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)

0
votes
1answer
39 views

Reference - formal characterization and analysis of Koch curve

I am studying the Koch curve but most resources I have seen do not describe the Koch curve formally and are similar to the Wikipedia page on the subject. For example, I have looked at books like ...
0
votes
1answer
19 views

Book on Lipschitz pointwise constant

Does anyone know of a book (or possibly an accessible paper) discussing Lipschitz pointwise constants and perhaps including some examples? Thank you
1
vote
1answer
62 views

References for a notion of “restricted adjoint”

A construction that I've been finding all over the place in studying the category of NF (Quine's New Foundations) sets and functions is a situation like the following: there's a functor ...
17
votes
1answer
361 views

Soviet Russian Mathematical Books

The introductory part of the book briefly describes the popularity of mathematics in Soviet Russia, touches on Russian mathematical circles and generally how Russian society took to mathematics in a ...
5
votes
2answers
118 views

How was the $3x+1$ problem checked up to $5 \times 2^{60}$?

The Wikipedia article for the Collatz conjecture states that: The conjecture has been checked by computer for all starting values up to $5 \times 2^{60} \approx 5.764 \times 10^{18}$. It gives ...
0
votes
1answer
65 views

What is the metric spaces needed to motivate concepts of general topology?

I intend to start learning some topology on my own. I wonder How much metric spaces I should know in order to motivate the concepts of topology? I know it's possible to learn topology without any ...
1
vote
1answer
33 views

What is Bush Mosteller algorithm?

I cannot find anything interesting on the internet. What is the Bush Mosteller stochastic model? ...
13
votes
2answers
461 views

Pure mathematics in our society

Is there some book or essay which deals with the sociological and economical justification of doing and funding pure mathematics? I'm looking for a modern version of Hardy's A Mathematician's Apology, ...
6
votes
1answer
101 views

best intuitive books/video lectures to read topology and functional analysis

What are the best intuitive books/video lectures to read topology and functional analysis ? I am aware of basic linear algebra, analysis and measure theory.
0
votes
0answers
129 views

Is there a way to find a steady state probability density for a given transformation?

I was looking at probability density transformations here. They use $g(y) = f(x(y))|dx/dy|$ where $x(y)$ is the inverse of the transformation. Is there a way to, given only the transformation, find ...
1
vote
1answer
68 views

Reference request, Descriptive set theory

I was wondering what a good text would be to learn descriptive set theory out of? Hopefully something more in the spirit of Kunen's text on the introduction to independence proofs.
0
votes
1answer
19 views

Pseudo-Theorem on parallel lines in a quadrilateral - Proof & Reference Request

Yesterday I asked a question concerning an argumentation, and keep on thinking about the problem I realized that what I was missing is probably a basic result in linear algebra. Actually I am not sure ...
1
vote
0answers
38 views

Extending a homeomorphism between subspaces

Lavrentiev's Theorem. Suppose $X$ and $Y$ are complete metric spaces, $A\subseteq X$, $B\subseteq Y$, and $f:A\to B$ a homeomorphism. Then $f$ can be extended to a homeomorphism $\overline f :G\to ...
1
vote
0answers
16 views

Example to show that presheaf maps agreeing on stalks are not necessarily equal

We know that if two maps $\phi,\psi : \mathcal{F}\to \mathcal{G}$, where $\mathcal{F} $ is a presheaf and $ \mathcal{G}$ is a sheaf, agree on stalks then they are equal. Can we find an example to show ...
0
votes
0answers
15 views

Scorecard validation on different performance window

I am trying to build a scorecard model which predicts probability of default over the next 2 years of observation. Can someone suggest me literature which shows: A scorecard with 2 years of ...
3
votes
1answer
43 views

Undistinguishable elements in posets

Given a finite partially ordered set $P = (V, <)$, I say that $x$ and $y$ in $V$ are indistinguishable in $P$ if for all $z \in V \backslash \{x, y\}$, I have $z < x$ iff $z < y$, and $x < ...
4
votes
0answers
211 views

Has this weaker version of Fermat's last theorem already had an elementary proof?

Recently I carried out an elementary proof of the following assertion, which is a special case of Fermat's last theorem: If $p$ is an odd prime and $x, y, z > 0$ are integers such that $(x, y) = ...
2
votes
1answer
31 views

Ramanujan's expansion of $\operatorname{li}(x)$

What are the steps to showing $$ \operatorname{li}(x)=\gamma+\log(\log(x))+\sum_{k=1}^{\infty}\dfrac{\log(x)^k}{k!k}? $$ Any pointers on where to look would be warmly appreciated.
2
votes
0answers
48 views

Quotient of smooth variety is smooth if fixed point set is a divisor?

I've heard (a variant of) the following result being mentioned , but haven't been able to find a reference. I would like to know if the following is true, and if so, I'd very much appreciate a good ...
3
votes
0answers
61 views

Resources about infinite primes of form $n^2 + 1$

Where can one find existing work on the following problem? Prove there are infinitely many primes of the form $n^2 + 1$. Resources about related work would also be appreciated.
11
votes
2answers
231 views

Why is Volume^2 at most product of the 3 projections?

Is there a simple proof for $$ \text{Vol}^2(P)\le \prod_{i=x,y,z} \text{Area}(\text{Proj}_i(P)), $$ where $P\subset \mathbb R^3$ and $\text{Proj}_z(P)$ denotes the projection of $P$ to the $z=0$ ...
4
votes
2answers
63 views

Probability that two random permutations of an $n$-set commute?

From this MathOverflow question: It is well known that two randomly chosen permutations of $n$ symbols commute with probability $p_n/n!$ where $p_n$ is the number of partitions of $n$. -- Benjamin ...
5
votes
0answers
79 views

Reference Request: Prereqs for Lecture Notes on “Abstract Linear Algebra”

I just found this set of lecture notes on linear algebra which seems to go over several things I've been wondering about as I study linear algebra. Unfortunately there are very few exercises in the ...
0
votes
2answers
113 views

Open Problems for High School Students

I am a homeschooled rising senior in high school, and I would like to research an open problem in mathematics. I have taken a number of undergraduate-level mathematics courses, including ...
3
votes
2answers
170 views

What to study from Eisenbud's Commutative Algebra to prepare for Hartshorne's Algebraic Geometry?

I surveyed commutative algebra texts and found Eisenbud's "Commutative Algebra: With a View Toward Algebraic Geometry" to be the most accessible for me. The book outlines a first course in commutative ...
1
vote
2answers
40 views

Do most nonograms not require backtracking?

I get the impression that most Nonograms are "line solvable", meaning a computer never has to guess or backtrack. My understanding of this is that a tree searching algorithm isn't even necessary, ...
2
votes
3answers
128 views

A mathematical approach to economics

Are there books or papers where economics is formalized and studied very rigorously? I am very interested in this topic. I would preferably like free online books and/or papers, but that is not ...
0
votes
0answers
15 views

Quadratic form between a full row rank matrix and a positive definite matrix

Let $A\in\mathbb{R}^{n\times n}$ be a positive definite matrix and $B\in\mathbb{R}^{m\times n}$ (with $n>m$) is a full rank matrix ($\text{rank}B=m$). Could you please give me a reference for ...
9
votes
3answers
207 views

Areas of contemporary Mathematical Physics

I have often heard that some developments in Physics such as Gauge Theory, String Theory, Twistor Theory, Loop Quantum Gravity etc have had a significant impact on pure Mathematics especially geometry ...
1
vote
1answer
36 views

Proof of existence of Delaunay triangulation in 2D

I want to know references(papers/books/online articles) to the proof of existence of Delaunay triangulation of arbitrary set of vertices(in general position) on 2D euclidean plane. I do find a ...
3
votes
2answers
81 views

Best textbook for Geometric Measure Theory

I was wondering what is the best textbook for Geometric Measure Theory for self study. I am looking for one that isnt excessively detailed or long either as I found Rana's Introduction to measure ...
7
votes
1answer
79 views

Who first proved the fundamental theorem of finitely generated (or finite) abelian groups?

The fundamental theorem of finitely generated abelian groups (or maybe just finite abelian groups) is well-known and can be found in just about any text on the theory of groups or abstract algebra. ...
1
vote
0answers
26 views

Reference: Computing Martin Capacity

For Borel set $A$ the Martin Capacity is defined as: $\mathrm{Cap}_{M}(A)=[\inf\{\int \int \frac{G(x,y)}{G(0,y)}d\mu(x)d\mu(y):\mu \mbox{ probability measure on }A \}]^{-1}$ and Green's function ...
2
votes
0answers
15 views

Sampling from a graph

Suppose you have a graph $G=(V,E)$ that is unobservable globally and you wish to take a sample from the vertices of that graph to infer something about its global properties from local properties. ...
1
vote
1answer
44 views

What is the difference between reinforcement learning, trial and error, and fictitious play?

I have three question about three algorithms. I have a game with $n$ players. The action space of player $i$ is given by $\mathcal{A}_i=\{a_1, a_2, \cdots, a_m\}=\mathcal{A}$. The joint action space ...
1
vote
1answer
46 views

When is a binary operation bipotent?

I learnt that $\max(-,-)$ is a bipotent binary operation but I'm not able to find a definition of bipotent operation. QUESTION A binary operation $*:M\times M \rightarrow M$ is bipotent if ...
2
votes
1answer
105 views

Best Less-Famous Texts for Forcing

There are many books, papers and lecture notes which give an introduction to forcing (e.g. Jech or Kunen's books) but here I am looking for some possibly less-famous useful comprehensive texts for ...
6
votes
6answers
221 views

Interviews of famous modern mathematicians

I was wondering, are there any good collections of interviews of famous modern mathematicians? It can be text interviews, or audio or video recordings. I am not sure what exactly I mean by "modern". ...
2
votes
3answers
64 views

Recommendations for books on complex analysis and on measure theory?

I'm looking for a book on complex analysis that has a similar writing style to either Terry Tao's Analysis II or Nathan Jacobson's Basic Algebra series. I have found both of these extremely easy to ...
0
votes
1answer
54 views

Where can I read about the topological properties of the perforated plane?

Anybody knows about perforated plane in topology? What is it? Where can I read about it? I'm talking about the plane $\mathbb{R}^2$ with the topology that have basis elements disks without finite ...
2
votes
1answer
53 views

Better than Casella and Berger's *Statistical Inference*?

I have just finished an undergraduate degree in statistics and am looking into a graduate degree in statistics. One textbook that I've found in my searching is Casella and Berger's Statistical ...
3
votes
1answer
59 views

Characterization of weak solution

5 Nonlinear elliptic variational inequalities Preliminaries In order to explain the importance of elliptic variational inequalities, first consider the weak solution of the linear ...
0
votes
0answers
18 views

Reference for Hölder space $C^{k,\beta}(X,Y)$, X and Y Banach spaces

Does anybody know of a reference for the Hölder spaces $C^{k,\beta}(X,Y)$, which treats the case where $X$ and $Y$ are (subsets of) Banach spaces? (Or something more general.) All books I have seen ...
1
vote
1answer
47 views

“Reparametrizing” a differential system of the first order (Vinograd theorem?)

Consider a continuous function $f:\Omega\subset\mathbb R^n\longrightarrow \mathbb R^n$ such that for every $x\in\Omega$ the Cauchy problem: $$(\ast)\left\{\begin{array} {ll} y'=f(y)\\ y(0)=x ...
0
votes
1answer
39 views

Lie rings: reference request

Dear friends: I am looking for a modern reference for Lie rings (In particular, I would like to have nice references for the structure of Lie ideals), let it be lecture notes or a book, in the sense ...
4
votes
1answer
35 views

Topological property: set-theoretically large subsets of an infinite space are not compact.

Let $X$ be an infinite topological space. Say that $X$ satisfies # if no subset of $X$ of cardinality $|X|$ is compact. So for instance it is clear that no (infinite) compact space satisfies # any ...
0
votes
0answers
25 views

Computing equilibrium measure for Borel sets eg. Ball

I am asking for methods to compute equilibrium measures. The more the better. Here is the definition of equilibrium measure in the Brownian motion setting: Let $\gamma=\sup\{t\in [0,T]: B_{t}\in ...
0
votes
1answer
36 views

how can I to write equations in format latex? [closed]

I need your help... how can I to write equations in format latex? i dont know how to do that example:
6
votes
1answer
33 views

Integer programming feasibility is NP-what

What is the complexity class of the general problem of integer programming feasibility? The sources I've looked at are, in my opinion, very confusing. Some say NP-hard, some say NP-complete. Some ...
2
votes
1answer
66 views

Descartes on imaginary unit.

I heard once that Descartes defining the imaginary unit had to talk about the imagining of rise of the spirit over the real numbers because definition based on square root of a negative number could ...