. An ...
2
votes
1answer
59 views

Representation of regular languages by monoids [closed]

I'm interested in representation of regular languages by monoids, and in particular of how to use this kind of representation to get a recognizer. I have found some references on the web, but does ...
1
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2answers
64 views

No Galois Theory in Godement's Cours d'Algebre?

I just procured an English translation of Godement's Cours d'Algebre and was interested in reading the treatment of Galois Theory. I started to look for the relevant chapter in the ToC, but to my ...
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0answers
17 views

Decidability of the theory $(\mathbb{R},+,*,\max,\leq)$

I know that the theory $(\mathbb{R},+,*,\leq)$ is decidable (Tarski 51) and I was wondering wether the decidability status is known when extending this theory with the $\max$ operator. Do you have ...
23
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2answers
349 views

A diophantine equation with only “titanic” solutions

I made a note some time ago that I had read in some book that the equation $$313(x^3+y^3)=t^3$$ has positive integer solutions, but that these are so large that it would be absolutely hopeless to ...
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1answer
44 views

Does this function have a name? What other properties does it have?

Let $x < y$ be real numbers and let $ a$ satisfy $0<a<1$, Does the function $ z = a y +(1-a)x$ have a name? What properties does this function have? This particular function has come up a ...
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2answers
48 views

how to find null space basis directly by matrix calculation

The problem of finding the basis for the null space of an $m \times n$ matrix $A$ is a well-known problem of linear algebra. We solve $Ax=0$ by Gaussian elimination. Either the solution is unique and ...
2
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1answer
35 views

Geodesics are minimizing in a simply connected manifold without conjugate points?

Let $\tilde M$ be a compact Riemannian manifold, without conjugate points. Denote by $M$ its universal cover. Then in this paper, it is claimed that every geodesic is globally length minimizing. Why ...
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0answers
40 views

Quick question about number of positive summands in a sum of $p$-adic integers

I've started reading recently on $p$-adic numbers online. Forgive me if the question is silly. Let $\mathbb{Z}_p$ be the ring of $p$-adic integers and let $a_1, \ldots, a_k \in \mathbb{Z}_p$. If ...
0
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2answers
57 views

Reference request on complex projective algebraic geometry

I am looking for a reference on complex algebraic projective geometry. Specifically, I would like to become more acquainted with notions like the dimension and the degree of a projective algebraic ...
0
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0answers
33 views

Prove that The set of Sentences over a theory $T$ is a Cartesian Closed Category

i am sorry to bother but, I have doubts with this problem: In some elementary theory $\;$ $T$ $\;$ consider the set $S=\{p,q,\ldots \}$ of sentences of $T$ as a preorder, with $p\leq q$ meaning "$p$ ...