Tagged Questions

This tag is for questions where the poster seeks references (books, articles, etc.) about a particular subject. Please do not use this as the only tag for a question.

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1
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0answers
18 views

Prerequisite to study smooth 4-manifolds

I am quite interested in understanding smooth 4-manifolds. What are the necessary prerequisites in order to start my study? Also can you please suggest me some good books from where I can start? ...
6
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2answers
34 views

Video Lessons in Complex Analysis

Does anybody have some link for good video lessons of a complete course in Complex Analysis? Grateful.
1
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1answer
33 views

Accounts of the proof of Fermat's Last Theorem

I would like to collect a set of references to pieces of Wiles' 1995 proof of Fermat's Last Theorem. Has anyone recompiled the proof into another paper? Are there any books or articles that describe ...
1
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0answers
41 views

Linear algebra and geometric insight: a rigorous approach to vector spaces, matrices, and linear applications

Could you point out some references (undergraduate level) that give a geometric understanding of vector spaces, matrices, and linear applications? As far as I know, many textbooks start with ...
1
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1answer
36 views

Definition of unipotent linear algebraic groups over non algebraically closed fields

Suppose we have a field $F$ with $\text{char}\ F=0$ and $F$ is not necessarily algebraically closed. What is the definition of a unipotent linear algebraic group over $F$? I'd really appreciate ...
0
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1answer
34 views

Inequalities textbook request [duplicate]

At university I have got a problem set with lots of inequalities. Unfortunately there are no explanations given how to do them. In Highschool we only did very easy inequalities. Therefore I am looking ...
0
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1answer
11 views

Relating maximal elements of downsets to minimal elements of the complement

Denote by $\mathcal{P}(S)$ the set of non-empty subsets of a finite $S$. Suppose that $A\subset \mathcal{P}(S)$ is a downset, i.e., every subset $Q$ of any $P\in A$ is also contained in $A$. We can ...
0
votes
1answer
49 views

Any algorithm or theorem to decide whether two functions are equivalent? [duplicate]

Any algorithm or theorem to decide whether two functions that are polynomials,rationals and analytic over $\mathbb{N}$ or $\mathbb{Q}$ or $\mathbb{R}$ or $\mathbb{C}$ are equivalent ?
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0answers
15 views

Combinatorial designs give triangulations of complete graphs

I recently attended a talk on combinatorial design theory. The speaker mentioned briefly that the Fano plane, and other designs give rise to triangulations of complete graphs (the Fano plane gives a ...
0
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2answers
64 views

Adding Substructures by Forcing

Consider a first order language $\mathcal{L}$ and an $\mathcal{L}$-structure $M$. Let $V$ be a model of ZFC (or ZF) the general question is that what would happen to classes, $Sub(M):=\{N~;~N~\text{is ...
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0answers
7 views

Reference: Differential operators and principal symbols

I am looking for good references about differential-/pseudodifferential operators and principal symbols. thanks
0
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0answers
15 views

Good Convex Analysis book

I am an average student and have just a very basic knowledge of this subject. Thank you
0
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0answers
19 views

Ref. request for Linear algebra over noncommutative rings

This is not a real question but more a reference question. I am looking for introductory articles/blog entries/books that discuss the obstructions to do linear algebra over a non-commutative ring $R$. ...
2
votes
1answer
44 views

Infinite direct sum of Hilbert spaces

Let $\{H_i\}_{i \in I}$ be an infinite collection of Hilbert spaces. I am trying to understand their "Hilbert space direct sum". $\bigoplus H_i$ (algebraic sum) is an inner product space in a ...
2
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0answers
25 views

Sampling theorem.

Let us consider \begin{equation} \hat{f}(x)=\sum_{n\in \mathbb Z}\left\langle\hat{f},e^{i n x}\right\rangle_{L^2[-\pi,\pi]} e^{i n x} \ \ \ \ \ \ \ \ (1) \end{equation} where $\langle g, ...
0
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0answers
36 views

Good source for my “language of math” class?

I'm having a hard time in my "language of math" class (proofs, sets, etc). Right now we're doing finite sets. Are there any good online resources for this class? Thanks
1
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3answers
54 views

Book recommendation for ordinary differential equations

This question has been posted before, but I need book with specific qualifications. I do not need books for engineers, book that is centered around calculations and stuff. I need to find a book that ...
0
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0answers
20 views

Compact hypersurface in $\mathbb{R}^n$

Let $S$ be an $(n-1)$ dimensional hypersurface in $\mathbb{R}^n$. If we say that $S$ is compact, does this necessarily mean that $S$ has no boundary? Eg. $S$ can be a sphere but not a sphere cut in ...
2
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1answer
24 views

Reference for this theorem: $a, b$ coprime, $f(k) := ka \bmod b$, then $f$ is bijection on $\lbrace 0, …, b−1 \rbrace$.

I need to use the following theorem in a paper but have to expect that some of the audience (physicists) is not familiar with it, so I would like to reference it: Let $a$ and $b$ be two coprime ...
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0answers
16 views

Equivalence of condition on function

In a book I am studying it states that a condition on a function $g$ as follows: Given the function $g: \Omega \times \mathbb{R} \mapsto \mathbb{R}$ is a Caratheodory function satisfying $$\sup_{|u| ...
0
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0answers
15 views

Standard examples of operator

In a text I am reading it says that we can consider an operator $A: X \rightarrow X^{*}$ (where $X := W^{1,p}(\Omega)$) which is defined as $$Au = -\text{div}(a(x,u,\nabla u))$$ where $a: \Omega ...
5
votes
0answers
37 views

Real affine variety of $d$ orthonormal vectors in $\mathbb R^n$

I'm interested in the affine variety $$ V = \left\{ \, A\in \mathbb R^{d\,\times\, n} \, \middle| \, A\,A^T = I \, \right\} \subseteq \mathbb R^{d\, \times\, n}, $$ where $n\ge d$ and $I$ is the ...
3
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0answers
76 views

Mathematics behind Mathematics! [on hold]

Mathematics is a social human activity which shares many points with other natural and social phenomenas. All of us have an intuitive sense of what is going on in different fields of maths. For ...
6
votes
2answers
81 views

Proving if A and B are matrices such that A, B, and AB are normal, then BA is also normal.

If A and B are matrices such that A, B, and AB are normal, then BA is also normal. I've seen this statement around, although I've only seen the site/publication/etc... state that it was proven by ...
1
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1answer
46 views

Fixed Point Equivalences of Axiom of Choice

Axiom of Choice has many known equivalences. Also there are many known fixed point theorems (unproved statements) which provide useful information about existence of fixed points for particular ...
4
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1answer
77 views

Theorems which later turned out to be vacuous

Has it ever happened that a theorem of the form If $P$, then $Q$ was proven and published, perhaps with great difficulty, only for someone to realize later that the condition $P$ of the theorem ...
1
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1answer
20 views

Free loop space of classifying space as a disjoint union of classifying spaces of centralizer proof reference request.

I am looking for a reference for the proof or explanation of why for a discrete group $G$ we have that the free loop space of its classifying space is the disjoint union of centralizeers of $g$ where ...
10
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4answers
179 views
+100

Open source lecture notes and textbooks

This question is inspired by the popular "Best Sets of Lecture Notes and Articles". Indeed, I would like to collect a "big-list" of open source (that is, with $\LaTeX$ code available) high-quality ...
0
votes
0answers
10 views

anisotropic vector valued function definition

Does anyone have insight into the significance of the following statement which defines an anistropic function $$a:\Omega \times \mathbb{R} \times \mathbb{R}^{N} \rightarrow \mathbb{R}^{N}$$ The ...
0
votes
0answers
46 views

series and inequality

I found this homework in an old paper written that's why I'm not sure about $\sum_{i=1}^{n}x_{i}=?$ Let $n\in \mathbb{N}^*$ and $x_1,x_2,\ldots,x_n \in \mathbb{R}$ such that $ ...
0
votes
1answer
29 views

What is the difference between Difference equations and Recurrence relations?

Is there any difference between Difference equations and Recurrence relations? Some people are use them as difference equations and some are use as recurrence relations. I couldn't find in anywhere. ...
4
votes
0answers
80 views

Flatness of homomorphisms of graded-commutative rings

Algebraic geometry offers some properties and criteria for homomorphism of commutative rings to be flat. What about homomorphisms of graded-commutative rings? You can define flatness as usual: $R \to ...
2
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0answers
36 views

Problem sets for Griffith and Harris?

Are there any problem sets floating around that correspond to the material in Griffiths and Harris' "Principles of Algebraic Geometry"? I find a good set of problems helps cement the concepts when ...
0
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1answer
26 views

Reference for Engineering Mathematics

I am a graduate Engineer looking to qualify a post graduate entrance examination (for Master's degree) where I have 'Engineering Mathematics' as one of my Subjects.I hereby paste my course syllabus: ...
0
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0answers
31 views

Good resources to learn Hopf algebras

I am finding it hard to find resources that can educate me in this subject. I have looked up this and I can't find anywhere to start. Any advice?
3
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0answers
30 views

amenable + without $BS(m,n)$+finite $K(G,1)$implies virtually cyclic? [migrated]

I heard from someone that the following problem is an open question. (Open Problem 1)For a countable discrete group $G$, suppose it does not contain any Baumslag-Solitar subgroups $BS(m,n):=\langle ...
0
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1answer
15 views

Literature: Derivations in C*-Algebras

Do you have some nice reference for dynamical systems in C*-algebras (including discussion of their derivations!) like notes, papers, books, etc.?
0
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0answers
34 views

Dedekind(?) representation lemma on posets?

Here's an easy lemma: Any poset $(S, \preceq)$ is order-isomorphic to a subset of the powerset $\mathcal{P}(S)$ ordered by set-inclusion. I seem to recall having seen this attributed to Dedekind. ...
0
votes
0answers
16 views

Existence of strong solutions to parabolic p-Laplace equation

Can I find a reference to where the existence of strong solution $u \in L^2(0,T;W^{1,p})$ with $u_t \in L^2(0,T;L^2)$ is proved to the equation $$u_t - \Delta_p u = f$$ $$u(0) = u_0$$ ...
2
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1answer
49 views

suggest a topic about history of mathematics

Can you suggest a topic (the history of mathematics) concerning the evolution of a given concept from a document written in English from varied scientific resources What do you think of the ...
0
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0answers
26 views

Is $F(x_1,x_2,\dots,x_n)$ where $(x_1,x_2,\dots,x_n)\in \Delta$,a semi-algebraic function?

Given $$F(t_1,t_2,\dots,t_n)=\int\frac{P_1(x_1,x_2,\dots,x_n)}{P_2(x_1,x_2,\dots,x_n)}dx_1dx_2\dots dx_n$$ where $P_1(x_1,x_2,\dots,x_n), P_2(x_1,x_2,\dots,x_n)$ are polynomials whose coefficients ...
0
votes
0answers
17 views

Is it decidable that any two computable function over reals $ f(x_1,x_2,\dots,x_n)\equiv g(x_1,x_2,\dots,x_n)$

Is it decidable that any two computable function over reals or over sphere of complex $ f(x_1,x_2,\dots,x_n)\equiv g(x_1,x_2,\dots,x_n)$ ?
0
votes
2answers
32 views

Is a intersection of chain of non enumerable dense sets non enumerable?

Let $M_1\supset M_2\supset \cdots$ sets such that each $M_k$ is a non enumerable set, all of then open and dense in $S^1$ and such that $Leb(M_k)\to 0$ when $k\to \infty$, where $Leb$ denote the ...
1
vote
1answer
17 views

Does every quasi-affine variety have an open cover of affine dense subsets?

Suppose you have a nonempty, quasi-affine variety $Y$. Does $Y$ always have an open cover of affine dense subsets? I know that every quasi-affine variety has an open cover by quasi-affine varieties ...
1
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0answers
18 views

Reference request: classification of simple Lie groups and simple real Lie algebras

I am trying to understand the classification of simple Lie groups and the theory of highest weights for semisimple Lie groups by first understanding the case for complex Lie algebras, then relating to ...
10
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2answers
521 views

Locating a paper in Euler's complete works

I'm currently reading Disquisitiones Arithmeticae and I keep seeing references to Euler such as "Comm. acad. Petrop., 8 [1736], 1741, 141". My question: How can I go about locating this paper in ...
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1answer
57 views

A comprehensive book on Applied Mathematics for beginners

The Princeton Companion To Mathematics is described on Wikipedia thus: The book concentrates primarily on modern pure mathematics rather than applied mathematics, although it does also cover both ...
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0answers
56 views

Does this lemma have a name or where can I find a proof?

Does the lemma at the bottom of this page have a name? Or could someone give me an idea of where I can find a proof? In case you can't access the link: Lemma $\ \ $ If $g$ is of class ...
3
votes
1answer
36 views

Hypercomputation & Higher Dimensional Variants of Conway's Game of Life

Conway's Game of Life is a simple and important mathematical game with some rules of evolution in a two dimensional space. It appears in many subjects in mathematics, artificial intelligence and ...
4
votes
1answer
59 views

Question about the Ascoli-Arzelá Theorem proof

Ascoli-Arzelá Thoerem: Let $K$ be a compact space and $M$ be a metric space and $C(K,M)$ be the set of continuous functions from $K$ to $M$. $H \subset C(K,M) $ is relatively compact if and only if ...