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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0
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1answer
30 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 ...
0
votes
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
votes
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 ...
0
votes
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 ...
0
votes
3answers
73 views

Textbook on group theory for physics student

I'm an undergraduate physics student and realize I should learn some group theory for physics. Does anyone know any good textbooks that would be good for this? I've found the following but am not sure ...
5
votes
4answers
245 views

The way into logic, Gödel and Turing

I have always read about the geniuses of Alan Turing and Kurt Gödel . Many websites mention their works in logic as revolutionary. I want to understand their works, but I don't exactly know the way ...
2
votes
0answers
17 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 ...
27
votes
20answers
2k views

Elementary books by good mathematicians

I'm interested in elementary books written by good mathematicians. For example: Gelfand (Algebra, Trigonometry, Sequences) Lang (A first course in calculus, Geometry) I'm sure there are many other ...
0
votes
0answers
6 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 ...
0
votes
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
vote
1answer
78 views

Finite groups of Mobius Transformations

Let $M_2(\mathbb{C})$ be the group of all Mobius transformations $z\mapsto \frac{az+b}{cz+d}$ from $\mathbb{C}\cup\{ \infty\}$ to itself. Let $PSU(2,\mathbb{C})$ be the group of all Mobius ...
2
votes
2answers
108 views

Generalizations of the Collatz to $(mx \pm 1)/2$ for $m=181$ gives two nontrivial cycles; are more examples $m$ known?

Generalizing the Collatz $T_{3,+}(n) = \left\{ \begin{array} {cl} {3n+1 \over 2} & \text{ when } n=2k+1 \\ \frac n{2^B} & \text{with maximal } B \gt 0 \text{ where } 2^B | n \end{array} ...
1
vote
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. ...
0
votes
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 ...
2
votes
1answer
52 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.
17
votes
3answers
387 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 ...
0
votes
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
votes
1answer
59 views

Representation of regular languages by monoids [closed]

I'm interested in representation of regular languages by monoids, and in particular of how to use this kind of representation to get a recognizer. I have found some references on the web, but does ...
0
votes
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 ...
7
votes
6answers
2k views

book with lot of examples on abstract algebra and topology

I have read a lot of blogs and forums to find out the best of the books on Abstract algebra and Topology but on going through the books I realized that they are full of proofs and all kind of theorems ...
1
vote
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 ...
8
votes
1answer
87 views

Diophantine equations for polynomials

I know that there has been work on diophanitine equations with solutions in poynomials ( rather than integers ) of the Fermat and Catalan type $x(t)^n+y(t)^n=z(t)^n$ ; $x(t)^m-y(t)^n=1$ and these have ...
0
votes
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
votes
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 ...
1
vote
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 ...
0
votes
0answers
42 views

What's the name of this problem? Interesting minimisation of a length.

There is a problem which has to do with minimising the length of a (possibly disjoint) barrier in a region of space (often a 2D circle) such that no straight line can pass through the particular ...
1
vote
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
votes
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 ...
2
votes
3answers
184 views

Book/article recommendations for an introduction to hypergroups and subsequent research

I'm a grad student and I'm choosing an area to follow on my doctorate (in?) and I've been thinking about extension of topological group theory results to topological hypergroups, but for that I need ...
0
votes
0answers
107 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 ...
2
votes
1answer
90 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 ...
17
votes
13answers
10k views

Requesting abstract algebra book recommendations

I've taken up self-study of math. (How smart can that be?) I've just about finished a course in real analysis which spent a lot of time on metric spaces and some time revisiting calculus. I was ...
28
votes
7answers
13k views

Game theory - self study

I want to self study game theory. Which math-related qualifications should I have? And can you recommend any books? Where do I have to begin?
5
votes
2answers
168 views

Book on applied mathematics

My Applied Mathematics course covers these subjects: -Calculus of Variations -Laplace Transform -Fourier Analysis -Special Functions -Integral Equations And as an introduction to the subject it has ...
18
votes
5answers
852 views

Categorical introduction to Algebra and Topology

At the moment I am reading books on Algebra and on Category theory. More exactly, I started working through the book Algebra by Serge Lang. I have read the chapters on groups and rings, but then my ...
3
votes
1answer
118 views

Book Recommendations for Picard Big and Little Theorems

I am looking for a book covering Picard's Little and Big Theorems, preferably, one that is intended for an undergraduate/first year graduate student who has a semester of complex analysis under ...
7
votes
0answers
153 views

Help requested to understand the abstract cotangent complex construction

I am trying to thoroughly understand one way of constructing of the cotangent complex (I am using here the Lichtenbaum's way) The first question I have is about the definition of an extension of ...
10
votes
3answers
987 views

Applications of Banach Algebras and Operator Algebras

I am trying to learn operator algebra theory (I am tempted to start with Douglas' "Banach Algebra Techniques in Operator Theory"). One aspect that I am curious about is whether there are significant ...
2
votes
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!
1
vote
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)) ...
4
votes
0answers
354 views

On the weak convergence in reflexive Banach space

Consider the following proposition: Proposition 1. Let $X$ be a reflexive Banach space and suppose that $\{x_n\}$ is a sequence in $X$ that is bounded and has at most one weakly sequentially cluster ...
1
vote
1answer
400 views

Comparison theorem for systems of ODE

Let vector-function $x(t)$ satisfy a differential equation $$ \dot x = f(x), $$ and a vector-function $y($t) satisfy a differential inequality $$ \dot y \leq f(y) $$ with starting positions $y(0) ...
9
votes
7answers
12k views

Good First Course in real analysis book for self study

Does anybody know of a good book in real analysis for self study for a beginner? What about Analysis 1 by Terence Tao?
1
vote
0answers
163 views

Linear algebra book for self study

I am not a complete beginner in the subject but I am not familiar with most of the linear algebra's topics. I have studied determinants and matrices, but I want to get a much deeper insight. I looked ...
0
votes
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.
4
votes
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 ...
7
votes
2answers
255 views

Definition of a polyhedral region

I believe the following two conditions on a subset $S$ of $\mathbb{R}^3$ may be equivalent. I would like to know if they are equivalent, and where I can find either a counterexample or a proof of ...
1
vote
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)? ...
0
votes
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 ...