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.

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Green functions

do you know some litterature about green functions for the heat equation ? in particular for the non-linear equation : $\frac{\partial u(x,y,t)}{\partial t}-\frac{\partial^2 \left[ f(u(x,y,t))u(x,y,t)...
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1answer
47 views

Are there any examples of consistent proper axiomatic extensions of classical logic?

By a proper axiomatic extension, I mean a logic with the same set of well formed formulas as classical logic, but with the set of theorems of the logic a proper superset of the theorems of classical ...
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0answers
20 views

Rappaports algorithm for the convex hull of multiple circles.

I would like to use D. Rappaports convex hull algorithm for discs in a JavaScript application, which I am developing. http://www.sciencedirect.com/science/article/pii/092577219290015K I found ...
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1answer
66 views

Books about the foundations of (calculus) functions?

I'm looking for a foundational book that builds up ideas like transcendental functions. For example, how the trigonometric functions are truly defined when plotted as continuous functions. I believe ...
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0answers
24 views

On a stronger property than being an Armendariz ring

A ring $R$ is said to be Armendariz if $f(x), g(x) \in R[x]$ are such that $f(x)g(x) = 0$, where $f(x) = a_nx^n + \dots a_0, g(x) = b_mx^m + \dots + b_0$, then $a_ib_j=0$ for all $i,j$. In other ...
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1answer
39 views

Reference request: $W^{2,2}$ estimates of elliptic PDE with measurable coefficients

I have some questions on solvability of the following elliptic PDE: in $\mathbb{R}^2$, for $f\in L^2$, $$a^{ij} u_{x^i x^j} +b^i u_{x^i} + c u = f.$$ Here $\{a^{ij}(x)\}_{i,j=1,2}$ is symmetric ...
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1answer
43 views

self teach algorithms [closed]

What are some good resources to self teach the subject of Algorithms for someone with background in mathematics? That is, does there exists a more theoretical and abstract approach versus practical ...
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0answers
15 views

Reference for the equivalence of categories between the categories of affine group schemes and commutative hopf algebras.

Where can I find the proof or a discussion that the category of affine group schemes is equivalent to the category of commutative hopf algebras? Thanks.
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0answers
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A “contraction” on tensor product spaces

Let $X$ be a topological vector space. Let $X'$ denote its continuous dual. Consider the (algebraic) tensor product $\mathbb{X} := X \otimes X'$. For simple tensors $x \otimes x' \in \mathbb{X}$ set $...
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1answer
46 views

Courant-Hilbert's Book: Weyl's asymptotic law for eigenvalues - Planar domains

In the book Strauss W.A. Partial Differential Equations - an Introduction (Wiley, 2008, 1st Ed.) page $311$, there is a comment Now an arbitrary plane domain $D$ can be approximated by unions of ...
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2answers
33 views

Curvature of curves on surfaces

Are there ways to know the curvature of a curve $\gamma$ that lives on a surface $\mathcal{S}$starting from the gaussian curvature of $\mathcal{S}$? In general, is it possible bound the curvature of ...
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1answer
89 views

Applications of PDEs in many variables

One reason that solving systems of partial differential equations is so important is the many applications of PDEs in science and engineering (eg. the heat equation, the wave equation, etc.). Often ...
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0answers
42 views

In which quadrant of the circle does the angle of $90^\circ$ lie?

By definition and with an authoritative reference, in which quadrant or quadrants does $90^\circ$ lie? (There are non-authoritative references which answer the question, and a related question which ...
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1answer
13 views

Decidability of quantifier-free formulae in Peano- and True Arithmetic

It is well-known that validity in Peano Arithmetic is undecidable. It is less well-known that validity is already undecidable in True Arithmetic (the theory of the standard model of Peano Arithmetic). ...
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1answer
20 views

Differential forms vector space over function field?

Let $V$ be a vector space and $V^*$ be its dual space. Then I know that $V^*$ is considered a vector space because we can scale the basis covectors by real numbers and add them together and all of ...
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0answers
27 views

Legendre's Conjecture Theme (Part II)

This is a continuation of this question. My main question is that, in the previous question we were mainly concerned about the sign of, $$f_{2}(n)=\pi\left((n+1)^2\right)+\pi\left(n^2\right)-2\pi\left(...
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1answer
20 views

On terms “Orientation” & “Oriented” in different mathematical areas?

The goal of this question is to help to deal with different meanings of the words such as "orientation" and "oriented" in different mathematical areas. Are different oriented concepts somehow ...
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0answers
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Are Oriented Graphs Related to Oriented Matroids?

My professor said that oriented matroids make it easier to investigate things such as connectivity. Recall that an oriented graph is a digraph without multiple edges or loops. Now Are oriented graphs ...
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2answers
40 views

Special Relativity-Book

I would a good book to study the Special Relativity. In my course the professor has treated the following topics: $(1)$ Lagrangian and hamiltonian dynamic of a charged particle; $(2)$ Relaticistic ...
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2answers
243 views

modern calculus or analysis text that emphasizes Landau notation?

Is there a comprehensive calculus or analysis textbook or problem book, written in the last twenty years, that emphasizes the use of Landau notation (big and little oh), especially for making ...
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0answers
13 views

Area of Operations Research on graph theory and reliability engineering? [closed]

I am confused by the jargon in Operations Research (OR) when it is the same as in Graph theory such as component but it can mean just a vertex. So I am confused to the extent that reliability ...
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0answers
66 views

Legendre's Conjecture Theme (Part I)

Main Question Recently I have been thinking about the Legendre's Conjecture. I noticed that a proof of the conjecture can be obtained if we can prove any one of the following, Conjecture 1. For ...
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0answers
36 views

Introduction to p-adic vector spaces

I'm interested in learning about vector spaces over $\mathbb{C}_p$ and $\mathbb{Q}_p$. Most textbooks on p-adic numbers (Koblitz, Schikhof) focus on analysis and number theory. Is there any ...
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0answers
38 views

Image of the norm map in imaginary quadratic fields

Let $K=\mathbb{Q}(\sqrt{D})$ be an imaginary quadratic field of discriminant $D<0$. I want to know the image of the norm map $$ N^K_{\mathbb{Q}}:\mathcal{O}_K\to\mathbb{Z} $$ and the values of $N^...
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1answer
31 views

Ultrafilter on $[0,1]$ consisting of closed sets

Today we learned about filters and ultrafilters in the General Topology course. I am trying to play around with these definitions. I wish to ask a question that I am unsure about. Let us say, we have ...
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0answers
48 views

Books on inference for stochastic analysts

I realize that book recommendations to learn statistical inference is a hackneyed topic but I have something more specific in mind. I work on diffusions and would like to quickly and effectively learn ...
3
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2answers
87 views

Maclane/Birkhoff's “Algebra” as a first book on the subject?

Would the more knowledgeable and well-versed members of this community be so helpful as to give their opinion on using Birkhoff & MacLane's famous "Algebra" for a first course in Abstract Algebra? ...
3
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2answers
99 views

Spivak's Calculus?

I have seen many users here asking questions about problems in what they call "Spivak's Calculus Book". I have never seen the book, and information online is scarce. From what I've gathered, it is ...
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1answer
35 views

A good reference for irreducible and noetherian spaces

I am looking for a comperhensive reference for irreducible and noetherian topological spaces. Also, a reference for prime spectrum of a commutative ring.
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2answers
85 views

Reference for Algebraic Topology

I know undergraduate algebra (groups, rings, fields, Galois etc), undergraduate differential geometry, undergraduate real/complex analysis and now I feel as though to get to the next level, i should ...
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2answers
59 views

Text for honors college algebra and trigonometry

I am looking for suggestions on algebra and trigonometry for students who are interested in majoring in mathematics. So typical texts written for average freshman who is forced to take math as a core ...
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2answers
42 views

References for the functor of points vision of schemes.

I recently discovered the idea of the functor of points. I would like to find a reference where the different visions of scheme are presented. It seems to me that the classical texts emphasize the ...
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1answer
70 views

Relation between tangent spaces of (un)stable manifolds in Morse theory

After asking this question about signs in the Morse complex, I realised that my confusion is really about how tangent spaces to different (un)stable manifolds are related. So suppose we have a Morse ...
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46 views

Reference for complex analysis for an engineer starting off mathematics

I am thinking of self studying complex analysis and would appreciate any recommendation for which book to use among Needham's visual complex analysis or Flanigan's complex variables. I am looking for ...
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1answer
36 views

Decision theory references for advanced undergrad/early grad students?

I'm studying measure theoretic stochastic calculus, and I was hoping to pick up some knowledge of decision theory along the way. I'm very happy with Rudin or Karatzas in level of rigor, and I was ...
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0answers
22 views

Request for reference about a few eigenvalue inequalities

Can someone kindly give me a reference for these two theorems? For $M_1$ and $M_2$ being two matrices such that $M_1^T M_2$ makes sense apparently the following is true, $\sum_{i=1}^k \sigma_i(M_1^...
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0answers
22 views

Spherical functions which are invariant under a finite rotation group

Is there a nice, clean reference which lists a basis in terms of (linear combinations of) spherical harmonics for the $L^2$ space of functions defined on the sphere $\mathbb{S}^2$ which are invariant ...
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2answers
111 views

Neighborhood chain in $\mathbb{R}^\mathbb{R}$

Edited after SamM's comment: Consider the topological space $\mathbb{R}^\mathbb{R}$, with the usual topology. Pick a point $x \in \mathbb{R}^\mathbb{R}$ and a neighborhood $V = V_0$ of $x$. I wish to ...
3
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2answers
118 views

A discontinuous function with smooth sections

I am searching for $f : U\rightarrow \mathbb R $ defined in an open square $U$ in $\mathbb R^2$ so that $(0,0) \in U$, $f$ is not continuous at $(0,0)$, for each $x$ the function $y\mapsto f(x,y)$ is ...
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1answer
36 views

How much can you minimize the overlap of intervals?

I'm wondering about the following (sorry I invented some terminology): Consider a collection of intervals $\{I_k\}_{k=1}^n$ such that $I_k\subset[0,1]$ and $|I_k|>1/3$. Define the order of $x\...
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0answers
35 views

Explicit degree two Artin L-function

Let $K$ be a cubic field, and $\zeta_K(s)$ the Dedekind zeta function. Then from here one has the factorization $$\frac{\zeta_K(s)}{\zeta_{\bf Q}(s)}=\sum_{n=1}^\infty\frac{a(n)}{n^s}$$ where $a(n)=\...
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0answers
24 views

On the Arrangement of Intermediate Subgroups

I am trying to find a journal paper 'On the Arrangement of Intermediate Subgroups' by M.S. Bah and Z.I. Borevich appearing Rings and Linear Groups, Krasnodar (1988), 14-41. This is a Russian text and ...
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2answers
91 views

How large must $S(5)$ be at least , if it is not $47,176,870\ $?

See here : https://en.wikipedia.org/wiki/Busy_beaver for more details about the maximum-shifts-function It is said that about $40$ machines with $5$ states have unknown status (it is not known ...
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1answer
57 views

Explicit verification of signs in Morse complex

I'm trying to check by hand that the signs in the Morse complex, defined via choices of orientations on the unstable manifolds, lead to $\partial^2=0$. The books I've looked in seem to say either ...
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2answers
88 views

Overly formal book on mathematical logic.

In the preface to his book on logic Dirk van Dalen talks about the duality between "profane" and "sacred" logic, referring to relaxed logic and extremely formalized logic. He then explains his book ...
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29 views

Weak elimination of imaginaries in the theory of the random graph

Let ${\cal U}$ be a countable random graph. Prove that for every formula $\varphi(x)\in L({\cal U})$, where $x$ has arbitrary finite arity, there are a positive integer $n$ and finite $C\subseteq{\cal ...
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1answer
30 views

References for the representation theory of $SU(2, 1)$

I couldn't find any reference with the representation theory of this specific case. I found some general stuff but never explicit computations or realizations. The only thing I found on $SU(2, 1)$ ...
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1answer
19 views

Best known inequality for the larger prime number of a product?

We all know given two prime number's $b$ and $a$ whose product is $c$: $$ c \geq b \geq \sqrt c \geq a \geq 2 $$ where, $ab=c$ I was wondering if the inequality for $b$ could be improved upon ...
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0answers
24 views

Probability reference after Billingsley's Convergence of Probability Measures

I've read through Durrett's Probability: Theory and Examples and Billingsley's Convergence of Probability Measures and was wondering what a good next step would be. I've taken graduate courses in ...
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1answer
37 views

Reference request: AI for mathematicians

I am looking for books on AI and Machine Learning written for PhD + level Mathematicians. Is there anything like this? Thanks, Vladimir