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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1answer
77 views

On the density of $\mathcal{C}^\infty(\Omega) \cap W^{1,\infty}(\Omega)$ in $W^{1,\infty}(\Omega)$

Let $\Omega$ be an open set of $\mathbb{R}^n$ ($n\ge 1$). We know that the Meyers-Serrin theorem isn't true in $W^{1,\infty}(\Omega)$. But is it true that $\mathcal{C}^\infty(\Omega) \cap ...
4
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1answer
37 views

Extension of ZFC models preserves cardinals

Let $M \subseteq N$ be countable transitive ZFC set models. Assume that this extension preserves cardinals, i.e. if $\alpha$ is an ordinal number (this notion is absolute) such that $(\alpha \text{ is ...
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0answers
34 views

Solutions to exercises in Nelson's “An Introduction to Copulas”

I am paving my way through Nelson's "An Introduction to Copulas". The book has exercises (quite good actually), but no solutions. Does anybody have a solution manual for (some of those) exercises? ...
2
votes
1answer
165 views

Resolution of Singularities: Base Point

Consider the curve $y^2=4x^3-ax-b$, where $a$ is a fixed constant and $b$ is a free constant. For each value of $b$ we get a family of curves. Part 1: Show that the family of curves intersect at ...
2
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1answer
50 views

Reference Request: Split-Complex Numbers

Does anyone have a recommendation for a good book on split-complex numbers? If it also covers dual numbers or the relation between split-complex numbers and special relativity or Minkowski 4-space or ...
0
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1answer
54 views

About connection and topology

I'm looking for a good book (or article) about history of topology, and specially about the connection concept. I appreciate all your suggestions!!!
2
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3answers
70 views

Very elementary number theory and combinatorics books.

I know the basics of logic, sets, relations and the like, so studying intros to abstract algebra and real analysis is not that hard. That said, I have a deficiency when it comes to elementary number ...
5
votes
1answer
66 views

Partial order on cardinalities without the axiom of choice

Cardinality can still be defined without choice, e.g. as equivalence class of equipotent sets, see Defining cardinality in the absence of choice. Injections define partial order on cardinalities by ...
0
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1answer
67 views

Where can I find a copy of the Project Euler questions?

The Project Euler page is currently offline, and I would very much like to do the problems still. Does anyone know where I can find a transcript of the problems?
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5answers
95 views

Book about different kind of logic

I'm searching for a book that talks about different kind of logic ( esoteric and particular one too ) and their uses and differences. Does such a book exist?
1
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1answer
34 views

Lower bound for $(x + y)^k $?

I'm wondering, is there a lower bound for $(x + y)^k $? For example, if $x,y,k > 0$, can we say that $(x + y)^k \geq x^k + y^k$? If anyone has a source/reference for this, that would be great.
2
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0answers
36 views

How I can make $\Bbb{C}[x]$ into a Banach algebra?

Let $\Bbb{C}$ the complex field. Define $\Bbb{C}[x]$ as the set of all polynomials with variable $x$. It is known that $\Bbb{C}[x]$ is a algebra. Now the question is this that how I can make it a ...
0
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1answer
28 views

Books and/or online resources on solving problems.

What are some good resources(online, books) that teach you how to tackle difficult and ugly problems in higher math arranged by subjects(analysis, topology, ODEs, groups etc) or topics(polynomials, ...
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0answers
22 views

Reference for introductory text on Homotopy Theory

Can anyone recommend a good introductory text on Homotopy Theory? Paid textbooks or free online material/lecture notes both welcome.
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6answers
230 views

Proving that $E=mc^2$

What are the axioms of special relativity? Is there a book or paper that introduces the theory of special relativity in a rigorous manner, and proves that $E=mc^2$ after appropriate definitions?
5
votes
1answer
35 views

Does the data of Galois group, ramified places, and inertia groups, determine a Galois number field?

Suppose I tell you that $K/\mathbb{Q}$ is a finite Galois extension, and I specify the Galois group $G$, and suppose further that I give you a finite list $S$ of places of $\mathbb{Q}$ and for each ...
37
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4answers
2k views

Why can't we define more elementary functions?

$\newcommand{\lax}{\operatorname{lax}}$ Liouville's theorem is well known and it asserts that: The antiderivatives of certain elementary functions cannot themselves be expressed as elementary ...
2
votes
0answers
39 views

A better Reference than Andre Weil's Basic Number Theory

I want to get a feel for Adeles. I have been suggested to read the first 4 chapters of Andre Weil's Basic Number Theory. I am very confused by the writing style and conventions (like a field need not ...
0
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0answers
72 views

Does such a mathematics book exist?

A book that is intuition and theory driven, with lots of exercises to practice. A book that goes over basic mathematics to more advanced topics (from say algebra 1 and 2 to calculus and beyond..) Or ...
0
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1answer
13 views

Reference for Time Series and Linear Filters

I am reading "Time Series, Data Analysis and Theory" by David R. Brillinger. I am sorry but it seems to me that the book is quite sketchy and loose about notations. For example in the first chapter ...
1
vote
4answers
373 views

Help for Mathematics High school

I'm looking for mathematics books, courses + exercises for high school level. My daughter was high school certificated but she has stopped her studies for 5 years. She would like to be involved in new ...
2
votes
1answer
82 views

How to get the domain of $x^x$?

The function $$f(x)=x^x.$$ is defined on $(0,\infty)$ because it is equal to $\exp\left(x\log\left(x\right)\right)$. But what happen when $x\leqslant0$? I tried for example $x=-1$, so ...
2
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1answer
53 views

Mathematics of genealogical trees

I really searched a lot but did not find anything meeting my needs: A place where questions of genealogy, especially the structural and combinatorial analysis of genealogical "trees" of descendants ...
1
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0answers
32 views

Less Terse alternative to Advanced Calculus by Folland.

I am currently in an advanced calculus class in university. We use Advanced Calculus by Folland. When I try to follow along the book I find that it is not verbose enough, and has too few examples. I ...
0
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0answers
31 views

Reference/confirmation of a result in analysis

Does anyone know of or have a reference for the following result: Let $X$ be a reflexive Banach space with dual $X^{*}$. If there exists a continuous mapping $f: K \rightarrow X^{*}$ on compact ...
1
vote
1answer
64 views

Primary decomposition of $I = (x^2, y^2, xy)$

I want to find a primary decomposition of the ideal $$ I = (x^2,y^2,xy) \subset k[x,y]$$ where $k$ is a field. How to proceed? Are there algorithms to find such decompositions? Where can I find ...
0
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1answer
32 views

References for Legendre's prime-counting function

This question is about Legendre's prime-counting function, the one that can be used to calculate the exact amount of prime numbers that are less than or equal to a given number (as long as the number ...
0
votes
1answer
69 views

Book recommendations for someone interested in higher mathematics?

Background: I am currently studying physics and except for high school mathematics I have experience with linear algebra, single- and multivariable calculus, differential equations (mostly ODE's, but ...
1
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5answers
80 views

Number theory problem book

Can anyone suggest me some good book that has problems on classical elementary number theory with solutions?
0
votes
1answer
32 views

The center of Sylow $p$-subgroups of a finite simple group of Lie type

Would some one please to introduce me an easy reference!! which contains the size of $Z(P)$(center of $P$), where $P$ is a Sylow $p$-subgroup of a finite group of Lie type over a finite field of ...
2
votes
2answers
69 views

Sylow $p$-subgroups of finite simple groups of Lie type

I need some information about the Sylow $p$-subgroups, and their normalizers, (specially their sizes), of a finite simple group of Lie type over a finite field (not necessarily algebraic closed) of ...
3
votes
1answer
59 views

Is there a garden of derivatives?

I've found a book called A Garden of Integrals, in which the author shows the evolution of the concept of Integral. I follow AnalysisFact on Twitter, some days ago, they posted the following: The ...
0
votes
0answers
32 views

Presentations that make the Todd-Coxeter algorithm blow up

Consider the presentation defined, for an integer $n > 1$, by $$G_{n} = \langle x, y \mid xy^n = y^{n+1}x, yx^{n+1} = x^{n}y\rangle .$$ The group defined by this presentation is trivial. Is it ...
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0answers
17 views

Citing a result on obstruction to Lagrangian Embedding

Let $L$ be a closed orientable Lagrangian embedding in $\mathbb C^n$. Then $\chi(L) = 0$, where $\chi(L)$ denotes the Euler characteristic of $L$. This fact is more or less stated in section 3.2 of ...
4
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0answers
49 views

Decomposition of Laplacian into tangental and normal components w.r.t. submanifold

If I have the covariant Laplacian operator acting on a tensor e.g. $\nabla^2 h_{\mu\nu}$ on a (pseudo-Riemannian) manifold, and I have (say a codimension-2) submanifold, how can I "decompose" the ...
3
votes
2answers
86 views

Introduction to Proper Forcing Reference

What is a good introduction to proper forcing? I am aware of Shelah Proper and Improper Forcing, but I heard this book may be somewhat challenging to read. There is also Devlin's The Yorkshiremen's ...
2
votes
0answers
48 views

Why has no body retypeset Ladyzhenskaya et al's “Linear and quasi-linear equations of parabolic type”? [closed]

The book "Linear and quasi-linear equations of parabolic type" is one of the ugliest books I have ever seen in my life. The fonts are awful, the notation is difficult to understand and recall and the ...
1
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1answer
62 views

Locally finite infinite field

Is there a place (a book maybe) where I can find some useful information on infinite locally finite fields? Especially when all of whose proper subfields are finite? I know, for instance, that a ...
2
votes
0answers
25 views

$\mathbb{Z}_p[\text{PGL}_2(\mathbb{F}_{p^n})]$-modules

Let $p$ be prime. Let $\mathbb{Z}_p$ be the $p$-adic integers. I'm intersted in $\mathbb{Z}_p[\text{PGL}_2(\mathbb{F}_{p^n})]$-modules of low rank over $\mathbb{Z}_p$ (rank $2$ is already very ...
3
votes
1answer
48 views

Sets that are equal to closure of its interior

Is there a standard name for set $M$ for which $M = \overline{M^0}$? $M^0$ is interior and $\overline{M}$ is closure. Often I work with well behaved sets and functions. I have in mind continuous ...
1
vote
1answer
66 views

Beggining in Algebraic Geometry

My question is about sources for start the study of algebraic geometry. I know that it requieres so much algebra, but, is there any book which can be readed without many tolos of modules, Galois, ...
6
votes
1answer
75 views

Follow up to Pinter's abstract algebra

I wanted to learn abstract algebra this summer so I bought Pinter's A book of Abstract Algebra. I was planning on reading it over the course of the summer, but just finished the last problem of its ...
0
votes
0answers
15 views

good text books for axiomatic solid geometry?

I read the book about plane geometry : Marvin Jay Greenberg Euclidean and non-euclidean but it's only for the plane geometry so I want know about axiomatic solid geometry. Can someone recommend a ...
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0answers
19 views

Reference request for papers proving the existence of a special function satisfying the following conditions

Previously in this site it has been proved that there exists at least one prime between $c_n$ and $n$ where $c_n$ denotes the $n$-th composite (see the question Prove that there exists an $m$ such ...
2
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1answer
57 views

Solving polynomial equations over finite fields

I have looked (a bit) at questions like finding the number of roots of $x^n =1$ over a finite field. Now I would like to understand how to solve polynomial equations over finite fields. From what I ...
46
votes
46answers
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 ...
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0answers
22 views

Endomorphisms of Groups - Book Recommendation

Which books dealing with group theory have considerable material on endomorphisms? The books I have seen usually have something on homomorphisms, isomorphisms, and automorphisms, but very little on ...
2
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0answers
24 views

When does weakly elliptic $\Rightarrow$ strongly elliptic?

While learning more about the analytic background for the Atiyah-Singer Index Theorem, I was curious about the following question (although not needed for the ASID): what are some general conditions ...
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0answers
18 views

Can anyone tell me more about this measure of asymmetry

I have a measure of asymmetry (Q ranging from $-1$ to $1$) between two paired variables (x,y; both positive integers) and would like to know more about where this equation comes from, where it's been ...
1
vote
1answer
34 views

Reference for $f \in L^{p,\infty} \cap L^{q}$ then $f \in L^r$ for $p < r \leq q$

Okay, so I think I've shown that if $f \in L^{p,\infty} \cap L^{q}$ with $p < q$ then $f \in L^r$ for $p < r \leq q$ where $L^{p, \infty}$ denotes the weak $L^p$ space. what I did was I wrote $$ ...