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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33 views

Universal Algebra: partial algebras and homomorphisms

I'm looking for an accessible introductory text on universal algebra, one which discusses homomorphisms in the context of partial algebras. I have been recommended the Grätzer book, "Universal ...
2
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2answers
66 views

Any “DIY Analysis” books?

Are there any good "analysis through problems" type books? I've tried reading analysis books but I literally get bored to death, and, until I manage to concoct a way of transforming a normal textbook ...
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0answers
73 views
+50

Supportive book(s) for unproven-theorems of General Topology by R Engelking?

I am studying General Topology by R Engelking. And, it has many theorems left without proofs. Some of them are very hard and I don't think the author had intention to leave them as exercises. Would ...
3
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1answer
51 views

Is there is any analogue of mean value theorem for integral when the range is whole $R$?

Is there is any analogue of mean value theorem for integral of a continuous function when the range of the integral is whole real line? By MVT: if a function $f$ is continuous on the closed interval ...
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0answers
33 views

Vector calculus vs Vector analysis?

I was just wondering, is vector analysis the same as vector calculus? What about multivariable calculus? Because my multivariable calculus book (which I assume is the same as vector calculus?) covers ...
6
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2answers
110 views

Generalized convex combination over a Banach space

The Question: Is the following true? If not, what further hypotheses do I need? Let $X$ be a Banach space, and let $C \subset X$ be closed and convex. Let $P$ be a probability measure over $D$, ...
1
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1answer
29 views

Example of polynomial in dynamics

I am looking for an example of a post-critically finite polynomial $P$ (i.e. all critical points have finite orbit), which has both the following: a critical point on its Julia set (such as the ...
2
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1answer
19 views

what is a spectral function?

My knowledge in spectral theory is very limited, but lately I heard talking about the spectral function of an operator and how it's important. By curiosity I tried to look for a definition and a ...
1
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1answer
36 views

Reference for Dynamic Arrays

I'm looking for a reference for the fact that dynamic arrays have random access in constant time and inserting or deleting an element at the end can be done in constant amortized time. What would be a ...
2
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1answer
50 views

A sum involving twin primes and Prime Number Theorem

This morning I've been watching documentary about asterorids, in a scene an astronomer explains the so called image subtraction process or pixel subtraction, a mathematical model used in computerized ...
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0answers
19 views

The basis induced by the nilpotent linear transformation

In Halmos's book, there is a theorem regarding the nilpotent transformation: If $A$ is a nilpotent linear transformation of index $q$ on a finite-dimensional vector space $V$, then there exist ...
2
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0answers
64 views

Inquiry about My Self-Study Plan for Real Analysis (associated with my undergraduate research) [closed]

S.E advisers, I am a college sophomore in US with a major in mathematics and an aspiring mathematician in the computation theory and cryptography. I recently got an undergraduate research in the ...
3
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0answers
56 views

Analogy between Galois groups and fundamental groups

I've heard that there is an analogy between algebraic field extensions and covers (in topology). In this analogy Galois extensions correspond to Galois covers and Galois groups correspond to ...
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0answers
40 views

On a modified least square.

Given a vector $y \in \mathbb R^n$ and real constants $x_{ij}$ ($i=1,\dots,n$, $j=1,\dots,p$), we consider a vector $\beta = (\beta_0,\dots,\beta_p)$ which minimize ...
3
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0answers
35 views

Proving those hard cyclic inequalities

From time to time some user asks for help to prove a cyclic inequality, that is, something like $$f(x,y,z)\le k$$ where $x,y,z$ are usually real positive numbers and $f$ is a 'cyclic function' (I ...
2
votes
1answer
33 views

A general method for solving systems of quadratic equations

For linear systems we have general methods (i.e. Gauss elimination). Is there a general method for solving systems of quadratic equations with many variables? I heard about Groebner bases; is there ...
1
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0answers
31 views

Product of complex numbers $m+in$ with $0 < m,n \leq N$

I am trying to look for a generalization of Stirling's formula to complex numbers. In the integer case: $$ \log n! = \sum_{k = 1}^n \log k \approx \int_1^n \log x \, dx = n \log n - n$$ For the ...
0
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0answers
11 views

Reference request for a mixed boundary value problem

Let $\Sigma$ be a compact Riemannian manifold with boundary and assume that $\partial\Sigma=Y_1\sqcup Y_2.$ Let $\Delta$ be the nonnegative Laplacian on $\Sigma.$ I am looking for the reference for ...
10
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1answer
78 views

Continued fraction estimation of error in Leibniz series for $\pi$.

The following arctan formula for $\pi$ is quite well known $$\frac{\pi}{4} = 1 - \frac{1}{3} + \frac{1}{5} - \frac{1}{7} + \cdots\tag{1}$$ and bears the name of Madhava-Gregory-Leibniz series after ...
3
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1answer
83 views

Looking for a good alternative to 'An introduction to manifolds' by Loring W. Tu

I'm currently studying some basic theory about manifolds from the book 'An introduction to manifolds' by Loring W. Tu. The problem I have with this book is that there are very little exercises, and ...
5
votes
3answers
287 views

What mathematical analysis book should I read (research, Putnam, personal enrichment)? [closed]

S.E advisers, I am a college sophomore in US with a major in mathematics and an aspiring mathematician in the fields of computation theory and cryptography. Recently, it became important matter that ...
3
votes
4answers
66 views

Are there any books with lots of questions of “Fill in The holes” type

Does anyone knows books which have lots of questions ,whose format are like fill in the holes type . . Same goes for theorems and exercises . I am looking on pure math especially Real analysis ...
1
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0answers
13 views

Maximal subalgebras of simple Lie algebras.

Does anyone know how I can access Dynkin's papers on the classification of maximal subalgebras of simple finite dimensional complex Lie algebras? V.V. Morozov also worked on this topic, how can I ...
1
vote
1answer
32 views

Books and sources concerning the mathematics of Leibniz and the feud with Newton

I am trying to find books and other sources concerning the mathematical history of Leibniz, including the controversy due to the independent discoveries of calculus by both Newton and Leibniz. I can't ...
1
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0answers
38 views

On two definitions of the nerve of a simplicial category

Let ${\mathcal C}$ be a simplicial category. Then there are the following two ways of constructing a simplicial set from ${\mathcal C}$: Form the simplicial nerve $\text{N}_\Delta({\mathcal C}) := ...
19
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1answer
371 views

What function satisfies $F'(x) = F(2x)$?

The exponential generating function counting the number of graphs on $n$ labeled vertices satisfies (and is defined by) the equations $$ F'(x) = F(2x) \; \; ; \; \; F(0) = 1 $$ Is there some closed ...
5
votes
1answer
68 views

Completeness for Infinitary Logic?

I have heard a rumor that there is a proof system for certain infinitary logics, given by Carol Karp (?) in her thesis, but I can't find a copy. The result that I'm told exists is the following: A ...
1
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0answers
25 views

Is there a treatment/development of the Stokes' Theorem using differential forms and the Henstock-Kurzweil integral i.e. the gauge integral?

I'm working through an analysis text independently to prepare for grad school, and the author has discussed the limitations of both the Riemann and Lebesgue integrals and only hinted at the power of ...
0
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0answers
16 views

Stability of ground state under positive (not relatively bounded) perturbations

This is about positive perturbations that are not necessarily relatively bounded, but where the perturbed operator is known (by some independent proof) to be self-adjoint. Is this a known result (or ...
0
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0answers
16 views

Survey, text for noncommutative Grobner basis.

This is a survey/ text request for noncommutative grobner basis. A googling gave me these: http://www.sciencedirect.com/science/article/pii/0304397594902836 ...
0
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3answers
80 views

Does $\Pr(\{X\leq x\})\geq\Pr(\{Y\leq x\})$ imply $\Pr(\{X\leq Y\})=1$?

Suppose that $(\Omega,\mathcal{F},P)$ is a probability space and $X,Y:\Omega\to\mathbb{R}$ are random variables satisfying $$ P(\{X\leq x\})\geq P(\{Y\leq x\}),\quad\forall x\in\mathbb{R}. $$ ...
4
votes
1answer
41 views

Is there anything special about a transforming a random variable according to its density/mass function?

Lets say that $X\sim p$, where $p:x\mapsto p(x)$ is either a pmf or a pdf. Does the following random variable possess any unique properties: $$Y:=p(X)$$ It seems like $E[Y]=\int f^2(x)dx$ is similar ...
5
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1answer
65 views

Haar measure on SO(n)

I am interested in describing the group of special orthogonal matrices SO(n) by a set of parameters, in any dimension. I would also like to obtain an expression of the density of the Haar measure in ...
1
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1answer
45 views

best introductory simple readable undergraduate book for algebraic geometry [duplicate]

I like to study algebraic geometry and what is the best introductory simple readable undergraduate book for it?
0
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0answers
24 views

Reference request: maximize the total weight along the path on the graph.

I am looking for the reference(s) where the following computational problem is discussed: Given a weighted graph $G$ where each vertex $v_i$ has some weight $w_i$ and a number of "vertices visited" ...
2
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0answers
65 views

What is the Best Introduction to Dedekind Cuts?

I'm looking for a clear, thorough, and easy-to-follow introduction to Dedekind cuts that is specifically geared towards those with an interest in foundational issues. So far, the discussions that I ...
4
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2answers
61 views

Proof: $Y$ stochastically dominates $X$ implies $E[\phi(Y)]\geq E[\phi(X)]$ for increasing $\phi$

Suppose $X$ and $Y$ are real random variables with CDF $F$ and $G$ such that $F(x)\geq G(x)$ (i.e. $Y$ exhibits (first-order) stochastic dominance over $X$). Then, for all increasing function ...
0
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2answers
61 views

A Series might be a number or a sequence – Is there a better notation?!

Take the expression $\sum_{k=1}^\infty a_k$. Sometimes this expressions refers to the sequence of partial sums $\left(\sum_{k=1}^n a_k\right)_{n\in\mathbb N}$ and sometimes to the limit of this ...
0
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0answers
10 views

Can Somebody Help Me Find A Certain Paper about Hybrid Proximal Extragradient method for Bregman Functions?

I have read these two papers by Svaiter and Solodov. The first one, published in 1999 (http://pages.cs.wisc.edu/~solodov/solsva99Teps.pdf) presents an error criterion for the hybrid proximal ...
0
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2answers
39 views

Indentifying $\sin(mx) = 2\cos(x)\sin\left[(m-1)x\right] - \sin\left[(m-2)x\right]$

I encountered in a work of Joseph Fourier's the identity: $$\sin(mx) = 2\cos(x)\sin\left[(m-1)x\right] - \sin\left[(m-2)x\right]$$ which holds for all real $m$ and $x$. I had trouble, however, ...
1
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1answer
45 views

Tensor power modulo cyclic group action

Let $M$ be some $R$-module and $n \geq 1$ be some positive integer. The cyclic group $\mathbb{Z}/n\mathbb{Z}$, with a chosen generator $t$, acts on $M^{\otimes n}$ via $t(m_1 \otimes \dotsc \otimes ...
0
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1answer
50 views

Mountain of coins

Let a mountain of coins be an arrangement coins in rows such that the coins in each row form a single block, and that in all rows (except the bottom row) each coin touches exactly two coins from the ...
0
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0answers
44 views

When are direct products exact in the category of quasi-coherent sheaves?

I would like to know if there is a description (or at least some sufficient condition known) of a (Noetherian) schemes $X$ such that the category $\mathrm{QCoh}_X$ does have exact direct products. I ...
3
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0answers
29 views

Looking for Math books recommendations to study Electronics

My background is the very basics, and I mean, literally, I can add, sub,mul,div and a little of algebra (near, nothing) and that's it. As you can see I need the best Total Beginner Book(s) that can ...
2
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1answer
30 views

How to express curvature of a level set in terms of derivatives of a function?

Suppose I have a smooth function $u:\mathbb R^n\to\mathbb R$. Assume that its gradient doesn't vanish (near any point where we investigate it). Is there a list of different (intrinsic and extrinsic) ...
2
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0answers
27 views

Gradient of Probability Distribution

Given a random walk on a lattice $L$ (not necessarily centered - we allow $E[X_i] \neq 0$ for the i.i.d. increments $X_i$), let $p_t(x)$ denote the probability measure of state $x \in L$ after $t$ ...
2
votes
1answer
37 views

Reference request for a theorem on maps to normal varieties with equidimensional fibers being open

I am requesting a reference for a proof.. I believe that it is due to Chevalley. A theorem by Chevalley says that if $f: X \rightarrow Y$ is a dominant morphism of irreducible varieties, then there is ...
-4
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1answer
39 views

Looking for a paper of Arhangel'Skii A V, Bella A. [closed]

I'm Looking for a paper of Arhangel'Skii A V, Bella A. Its title is this: The diagonal of a first countable paratopological group, submetrizability, and related results[J]. Applied General ...
1
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0answers
42 views

special kinds of homotopies

Let $X$ and $Y$ be two homotopy-equivalent topological spaces. That is, there exists maps $f:X \to Y$ and $g:Y \to X$ such that $g \circ f \simeq 1_X$ and $f \circ g \simeq 1_Y$. $1_X$ and $1_Y$ are ...
2
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0answers
38 views

Expected maximum degree Erdős–Rényi graph

Consider an Erdős–Rényi random graph $\mathrm{ER}(N,p)$, where $N$ is the number of nodes and $p$ the probability of placing an edge between each distinct pair of nodes. I'm interested in finding ...