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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3
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0answers
52 views

Generalization of the Frenet-Serret frame.

Consider $\alpha : I \rightarrow \Bbb R^n$ a differentiable curve, $\mathscr{C}^\infty$ and parametrized by arc-length, to make our lives easier. If $n = 2$, we have only one signed invariant, the ...
0
votes
0answers
17 views

Maximum principle for linear elliptic operators of arbitrary order

What is known about maximum principles for strongly elliptic linear differential operators of even order (possibly higher than $2$)? By such an operator, I mean a linear differential operator with ...
7
votes
0answers
77 views

Infinite sum involving $q$-adic representations of whole numbers and $q$-factorial numbers

Let $q \in \mathbb{N}_{\geq 2}$. For $n \in \mathbb{N}_0$, let $$\mathrm{fac}_q(n) := \prod_{i=1}^n (1+q+\dots+q^{i-1}) = \prod_{i=1}^n \frac{q^i-1}{q-1}$$ be the $q$-factorial of $n$. In particular, ...
3
votes
0answers
41 views

cov(meager) strictly between $\aleph_1$ and $2^{\aleph_0}$

Is is consistent that $\aleph_1 < \text{cov(meager)} < 2^{\aleph_0}$? I can only seem to find references for results that assert it is consistent that it (or other cardinal characteristics) is ...
1
vote
0answers
22 views

Reference for construction on Riemannian Manifolds

I would like to know a book or an article where the connected sum of Riemannian manifolds is explained with some detail. I roughly know how to do the construction but I want to be able to check a more ...
0
votes
0answers
23 views

Matrices with functions as entries

I am interested is studying matrices which have functional entries. Specifically I am looking at quadratic forms of the type $x^T Q(x) x$ where $Q(x)$ is a matrix whose entries are functions of $x$. I ...
1
vote
2answers
22 views

Text on convergence theorems in probability theory (various modes of convergence)

I need a text reviewing theorems and discussing with details ALL the types of convergence in probability theory such as almost sure convergence, convergence in probability, weak convergence, $L^p$ ...
1
vote
1answer
49 views

Real Analysis Help [on hold]

I have done a two semester undergraduate course in Real Analysis. But still I have no feel for the subject and I have no idea how to approach a new problem.I cannot visualize the concepts easily. ...
1
vote
1answer
32 views

References for coordinate-free linear algebra books

I'm looking for some (or one) good book(s) that teach linear algebra either purely coordinate-free or ones that present the standard bag-of-tools alongside coordinate-free alternatives or discussions. ...
0
votes
2answers
57 views

Looking for a book: $B(H)$ not reflexive

I'm looking for a book with a proof that for an infinite dimensional Hilbert space, $B(H)$ is not reflexive. Thank you.
2
votes
3answers
80 views

If $I_{n+1}\subset I_n$, show that $\bigcap_{n=1}^\infty I_n$ is nonempty

Question: If $I_n$ is closed and bounded, $I_{n+1}\subset I_n$, and $I_n\neq\emptyset$, show that $\bigcap_{n=1}^\infty I_n$ is nonempty. This is not a homework help question. I'm actually looking ...
3
votes
0answers
41 views

Conjectured Value of Ramsey Number $R(3,10)$

It is known that the value of the Ramsey number $R(3,10)$ is either 40, 41, or 42. Have any experts in the field offered a conjecture as to which it might be?
0
votes
0answers
22 views

Probability of hitting a Borel set by transient Brownian motion ($d\geq 3$)

I am looking for references/progress made in estimating the hitting probability for Borel sets. For spheres we have $P_{x}(T_{B_{r}(0)}<\infty)=(\frac{|r|}{|x|})^{d-2}$, where $x=B_{0}$ for ...
3
votes
1answer
61 views

Textbooks on graph theory

I've read the textbook Groups and Their Graphs by Grossman, and I'm interested in learning more about graphs. I know about O. Ore's book in the same series (Graphs and Their Uses), but I'm interested ...
3
votes
1answer
37 views

Book Recommendations for Picard Big and Little Theorems

Does anybody have book recommendations for reading about Picard's Little and Big Theorems? Preferably, I am looking for a book that is intended for an undergraduate/first year graduate student who ...
0
votes
0answers
24 views

About product order [on hold]

Are there any references talking about product order on this wikipeida link? thanks!
6
votes
1answer
121 views

Mathematical background for TQFT

I am physicist. I`ve started studying Topological QFT. What would you recommend to read in mathematical field for understanding Witten’s old articles of 80s-90s? What books/articles could help form ...
0
votes
0answers
44 views

can somebody provide me this paper by NIVAN? [on hold]

equations in quaternions by I. Nivan published in AMM Vol 48 , 654-661 (1941). please i need it, and could not find it online anywhere.
1
vote
1answer
38 views

References for mathematics enthusiasts?

I'm willing to give a mathematics Olympiad [syllabus] and I can't buy all the book(or even some of them) and am looking for some online resources like questions, articles, or more prefably some single ...
1
vote
2answers
66 views

Typed version of Newton's Principia Mathematica

I need a typed pdf version of Newton's Principia. Is it available for free online? And I also need the proof of universal law of gravity and the elliptical orbits of planets(If there's no typed ...
2
votes
0answers
29 views

Meaning of “Canonical System of the First Order”

I am learning about PDEs and came across the following. "Convert a partial differential equation of higher order into a canonical system of the first order" What does the above statement mean/imply? ...
5
votes
1answer
63 views

Limit everywhere, limit function is continuous, specific proof.

Suppose $f:[a,b] \to R$ is a function such that $\lim_{t\to x} f(t) = g(x)$ exists $\forall x \in [a,b]$. It can be shown that $g(x)$ is a continuous function. I seem to remember that there was a ...
1
vote
1answer
39 views

Where can I find introductory video lectures about calculus and analysis?

I am having calculus classes that are titled as Calculus for Mathematicians, for the rest of the students who are studying calculus, they use Stewart's book. In our classes, we're having something ...
1
vote
0answers
31 views

For starting the studies in Mathematical-Biology

I will take an undergraduate course in Mathematical Biologylearn themes like: population dynamics; the emergence of patterns of Philotaxia; Turing´s bifurcation; Genetics; Chaos; Neural networks; ...
0
votes
0answers
32 views

Koblitz - Are chapters III & IV independent of I & II

I am interested in learning about Modular forms and have heard many great things about Neal Koblitz's Introduction to Elliptic Curves and Modular Forms. However, Koblitz doesn't discuss modular forms ...
1
vote
1answer
22 views

References dealing with function spaces in pde like $C^k(\mathbb R^n)$, $C^\infty_c(\mathbb R^n), \ldots$?

What would be nice references for function spaces like $C^k(\mathbb R^n$), $C_0(\mathbb R^n)$, $C^\infty_c(\mathbb R^n), \ldots$ and most common function spaces which are offen employed in partial ...
0
votes
1answer
43 views

Suggestions for a real analysis reference.

Can anyone suggest some real analysis book which has a geometric presentation of the concepts with pictorial representation.
0
votes
2answers
22 views

What are the complex solutions of a linear homogenous ODE of order $n$ with constant coefficients?

What are the complex solutions of a linear homogenous ODE of order $n$ with constant coefficients? Where can I read a proof? p.s. I don't even see the answer to the first question with a google ...
2
votes
2answers
74 views

Distinguishing sets according to more fine-grained notions than cardinality.

I'm interested in distinguishing sets according to more fine-grained notions than cardinality. Now I don't know a thing about computability theory, but it seems to me that considering sets up to ...
2
votes
1answer
33 views

References on estimating capacities (Newton, Martin etc) for sets & alternative formulations.

By G-capacity for capacitable set K I mean: $Cap(K)=[inf\{\int\int G(x,y)d\mu(y)d\mu(x):\mu$ probability measure on K$\}]^{-1}$. where G(x,y) is any kernel eg. the Green kernel. Q1:We've calculated ...
0
votes
0answers
34 views

Which Trigonometry Book is Recommended? [duplicate]

I'm taking trigonometry for this upcoming fall, and I want to get a good head start like I did with statistics a while back. I was recommended Cynthia Young' s Trigonometry book and Loney's book. ...
0
votes
1answer
24 views

Wasserstein metric: conditions for the existence of minimizer and duality

Let $(X,d)$ be a metric space and let $\mathcal P(X)$ be the set of all Borel probability measures on $(X,d)$. The Wasserstein distance on $\mathcal P(X)$ is given by $$ W_d(\mu,\bar\mu):=\inf_{M\in ...
4
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0answers
43 views

Adjunction between cocomplete categories

Let $C$ be a small category. Let $D,E$ be cocomplete categories. Let us denote by $\hom$ (resp. $\hom_c$) the category of (cocontinuous) functors. Then there is an equivalence of categories ...
0
votes
0answers
30 views

Reference Request: Fubini's theorem for non-negative functions

I have never seen this (1st page) formulation of Fubini's theorem in the literature. Does anyone know where I can find it? In every calculus book (e.g. Apostol, Courant, etc.) I looked, the authors ...
5
votes
2answers
249 views

Curious gamma identity

I found the following curious identity for the gamma function on Wikipedia for which I'd like to know some references (proof, history, etc). The identity is as follows: $$\Gamma(t) = x^t ...
4
votes
1answer
51 views

References for mathematical theory of summability of divergent series

Once in a while, I can't help it to ask very broad questions. I have read (a portion of) Hardy's Divergent Series. Back then, I think besides in mathematics, divergent series and the need to assign ...
1
vote
1answer
60 views

The relationship between each harmonic numbers

In Knuth's "Concrete Mathematics" in chapter about numbers below equality is given $$H_n = \ln n + \gamma + \frac{1}{2n} - \frac{1}{12n^2} + \frac{\epsilon_n}{120n^4} $$ where $0 < \epsilon_n < ...
1
vote
0answers
21 views

Defining cardinals as fixpoints of the cardinality function [closed]

I am fond of non-standard approaches to various concepts. So, is there some paper or book that first defines a cardinality function # (as in #({1,4,6})=3), and then defines the cardinal numbers as ...
-1
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0answers
34 views

Behavior of groups under extension

We know that an extension of a solvable group by a solvable group is solvable. Similarly we can find other properties of group extensions here Can someone provide a reference to these statements where ...
4
votes
0answers
48 views

Does anyone have a good reference on calculating contour integrals around the unit circle (numerically or otherwise)?

I am looking for a reference that will help me calculate contour integrals around the unit circle or other curve. I have a particularly ugly function which isn't likely to have a nice closed form so I ...
0
votes
0answers
26 views

Reference for understanding Frechet and Gateaux derivatives

In multivariable calculus, when we were discussing directional derivatives, we were told that the fact that the directional derivative equals the gradient times the direction vector $( \partial^{\vec ...
2
votes
0answers
50 views

Simplifying a Vector Integral

While reading the book - Cercignani, Theory and Applications of Boltzmann Transport Equation (I am not a math student), I found this integral which I am unable to understand. Note that $\xi_i , \xi_l$ ...
0
votes
1answer
32 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
17 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
61 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 ...
10
votes
1answer
174 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
113 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
63 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
30 views

What is Bush Mosteller algorithm?

I cannot find anything interesting on the internet. What is the Bush Mosteller stochastic model? ...
12
votes
2answers
428 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, ...