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.

learn more… | top users | synonyms (3)

3
votes
0answers
14 views

Is there a name for this partial order between metrics?

Suppose we have a set $X$ and two metrics $d_1,d_2$ on it (which may or may not attain $\infty$). Assume furthermore that $d_1,d_2$ have the same metric components (where a metric comoponent is a ...
0
votes
1answer
8 views

book info needed about game theory

can you suggest me a good book on game theory undergrad/grad course,that may provide insight instead of preaching about computation?it would be better if the works of Neumann & Nash are explicitly ...
0
votes
0answers
29 views

A book suggestion -Algebraic geometry. (Arf rings and Hilbert Function)

I am studying algebraic geoemtry. And I need to learn Arf Ring & Hilbert funciton. Please suggest me books / lecture notes...etc. that explains this topic in detail. Thank you.
0
votes
1answer
26 views

Why all games are not Potential?

A definition given in wikipedia of an exact potential game as follow: A game $G=(N,A=A_{1}\times\ldots\times A_{N}, u: A \rightarrow \mathbb{R}^N)$ is: an exact potential game if there is a ...
1
vote
0answers
13 views

Original publication of P.A.M. Dirac

For an article I am looking for the original publication of P.A.M. Dirac where he explained the difference between a $2\pi$ and $4\pi$ rotation by using a model with strings. This is sometimes called ...
0
votes
0answers
44 views

Real Analysis and dynamics

I am looking for a textbook or similar resource that addresses the content in a rigorous graduate course in real analysis(at the level of Rudin/Royden) with the following criteria: No hand waving - ...
0
votes
0answers
14 views

Elliptic regularity of Dirichlet problem

Suppose $\Omega\subset\mathbb{C}$ is a simply connected domain with $C^\infty$ boundary. Consider the following Dirichlet problem $$\Delta u |_{\Omega}=0 $$ $$u|_{\partial\Omega}=f$$ Under what ...
1
vote
1answer
30 views

Why optimization problems cannot be solved by simple derivative?

Let $f(\cdot)$ be a linear function. $f:\mathbb{R}^n\rightarrow\mathbb{R}$ $\;\quad\;\mathbf{x}\;\rightarrow f(\mathbf{x})$. Let $\mathbf{A}$ be a matrix in $\mathbb{R}^{m\times ...
0
votes
1answer
23 views

Matrix representation of complex numbers in exponential form

Do there exist matrices M and P for this equation? Or perhaps M and P dont need to be matrices? I saw this and this question after googling which made me wonder about whether the exponential form of ...
1
vote
2answers
64 views

Gödel's incompleteness theorems: where to learn? Is there a straightforward relation between the two?

What would be a good textbook or paper to learn the proofs of the two Gödel's incompleteness theorems from? I would prefer it to be as close to the original proofs as possible. I have not tried to ...
3
votes
2answers
39 views

Arbitrary (i.e. not necessarily finite-dimensional) vector spaces; reference request.

Its virtually impossible to complete an undergraduate degree these days without studying finite-dimensional vector spaces in quite some detail. So like most of us, I've done all that; however, just ...
2
votes
1answer
52 views

Twin Prime conjecture current status

Can someone help me with a link to read about the status of the Twin Prime conjecture. I have browse on the internet and have read some articles but still I have no clue of the updated status of Twin ...
1
vote
0answers
14 views

Arrow's Impossibility Theorem Using Boolean Algebra

I am currently working on a research project which involves using Boolean matrices for the proof of Arrow's Impossibility Theorem and various other lemmas and results related to quasi ordered sets. In ...
1
vote
0answers
35 views

Applications of PDEs

I teach an undergrad ODE course. As I have completed basically all the material, I thought it would be nice to give the students a brief introduction to PDEs. At the end of the lecture, I said that ...
0
votes
1answer
75 views

When graph theory cannot model the most basic problem in wireless networks. Why?

I have a set of wireless links. These links are denoted by $\mathcal{L}=\{\ell_1, \dotsc, \ell_n\}$. Every link $\ell_i$ is composed of one transmitter $s_i$ and one receiver $r_i$. Initially, all ...
0
votes
1answer
18 views

Find a conformal map from the exterior of the closed unit disk to the unit disk

Question: Find a conformal map from the exterior of the closed unit disk to the unit disk. Also, prove that it is indeed a conformal map (bijective and holomorphic along with its inverse). I missed ...
0
votes
0answers
15 views

What is the convergence criterion for linear fixed-point iteration in Banach space?

Consider an iterative process of the form $x^{n+1}=A x^n + b$. When $A$ is a linear operator in $\mathbb R^n$ then the criterion of convergence is $\rho(A)<1$, where $\rho(A)$ is spectral radius of ...
0
votes
0answers
28 views

Riesz Representation Theorem

I am unfamiliar with Quantum Mechanics and all that stuff. I have recently studied Riesz Representation Theorem , I got to know that it justifies ket and the bra notation. Can anyone please give an ...
0
votes
0answers
6 views

Literature on 3 dimensional image segmentation

Currently I am working on a paper on 3d image segmentation and finding my way into the topic. However I can not find good mathematical literature on the topic. I am looking for a books or scripts that ...
2
votes
0answers
56 views

Calculus book advice

I'm reading Thomas Calculus now but I don't think it includes Mellin transform or Riemann-Stieltjes integration... Can you recommend an advanced calculus book which includes all of this stuff?
1
vote
0answers
24 views

Application of Kodaira Embedding Theorem

I am going to give a talk on Kahler manifold. In particular, I will outline a proof of the Kadaira Embedding theorem. I also wish to give some applications of the theorem. One of the application ...
1
vote
0answers
27 views

Regularity of Dirichlet Eigenvalues on Lipschitz Domain

What kind of regularity do we generally have for weak solutions to the Dirichlet problem? $$(\Delta+\lambda)u=0 \textrm{ in }U$$ $$u=0 \textrm{ on }\partial U $$ where $U$ is a planar domain with ...
0
votes
0answers
14 views

Subsets of immersions that are embeddings

Let $X$ be a manifold and let $Y$ be a submanifold, possibly with boundary. I am dealing with a situation where $f:X\to \mathbb{R^3}$ is an immersion, but $f\vert_Y:Y\to \mathbb{R}^3$ is an embedding. ...
0
votes
1answer
13 views

what are some typical systems of equations generating from practical problems?

I want to know some typical forms of system of equations generating from practical problems in engineering/economics/physics,etc. Some examples or research articles would be good. Specifically, I am ...
0
votes
0answers
15 views

Geometric introduction to exterior algebra

Could anyone point me to a geometric introduction to exterior algebra (meaning, one with a good number of figures and/or verbal descriptions of geometric objects in it)? Thanks!
4
votes
2answers
109 views

Modern book on Gödel's incompleteness theorems in all technical details

Is there a modern book on Gödel's incompleteness theorems that goes into each and every technical aspect of the proof of them (a classical one, if such exists)? I'm not interested in popular ...
1
vote
0answers
18 views

Historical context: The Fresnel integrals

The evaluation of the Fresnel integrals has been done a plethora of times both on this site, and numerous other places. The two main ways of evalutating these integrals has either been with some ...
0
votes
0answers
11 views

Weak stochastic integral

I recently encountered the following object, referred to as "weak stochastic integral" in the book of SPDE's by Prevot/Rockner [PR07]: $ \int_0^T { \langle \Psi dW(t), \Phi(t)\rangle }$ A few useful ...
3
votes
0answers
41 views

Lefschetz duality for non-compact relative manifolds

I'd like to use the formulation of Lefschetz duality stated here, but I can't seem to find a reference for this particular version of it, and it doesn't seem quite right to me. The exact statement in ...
0
votes
2answers
22 views

Requested material on Bilinear Pairing

Bilinear map/pairing is widely used in Pairing based Cryptography. I am new to this area. Can anyone suggest me some good reference on Bilinear pairings? I need at least an example of Bilinear map ...
0
votes
0answers
9 views

Books in spectral theory for finite dimensional spaces

I'm looking for beginner books of spectral theory for finite dimensional spaces. I've already heard about this subject, but I don't know where I can find it. What's the domain of this subject? (Linear ...
0
votes
1answer
27 views

Text of differential geometry

I would like to ask for suggestions for a differential geometry text book, reaching the theory of $n$-dimensional (not only cuves and surfaces) differentiable and Riemannian manifolds in sight of ...
1
vote
1answer
85 views

Foundations book using category theory?

I'm about to embark on a PhD in mathematical biology. My major is in computer science. I would like to acquire a more rigorous understanding of math, which I am going to need to tackle some research ...
0
votes
3answers
65 views

Is there any book about inequality? [on hold]

I heard there is a book name 'inequality'. But I couldn't find the book. Is there any site or book about inequalities? What i want is collection of inequalities.
2
votes
0answers
19 views

Reference Request: Algebraic Serre's Duality Theorem for Curves

Serre's Duality Theorem is well known and well studied and, as far as I know, there is a "big" algebraic proof for the general case, which is now kind of standard, and can be found in Hartshorne and ...
1
vote
3answers
76 views

What is the “Principle of permanence”?

While reading the book "The Number-System of Algebra (2nd edition)." term "Principle of permanence" occurred to me. I remember I had read this in the book "Beginning algebra for college students.". I ...
8
votes
1answer
107 views
+50

Homology Whitehead theorem for non simply connected spaces

(One version of) the Whitehead theorem states that a homology equivalence between simply connected CW complexes is a homotopy equivalence. Does the following generalisation hold true? Suppose ...
0
votes
0answers
291 views

How to present calculus? Asking for some excellent intuitive referance.

$\text{Dear}$ mathematicians, amateurs, learners, students et al; I learned calculus when I was 13 years old, I was at the time able to evaluate some easy derivatives, integrals, some tricky limits ...
0
votes
0answers
57 views

Recommended Textbook/Resources

I'm looking for a textbook or resources my younger brother could use. (He is in year 9, equivalent to US high school freshman) He is wanting to advance upon his math, he currently does exercises out ...
-4
votes
1answer
60 views

Lee, Introduction to Smooth Manifolds Solutions

Does anybody know where I could find the solutions to the exercises from the book Lee, Introduction to Smooth Manifolds? I use the freely available online version ...
8
votes
2answers
152 views
+100

Putting down axioms for some symbols. Playing with their consequences qualitatively and symbolically. Building theories. The book?

I am interested in the design and building of theories. By building theories, I mean putting down axioms of various kinds, over various fields, exploring their perhaps interesting, or probably boring, ...
3
votes
1answer
46 views

Intuitionistic Linear Logic

I am currently going through some papers that use the "intuitionistic version" of Girard's Linear Logic. Problem is, i seem to find very little literature on it. There is a lot done on Linear Logic ...
2
votes
0answers
30 views

uniform equivalence to unit vector basis of $\ell_p$

Let $(e_n)$ be the unit vector basis of $\ell_p$, $1\leq p<\infty$. It is well-known that if $(x_n)\subset\ell_p$ is seminormalized and weakly null then it contains a subsequence equivalent to ...
3
votes
2answers
58 views

What is the best book to learn statistics?

Right now I'm taking a 3 part course on probability and statistics using Schverish & Degroot Probability and Statistics and it is just not helpful. For the first part, which was on Probability, I ...
0
votes
0answers
12 views

Space of almost complex structures on a compact manifold

According to the book by Huybrechts, Complex Geometry: An Introduction, this is a nice space and may be regarded, after some form of completion, as an infinite-dimensional manifold. How is this done, ...
4
votes
0answers
27 views

Looking for a a measure-theoretic treatment of “differential entropy”

If $X$ is a discrete random variable, its entropy $H(X)$ is usually defined as something along the lines of $-\sum \def\P{\mathbb{P}}\P(x) \log_2( \P(x))$, where the sum ranges over all the possible ...
0
votes
0answers
7 views

Homological Algebra for Characteristic Classes

how much homological algebra should I know to make a rigorous study of characteristic classes? Furthermore, what would be other requisites? References on both homological algebra and characteristic ...
0
votes
0answers
32 views

Module and bimodule categories equivalent to a 2-functor

Let $A$ be a tensor category (i.e. monoidal category). A (right) module category of $A$ is a category $M$ with a coherent action $\mu\colon M\otimes A\to M$. Denote $BA$ be the one-object bicategory ...
2
votes
1answer
20 views

Fourier series with a weighted mean square norm

I am interested in Fourier series with a non-uniformly weighted error norm. What I mean by this is that the usual Fourier series of a periodic function is a minimizer of the mean squared error: $$ J_N ...
2
votes
2answers
50 views

Odd and even functions.

I have a book which says: If a function $f$ satisfies $f(-x)=f(x)$ for all $x$ in its domain, then $f$ is called an even function. However, if $f(-x)=-f(x)$ for every $x$ in the domain of $f$, ...