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.

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4
votes
1answer
27 views

Generalize logarithmic coincidences

After playing around with logarithms, I've found the following coincidences: $\log_{10}{2} \approx 0.3$, since $2^{10} \approx 10^3$, and $\log_{10}{5} \approx 0.7$, since $5^{1000} \approx ...
0
votes
0answers
18 views

Spectral Theory of Differential Operators References?

What are some nice references about spectral theory of differential operators? Some more details: I'm looking for an exposition about linear partial differential operators both with constant and ...
3
votes
1answer
41 views

Text defining length, area and volume

I am looking for a geometry textbook that axiomatises concepts such as length, area and volume of objects in Euclidean space; for example, the surface area of a 2-sphere in 3-space. Such a text would ...
1
vote
2answers
29 views

Logic with finite symbols

What obstructions do you run into if you're trying to develop first order logic when you only have finitely many constant, relation, and function symbols? Are there any cases where you actually need ...
1
vote
3answers
79 views

A resource for Trigonometric Inequalities

I'm looking for a good and detailed guide for trigonometric inequalities in pdf if possible. Any recommended resources?
5
votes
1answer
70 views

group-like structure texts.

I was reading Dummit and Foote to be ready for my group theory text, but my teacher seems to be paying special attention to things with less structure than groups, for example monoids, semigroups, and ...
2
votes
0answers
35 views

References on the relations between Top, Diff and PL

I have heard many times informal statements like "differentiable and pl manifolds are essentially the same for such and such dimensions", but I would like to know what they mean exactly and how such ...
1
vote
0answers
18 views

What is the definition of period number and any relation between Abelian integral and such a kind of period number

I recall there is a kind of real or complex number called period number which is defined by integral and algebraic function.But now,I search it again and again having gotten no result.Now any one can ...
1
vote
0answers
27 views

In regards to metric spaces, does $d^\star$ have an accepted name, or notation? Do any authors use it?

(I write $\omega$ for the set $\{0,1,2,\ldots\}$.) Let $X$ denote a metric space with metric $d$. Define a function $d^{\star} : X^\omega \times X^\omega \rightarrow [0,\infty]^\omega$ by writing ...
0
votes
1answer
41 views

What are those functions

what are such functions $$f(x) = \int_{c}^{x} R \left(t, (P(t))^{\frac{1}{n}} \right) \, dt,$$ where $R$ is a rational function of its two arguments, P is a polynomial with no repeated roots, $n \geq ...
5
votes
1answer
85 views

Category theory for knot theory

Where would I start to learn category theory for its use in knot theory? I have a background in physics and Ive read Adams Knot book. I know nothing about category theory. Eventually I want to learn ...
0
votes
1answer
28 views

Books for a beginner (Pseudoconvex Domains)

Can anyone recommend me a book on Pseudoconvex Domains with include definitions, as well as a few examples? I have some course notes on that subject, but it's really abstract and theoretical. I want ...
0
votes
0answers
9 views

Reference request: result concerning Leray trace

Let $V$ be a vector space (possibly of infinite dimension). For a linear homomorphism $f\colon V\to V$ define $$N(f)=\bigcup_{n\in\mathbb{N}} \operatorname{ker}(\underbrace{f\circ\ldots\circ ...
5
votes
2answers
75 views

Reference Request: Characters of Finite General Linear Groups

I've been looking at J.A. Green's article The Characters of Finite General Linear Groups and it seems that Green in this article comes up with a way of calculating all irreducible characters of a ...
1
vote
0answers
24 views

Taking multisets as fundamental

I have heard that it is possible to axiomatize the concept of multisets as a primitive idea. Is there some text where this is actually done?
0
votes
0answers
25 views

Examples of elements in the Dirichlet space

By Dirichlet space we mean $\{F\in C_{0}[0,1]:\text{ there exists }f\in L^{2}[0,1]\text{ with }F(t)=\int_0^t f(x) \, dx$, $\forall t\in [0,1]\}$. The more the better. Any famous examples? Using the ...
2
votes
1answer
47 views

Unit circle can't be covered by one chart

I am hoping that someone can give me a proof showing why the unit circle cannot be covered by one coordinate chart, or a reference where I can find a proof.
2
votes
0answers
31 views

Research papers of monotone/pseudomonotone operators with applications to PDEs

I have recently been studying how coercive, pseudomonotone operators are used to prove the existence of solutions to elliptic boundary value problems. I have been studying the book "Nonlinear Partial ...
2
votes
0answers
82 views

K-theory of $\mathbb{RP}^{\infty}$

what are the $K_0$ and $K_1$ group of $\mathbb{RP}^{\infty}$? Any reference would be good enough.
0
votes
0answers
34 views

Reference: Fields of characteristic p

I am interested in learning more about fields of characteristic $p\neq 0$. Does anyone know of a good reference that covers the basics of this topic and possibly galois theory over fields of prime ...
1
vote
1answer
40 views

Generalization for Stirling numbers 2nd kind to negative column-indexes?

The exponential generating functions for the Stirling numbers 2nd kind are the n'th powers of $f(x)=\exp(x)-1$ (where this is understood as formal power series, Abramowitz&Stegun, 26.8.12). ...
2
votes
1answer
41 views

Global bounded solution of $u_{tt}=\Delta u-mu+h$ in the Hilbert space $X=H_{0}^{1}\left(\Omega\right)\times L^{2}\left(\Omega\right)$

Let $\Omega$ be an open subset of $\mathbb{R^n}$. Consider the linear wave equation $$\begin{cases} \dfrac{\partial^{2}}{\partial t^{2}}u\left(t,x\right)=\Delta ...
0
votes
0answers
24 views

Book for asymptotic behavior of an ODE

I want a good book to master the concepts of limit point, equilibrium point, stability (lyapunov, global, local etc.). I am aware of real analysis. Not aware of ODE.
2
votes
1answer
59 views

Starting with ring theory

Can anyone suggest a book on rings explaining concepts using visual diagrams, similar to the one visual group theory book by Nathan Carter for groups.The problem with me is that after reading that ...
0
votes
0answers
11 views

Reading on Laurent Polynomials

I'm interested in reading about Laurent Polynomials. Does anyone know a good resource/book that I can read about Laurent polynomials? Thanks.
0
votes
2answers
43 views

Looking for some decent math books and solutions

I am a graduate student in engineering pursuing computational mechanics. I have learned very quickly that the math required to study in this area is very sophisticated and complicated. I need some ...
4
votes
1answer
447 views

Moment generating functions/ Characteristic functions of $X,Y$ factor implies $X,Y$ independent.

This is solely a reference request. I have heard a few versions of the following theorem: If the joint moment generating function $\mathbb{E}[e^{uX+vY}] = \mathbb{E}[e^{uX}]\mathbb{E}[e^{vY}]$ ...
4
votes
1answer
83 views

Proof for and Intuition behind Taylor's Theorem

I notice that multiple versions of a theorem are called Taylor (univariate/multivariate, approximate/exact). But I do not find it trivial to infer proof of one version from the rest. So looking for a ...
3
votes
1answer
65 views

Best algebra text for Model Theory

I'm looking for an algebra book that is tailored towards some of the ideas in Model Theory, I'm currently slogging through Hodges' Model Theory. I'm a bit rusty with my algebra and was curious if ...
6
votes
1answer
144 views

Does $\sum\limits_{n=1}^{\infty}\frac{1}{P_n\ln(P_n)}$ converge to the golden ratio?

The sum $\displaystyle\sum\limits_{n=2}^{\infty}\frac{1}{n\ln(n)}$ does not converge. But the sum $\displaystyle\sum\limits_{n=1}^{\infty}\frac{1}{P_n\ln(P_n)}$ where $P_n$ denotes the $n$th prime ...
0
votes
0answers
18 views

A remark on representable functors in May's Concise Course

On page 206 of May's Concise Course there is a lemma stating that for well pointed space $X$ and $Y$ and a particular representable functor $A:Spaces \to Groups$ (in particular reduced K-theory) that ...
8
votes
2answers
87 views

Ways to calculate the spectrum of an operator

Friends, I am learning some very basic stuff of spectral theory and kind of lost, in some sense. I am trying to find ways to compute the spectra of different operators, when they work and don't work. ...
0
votes
0answers
13 views

On the definition of subharmonic functions

An upper semicontinuous map $f:\mathbb C\to\mathbb R\cup\{-\infty\}$ is said to be subharmonic if it satisfies the following average inequality property: For any $z_0\in\mathbb C$ and $\delta>0$, ...
3
votes
1answer
26 views

Generalisation of cochain complexes and “curvature”

Someone has mentioned to me that generalizations of co-chain complexes and their cohomology have been studied, where instead of $d^2 = 0$ we have something like $d^2 \alpha = q \alpha $, which is ...
5
votes
1answer
84 views

What are the prerequisites for Fulton's “Intersection Theory”?

Is it necessary to read SGA VI to understand "Intersection Theory" by William Fulton?
1
vote
1answer
42 views

Introduction to Localization of Topological Spaces

I am trying to learn localization of topological spaces but am not sure where to start. Can anyone recommend some introductory materials? It would be great if it contains detailed motivations, ...
0
votes
2answers
79 views

Which functional analysis book is good?

Which functional analysis book is good ? I am aware of linear algebra, real analysis, measure theory and a little bit of topology. It should be intuitive and with full of motivation.
0
votes
0answers
21 views

Extending a trace on algebra to a trace of systems of algebras

Suppose, we have a trace $\tau$ on some algebra $\mathcal{A}$, i.e. $$\tau(aA+bB)=a\tau(A)+b\tau(B)\ \forall A,B\in\mathcal{A}, \forall a,b\in\mathbb{C}$$ The question rises, what are then the ...
7
votes
3answers
302 views

Video lectures of algebraic geometry (Hartshorne, Shafarevich, … )

I am a commutative algebra student. I wonder if there is some video lectures of algebraic geometry courses available online for free? I'd like the lectures to cover main topics of the books ...
1
vote
2answers
41 views

Compendium of elliptic curves?

does anyone know where I can find a collection of elliptic curves and their integral solutions? EDIT: Removed additional useless info. Thanks!
3
votes
1answer
55 views

Rank of Elliptic Curves

Recently, I have heard of some heuristics that would suggest that the rank of elliptic curves are bounded (specifically in the congruent number family). I always though that the best way to prove ...
7
votes
2answers
266 views

Graduate level elementary logic books

I've done two courses on Logic during my Bachelor course, but they were very basic. Now I'm going to start by PhD, and I'm interested in learning "real Logic". Could you please provide some references ...
10
votes
1answer
361 views

Looking for an easy lightning introduction to Hilbert spaces and Banach spaces

I'm co-organizing a reading seminar on Higson and Roe's Analytic K-homology. Most participants are graduate students and faculty, but there are a number of undergraduates who might like to ...
2
votes
0answers
42 views

Propositions as sets of witnesses

Under the propositions-as-types paradigms, a proposition is identified with the type of all its proofs. From a more classical perspective (and assuming the full-blown axiom of choice), it sometimes ...
6
votes
2answers
58 views

Existence of a random variable satisfying a condition on its distribution

Let $X, Y : [0,1] \to \mathcal{X}$ be two random variables. Here, $[0,1]$ is the interval with the Lebesgue $\sigma$-algebra and $\mathcal{X}$ is a topological space with the Borel $\sigma$-algebra. ...
9
votes
5answers
507 views

Reference request: Chern classes in algebraic geometry

I have encountered Chern classes numerous times, but so far i have been able to work my way around them. However, the time has come to actually learn what they mean. I am looking for a reference that ...
1
vote
0answers
41 views

basic sequence in the complexification induces a basic sequence in the underlying real space?

This should be easy to prove if it is true, but, alas, what SHOULD be easy is not always easy for me ;) Conjecture 1. Let $X$ be a real Banach space and let $X_\mathbb{C}$ denote its ...
4
votes
1answer
36 views

Cramer's theorem reference request

I'm looking for a proof of Cramer's theorem that states the following: Let $X,Y$ two independent random variables such that $X+Y$ is normal distributed, then $X$ and $Y$ are normal distributed. ...
46
votes
49answers
4k views

What was the book that opened your mind to the beauty of mathematics?

Of course, I am generalising here. It may have been a teacher, a theorem, self pursuit, discussions with family / friends / colleagues, etc. that opened your mind to the beauty of mathematics. But ...
1
vote
4answers
137 views

Suggestion for a book on Linear Algebra [duplicate]

Please suggest a Linear Algebra book with an introduction and rigorous theory (description) on Eigenvectors , eigen-values , Cayley-Hamilton theorem , Diagonalisation of matrices ; Quadratic forms ( ...