Questions tagged [reference-request]

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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Uniqueness of the ternary Golay codes

In [Van Lint - Introduction to Coding Theory] the uniqueness of the binary Golay codes is shown quite easily. In essence, the proof boils down to the fact that there is only one 2-$(11,5,2)$-design up ...
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References for me to understand current approaches to settle $P$ vs $NP$

I am an undergrad student that likes to study approaches to settle $P$ vs $NP$. I know that there is GCT method, and another way is to attack it by logic equivalent. I am a double major student in CS ...
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Books about operator algebra and number theory

Does anyone know books that covers both operator algebras and number theory. Actually, a number theory books that has operator algebraic approaches.
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Reference for time dependent traces

Consider the spaces $H^{1/2}(0,T; L^2(\partial\Omega))$, or $L^2(0,T;H^{3/2}(\Omega))$ and what not. I'm interested in a reference book illustrating the meaning, properties of these spaces (so, ...
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Absolute value of functions in $H^1(\mathbb R^n)$

Let $f$ be a function in the atomic Hardy space $H^1_{at}(\mathbb R^n)$. That is, there exists a sequence of atoms $a_j$ satisfying supp $a_j \subset B_j$ for some ball $B_j$, $\int a_j dx = 0$, $\...
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Vladimir Zorich an ideal substitute for Baby Rudin?

I am currently ploughing through Zorich's Analysis Volume I, after which I plan on reading the Volume II. Truth be told, I am truly enjoying this read. A little background: I am a first year math ...
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Is there a solution manual for GMT Graph Theory ( Adrian Bondy, U.S.R. Murty)? [closed]

I am looking for an offical solutions manual for Graph theory. There is S&M for another Graph theory with Apps. However it seems no S&M for GMT Graph theory(the yellow front), considering ...
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Books for learning Hyperbolic Dynamical Systems and differentiable manifolds

I am looking for some books/lectures that cover Hyperbolic Dynamical systems and supplemental materials that cover the very basics of differentiable manifolds, enough to understand everything relevant ...
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2 answers
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Does the set of convex combination of points in Cantor set contains a non empty open interval?

$\mathcal{C}$ denote the cantor middle third set. $$\mathcal{C}_t=\{(1-t)x+ty : x, y\in \mathcal{C} \}$$ $\mathcal{C}_0=\mathcal{C}_1=\mathcal{C}$ and we can prove that that $\mathcal{C}$ contains no ...
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Let $f:\Bbb N^2\to\Bbb R:(m,n)\mapsto a^mb^n$, with $0<a<1<b$. Is $\operatorname{im}\! f$ dense in $\Bbb R_{>0}$?

Given real $a$ and $b$ with $0<a<1<b$, can every positive real number be arbitrarily well approximated by a number of the form $a^mb^n$ ($m,n\in\Bbb N$), provided that $a^mb^n=1$ only when $m=...
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What are some topics in undergraduate mathematics to write about?

As a high school student, I will soon be going on to do the IB(college equivalent). As part of the IB curriculum we are expected to write an Extended Essay(EE) that counts towards our grade. For the ...
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1 answer
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Am I learning math wrong?

This may be not really related to math. I'm currently learning differentiation, and no matter how many math problems I do, it seems that I always get it wrong in the exam, either having calculated ...
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1 vote
1 answer
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Dual of $L \log L(\mathbb{R})$

Consider the space$$L\log L(\mathbb{R})=\left \{f\in L^1(\mathbb{R}):\int \limits _\mathbb{R}|f(x)|\log ^+|f(x)|\,dx<\infty \right \}.$$Is it known what its dual and predual spaces are? Also any ...
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Attempting to restate the question of whether the collatz conjecture has a nontrivial cycle as a combinatorics problem

It occurs to me that the question about whether non-trivial cycles exist for the collatz conjecture can be restated as these two questions (details on how this relates to the collatz conjecture can be ...
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Reference request for books on Sieve Theory

For various reasons, I am hoping to study sieving methods some during this summer. My general goal would be to read a book on the topic, complete relatively large amounts of questions in my own, and ...
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Multidimentional real analysis.Reference request.

I wanted a rigorous self contained book on multivariable calculus. I found someone recommending this book "Multidimensional real analysis" by Duistermaat,Kolk on mSE but couldn't find any ...
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4 votes
2 answers
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Build a "rich" first-order logic within a given category

I would like to know a mathematical framework with an internal logic where isomorphic objects can be considered equal. For example, consider the rationals $\mathbb{Q}$. With this set we can construct ...
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Reference request: Bounded operators are not a Hilbert space

I believe that the following is true: Let $X$ and $Y$ be normed spaces, both of dimension at least $2$. Then, the space of bounded linear operators $L(X,Y)$ is not a Hilbert space. Is there a nice ...
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Where can I find matrix topology problems?

I am an NBHM aspirant. I am currently studying MSc in Mathematics. In NBHM, I have seen questions from topology of the space of matrices for example compactness, connectedness, openness, closedness ...
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2 votes
1 answer
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Pseudo-periodicity of analytic self-maps of the upper half-plane

I have a couple of questions, in increasing order of softness: Consider an analytic map of the upper-half plane into itself $f: \mathbb{H}\to\mathbb{H}$. When this function is $1$-periodic, i.e., $f(z+...
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Is there a probabilistic concept or theory for infinitesimal logarithmic product interpretation of integral?

If we have a number of independent events in probability, we can calculate it's likelihood : $$\prod_{\forall i} p_{i}$$ We can also consider ( where $H$ is the Heaviside step function ) $$\int L(t) H(...
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When is an SDE solution differentiable in its starting value?

Let $W=\{W_t\}_{t\in[0;T]}$ be a real-valued Brownian motion, $\{F_t\}_{t\in [0;T]}$ the filtration generated by $W$, augmented with the nullsets, $\mu,\sigma\colon [0;T]\times\mathbb R \to \mathbb R$ ...
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Name for triangle with vertices on and sides perpendicular to acute triangle $ABC$

Given an acute triangle $\Delta ABC$ there is a unique triangle $\Delta XYZ$ where $X$ lies on $\overline{AB}$, $Y$ on $\overline{BC}$ and $Z$ on $\overline{AC}$ such that $XY \perp AB$, $YZ \perp BC$,...
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Ratio of products of line segments

The points $A,B,C,D$ are collinear. The point $P$ sits off the line, and $\angle{APB}=\angle{CPD}=\theta.$ I'd like to show that if the points $P,A,D$ are fixed, the ratio $\dfrac{AB\cdot AC}{DC\...
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2 votes
1 answer
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Is There a Notion of Diagram in Multicategories and/or Operads?

In ordinary category theory there is a notion of a diagram in a category $\mathsf{C}$ which is usually described as a functor $F: \mathsf{J \to C}$ where $\mathsf{J}$ is some small category. Based on ...
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3 votes
1 answer
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Is the complement of a set with vanishing $(d-2)-$dimensional Hausdorff measure simply connected?

In the same vein as this question, I want to ask whether $\mathbb{R}^d\setminus A$ is simply connected if $A\subseteq \mathbb{R}^d$ has vanishing $(d-2)-$dimensional Hausdorff measure, i.e. ${\cal H}^{...
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3 votes
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If $A$ and $B$ have the same measure, are they isomorphic?

During a discussion, the following result was mentioned. Theorem. Let $A$ and $B$ two Borel-measurable subsets of $\mathbb R$ with the same (positive and finite) Lebesgue measure. Then, there exists a ...
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1 answer
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Reference request for studying product measure.

I am a graduate student of Mathematics.I am self-studying measure theory.I have already completed measure,integration,convergence theorem etc.I am yet to study product measures but I am not finding ...
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2 votes
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Alternative reference request for Kato's Perturbation Theory

I am studying Analytic Perturbation Theory from Kato's book.But sometimes I find it really difficult to follow.(e.g. In Chapter 2 , he directly talks about algebraic singularities without defining it ...
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What are the classical mathematics textbooks? [closed]

I have some classical books such as Richard Courant Differential and Integral Calculus both volumes I and II (English version). I also have Hardy’s Pure Mathematics. Apostol Introduction to ...
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5 votes
1 answer
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Reference request for perfection of schemes over finite fields

I am currently reading a paper from 2021 which uses "perfection" of schemes over finite fields. If $X$ is such a scheme over $\mathbb F_q$, the associated perfection is denoted by $X^{\...
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2 votes
1 answer
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What kinds of graphs are known to exhibit sharp threshold for bernoulli percolation?

What kinds of graphs are known to exhibit sharp threshold for independent bernoulli percolation? Here, sharp threshold stands for exponential decay of the probability of the cluster range below the ...
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5 votes
1 answer
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Formalizing Natural Languages

I've been interested in the subject of metalanguages and how (if) we can formalize them. Most metalanguages I've encountered use some variation of a natural language (such as English, German or French)...
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Tor functor using tensor product of free resolutions

I was studying these notes by Huneke: https://home.adelphi.edu/~bstone/commalg-notes/commalg-2/algebra-notes-II.pdf He considerar $M$ and $N$ $R$-modules over a commutative ring $R$. Then, he says ...
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What is this concept called (differentiating a matrix, NOT talking about Jacobians)

In my differential geometry course, we try to prove that the set of orthogonal matrices is a smooth-submanifold. The submersion we use is $f(A) = A^TA - I$, where $I$ is the identity. For $f$ to be a ...
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1 vote
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Prove that if $f\in C^{r}$ then the map $g(u,x):=(df)_u(x)$ is of class $C^{r-1}$

Let $X,Y$ be two finite dimensional $\mathbb{R}$-banach spaces and $U\subseteq X$ an open subset. Suppose that $f:U\to Y$ is of class $C^{r}$ with $r\geq 1$. Show that the map $g:U\times X\to Y$ given ...
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Is there any solutions manual to N Piskunov - Differential and Integral Calculus [closed]

Just as the questions says, is there any solutions manual or repository of solutions of the book N Piskunov - Differential and Integral Calculus.
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2 votes
0 answers
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Do the global minima of a continuous function vary continuously?

Let $\|\cdot\|$ be any norm on $\mathbb{R}^n$, and $f : \mathbb{R}^n\rightarrow\mathbb{R}$ a continuous function. Let further $B_r:=\{x\in\mathbb{R}^n\mid \|x\|\leq r\}$ be the zero-centered closed $\|...
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Explicit equations describing complex spin groups as affine algebraic groups

Although there are tons of questions about spin groups here on math.SE, I could not find there what I want. What I want is this. Take the complex spin group $\operatorname{Spin}(2n,\mathbb C)$. It has ...
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1 vote
1 answer
51 views

Reference for Analysis book in which natural numbers constructed from sets

Could anyone suggest books on Mathematical/Real Analysis that construct natural numbers through sets not Peano axioms? I find construction of natural numbers through sets more convenient. So I ...
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-2 votes
0 answers
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An article of F. Harary

I have searched in the Web many times to get the following article of F. Harary but all to no avail. Could anyone help? "On arbitrarily traceable graphs and directed graphs" Scripta Math. 23 ...
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Finding an article of Harary

I am searching for the following article from F. Harary: On arbitrarily traceable graphs and directed graphs. Scripta Math. 23 (1957), 37-41 I have searched many different sites but to no avail. I ...
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1 vote
0 answers
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Reference request for parabolic equations in weak formulation

I want to learn about parabolic equations, and its regularity theory. I'm interested in non-homogenous boundary value problems, with Neumann, and Dirichlet conditions, and mixes of them (on different ...
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6 votes
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A direct proof of the Vandermonde decomposition of a nonsingular Hankel matrix?

I have been doggedly searching for a direct proof of the following theorem: Theorem 1: Let $H$ be a complex nonsingular $n\times n$ Hankel matrix. Then $H$ can be factorized $H = V^\top DV$ where $V$ ...
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4 votes
1 answer
70 views

Cohen reals satisfying a formula

Consider the Cohen forcing $\mathbb{C} =Fn(\omega,2)$, the one that adds a Cohen real, and now suppose that for a Cohen real $r$ generic over $V$ we have $$V[r]\models \exists x (x \in \mathbb{R} \...
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0 votes
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A new (?) infinitely nested radical equals $1$

Let $x$ be a real number such that $x\ge{0}$, then $$1=\sqrt{\frac{\sqrt{\frac{\sqrt{\frac{\sqrt{\frac{x+1}{2}}+1}{2}}+1}{2}}+1}{2}}+...$$ At least I haven't seen it on the internet. Questions: a) Is ...
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6 votes
1 answer
90 views

Good applied differential geometry books

I'm searching a book which goes about how Differential Geometry can be applied to solve Real world problems. I tried William L Burke's book, but I found it to be all over the place. The information, ...
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3 votes
1 answer
103 views

A Reference From Andrej Bauer's Recent Talk on Countable Reals

Andrej Bauer gave a talk today in the topos institute colloquium (video here) announcing a proof that the dedekind reals can be countable in the absence of LEM and CC. At roughly the 27 minute mark, ...
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3 votes
1 answer
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Natural Deduction: An unusual presentation?

1. Context On page 241 of their paper Natural deduction and coherence for weakly distributive categories Blute et al give the right- and left-introduction rules of multiplicative conjunction for (...
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1 vote
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Is Hubbard& Hubbard good for learning analysis?

I am currently using that book for learning multivariable calculus and linear algebra and I am really liking it. The author said on preface that this book could be used in a course of analysis by ...
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