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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Normalizer problem for finite Metabelian Groups with abelian sylow 2-subgroup

I am studying Normalizer problem (which states that given an integral group ring $\Bbb{Z}G$, $N_{\cal{U}}(G)=G\frak{z}$ where $\frak{z}$ denotes centre of $\cal{U}$ = $\cal{U}$$(\Bbb{Z}G))$ and I came ...
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0answers
15 views

Learning outcomes of reading textbooks [on hold]

So I've densely mined this site for the scholarly materials I need most. And have prudently written many of them down, so I can sort them if I see fit. But, are the books always the preferred method ...
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2answers
58 views

recommend math books [on hold]

So i completed an year ago my schooling and i am pretty good at maths well at my level and i am very interested in maths and want to learn as much maths as possible and i like stuff like number ...
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0answers
10 views

Source for Space-Time Fourier transform theory

I need to do research on Space-Time Fourier transforms (specifically applications within EM theory). Since the resources for learning this digitally seem to be limited (by my very advanced Google ...
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3answers
47 views

A good companion to Axler's “Linear Algebra Done Right”?

Seeing as Axler is very reluctant to talk about determinants and generally avoids computations and playing around with algebra, I'd like to get a book that will serve as a companion to Axler's ...
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0answers
21 views

Pell's Equation sources

I am researching about Pell's equation and wanted to ask what the best resources are for it? So far I have Stopple's book and Hardy's book.
0
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0answers
37 views

Reference request for a very particular problem solving skill

I want to start with an apology for a very verbose description of my question but if there is a way to cut it down, please let know and I will do so right away. I have been trying to get better at ...
1
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1answer
29 views

Where can I find a proof of the Presentation for Semidirect Products?

I have seen it claimed online that: Given two groups $G = \langle X \mid R \rangle$ and $H = \langle Y \mid S \rangle$ with some action $\theta \colon H \to \text{Aut}(G)$, then $$ G\rtimes_\phi ...
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1answer
41 views

References for information theoretic statistical tools

Strange statistical concepts like spaces of probability distributions, "metrics" like Fisher information or relative entropy, and convergence with respect to these quantities are necessitated in my ...
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5answers
2k views

Proving the existence of a proof without actually giving a proof

In some areas of mathematics it is everyday practice to prove the existence of things by entirely non-constructive arguments that say nothing about the object in question other than it exists, e.g. ...
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1answer
56 views

Are weakly étale ring homomorphisms of finite presentation étale?

Following [Stacks, 092A], say a ring homomorphism $A \to B$ is weakly étale if both $A \to B$ and $B \otimes_A B \to B$ are flat. Question. Are weakly étale ring ...
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1answer
54 views

The eigenvalues of $AB$ and of $BA$ are identical for all square $A$ and $B$ …a different approach

The eigenvalues of $AB$ and of $BA$ are identical for all square $A$ and $B$. I have done the proof in a easy way… If $ABv = λv$, then $B Aw = λw$, where $w = B v$. Thus, as long as $w \neq 0$, it is ...
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2answers
24 views

reference request Schur Zassenhaus Theorem

I am looking for a reference for the Schur Zassenhaus Theorem, saying that any normal Hall subgroup admits a complement. An on-line search show that it is supposed to be in "The theory of groups" by ...
-2
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1answer
47 views

How good is Naive Set Theory by Halmos? [on hold]

I happened to run into this book in an old shop and got it for like half a dollar. Has anyone read this book? Is it worth the time? (Please don't respond things like "every math book is worth the ...
0
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0answers
13 views

Material on Koszul complex

I have tried a lot of books to understand Koszul complex but eventually failed. I have tried Eisenbud's book, Weibel's homological algebra, but I just can not how to construct Koszul complex by tensor ...
0
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0answers
11 views

Infinite series, continued fractions, nested radicals and such - is there a general recursive algorithm theory?

The nature of infinity and irrational numbers (among other things) always gave me trouble. But recently I learned to think about infinite sequences in terms of recursive algorithms and their time ...
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1answer
29 views

Partitioning a convex object without cutting existing convex subsets

$C$ is a convex object in the plane. $D_1,\dots,D_n$ are pairwise-disjoint convex subsets of $C$ such that $D_1\cup\dots\cup D_n \subsetneq C$, like this: Is it always possible to partition $C$ to ...
2
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0answers
15 views

A sufficient condition for factorization in a complete local ring

I think something like the following statement is true, but I don't recall a reference. Suppose $f(x,y)\in k[[x,y]]$ is power series with no constant or linear terms. Then, if the quadratic terms ...
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0answers
42 views

Estimates for the Dedekind number $M(9)$

The Dedekind number $M(n)$ is the number of antichains in the partial order of subsets of $\{1,\dotsc,n\}$. It is only known for $0 \leq n \leq 8$. Question. What are some known upper and lower ...
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1answer
44 views

Using derivatives to get some trigonometric identities

Is there a way of using derivatives to get some trigonometric identities in a straight-forward fashion? I use to forget them, so that would help me a lot... For example, since when we get the ...
2
votes
1answer
54 views

Why is even codimension necessary to apply excision for the Euler characteristic?

In this answer on MathOverflow, it is claimed that $$\chi(X/Z)=\chi(X)-\chi(Z)$$ holds for complex subvarieties $Z$ only because $Z$ has even codimension. It is implied that for $Z$ with odd ...
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1answer
46 views

On groups with presentations $ \langle a,b,c|a^2=b^2=c^2=(ab)^p=(bc)^q=(ca)^r=(abc)^s=1\rangle $…

$$ \langle a,b,c|a^2=b^2=c^2=(ab)^p=(bc)^q=(ca)^r=1\rangle =\Delta(p,q,r) $$ This is a presentation of a triangle group $\Delta(p,q,r)$, a special kind of Coxeter group. What about the following ...
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3answers
110 views

Book on foundational reasoning of standard arithmetics “curriculum”

I am interested in a book that is about arithmetics but the presentation is not just the known to all formulas but the foundational logic behind it. The closest example I can think about is the way ...
10
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0answers
78 views

Category Theory Zoo

There are a few very useful websites when it comes to either finding a specific object with certain properties (and maybe lacking other properties) or finding out which properties a certain object ...
3
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0answers
82 views

Name for categories with a certain property on coproducts

Is there a name for categories with the following property: The category has zero morphisms, coproducts, and for each family $(X_i)_{i \in I}$ of objects the natural map $$\hom(Y,\bigoplus_{i \in I} ...
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0answers
27 views

“Peak lemma” and explicit monotone subsequence

Looking at the proof of Bolzano–Weierstrass theorem, it found an interesting lemma (called the peak lemma here) : Every sequence $(x_n)_{n\in \mathbb{N}}\in \mathbb{R}^\mathbb{N}$ has a monotone ...
0
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1answer
18 views

Asymptotic bounds on sum of primes

Let $p_i$ denote the $i$th prime number, and let $p_k\#$ denote the $k$th primorial, $p_k\# \overset{\textrm{def}}= \prod_{i \le k} p_i$. I am interested in asymptotic upper bounds for the ...
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1answer
27 views

Is the braid category biclosed and bicomplete?

Let $\mathcal{B}$ be the braid category, as in Categories for the Working Mathematician §XI.4 p.262 (objects are natural numbers and morphisms are the braids $n\to n$). Then this can be given a ...
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0answers
9 views

Regarding Smirnov domains

Suppose $G$ is a Smirnov domain that contains infinity in the plane (we can think of it as the exterior to a closed Jordan curve) and $\phi$ is a conformal mapping from $\mathbb{D}$ onto $G$. Can we ...
0
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0answers
21 views

Best resources for learning about regular and context free languages

I would like to train myself when it comes to finding out if a language is regular or context free. I would be grateful for pointing what are the best places/books for training.
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0answers
65 views
+50

Complex Root of Unity Analogue of Forward Difference Operator

In my studies I have come across a couple of operators; in particular; $$\Delta[f(x)]=f(x+1)-f(x)$$ $$\Delta^*[f(x)]=f(x+1)+f(x)$$ $\Delta$ has been called the Forward Difference Operator. I was ...
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0answers
21 views

Reference request for numerical invariants of modules which are not finitely generated

Suppose that $R$ is an integral domain with subring $S$ and that both rings are finitely generated $k$-algebras ($k$ an algebraically closed field). $R$ is integral over $S$ if and only if $R$ is ...
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1answer
50 views

Survey of varieties of non-standard analysis?

Is there a reliable, reasonably up-to-date, survey article doing a "compare and contrast" on varieties of non-standard analysis?
6
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1answer
52 views

Classification of homomorphisms $\mathbb Q \to \mathbb C^\times$

Are there any textbooks which discuss/classify the injective group homomorphisms from $\mathbb Q$ (under addition) into $\mathbb C \setminus \{0\}$ (under multiplication)?
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0answers
14 views

Hamioltonian Circuit of Planar Graph of Order $2^n$

$G$ is a planar graph of order(= number of vertices) $2^n$. Questions: When $G$ has a Hamiltonian Circuit? Is there a polynomial or quasi polynomial time algorithm to decide whether $G$ has a ...
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0answers
54 views

Circle is similar to a polygon with infinite number of sides

It is know from the time of Euclid, that a circle is similar to a polygon with infinite number of sides. But this ^^ is informal. Do you know any formalization where it appears that a circle is a ...
1
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1answer
58 views

Where does the group $\mathbb Z/(a)\oplus \mathbb Z/(a^2)\oplus \cdots $ arise?

Let $a>1$ be an integer, and consider the infinite abelian group $$ V_a=\bigoplus_{j=1}^{\infty}\mathbb Z/{a^j\mathbb Z}. $$ Can anyone provide references to places where this (or related) groups ...
4
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0answers
41 views

Open problems in Lie theory

I been studying lie theory for some time. Beside classification related problems what are some examples of open problems in the lie world? Especifically in the topological/differentiable structure of ...
0
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1answer
15 views

Formula for choosing $x$ elements from a set containing $n$ elements, with repetition allowed

I've been searching around for a formula for the number of cmbinations for choosing $x$ elements from a set containing $n$ elements. For instance, for the set $(1,2,3)$ we have $10$ different ways of ...
1
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0answers
38 views

Is there a formula for the $i$th Chow group $CH_i(X\times\mathbb{P}^n)$?

Is there a formula for the $i$th Chow group $CH_i(X\times\mathbb{P}^n)$ for a variety $X$? I heard there was a formula in one of Fulton's texts, but I've been scouring them and can't find one.
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0answers
24 views

How do I prove shoenflies theorem for $\mathbb{R}^2$?

I studied the contents in Munkres-Topology. In this text, the author uses basic algebraic topology to prove Jordan curve theorem. Then, he wrote that "If $C$ is a simple closed curve in $S^2$, the ...
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4answers
41 views

Introductory text on nets

I have learned point-set topology using filters. Now I do functional analysis where we are using nets to do topological stuff. Therefore I search an introductory text on nets that is suitable for this ...
2
votes
3answers
33 views

Suggestions for readings; Elliptic curves over function fields

I would love to know some good refercences about Elliptic curves over function fields. Especially in view with Mordell-Weil's Theorem. I am already familiar with the main proof of Mordell's theorem in ...
0
votes
1answer
43 views

Can one use the Hilbert-Ackermann Consistency Theorem to prove the consistency of $PRA$?

In his textbook Mathematical Logic, Shoenfield states the Hilbert-Ackermann Consistency Theorem as follows: "Consistency Theorem (Hilbert-Ackermann): An open theory $T$ is inconsistent iff there is ...
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1answer
17 views

Existence of hypergraphs with large parameter values

By a result of Erdös, proved using the probabilistic method, there exist graphs of arbitrarily large chromatic number and girth. What are the corresponding results for hypergraphs (given some ...
3
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2answers
234 views

Resources to understand real world usage of linear algebra

I've learned linear algebra basics at university and really liked it, so I decided to learn it more deeply. Secondly, I want to work in computer science and I think linear algebra knowledge could be ...
3
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1answer
72 views

Lie groups pre-requisites and reference

What are the minimum pre-requisites in analysis (differential geometry) required to study Lie-groups? And for that material, what are some good references? I have done basic courses in Metric spaces, ...
0
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1answer
40 views

Translate this theorem from Endliche Gruppen

In a paper I was doing a reference is given from "Endliche gruppen" by Huppert. I do not understand german and google translator was also not much helpful. Can some translate this theorem or much ...
1
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0answers
62 views

Assigning values to a divergent integral?

Question If I can assign the series of the zeta function to: $$ \zeta(-1) \to 1+2+3+\dots$$ why can't we assign the integral $$ \int_{0}^{\infty} x dx \to 0$$ and it still have some physical ...
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0answers
41 views

Some questions about S.Roman, “Advanced Linear Algebra”

Question for those who have studied Roman's book "Advanced Linear Algebra". How self-contained is this book. Can I study determinants directly from this in context of exterior algebra and tensor ...