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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1answer
31 views

Differential geometry of projective bundles

Can someone give me a reference about projective bundles from a differential-geometric point of view? I am not very familiar with algebraic geometry. I would like, for example, some theory about when ...
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0answers
31 views

A. A. Markov's paper on insolubility of the homeorphy problem [duplicate]

I am aware that this has been asked before, but the paper is nowhere to be found online, the provided link in the old thread leads to nowhere, and I'm really at wits end to find this paper, can anyone ...
3
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1answer
32 views

Formal theory on floating point numbers?

Is there a formal theory involving the set of floating point numbers? Like topological properties, analytic properties, etc. There's no abstract theory involving floating point set? I usually find a ...
1
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0answers
41 views

Ideas for approaching set theory when you've already studied higher abstractions?

I've come to acknowledge (or so I think). That many of the concepts e.g. in real analysis (like, say, continuity), actually don't (in modern times) boil down just real analysis. But rather, e.g. set ...
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0answers
10 views

Homogenous Sobolev Space definition

Consider the expressions $$ \|u\|_{A}^2:=\sum_{|\alpha|=2}\|\partial^\alpha u\|_{L^2(\mathbb{R}^d)}^2 $$ and $$ \|u\|_{B}^2:=\|\Delta u\|^2_{L^2(\mathbb{R}^d)}. $$ I think I have seen both used to ...
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0answers
39 views

On even almost perfect numbers other than the powers of two, as compared to odd perfect numbers given in Eulerian form

(Note: I have edited this question to conform to the further details added in the cross-post to MO.) Let $\sigma(x)$ be the sum of the divisors of $x$. We say that $X$ is almost perfect if ...
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0answers
9 views

Books for large deviations and maximum entropy principle?

What are some good introductory resources for learning more about the theory of large deviations and the maximum entropy principle?
2
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2answers
47 views

Rigorous Probability/Statistics Book reference?

Im wondering if anyone could recommend a book (or a few books) about statistics/probability for someone at the advanced undergraduate level who has taken some real analysis (at the level of baby ...
2
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1answer
39 views

Linear systems of equations and vector spaces

I'm looking for references that explicitly (and in an accesible way: -I come from engineering-) handle the connection between solving a linear system of equations and the abstract geometry involved.
2
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1answer
132 views

Regularity of heat kernel

I'm trying to find some references dealing with regularity and properties of the heat/Gaussian kernel $$ G_t\left(x,y\right) = \frac{1}{\sqrt{2\pi t}}\, e^{-\left.\left(x-y\right)^2\right/2t}, ...
1
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1answer
24 views

Suggest books on Combinatorial Graph Theory

I am going to start self-studying Combinatorial Graph Theory. Kindly suggest books or study materials available online. I have been told that it is basically application of linear algebra , mainly ...
1
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1answer
33 views

“Guesstimation” problems within pure mathematics

Wikipedia defines a “guesstimate” as “an estimate made without using adequate or complete information, or, more strongly, as an estimate arrived at by guesswork or conjecture.” Guesstimation problems ...
0
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1answer
31 views

References on completion and Tor/Ext

I am currently working on a thesis that relates to the Functors $\text{Tor}$ and $\text{Ext}$. I have found some work on localization with respect to them when it comes to information in my books but ...
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0answers
43 views

Single reference to classical results in analysis.

I am writing an expository work. And I need classical references (books or articles) that simultaneously proof the three classical results below. Any suggestion? Theorem. Let ...
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0answers
5 views

Looking for references of sobolev spaces involving time

I am looking for references which introduce the the sobolev spaces involving time. What I have at the moment is only a short chapter from Evan's PDE-book. Is there any other similar literature but ...
0
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0answers
33 views

Harmonic map and pullback metric

Let $\phi : M \to \mathbb{R}^n$ be a harmonic map, where $M$ is a Riemannian manifold. Let us take coordinates $(u_1, u_2,..., u_n)$ on $\mathbb{R}^n$ and express the Euclidean metric as $g = \Sigma ...
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0answers
103 views

Are “$S$-monoids” known to be good for anything?

I came up with the following... ...Definition. Let $(S,\wedge,1_S)$ denote a fixed but arbitrary monoid. (In the examples I have in mind, $S$ is always commutative and idempotent. But ...
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0answers
27 views

Does the antipode of a f.d. Hopf algebra have finite order

In a lecture I have heard that the antipode of a finite-dimensional Hopf algebra is conjectured to be finite, and that this has only been proven in characteristic $0$ by Larson and Radford in 1988. I ...
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0answers
28 views

Change of coordinates in target space of map

Consider a function $\phi = (\phi_1,....,\phi_n) : \mathbb{R}^m \to \mathbb{R}^n$. Suppose that $\phi_i$ is harmonic for each $i$, that is, $-\Delta \phi_i = 0$. Suppose we change from Cartesian to ...
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0answers
24 views

The image of a continuous derivation on a Banach algebra is contained in the kernel of a character.

It is known that if $D$ is a continuous derivation on a commutative Banach algebra $\mathcal{A}$, then for any nonzero character $\theta$ on $\mathcal{A}$ we have $D(\mathcal{A})\subseteq ker ...
2
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0answers
18 views

Comparing two textbooks for machine learning

I am a Ph.D student in Electrical Engineering. I am going to study the field of machine learning and I found some textbooks to study this field. 1) Probabilistic Graphical Models: Principles and ...
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0answers
7 views

Resources for free groups and surfaces

I'm looking for a good, clear, undergraduate level (if possible) reference (book, article, notes, etc) for the study of free groups, their topology and their relationship with surfaces. Thanks for ...
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0answers
12 views

What is the name of these elliptic surfaces E(n)?

I am referring to the elliptic surfaces $E(n)$, with fibration over $\mathrm{C}\mathbb{P}^1$. They are common in 4-manifold theory and complex geometry. See for example Chapter 7 in Akbulut`s ...
1
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1answer
23 views

An elementary introduction to Puiseux series?

While studying Analytic combinatorics of Flajolet and Sedgewick (to be more specific, the coefficient asymptotics of algebraic functions), I have come across the concept of Newton-Puiseux expansions. ...
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0answers
82 views

best books, lecture notes, for studying pullback rings

Does anyone have suggestions for books, or lecture notes, (or videos) for studying pullback rings? I know definition; and a few facts about it (for example when it is Noetherian). Now I ...
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0answers
32 views

Looking for an article that was only available as Bell Labs Technical Memo

I'm not even sure if this is the right place to ask and even if it is, I'm well aware it is a bit of a stretch, but anyways: I'm looking for the article "Asymptotic properties of robust generalized ...
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0answers
38 views

A math book that covers the all the math required for an undergraduate engineer in an interesting way

I am from the electrical engineering background. I have started my course in electrical engineering. I would like a book that covers the entire math that I have studied till now ( that is high school) ...
2
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1answer
53 views

Algebra and calculus's books for master [closed]

I want to prepare myself for entrance master exam for one of the universities in America, I will be grateful if you tell me which books are good to study linear algebra and calculus? Thanks.
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0answers
17 views

Raney's Lemma for non-negative real numbers in the interval $[0,1]$?

The Raney's Lemma is true with integers, below a variant with m-Raney sequences. Does there exist any variant about Raney's Lemma where the number sequence has only real numbers within the interval ...
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0answers
51 views

A rather special monoid

While implementing an embryo of computational algebra on my blog I ran into a rather special monoid and I wonder if it's studied before. After implementing a very simple concept of dynamic sets I ...
3
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1answer
60 views

Rank 2 vector bundle

$E$ is a rank $2$ vector bundle. Why is $E\simeq E^*\otimes \det E$? Any generalization (arbitrary rank, $E$ non locally free etc.)?
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0answers
15 views

Large sparse binary matrices with little row overlap

How can I construct sparse binary matrices $A : M \times N$, with ~ $N p$ ones in each row, so that rows don't overlap much, i.e. the maximum $\qquad \text{size} (\ A \text{ row } i \ \cap\ A ...
3
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0answers
24 views

Good book on quantum probability

Who can suggest me a book on quantum probability? I'm mostly interested in its geometric aspects (complex projective space, Fubini-Study...). I have a background in quantum mechanics and differential ...
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0answers
23 views

Evolution of a closed set under a differential equation

I consider an ordinary differential equation $$ \dot x = f(x), \quad x(0) = x_0 \in X_0 \subset \mathbb R^n. \quad (*) $$ Let $f$ allow for a unique solution on $X_0$ and on the whole time interval ...
1
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1answer
49 views

Recommended Algebra Books to read? [duplicate]

Can somebody recommend me any books to read that cover the following topics? Chapter 1. Vector Spaces 1.1. Solutions of Simultaneous Linear Equations 1.2. Fields and Vector Spaces 1.3. ...
4
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1answer
25 views

Study of algebraic structures analogous to the ring of smooth functions and module of vector fields

$\newcommand{\Ga}{\Gamma}$ Let $M$ be a smooth manifold. $\Ga(TM)$ is a module over the ring of smooth (real) functions (which is also an algebra, and denoted by $C^{\infty}(M)$). Also, each $X \in ...
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1answer
66 views

Is “Generalized functions” by Gelfand published in 5 or 6 volumes?

From what I know, "Generalized functions" by Gelfand is published in five volumes. Do you know whether there exist a 6th volume? Thanks a lot!
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0answers
92 views

References about Iterating integration, $\int_{a_0}^{\int_{a_1}^\vdots I_1dx}I_0\,dx$

Are there any references that discuss Iterating integration in general, $\int_{a_0}^{\int_{a_1}^\vdots I_1dx}I_0\,dx$, conditions in which they converge, some special values, some special tricks to ...
2
votes
1answer
91 views

How important is the choice of books in studying Analysis?

I am in a fix. I have done a graduate course in Pure Mathematics.I love to study abstract algebra.I want to do postgraduate in Mathematics especially in Abstract Algebra . In order to enter a ...
4
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1answer
40 views

Basic question on cohomology ring

To show (1) $S^2\vee S^1\vee S^1$ is not homotopy equivalent to $S^1\times S^1$ (2) $S^1\vee S^2\vee S^3$ is not homotopy equivalent to $S^1\times S^2$ I use the same method: For (1) the ...
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0answers
12 views

Reference request: 2D conformal field theory and the honeycomb lattice

Would anyone know what is meant by "conformally invariant" functions defined on the plaquettes of the honeycomb lattice (ie the function is defined on the vertices of the dual tringular lattice)? ...
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0answers
12 views

Request: superposition of triangular lattice and its dual graph

Does anyone know where I could find a pdf of graph paper with both the triangular lattice and its dual hexagonal lattice superimposed? I'd like my students to have something they could easily doodle ...
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0answers
36 views

Reference for an isomorphism

Let $A$ be a finite dimensional algebra over a field $K$ and $D:=Hom_K(-K)$ the natrual duality of mod-$A$. Let $M$ and $N$ be $A$-bimodules. Then there is an isomorphism $A$-bimodules: $Hom_A(M,D(N)) ...
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0answers
18 views

What is the most accessible reference on wall-crossing?

I am looking for a nice and easy to read reference on wall-crossing (in the context of Donaldson theory). Is there some accessible reference you have to suggest? I am interested in studying Donaldson ...
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0answers
49 views

converting to math from economics major

Recently, i'm majoring in honour track of economics taking econometrics statistics courses and minoring in mathematics taking advanced calculus, real analysis ,linear algebra courses. Upon research on ...
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1answer
78 views

A Real Analysis book which is in both French and English Languages.

I need a real analysis book which is in both French and English languages. So, it would be great if anybody does have any idea of this issue.
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3answers
389 views

How, if at all, does pure mathematics benefit from $2^{74207281}-1$ being prime?

So a couple of days ago the $17$ million digit number $2^{57885161}-1$ was beaten by the $22$ million digit number $2^{74207281}-1$ at being the largest known prime number. Are there any specific ...
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0answers
109 views

Atiyah-Guillemin-Sternberg convexity theorem

I would like to study the Atiyah-Guillemin-Sternberg convexity theorem: proof and applications. I am already familiarised with hamiltonian actions, moment maps...and with elementary Morse theory. So ...
3
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1answer
64 views

What is the definition of a presheaf in EGA?

In EGA I, Grothendieck says he is not going to bother recalling the definition of a presheaf (on a given topological space $X$ with values in some category $\textbf{K}$). I was just wondering what ...
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1answer
44 views

Textbook Accompanying Naive Set Theory

I'm in the process of self-studying from the very popular Halmos book "Naive Set Theory" and I must say I can say only the best about the book. However, although the book has some excercises I would ...