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.

learn more… | top users | synonyms (3)

0
votes
0answers
46 views

Is a tight concrete bound for the error-term in the prime-number-theorem known?

Here : https://en.wikipedia.org/wiki/Prime_number_theorem it is mentioned that $$\pi(x)=Li(x)+O(xe^{-a\sqrt{ln(x)}})$$ What is a tight upper bound for $|\pi(x)-Li(x)|$ in concrete terms ? The ...
1
vote
0answers
36 views

Equation of Sun Orbit Spiral on Azimuthal Equidistant Earth Map

From the perspective of the AE map: The sun circles the earth. Every complete circle it makes is approximately one day. However, the sun is not always on the circle of the equator. It spirals inward ...
2
votes
0answers
34 views

Zorich's Mathematical Analysis, Volume II

Springer just published a new English version of Vladmir Zorich's two-volume Mathematical Analysis. I was looking at the second volume. It seems to have sections on both Multivariable/Vector Calculus ...
1
vote
1answer
38 views

References on Hauptmoduln

Here it is said that a Hauptmodul (a generator of a modular function field) is unique up to a Möbius transformation. My impression is that it is really hard to find references on Hauptmoduln and ...
6
votes
1answer
75 views

Perfect circles in the Mandelbrot set?

It is known that the boundary of the period 2 hyperbolic component of the Mandelbrot set is a perfect circle of radius $\frac{1}{4}$ centered at $-1$. Moreover it is known that the boundaries of the ...
1
vote
0answers
30 views

Textbook Recommendation for Brushing up on Elementary Freshman/Sophomore Level Mathematics

As is the case with most students (I suppose), I seem to have lost touch with the do doing some "basic" math -- calculating integrals, playing around with matrices and doing some linear algebra etc. --...
3
votes
2answers
56 views

Elementary question: local computation of curvature on principal bundle

Let $G$ be a Lie group and $S=[0,1]^2$. Let $\omega$ be a connection $1$-form on the trivial principal $G-$bundle $P=S\times G$ over $S$. Let $(x_1,x_2)$ be coordinates on the base $S$. We can choose ...
1
vote
0answers
19 views

Representing a positive definite function as the absolute value squared of a fourier series?

For the closed surface of some (pseudo)Riemannian manifold M , we're interested in a function $\rho$ which satisfies: $$m=\int_{\partial M}\rho(x,y,z) \, d\mathrm{vol}$$ Where $dvol$ is the ...
0
votes
0answers
17 views

where can i learn more about primitive recursive arithmetic (PRA)?

The references on the wiki page are articles in journals, which are not easily accessible. I can find the first reference (by Skolem) online... but it is in German. I would expect this to be in a ...
3
votes
0answers
78 views

Relearning differential geometry

I will shortly describe my situation and than formulate the problem. From around year I am working under supervision of my professor on master thesis in differential geometry (mainly discussion of ...
0
votes
0answers
27 views

Elementary literature on Group theoretic Power Diophantine Equation

I am looking for an elementary books/pdf notes on group theory related to Power Diophantine Equation. I have read elementary group theory. Please advise some books/pdf notes. Also, it would be ...
1
vote
0answers
30 views

Further references on number theory paper.

Courtesy of the wonderful Canadian Mathematical Society which allows free access to their back issues, I discovered a paper written in 1959 in the Canadian Mathematical Bulletin. The paper answers the ...
-2
votes
1answer
100 views

What are some good books and materials for studying rings and fields theory? [closed]

I will very soon be introduced to the subject. I have heard this is one of the most important part of undergraduate algebra. I want to develop clear understanding in it from the beginning. I have ...
6
votes
5answers
249 views

List of theorems named after non-human animals [closed]

I think it would be entertaining if we could come up with a list of theorems named after non-human animals (so excluding names like "Gauss's lemma" and the like). So far, I have only encountered two, ...
2
votes
1answer
44 views

Stabilization of embedding?

In D. Freed's lecture notes he mentions "stabilization of embedding" in theorem 4.48. Does anyone know the definition? I can't find it online.
1
vote
1answer
81 views

Distribution on a collision variant of Hypergeometric distribution?

I have the following scenario: there is a set $\Omega$ of $N$ elements, among which $K$ are marked — let $M\subseteq \Omega$ be this subset. Alice select uniformly at random (i.e., sampling without ...
1
vote
0answers
32 views

Number-Theory Books to read before studying Analytic Number Theory

S.E friends, Due to my genuine interest to Goldbach's conjecture, I decided to self-study the subject of additive number theory on this upcoming Fall. Before jumping to such fascinating field of ...
0
votes
1answer
96 views

Number of urns containing a ball of each color: is there a probability distribution describing this?

There are $B$ urns. There are $n$ red balls and $n$ white balls with $n\leq B$. Each ball is independently put into each urn with equal probability. An urn can get at most one ball with the same color ...
4
votes
3answers
67 views

Textbook for Multivariable and/or Vector Calculus

I'm looking for a tetxbook that covers Multivariable Calculus and/or Vector Calculus theoretically. I have done Analysis (single-variable) at the level of Introduction to Real Analysis by Bartle and ...
4
votes
2answers
37 views

Ring of algebraic integers as lattice points in the complex plane

Let, $i=\sqrt{-1}$ and $\omega = e^{\frac{2\pi i}{3}}$. I know that we can represent the ring of integers $\mathbb{Z}[i]$ and $\mathbb{Z}[\omega]$ as square and triangular lattice on complex plane ...
0
votes
0answers
18 views

About functions with its codomain being the power set of its domain

Can you recommend me some articles or textbooks about functions whose codomain is the power set of its domain (i.e. a function $f:M \to 2^M $ where $M$ is a non-empty set)? In fact, I want to know ...
2
votes
0answers
31 views

Determining a function is harmonic from mean value property for just three(?) radii.

This theorem is well-known (maybe it can be called Morera's theorem): A continuous function satisfying the mean value property on balls is harmonic. I was recently surprised to hear in a talk ...
0
votes
1answer
19 views

Spectral radius of block-skew-hermitian matrix equals norm of block

$$\rho\left(\left[\begin{matrix}0 & A \\ -A^{\dagger} & 0\end{matrix}\right]\right)=\|A\|$$ where $\rho(\cdot)$ is the spectral radius, $\|\cdot\|$ is the induced 2-norm. Question: I am ...
2
votes
1answer
113 views

What branch/field of mathematics is this? [closed]

I do not want solutions, I just want the field/branch of mathematics that these problems deal with, and possibly a good online source or two to learn it. Problems :- 1:- 2:- 3:- 4:- ...
0
votes
1answer
41 views

solve a specific word problem in free groups

Let $F_2=\langle a, b\rangle$ be the non-abelian free group with two generators and $e$ is the neutral element in $F_2$. Given $g\in F_2, k\geq 2$ an integer. I want to know how to solve the word ...
1
vote
1answer
64 views

Can someone suggest books on mathematics and problem solving which nurtures the reader? [closed]

Can someone suggest books on mathematics and problem solving which nurtures the reader like Alexander Soifer's books? Thanks in advance
1
vote
2answers
54 views

Fibered categories, introduction or notes

I would like to learn about fibered categories, I know basic category theory, but not algebraic geometry. Is there a text, or lecture notes, which motivate the definitions from fields other than ...
0
votes
0answers
25 views

Sylow tower theorem involving supersolvable groups

I just want to find out if anyone has a reference to the result that states that if $G$ is a finite supersolvable group then it has a normal Sylow subgroup.
3
votes
3answers
133 views

Where to read about sheaves?

I'm working through Mumford's Red Book, and after introducing the definition of a sheaf, he says "Sheaves are almost standard nowadays, and we will not develop their properties in detail." So I guess ...
1
vote
0answers
26 views

Exercises with solutions for mathematical statistics

I'm currently studying the statistics part of the book Georgii: Stochastics, contents are here (chapters 7 - 12). Sadly, there are no solutions for the exercises given in this book. Do you know a ...
1
vote
1answer
72 views

Linear Algebra Textbook

I'm looking for a textbook on Linear Algebra and I seem to have narrowed down the list to: Linear Algebra by Hoffman and Kunze; and Linear Algebra by Friedberg, Insel and Spence. I'm not ...
0
votes
1answer
25 views

Reference for results p-adic integers Z_p as abelian group

I have two facts I want to use in my thesis about $\mathbb{Z}_p$. To be precise: automorphism group is $\mathbb{Z}_p \times \mathbb{Z}/(p-1)\mathbb{Z}$, except for 2, and that any subgroup with finite ...
2
votes
0answers
42 views

Generalisation of the Poincaré Lemma

Let $\Omega \subset \mathbb{R}^3$ be an open but not simply connected domain and let $v \: \colon \Omega \to \mathbb{R}^3$ be a continuously differentiable vector field. Assume that $\textrm{curl} \, ...
3
votes
1answer
68 views

Does a sequence based on hereditary factorisation always terminate?

The well-known Goodstein sequences are based on the hereditary base-$b$ notation, where you don't just present the digits in base $b$, but also the corresponding exponents etc. That lead me to the ...
2
votes
1answer
79 views

Good, relatively short math textbooks? [closed]

Recently I've been trying to decide on some fun math summer reading on some areas of math which I have less experience with. I'm an undergrad studying mathematics with a focus in actuarial science, ...
2
votes
1answer
42 views

To distinguish among the various subsets of $M_n(\Bbb R)$

I am having problem in doing a certain type of problems relating to matrices: To distinguish among the various subsets of $M_n(\Bbb R)$ such as symmetric, diagonal, diagonalizable, upper triangular, ...
2
votes
1answer
36 views

Lines in a metric space - a metric space?

In a metric space, a point $x$ is between points $u$ and $v$ if $d(u,v)=d(u,x)+d(x,v)$. The line determined by points u and v consists of $u$, $v$ and all points $x$ such that one of $x,u,v$ is ...
3
votes
0answers
63 views

Which books or subjects would you recommend for undergrads for grad school? [closed]

I am an undergraduate mathematics student in my third year. Most undergrad programs don't completely prepare you for grad school. I know Ph.D. students are telling me that there is a lot of crucial ...
3
votes
0answers
46 views

Possibly new solution to equal-mass three-body problem; refinement required

(Since I didn't know which authorities to contact, I thought I'd post this here.) While messing around in this Wolfram Demonstrations applet, I found a suspicious pattern, in which I could see ...
1
vote
0answers
26 views

Constructing a Collection of Sets Satisfying Certain Intersecting Properties

I am trying to solve the following problem. We would like to construct $\{A_1, \ldots, A_n\}$, where $n$ is even, and each $A_i \subseteq [m]$, with $|A_i| = k$ and $m = \text{poly}(n)$. Now, I would ...
1
vote
0answers
21 views

Is this (open) neighborhood graph of a graph a known concept?

Let $G$ be a graph, and for a vertex $v \in V(G)$ let $N(v) = \{ u \mid uv \in E(G) \}$ be the open neighborhood of $v$, i.e., the set of adjacent vertices not including $v$ itself. Let $N'(G)$ be ...
0
votes
0answers
9 views

Contraction clique number of certain Turan graphs

What can we say about the size of the largest clique that is a minor of the complete $r$-partite graph with all vertex classes of size $n$?
0
votes
0answers
18 views

Lattice theory textbooks that do not mention diagrams?

Many lattice theory texts extol the virtue of diagrams (which are also "formalized" as a concept for finite sets). However, I am curious to know of texts which do not mention diagrams (or mention them ...
1
vote
0answers
26 views

Brownian motion hitting probability of boundary and going outside

I was solving an exercise which asks the reader to calculate the probability that a Brownian particle $B(t) = (B_1(t),...,B_n(t))$ starting at the origin in $\mathbb{R}^n$ will strike the surface of a ...
-1
votes
1answer
13 views

Reference request for a theorem of Schlessinger

I am reading The unbearable lightness of deformation theory by Balázs Szendröi (sorry, the umlaut should be a kind of double accent, but I have no idea about how to do it with my keyboard). At page 9 ...
2
votes
0answers
21 views

Introduction to morse theory with applications to optimization

I am wondering if there are any easy-to-read introduction materials on morse theory (especially with applications to nonconvex optimization) for people with non-math background.
4
votes
0answers
145 views

Restriction of irreducible unitary representation to normal subgroup of finite index [migrated]

Let $G$ be a Lie group (or more generally a locally compact group), let $N$ be a closed and normal subgroup of $G$ of finite index. Let $H$ be an infinite dimensional complex Hilbert space, and let $\...
3
votes
3answers
85 views

Differential Geometry for General Relativity

I'm going to start self-studying General Relativity from Sean Caroll's Spacetime and Geometry: An Introduction to General Relativity. I'd like to have a textbook on Differential Geometry/Calculus on ...
0
votes
0answers
32 views

Reference for monodromy theorem in SVC

I am looking for a reference for the Monodromy Theorem in several complex variables. I found plenty in the case of one variable, and some other versions who are purely topological and concerned with ...
0
votes
0answers
28 views

Beginning master's student with gaps - References for Riemann Surfaces

I currently have Jost (as well as a few other texts), and have been working through it - I am a master's student who is trying to prepare for thesis work in closely related areas. However, it is far ...