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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Testing a sub component of a state space model

I am building a discrete time linear Gaussian state space model where the state ($x_k$) is of dimension $p\geq 2$: $$x_k = A x_{k-1} + v_k\quad k = 1, \ldots, N$$ $$y_k = F x_{k-1} + w_k\quad k = 1, ...
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0answers
19 views

What is an automata network?

I've tried Wikipedia and Google as first steps, but while I've found some interesting papers and articles, and a couple expensive textbooks, I've yet to find a clear definition of an automata network ...
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0answers
27 views

Applied nonlinear dynamics: the onset of chaos in biological cycles (reference request)

I have seen some applied research in the onset of chaos in the study of current regulation in the human heart and the transition into cardiac arrest. I would like to review any literature that exists ...
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0answers
31 views

Book on Random Group Theory

I'm looking for a book on random group theory. I haven't had any luck in finding books specifically on this topic.
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1answer
61 views

What is a good first book on Algebra? [duplicate]

I'm planning to take a phd-level Algebra class this fall semester and so I want to spend some of the summer going through a good first book. The phd course will assume knowledge of undergrad Algebra. ...
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0answers
19 views

Convergence of sum of reciprocal of powers of linear combinations of integrs

From calculus comparison theorems, we have the following well-known result: $\displaystyle\sum_{n\ge1} \dfrac{1}{n^k}$ is absolutely convergent iff $k>1$, where k is a real number. I'm currently ...
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0answers
22 views

Book or lecture note on presymplectic-manifolds

I'm looking for a book/ lecture note in which presymplectic manifolds and matters relating to them (specially dynamics of Hamiltonian systems) has been fully explained. Does anyone know such a book? ...
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0answers
56 views

Where is Apostol's Mathematical Analysis being used?

I have noticed that Walter Rudin's Principles of Mathematical Analysis, third edition, is being used at many universities in the US. I'm wondering which of the world's top ranked universities, ...
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1answer
37 views

Mcgehee transformation, conversion to polar coordinates and blowing up the singularity

I am looking for any reference on the above topics as I am struggling to convert the below to polar coordinates in phase space: The system is: \begin{equation*} x''=\frac{-\mu x}{(\mu x^2 + ...
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0answers
23 views

Looking for examples of Discrete / Continuous complementary approaches

Among many fascinating sides of mathematics, there is one that I find very rewarding, especially in teaching at undergraduate level: the parallels that can be drawn between a "Continuous world" and a ...
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1answer
38 views

Documentary on number theory

Can anyone suggest documentaries on Number theory ? Looking to show it to high school and undergrads Thanks
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1answer
68 views

Collected works of Mathematicians

The collected work of any mathematician is, in my opinion, more than collection of his works. Since it is edited (collected) by some people which have passed through many papers of the mathematician, ...
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1answer
41 views

Reference for real analytic manifolds

I'm trying to find a reference for some introduction to real analytic manifolds. I'm especially interested in the fact, that the set of regular points of an analytic function $F \colon M \to ...
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0answers
30 views

A calculation in polar coordinates in $\mathbb{R}^n$; pointwise gradient bounds

Suppose we have a smooth function $f : \mathbb{R}^n \to \mathbb{R}$, and it is given that $f(0) = 1$. It is also known that $|\nabla f| \leq \gamma |f|$ everywhere. The question is, what is the radius ...
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3answers
96 views

If $ab^2+1 = c^2+d^2$ with $a$ squarefree, what [else] can be said about $a$?

What is known about squarefree integers $a$ where there exist non-zero integers $b$, $c$, and $d$, with $\gcd(b,c)=\gcd(b,d)=1$, such that $$ab^2+1=c^2+d^2$$ ? EDIT: As pointed out by individ, if an ...
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0answers
25 views

What is the Prerequisite to Understand Mathematical Analysis I?

I am a teenager looking to learn analysis over the summer. I have taken an interest in Mathematical Analysis I and Mathematical Analysis II by Vladimir Zorich. I have taught myself the techniques of ...
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0answers
55 views

QFT for mathematicians

I have a graduate degree in mathematics, I want to learn enough QFT to understand whats going on in Wittens paper about QFT and the Jones polynomial. So I need some QFT and maybe Chern-Simons theory. ...
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0answers
32 views

Is there any book which contains only examples and counter examples [duplicate]

I am asking this question from interview perspective. Say we know that convergent sequence is bounded but IS bounded sequence convergent ?. As given in standard books counter example of $(-1)^n$. Is ...
1
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1answer
17 views

Reference for table of cubes modulo $m$?

Is there an online table with all the cubes in $(\mathbb{Z}/m\mathbb{Z})$ (with $m$ up to (say) $100$, at least)? I didn't find anything googling it. Thanks.
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1answer
22 views

Building a hidden markov model with an absorbing state.

I'm working on trying to implement a hidden markov model to model the affect of a specific protein that can cut an RNA when the ribosome is translating the RNA slowly. Some brief background: The ...
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0answers
27 views

Looking for a certain proof of the Fundamental Lemma

The following is called the fundamental lemma: Let $\gamma$ is a closed path in $\Bbb C$ and $\varphi:$ Im$\gamma \to \Bbb C$ be continuous, and let $f_m: \Bbb C \setminus $ Im$\gamma \to \Bbb C$, ...
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1answer
49 views

Are there any large cardinals that are not ordinals? [closed]

In ZF, are there any useful large cardinal that cannot be well-ordered? I think that some of the partition cardinals are that way, since with AC, we cannot have $\kappa \to (\omega)^{\omega}$. Are ...
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0answers
11 views

How to describe scalar fields over graphs

I am trying to find the section the literature that dwells on the propagation of scalar fields over random graphs. Think of a network of ideal resistors for example, with a voltage source at a ...
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0answers
33 views

Need a book on Algebra but having these properties for self study and beginner

I have recently read a book called Understanding Analysis by Stephen D. Abbott . I really liked that book because of scratch work for proof of theorems he had presented before going over to formal ...
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0answers
22 views

Is there a broad map, guide or list of all or most of math's fields? [duplicate]

Has someone ever garthered all the different fields in maths (single variable function analisis, multivariable analisis, complex number analisis, number theory, graphs, succesions, etc) and made a ...
3
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0answers
37 views

Why do we know that , besides the known idoneal numbers , there is at most one more?

Here https://en.wikipedia.org/wiki/Idoneal_number the definition of an idoneal number is given : A number $n$ is idoneal if there are no integers $a,b,c$ with $0<a<b<c$ and $n=ab+ac+bc$ A ...
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1answer
59 views

How to represent tripartite graphs algebraically (as matrices)?

A bipartite graph can be represented by an adjacency matrix, or specifically, by a biadjacency matrix. Formally, let $G = (U, V, E)$ be a bipartite graph with parts $U = \{u_1, \ldots, u_r\}$ and $V ...
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0answers
83 views

Does anyone know a reference to best-fitting lines with integral coefficients?

I'm writing up a manual on how to generate "nice" Linear Algebra problems; that is, where the solutions tend to be integral. I "discovered" the following fact about the best-fitting line: Theorem. ...
3
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0answers
76 views

Where can I learn more about “topological germs”?

Definition 0. By a topological germ, I mean a pointed topological space. Whenever $X$ and $Y$ denote topological germs, by a morphism of topological germs $X \rightarrow Y$, I mean a neighbourhood ...
3
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0answers
52 views

What do you call the category of groups with surjections (injections)?

Take the category $Grp$ and throw out all morphisms that are not surjections. I think what's left is still a category. The composition of two surjections is surjective, and identities exist ...
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0answers
31 views

(Readings on) fundamental group and boundary identifications

I'm trying to solve some problems on topology, and I'd like to know where to find methods to calculate fundamental groups of objects like, e.g., the union of two solid tori where the two boundaries ...
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3answers
39 views

Reference Request: Parameter Dependent Center Manifold Theorem for ODEs

Suppose we have an $n$-dimensional first order ODE of the form $\frac{dx}{dt}= f_{\mu}(x)$ with $\mu \in \mathbb{R}^k$ a parameter and with an equilibrium at $x=0$ $(f_{\mu}(0) =0)$. For fixed $\mu$ ...
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0answers
19 views

Are there infinite self-locating strings in the decimal expansion of $\pi$?

I came across the following interesting objects. Self-locating strings within $\pi$: numbers $n$ such that the string $n$ is at position $n$ (after the decimal point) in decimal digits of $\pi$. The ...
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0answers
17 views

Video Lectures on Multi variable Calculus in n dimensions

I am teaching myself multi variable calculus from various resources on the internet. I have completed the famous 18.02 offered at MIT. This is an introductory course on Multi variable Calculus and is ...
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2answers
59 views

What are the books that I should study for college? [closed]

Baccalaureate exam approached Real Analysis (limits, differentiation and integration), Abstract Algebra, Functional Algebra, Linear Algebra, Combinatorics, Complex numbers, Vector Geometry, Analytical ...
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0answers
36 views

Reference for Coefficient Extraction of Multiple Sum

In a post here, the final answer is obtained by coefficent extraction of the quadruple sum. ...
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1answer
87 views

Book recommendation and online learning resources for mathematics as a hobby.

The career and field of study I am choosing is not related to maths much.But I am still interested and I love maths.But I just know math up to highschool level.So I wish to learn more,say as a hobby ...
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1answer
23 views

Reference request for Prof. Wilhelm Blashke's DG book

Please suggest how can one get a copy of the book mentioned here: TA Guess_on_W Blashke Is there an English translation of Professor Blashke's book on Differential Geometry? (Einführung in die ...
3
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2answers
31 views

Isometric embedding of $\ell ^ 1$ in $\ell ^\infty$ in finite dimensions

It is well known that $\mathbb{R}^n$ with $\ell ^1$ norm can be embedded into $\mathbb{R}^k$ with $\ell^\infty$ norm for some $k\in \mathbb{N}.$ But I guess, this is not true in complex case that is ...
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0answers
19 views

Transformations between Pell[-like] equations

I’m looking for [non-trivial] transformations that take a Pell-like equation $$ u^2-dv^2=w $$ and turn it into another Pell-like equation $$ x^2-my^2 = z. $$ Best-case scenario, one could always use ...
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0answers
27 views

On Kapranov's “On the derived categories of coherent sheaves on some homogeneous spaces”

As a graduate master student I am reading Kapranov's paper "On the derived categories of coherent sheaves on some homogeneous spaces" (1988). One problem is that the paper assume lot of notations and ...
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2answers
36 views

Probability of a number in the real line

I have read that the probability to pick a rational number in the real line is null. My problem is: If $S$ is a dense set in the real line, what is the probability to pick an element of $S$? There ...
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3answers
29 views

Algorithm: Intersection of two conics

I am looking for a detailed description of an algorithm for the classical problem of computing the intersection of two conic curves. The curves are given by two equations of the form: $$ a x^2 + b ...
0
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1answer
27 views

Reference for finite sum of $k^{\alpha}$

in this answer, we are given a great formula for $\sum\limits_{k=1}^n k^{\alpha}$ for all real alpha. For a paper I'm writing, I need a reference for a textbook or a paper which contains this result ...
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1answer
75 views

Reference for zero sum problems?

I am looking for books/ references which deal with the analysis of zero sum problems and weighted zero sum problems. I have found some articles on the internet, but they seem insufficient. Any ...
2
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2answers
55 views

References on probability theory, stochastic processes, Monte Carlo and convex optimisation, with similar writing style to Terence Tao

I learned a lot from prof Tao's notes and books because unlike many authors, he seems to prefer writing more words, explanations and intuitions rather than just mathematical formulae. His approach is ...
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1answer
54 views

reference request: Category theory

I am sure that a similar question has been asked before, but I make my ideal textbook and situation more specific. I would like a textbook on category theory designed for someone who knows basically ...
2
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1answer
30 views

General property of Fitting series

Let $G$ be a finite solvable group. $F(G)$ (Fitting subgroup) is defined to largest normal nilpotent group contained in $G$. Then $F_2(G)$ is defined to be inverse image of $F(G/F(G))$. i.e ...
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1answer
65 views

How can the Bessel function of the second kind be in the radial eigenfunction?

Let $0<a<b<\infty$. Consider the heat equations or wave equations on the annulus or the spherical layers $$\Omega:=\{x\in\mathbb{R}^d\mid a<\|x\|_2<b\},$$ ...
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0answers
42 views

“Closure” of a polynomial ring by fraction field

Let $k$ be an algebraically closed field of characteristic $p>0$, $A$ a regular noetherian $k$-algebra, $K$ the fraction field of $A$ and $\bar{K}$ an algebraic closure of $K$. Does there exist a ...