# Tagged Questions

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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### Practise with Smooth Functions and Manifolds

I'm trying to get an intuition for smooth manifolds, and in particular the smoothness of transition functions. I haven't done that much calculus on $\mathbb{R}^n$ before, and would like to practice ...
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### Sampling and probability generating functions - reference wanted

Suppose I have a huge (effectively infinite) population of widgets. The number of widgets that are broken is given by a random variable $X$, whose probability generating function is $p(z) = E(z^X)$. ...
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### Exterior Derivative vs. Covariant Derivative vs. Lie Derivative

In differential geometry, there are several notions of differentiation, namely: Exterior Derivative, $d$ Covariant Derivative/Connection, $\nabla$ Lie Derivative, $\mathcal{L}$. I have listed them ...
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### Longest Odd/Even Sequence in Composite Patterns

NOTE I have completely reworded this because I made a complete hash of it the first time, it got worse as I added to it. I apologize to anyone who might have been confused, and hope that this will be ...
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### Short First Course in linear algebra text

I am currently reading a bit of real analysis from Dr Pugh's book and I intend to study abstract algebra from Dummit and Foote in a short time. However, I wish to explore linear algebra in the ...
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### Poisson integral on $\mathbb{H}$ for boundary data which is orientation-preserving homeomorphism of $\mathbb{R}$

Let $f$ be a real-valued function (in my case, an orientation-preserving homeomorphims of $\mathbb{R}$) on the real line $\mathbb{R}$ which is not in any $L^p$ -space. Let us take the simplest example ...
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### reference recommendation on mathematical logics

It is a bit of strange that I haven't be trained on such a topic. It wouldn't influence my daily work but I would like to study some materials on my own. So, dear fellows, you got any classic ref in ...
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### Prerequisites for understanding the Hodge conjecture

The Hodge conjecture is a major open mathematical problem that states that on a complex manifold $X$ and its respective Hodge classes, defined as $Hdg^k(X)= H^{2k}(X,\mathbb{Q})\cap H^{k,k}(X)$ that ...
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### A good introductory discrete mathematics book.

I am professor of mathematics and I am scheduled to teach a newly designated discrete math class for computer science majors. The prerequisite for the class is only Calc 1 and Id like a book that ...
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### Has the $\Gamma$-like function $f_p(n) = 1^{\ln(1)^p} \cdot 2^{\ln(2)^p} \cdot \ldots \cdot n^{\ln(n)^p}$ been discussed anywhere?

In an older fiddling with the gamma-function (expanding on the idea of sums of consecutive like-powers of logarithms, similarly as the bernoulli-polynomials for the sums of like powers of consecutive ...
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### products of logarithms

(When one says several things in a question, then several things may get answered and others neglected. Hence this posting overlaps with one of my earlier ones, but (I hope) this one will be short, ...
108 views

### Existence and Unicity Weak, Strong, Pathwise, In Law, etc… for SDE's

I feel always confused with weak, strong, pathwise unicity and or existence for Stochastic Differential Equations. It is mainly my own fault and I should do something about it. But it would be much ...
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### How should I understand probability distribution defined as $P^X(A)=\frac{1}{3}\delta_0(A)+\frac{2}{3}P_2(A)$?

I get the following question from Zastawniak's Probability Through Problems: Assume that the distribution function of a random variable $X$ on a probability space $(\Omega,{\mathcal A},P)$ is ...
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### Project in computer science and mathematics.

My background I'm a third year student. I study mathematics combined with computer science (with focus on modeling, simulations and visualization). In order to get my degree, I have to make a ...
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### Simpler definition of manifold

I'm new to topology but I must understand how it works to progress in my research. First, can anybody point me to a document that introduces topology in a "gentle" way. What pre-requisites do I need ...
584 views

### Good textbooks for lattice and coding theory

I am looking for good textbooks for lattice and coding theory. Lattice and coding theory are very interesting on their own, but I have application of the theory to K3 surfaces & modular forms (and ...
729 views

### Ways to solve a 2D Laplace equation

I'm looking for a survey of methods to solve Laplace equation in two dimensions. Is there a book describing them with hints regarding their applicability for various cases? I mean analytical methods,...
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### What is a good resource for functional derivatives and functional determinants?

What is a good resource for functional derivatives, functional determinants, etc.? What is the branch of mathematics dealing with those things? It is not in my functional analysis book. What is a ...
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### Good substitutes for Ross's book on Probability Models

I was wondering if there are any FREE good alternatives to Sheldon Ross's Probability Models which are more succinct? Are there any free online resources (websites/PDFs/course notes) which cover more ...
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### Polynomials as concrete structures

Motivation The structuralist point of view on mathematical objects has two aspects: On the one side, a mathematical object is seen as a concrete structure of abstract dots, e.g. a graph. On the ...
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### Generalization of groups of the form (R-{0}, regular multiplication)

Result: Fix $a \in \mathbb{R}$. Then $(\mathbb{R} \backslash \{a\}, *)$ is a group, where our group operation is defined by $x*y = (x-a)(y-a) + a$. One consequence of this is the standard fact that ...
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### Where read recent developments in Math presented in a way that is easy to understand?

I posted a similar question a few months ago, but I don't think people understood my question. I often find articles such as this which discuss exciting developments in science. I have a great ...
339 views

### Do lay persons really believe that all of mathematics is known?

I once found a professor of medicine to be under the impression that everything in mathematics is already known. It's probably commonplace to hear that the masses labor under that misconception. In ...
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### How to compute rational or integer points on elliptic curves

This is an attempt to get someone to write a canonical answer, as discussed in this meta thread. We often have people come to us asking for solutions to a diophantine equation which, after some clever ...
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### Reference for l-adic Lie algebras

I don't know much at all about Lie algebras or representation theory, and I'm trying to read Ribet's `Review of Abelian l-adic Representations and Elliptic Curves'. Is there a standard reference for ...
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### Cyclic Algebras over local fields- reference request

I am looking for an introductory text to the subject of Cyclic Algebras, and in particular ones defined over a local field. A cyclic Algebra, to the best of by understanding is defined as follows: ...
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### Has the notion of a unique factorization category been defined and studied?

I am using a this notion in a paper that I am writing. The notion is that $(\mathcal{C},\otimes, I)$ (which we will just call $\mathcal{C}$) is a symmetric tensor category, with a unit $I$. Then a ...
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### What are the required backgrounds of Robin Hartshorne's Algebraic Geometry book?

It seems that Robin Hartshorne's Algebraic Geometry is the place where a whole generation of fresh minds have successfully learned about the modern AG. But is it possible for someone who is out of the ...
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### Good resources for learning Probability [duplicate]

Possible Duplicate: probability textbooks I recently started taking Probabilistic Graphical Models on coursera, and 2 weeks after starting the course I am beginning to believe that I am not ...
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### Polynomial behavior on hyperbolic plane

More a reference request / more information. I was reading some websites about hyperbolic geometry and got to thinking about how would polynomials $(x^2-2)$ behave in such a geometry. So, I need ...
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### Connection between modular forms and line bundles

I need a good reference about the connection between modular forms and line bundles. I found only Milne's note that treats briefly this argument. I've already checked, but without finding anything, ...
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### Smallest dimensional irreps of semi-simple Lie algebras

I'm wondering if there is a reference that lists the first couple smallest dimensional irreducible representations of each semi-simple Lie algebra. I know these can be found using the Weyl dimension ...
271 views

### de Rham Cohomology of Non-Flat Bundle

Let $E$ be a smooth vector bundle on a smooth manifold $M$. If $E$ is flat, there is a connection $\nabla$ which is a differential which we can use to define the de Rham cohomology of $E$. If $E$ ...
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### Necessary and sufficient conditions for $G$ to have $A(G)$ isomorphic to an operator algebra?

Let $G$ be a locally compact group. We denote by $A(G)$ the Fourier algebra of $G$. An operator algebra is a closed subalgebra of $B(H)$ where $H$ is a Hilbert space. What are the necessary and ...
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### Fluid mechanics resources for pure mathematicians?

I'm currently taking a course on fluid mechanics, and I'm finding it very difficult to become motivated and interested. I've always been more interested in the pure math side of my courses, and love ...
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### Complex analysis book with a view toward Riemann surfaces?

I am considering complex analysis as my next area of study. There are already a few threads asking about complex analysis texts (see Complex Analysis Book and What is a good complex analysis textbook?...
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