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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3
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1answer
34 views

Further examples of Principal Ideal Domain that are not Euclidean Domains

In several courses of algebra, I've heard that not all PIDs are EDs, and the canonical example is $\mathbb{Z}\left[\dfrac{1+\sqrt{-19}}{2}\right]$ which I've heard over and over. Some cursory research ...
3
votes
1answer
105 views

Mathematics books that tell you what is really happening? [closed]

Many book I've read teach you symblobic manipulations instead of pointing out what's really happening. So my question would be: what mathematics textbooks don't do that? Books that rather than listing ...
3
votes
2answers
63 views

A reference for a combinatorial identity

I have come across this identity from study of species. I am not posting my method but I am interested in knowing whether it arises in some other contexts as well. The identity is: $$\sum ...
12
votes
2answers
316 views

Interpolated Fibonacci numbers - real or complex?

The common Binet-formula for the Fibonacci-numbers $$ f_n = {\varphi^n- (1-\varphi)^n \over \sqrt 5 } \small {\qquad \qquad \text{ where }\varphi={1+\sqrt 5\over 2}}$$ allows interpolation to ...
3
votes
0answers
14 views

Which subject deals with questions about texture mapping in computer graphics? [migrated]

When we do texture mapping in computer graphics, we care about following questions: How are texture coordinates(also called UV coordinates) generated for a specific geometry? How can we measure the ...
1
vote
3answers
506 views

Introduction to Mathematical Thinking: Algebra and Number Systems

I'm currently in my final year of high school, and want to pursue some recreational maths before I go to university. I've been scouring the internet and various book stores for a nice textbook to ...
3
votes
1answer
117 views

A textbook for a rigorous introduction to Stochastic Analysis with emphasis on stochastic differential equations

I'm looking for a good textbook for an introduction to Stochastic Analysis, preferably one that focuses on rigour. I am familiar with measure theory and basic probability theory. The direction I am ...
17
votes
2answers
224 views

To whom do we owe this construction of angles and trigonometry?

I've come across what is, to me, the most precise, beautiful and thorough definition of what we know of as the angle between two vectors. I say this because most literature either skims over things ...
0
votes
0answers
29 views

Open conjectures in number theory that is easy to do some programming for

I have a to do a project in number theory that we are assigned that we should do some programming for that is not the collatz conjecture, so any suggestion would be really great.
1
vote
1answer
17 views

Let $V$ be a finite dimensional vector space over a field $F$. Prove the dependence of a set of vectors $\in V$ and reference request

Let $V$ be a finite dimensional vector space over a field $F$. Show that if $u_{1}, \dots, u_{n}, v_{1}, \dots, v_{n} \in V$ and $u_{1}, \dots, u_{n}$ are linearly independent, then there are only ...
4
votes
1answer
53 views

Centralizers of reflections in parabolic subgroups of Coxeter groups

Let us consider a (not necessarily finite) Coxeter group $W$ generated by a finite set of involutions $S=\{s_1,...,s_n\}$ subject (as usual) to the relations $(s_is_j)^{m_{i,j}}$ with ...
1
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0answers
23 views

Learning about Markov Chains

I am trying to learn about how to use markov chains for complicated probability problems. I have been looking for different materials to learn these but haven't had much luck. Does anyone have any ...
2
votes
1answer
59 views

Chain rule in several complex variables: Wirtinger derivatives

Let $\Omega,\Omega'\subseteq\Bbb C^n$ open, $F:\Omega\to\Omega'$ holomorphic invertible function; it's a variable change, so let's call $F(z)=\tilde z$. Let $r:\Omega\to\Bbb R$ twice differentiable, ...
3
votes
1answer
80 views

Affine variety and dimension

I'm working on a paper about representation of quivers and Gabriel's theorems. See this .pdf if you're interested ; but I guess you can answer my question without knowing anything about quivers, or at ...
2
votes
0answers
49 views

20th century books on geometry

I've heard something about the fact of some old geometry textbooks, dated to the beginning of the 20th century approximately, have a structure composed by a problem, the solution and then something ...
0
votes
0answers
23 views

Table of Fourier series

I found that there are very good references on Fourier integral transform but none on Fourier series. Do you happen to know one?
0
votes
0answers
26 views

Identifying a sequence of numbers from an optimization problem in $L^1$

Question Does there exist general closed form solutions (or some sort of recurrence relation) to the system of equations: $$\begin{align} x_0 &= -1\\ x_{k+1} &= 1\\ \sum_{j = 0}^k (-1)^j ...
1
vote
2answers
84 views

How can we detect if a topological space has “holes”.

I realize that this question might seem ambiguous, is there a topological notion for what a Hole is? I think it has something to do with the fundamental groups of the topological space but I don't ...
7
votes
1answer
202 views

Do hom-sets really live in the category Set?

In familiar introductory books on category theory, one of the first examples of a category given is Set. And what category is that? Typically no explanation is given at this stage. But of course ...
8
votes
2answers
256 views

Where can I find linear algebra described in a pointfree manner?

Clearly, some of linear algebra can be described in a pointfree fashion. For example, if $X$ is an $R$-module and $A : X \leftarrow X$ is an endomorphism of $X$, then we can define that the ...
1
vote
1answer
20 views

Reference request: Right pseudo inverse

Suppose, I have a matrix $P\in\mathbb{R}^{m\times n}$ with $\text{rank}(P)=m$ and I'm searching for a right pseudo inverse $P^{+R}$. Since I'm working with symbolic matrices in a computer algebra ...
1
vote
4answers
127 views

Calculus books recommendation (intermediate level)

:) I would like to ask for some intermediate level textbook for calculus (single variable), or, at least, some supplement to Spivak's Calculus for better understanding on how to approach and solve ...
0
votes
0answers
17 views

Domains whose Green functions is explicit or can be approximated explicitly?

The only examples I keep finding are upper half plane (and tilted) and sphere (eg. Evans). Can you suggest some other domains? If not, how about any good books or papers documenting the progress ...
2
votes
2answers
161 views

Quasi-hereditary algebras

Can anyone please recommend a reference (I prefer a book chapter) on Quasi-hereditary algebras? and if it is possible tell me how to prove that Schur algebras are Quasi-hereditary (or any other ...
2
votes
1answer
49 views

Reference request: Derived category of category with sufficiently many injectives

I'm studying derived categories and have encountered problem with references I have. Namely, proof of the following theorem: Theorem: Let $\mathcal A$ be Abelian category and $\mathcal I$ full ...
8
votes
5answers
453 views

categorical interpretation of quantification

Many constructions in intuitionistic and classical logic have relatively simple counterparts in category theory. For instance, conjunctions, disjunctions, and conditionals have analogues in products, ...
1
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0answers
21 views

If $R$ is a noncommuative Noetherian ring, is it true that $R[[x]]$ is a Noetherian ring?

I am looking for a reference in order to answer the following question: If $R$ is a noncommutative Noetherian ring, is it true that $R[[x]]$ is a Noetherian ring? The answer is well-known in the ...
0
votes
0answers
51 views

Calculus book with interesting examples

I need to prepare presentation about calculus, paying special attention for examination of function of one variable. I am not very advances in the topic, but I'm looking for book which contains ...
1
vote
0answers
28 views

Reference request: extending tensor product of modules

I'm looking for a reference to a construction similar to the following. I have a right R-module, $A_{K'}$, and a left R-module, $_KB$, where $K$ and $K'$ are fields and $K'\subset K$. I want to take ...
0
votes
0answers
37 views

what are mathematical and scientific website & database?

I have seach mathematical website, which are http://scienceworld.wolfram.com or http://www.mathforum.com and many more which are given by http://www.tifr.res.in/~base/links/website.html. Can anybody ...
0
votes
0answers
10 views

Finitely generated modules over completed group rings

Let G be a profinite group. Let $M$ be a finitely generated $\Bbb{Z}_p[[G]]$ (completed group ring). How to show the following facts: $M$ carries a unique Hausdorff topology(called its canonical ...
14
votes
0answers
113 views

Representability of diagonal of $\mathscr{M}_g$

Let $\mathscr{M}_g$ be the moduli stack of genus $g$ curves ($g \geq 2$). That is, $\mathscr{M}_g$ is the category whose objects are proper smooth morphisms $f: C \to S$ whose geometric fibers are ...
1
vote
2answers
195 views

(Updated) Geometric Illustration of Monotone and Maximal Monotone Maps

I am writing a note about the Monotone and Maximal Monotone maps from the following book http://link.springer.com/book/10.1007%2Fb97594 In this book we read a map ...
1
vote
0answers
19 views

Can anyone suggest a reference to learn about relative log-likelihood and likelihood intervals?

I want to understand how to calculate the 10% likelihood interval for a Poisson model of count data. It is an old assignment where they give you 20 counts, tell you it is a Poisson model and ask you ...
2
votes
1answer
56 views

Problem Books with Problems less “intense” than Putnam Problems

As the title indicates, I'm looking for a few suggestions on problem books. The problems should be a bit less demanding than Putnam problems. Like the Putnam, however, the prerequisites should be ...
-1
votes
0answers
47 views

I need a reference in topology [duplicate]

Can someone please give the title of a good topology book with exercises, preferably written by a master in the field? Actually, I have basic notions like compactness, completeness, connectedness and ...
0
votes
0answers
39 views

I need a good reference in topology [duplicate]

Can someone please give the title of a good topology book with exercises, preferably written by a master in the field Actually, i have basic notions like compactness, completeness, connectedness and ...
1
vote
0answers
32 views

Sets that are convex in two different metrics

Let $(M,g)$ be a complete Riemannian manifold, and let $C$ be a subset of $M$. We will say $C$ is convex if for any points $p,q \in C$, there exists a unique normal minimal geodesic $\gamma$ joining ...
1
vote
1answer
59 views

Analogue of splitting field in several variables

Let $k$ be a field, and $P \in k[X]$. Consider the extensions $k \subset L \subset K$, where $L$ is a splitting field for $P$ over $k$ and $K$ is the algebraic closure of $k$. Then (by definition) all ...
2
votes
1answer
40 views

Group generated by self-inverse elements

Given objects $x_1, \dotsc, x_n$, is there a name for the group generated by $x_1,\dotsc,x_n$ subject only to the relations $x_i^2 = 1$ for all $i \in \{1,\dotsc,n\}$? The dihedral group seems ...
2
votes
2answers
130 views

An analogous definition of Fourier transform $\hat f(u) = \int_{-\infty}^{+\infty} f(t) \exp(- i u t) dt$ for sinc-function.

We know the definition of Fourier transform $$\hat f(u) = \int_{-\infty}^{+\infty} f(t) \exp(- i u t) dt \ \ \ (*)$$ It is widely used in the analysis in the frequency of dynamical systems, in the ...
4
votes
0answers
48 views

What is the automorphism group of the field of all constructible numbers?

Let $\Omega\subseteq \mathbb{C}$ be the field of all constructible numbers (i.e. $\Omega$ is the smallest subfield of $\mathbb{C}$ which is closed under taking square roots). What is known about the ...
6
votes
2answers
177 views

Pre-requisites and references for $K3$ surfaces

I would like to know the "roadmap" to study $K3$ surfaces. Perhaps, my background might be helpful: I am an undergraduate student, who knows the basics of Differential Geometry, Topology, Complex ...
1
vote
0answers
30 views

Runge-Kutta methods for PDEs

How are RK methods for solving time-dependent PDEs implemented? I am trying to reproduce results of a thesis. It is a advection-diffusion unsteady equation. It is clearly mentioned that they have ...
1
vote
1answer
25 views

Domain of square root of a self-adjoint positive operator

Let $A \geq 0$ be a densely defined self-adjoint positive operator on a Hilbert space $H$ obtained by Friedrichs extension, and let $Q$ be the densely defined quadratic form associated to $A$, that ...
0
votes
0answers
29 views

Sobolev spaces on compact manifolds

Let us consider a self-adjoint elliptic pseudodifferential operator $P \in OPS^2$ on a compact manifold $M$ such that $spec(P) \subset (0, \infty)$. Is the norm $(Pu, u)^{1/2}$ on $H^1(M)$ equivalent ...
2
votes
0answers
37 views

Is the analytic version of the Whitney Approximation Theorem true?

The Whitney Approximation Theorem states that any continuous map between smooth manifolds is homotopic to a smooth map. If the manifolds are real analytic, is every continuous map between them ...
0
votes
0answers
25 views

Books on Complex analysis and Probability

Any books exploring the connections between Complex analysis and Probability in the spirit of Dudley's book? In this forum I found Watanabe's "Algebraic Geometry and Statistical Learning Theory" ...
0
votes
0answers
11 views

Prime ideals in Iwahori-Hecke algebras

Results on the ideals (especially the prime, completely prime ones) of Iwahori-Hecke algebras (espcially the ones with finite order) is needed. Thank you very much.
1
vote
2answers
52 views

Sets of “Isolated” Cardinals

Let $C\neq\emptyset$ be a set of infinite cardinals with the property that NO member of $C$ occurs as the supremum of strictly smaller members of $C$. So the cardinals in $C$ are sort of "isolated". ...