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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16 views

Ahlfors Complex Analysis solutions for reference

I am a math major and currently I am self studying complex analysis from Ahlfors Complex Analysis - third edition. I prefer working on problems first by myself and then refer back to see if I am right ...
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0answers
11 views

Maximal even sub-lattice in $\mathbb{Z}^n$ (reference)

Lemma: The maximal even sub-lattice in $\mathbb{Z^n}$ is $$ \Big\{ (x_1,\cdots,x_n)\in \mathbb{Z}^n ~~\big|~~ \sum_{1 \le i \le n} x_i \in \mathbb{2Z} \Big\} $$ I found the above lemma in an ...
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0answers
10 views

Elliptic quadrilaterals (Cyclic quadrilaterals)

I've just come back from the magical corridor. They showed me an elliptic quadrilateral and cow-sheep's inequality. But first, elliptic quadrilaterals. I only had a glimpse. Unfortunately, it was the ...
1
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0answers
24 views

Endomorphism ring of semisimple modules

Can someone help me to prove the following statement, or introduce some reference about it? Statement: Suppose that $M$ is a semisimple $R$-module of finite type. There are division rings $D_1, ... ...
2
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1answer
29 views

I need to show the following two limits

First, for $a>-1$: $$\lim_{n\to\infty}\frac{a+1}{n^{a+1}}\sum_{j=1}^nj^a = 1$$ Second, for $p>0$: $$\lim_{n\to\infty}\frac{e^a-1}{e^{a(n+1)}}\sum_{j=1}^ne^{aj} = 1$$ In particular, why do we ...
0
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0answers
16 views

A question about $(\exists x: p(x) \supset q(x)) \equiv ((\forall x: p(x)) \supset (\exists x: q(x)))$

Conider the usual logical connectives $\wedge$ for "and", $\vee$ for "or", $\supset$ for material implication, $\equiv$ for material equivalence, $\neg$ for "not" et cetera. We all know and use laws ...
3
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0answers
62 views

Cell theory - What is it? - Reference request

A user with $>10,000$ posts on sci.math called 'plutonium.archimedes' or 'AP' is constantly ranting about some theory he deems superior to calculus(a.k.a 'old math' I believe). I can't find any ...
2
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1answer
24 views

Representations of a product of Lie groups

Let $G=G_1\times G_2$ be a product of two compact Lie groups. Is every finite dimensional irreducible representation of $G$ a tensor product of irreducible representations of $G_1$ and $G_2$? This ...
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3answers
327 views

Undergraduate research thesis

$$\color{#0a0}{\text{1. General background information}}$$ $\color{#0a0}{\bigstar} \ $ At my university [whose name I will omit] the following practices are customary: $\color{#ac0}{\bullet}\ $ ...
5
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0answers
85 views

How to become a mathematcian? [on hold]

I study Electric engineering and I have always loved Mathematics and now I want to study math and dont know where to start, I want to be like a one who graduated from a math departement with no ...
0
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0answers
70 views

A roadmap to read Knuth's The Art of the Computer Programming

I want to read the Knuth's TAOCP books but I think I need fill in some Math gaps first, in order to fully understand the text and the problems in the books. My education is almost good at ...
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0answers
19 views

Solving Diophantine equations of the form $am^x +b n^y = ab z^2$

How can Diophantine equations of the following form be solved? $$am^x +b n^y = ab z^2$$ Can you suggest articles dealing with this type of problem
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0answers
18 views

Regularity when Dirichlet conditions are posed on the interior of a domain.

Problem: Let $\Omega_1,\Omega_2\subseteq \mathbb{R}^2$ be two domains, define $\Omega:=\Omega_1\cup\Omega_2$ as their union as well as $\Gamma:=\partial\Omega_1 \cap \partial \Omega_2$ as their common ...
0
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1answer
50 views

Is there a Set Theory textbook which include visual explanation?

Right now I am taking a class in set theory, The professor in many cases draw a diagram,pic or anything which help you intuitionally understand the material better. What was surprised me many (at ...
0
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1answer
9 views

Approximation theory in multiple dimensions (reference request)

I understand the following from approximation theory: if $f(x)$ is a well-behaved function on some interval $[a,b]\subset\mathbb{R}$ then for any tolerance $\varepsilon$, there exists an $N$th-degree ...
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0answers
26 views

Nilpotent completion of a free group

Let $F$ be the free group on $m$-generators ($m\geq 2$). Denote the $k$-th lower central subgroup of $F$ by $F_k$. (That is, $F_0=F$ and $F_{r+1}=[F_r,F]$.) Then, using the inverse system consists ...
2
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1answer
31 views

Reference request: Riemann-Hilbert problems

I am trying to learn more about the applications of complex analysis in solving spectral problems and came across applications of theory built around Riemann-Hilbert problems. So far I have only read ...
2
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0answers
31 views

GRE Mathematics Practice Exams

I will be taking the subject test in the near future. Can you recommend me some sources (online or print) from which I can find realistic practice exams? I would like to get my hands on as many ...
0
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0answers
25 views

Physical interpretation of logarithmic potential

Whats a physical interpretation of single layer potential in dimension two? $$Sf(x)=\int_{\Gamma}f(y)\log|x-y|ds_y$$ In here $\Gamma$ is a planar closed smooth curve, and $ds$ is the arc length.
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0answers
13 views

Reference for Learning about Nuclear Operators on Banach Spaces?

What would be a nice references for learning about nuclear operators on Banach spaces? I can't give more details of what I'm looking for since I know nothing about those operators. I don't care ...
2
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0answers
44 views

What kind of integral equation is this?

What kind of integral equation is this $$g(x,y) = \int f(z,y)k(z,x)dz$$ where $k$ is a known kernel function, $g$ is known and $f$ is unknown. It reminds the equation of the first kind: ...
2
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0answers
26 views

$GL(V)$ representations and Schur modules.

Let $W$ be a fine dimensional complex vector space of dimension $n$ and $L_{\lambda}W$ the Schur module associate to the partition $\lambda=(\lambda_1, \cdots,\lambda_{n-1})$, where $\sum_i ...
4
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0answers
106 views

Mathematical Canon [on hold]

Sometime ago I resolved to read through a prodigious book collection known as the The Great Books of the Western World--a rather lovely collection which I would encourage anyone to read through, if ...
0
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1answer
26 views

What is math branch that studies general populations.

A population is a summation of all the organisms of the same group or species, which live in a particular geographical area, and have the capability of interbreeding so i would like to understand the ...
2
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0answers
29 views
+50

Reference Request - Introductory book on Mathematical Modelling in Economics and Business

I have to take a compulsory course named Mathematical Modelling in Economics and Business this semester and have absolutely no background on the subject. I also noticed there is no post on this site ...
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2answers
34 views
+50

Theory and problems book in euclidean, affine, and projective geometry

Could you recommend a rich clear and complete theory book on euclidean, affine and projective spaces ("geometry"); and an interesting exercise book full of non-trivial problems and exercises?
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0answers
14 views

Video lecture on multivariate analysis?

Preferably covering the second half of Rudin's Principles of Mathematical Analysis. I've been looking for such a course within my university but couldn't find it. Does anyone know of any decent video ...
0
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2answers
27 views

Integration and measure theories, a reference list

This is a rephrase of the questions posted regarding measure theory but also including integration. (Reference book on measure theory) I have to review the knowledge of measure and integration ...
1
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0answers
15 views

What are the differences between the three editions of the book “The Structure of Compact Groups”?

meta pre-clarification: I looked into another question like this but the guy didn't mark any specific tags for this type of question. Here's a link to the amazon book: ...
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0answers
41 views

Book recommendations for the following topics in real analysis [on hold]

Topics are Countable and uncountable sets Riemann integral. Integrability of continuous and monotonic functions. The fundamental theorem of integral calculus. Mean value theorems of integral ...
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0answers
51 views

Reference for easy understanding of calculus

Can you please suggest some books or websites for higher secondary school student for easy understanding of calculus?(Just I want to learn to carry out basic calculations)
3
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2answers
41 views

Properties of Sobolev spaces $W^{k,\infty}(\Omega)$

I'm looking for different properties of spaces $W^{k,\infty}(\Omega)$ for bounded domain $\Omega \subset \mathbb R^n$ and $k \geq 1$ that I couldn't find in literature. References are wery welcome. ...
0
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1answer
30 views

What are all the standard methods available to solve a general ODE into infinite series? [closed]

What are all the standard methods available to solve a general ODE into infinite series? For example, the Taylor method. I am very curious.
2
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1answer
171 views

What is an ordinary differential equation equation that is yet to be solved?

In another word, the ODE i am talking about is very special that an special method must be developed in order to solve solely that ODE approximately in infinite series. An standard method mean it ...
1
vote
1answer
54 views

Concise Introduction to Galois Theory

I'm looking for a short, concise introduction to Galois Theory (but please don't assume I know anything about Galois Theory). I don't want a complete and "fat" Bourbaki-style book. My main motivation ...
1
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2answers
24 views

Tate-Shafarevich groups and Hasse principle (reference)

I'm looking for a proof of the fact that the Hasse local-global principle holds for an elliptic curve $E$ defined over $Q$ if and only if the Tate-Shafarevich group of $E$ vanishes. I just need to ...
1
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1answer
39 views

Applied/Numerical Linear Algebra-Suggestions for Project

I am looking for suggestions for a research project in applied/numerical linear algebra. As far as requirements, there really aren't any except that the topic has to tie in somehow with numerical ...
2
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0answers
28 views

Get function definition from an equation

My question: I have to find a function $g$ fulfilling the equation $$2\frac{t_k \cdot t_0 - 1}{t_k-t_{-1}} = g(t_k) + g(t_{k+1}) + t_{k+1}\cdot g(t_k)g(t_{k+1})$$ Whereby $t_{n+1}=t_n + h$ with $t_0, ...
2
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1answer
28 views

System of linear diophantine inequalites

are there any papers that deal with System of linear diophantine inequalites? I have a hard time finding any. The wikipedia entry calls it diophantine approximation, but i am not sure if this is the ...
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0answers
60 views
+50

Convergence of a certain matrix product representing a class of piecewise linear dynamical systems.

Consider a discrete-time dynamical system of the following kind. Assume $x(t) \in \mathbb{R}^n$. $x(t+1) = A_{\Omega(x(t))} x(t)\quad$ where $\quad A_i = \left [ \begin{array}{c|c} 1 & 0\\ \hline ...
1
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0answers
37 views

Artin Algebra Representation Chapter Resource Request

I am working through chapter 10 of Artin's Algebra 2ed which introduces Group Representations. However, I've found that the approach to introducing groups is unlike the usual method used by more ...
0
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0answers
35 views

General versions of Stokes theorem

I am preparing to write a short paper about general versions of Stokes' theorem. During our real analysis lectures we were presented with the following generalization of Stokes' theorem: Suppose $ ...
0
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1answer
42 views

A reference for a result by A. Casson

I was reading this article about the disproof of Triangulation conjecture: it says that A. Casson disproved this conjecture in dimension 4 in the '80s In 1982, Michael Freedman, then at the ...
4
votes
4answers
198 views

problem book on Group theory after doing Fraleigh.

Please refer a problem book on Group Theory:TOPICS: Groups, subgroups, Abelian groups, non-abelian groups, cyclic groups, permutation groups; Normal subgroups, Lagrange's Theorem for finite groups, ...
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0answers
23 views

heliophysics question [closed]

Are there any mathematical models out there describing the dynamics of space weather? Any good references are most welcome. I'm interested in models that involve differential equations.
2
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0answers
44 views

Blowing up the Grassmannian at a point

I want to better understand what the blow-up of the Grassmannian at a point looks like. Consider $G=Gr(r,n)$ and $V\in G$. I want to understand more explicitly what $Bl_V(G)$ should mean. Of course ...
5
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1answer
74 views

What is the Spivak of Probability?

I'm looking for a rigorous introduction to probability to help prepare me for a future course I plan on taking, "Advanced Introduction to Probability". Something possibly like Spivak's, where proofs ...
0
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0answers
13 views

Finite differences

I don't know finite differences but I have reached a step in a proof where I need them. In particular, I need to know the $3k$th differences of $4\cdot 1^{3k}, 4\cdot 2^{3k},...,4\cdot (3k)^{3k}$. I ...
1
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1answer
17 views

Does continuity on rays imply measurability?

Let us define a function on $\mathbb{R}^n$ by defining it on all lines crossing the origin $y=tx$, $t\in\mathbb{R}$. It is defined to be continuous on these lines. Is it known to be measurable?
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0answers
48 views

Euler's proof of $3m+1\in \mathbb{P}\implies 3m+1=x^2+3y^2$?

as the title suggests I am looking for Euler's descent proof of the fact that all primes of the form $3m+1$ can be represented as $x^2+3y^2$. Note: I am not interested in any other proofs but Euler's ...