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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31 views

Congruence numbers

Having read about Stirling numbers of the second kind I am curious. The article says it shows the number of equivalence relations on a set $n$ with $k$ equivalence classes which makes sense to me from ...
-2
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0answers
39 views

Solving Math problems for entrance exams [closed]

Could you please share what are the ways one goes about to solve the problems in various books. I will take an example but this would be true for any book. Arthur Engel's book on problems. I have seen ...
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0answers
16 views

Examples where ostragodsky's method is needed for integrating rational functions

I found out about Ostragodsky's method for integrating rational functions and thought it was pretty cool. However, I have never encountered any examples where it seemed needed (rather than just ...
2
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0answers
51 views

How does one read a formula with subscripts and superscripts?

An expression like $\Gamma_{ij}^k$ seems to be pronounced "gamma sub i, j upper k". Is this a generally accepted usage? Question. Is there a quotable source for such usage? Note that $k$ is not a ...
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0answers
19 views

Combination of certain linear-programming topics new?

I am writing a book on Linear Optimization. Its goal is to present material in a particular form which has not been encountered yet in the literature to the best of my knowledge. I am aiming at the ...
1
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0answers
23 views

Return probability of a SRW in an even number of steps

I am looking for some references for the following problem. Consider a graph $G$ and a simple continuous time random walk $(X_t)_{t\geqslant 0}$ on this graph. Consider the family of events $(e_t)...
5
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1answer
91 views

Ref. Requst: Space of bounded Lipschitz functions is separable if the domain is separable.

I have been scouring the internet for answers for some time and would therefore appreciate a reference or a proof since i'm not able to produce one myself. Let $(\mathcal{X},d)$ be a metric space, ...
0
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0answers
25 views

Fisher information for exponential family: Regularity conditions

for the Fisher-Information to be defined certain regularity conditions have to be fulfilled (like in Lemma 5.3. in Theory of Point Estimation by E.L. Lehmann or on slide 2 here: http://www.stat.nus....
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0answers
10 views

References request: two-queue, one-server model with pre-emptive queue priority and finite buffers

Sorry of the title is a mouthful. I'm developing a queue model with the following characteristics: Two queues: One contains an infinite number of people (Queue A) while the other (Queue B) is ...
0
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1answer
36 views

Good reference for partitions of unity?

I am reading about Sobolev Spaces and regularity theory of PDEs. The partition of unity lemma, as stated in Haim Brezis' Functional Analysis, Sobolev Spaces and Partial Differential Equations, is as ...
2
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0answers
26 views

Introduction to flag manifolds

What is a good self-contained introduction to the geometry of complex flag manifolds?
2
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2answers
73 views

Introductory Topology Book Recommendation for Economics

Would you please share your 2 cent on book recommendation for introductory topology book to graduate student in Economics. Have exposure to the first half of the yearlong analysis course in the ...
-3
votes
1answer
65 views

Help finding an article [closed]

Hello Recently I have been studying algebra and am in search of the following paper : Kac, V. G. Classification of simple $Z$-graded Lie superalgebras and simple Jordan superalgebras. Comm. Algebra 5 ...
2
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1answer
42 views

Uncertainty in a theorem about Sarrus numbers

From https://oeis.org/A001567 there is a theorem of Ray Chandler formulated: An odd composite number $2n + 1$ is in the sequence if and only if multiplicative order of $2\;(\text{mod}(2n+1))$ ...
2
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0answers
51 views

proof of Triangle Removal Lemma

Where can I find a proof of the following version of Triangle Removal Lemma (or any version equal to it)? Let $G(V,E)$ be a graph on $n$ vertices such that it contains $\varepsilon n^3$ triangles, ...
1
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1answer
54 views

Calculus of 1 variable [closed]

What are some good web link or pdf link to understand(self study) calculus of variable intuitively?I am a 12 th grade student with some notions of maxima and minima and some other notions in one ...
1
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0answers
18 views

Books / lecture series on Homotopy theory

I want to read homotopy theory on my own so I want to know prerequisites, good books and if there is any lectures available which can help me. Links are welcome. Till now I have done point-set ...
2
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0answers
51 views

Problem sets on Abstract Algebra

Many times we ask about what books should we read to learn or know more about a math topic (Abstract Algebra, in this case). However, I would like to get a list of the exercises what should we solve ...
1
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1answer
89 views

Hailstone collatz max sequence length upper bound of $260.5+x^{.43}$?

Let the Collatz function be defined as if $x$ even $c(x)=x/2$, if $x$ odd then $c(x)=3x+1$ over the naturals. Each operation is defined as a step. For example $3$ goes $(3,10,5,16,8,4,2,1)$ and takes ...
3
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1answer
56 views

Unsure on which sources to choose related to Calculus

I tried to get into Spivak's Calculus only to find that I've never been taught the type of Math presented there. First chapters talk about the properties of numbers, then mathematical induction, ...
1
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1answer
35 views

I've been working on Spivak and I'm on chapter 7. What are some good books to supplement Spivak for someone beginning to learn pure mathematics.

If I have too much difficulty with a concept/problem, then I'll just press on and solidify my understanding when the concept arises later by going back to it. This seems to be a lucrative method at ...
0
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0answers
14 views

Sheaves of Simplicial Rings?

Could someone provide me a reference for a treatment of sheaves of simplicial commutative rings? As in simplicial sheaves with a ring structure.
0
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0answers
17 views

Mapping cylinder of chain complexes via $-\otimes \Delta$

An instructor gave me a homework set where the mapping cylinder of a chain map $C_\bullet \xrightarrow{f} D_\bullet$ is defined as $(\Delta^1_\bullet \otimes C_\bullet) \oplus_{C_\bullet} D_\bullet$, ...
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0answers
59 views

Cardinallity increasing constructions

If we start with $\mathbb{Z}$ we can through localization get $\mathbb{Q}$, but that has the same cardinallity as $\mathbb{Z}$, so it doesn't increase cardinality for infinite sets, which is what I am ...
1
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1answer
42 views

Comparison of capacity of sets in $\mathbb{R}^n$

This is mainly in reference to this MSE post. Let $B_r \subset \mathbb{R}^n$ denote the ball of radius $r$ centered at the origin. Consider any set $F \subset B_1$. For all sets $\Omega \subset \...
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0answers
22 views

minimum distance of a linear codes

My question is about computing the minimum distance (weight) of a linear code. Assume that we have the generating matrix of the code. Then we can easily compute the weights of each row and of course ...
0
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0answers
28 views

Limit of the commutator of two elements?

Given a Lie group $G$ such the $\mathfrak{g}$ denoted its Lie algebra. Let $[g,g']_{G}$ the commutator of two elements $g,g' \in G$ and denoted by $[X,X']_{\mathfrak{g}}$ the Lie bracket of two ...
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2answers
41 views

Order Theory and Lattice Theory Synonymous?

Is Order Theory the same as Lattice Theory? Can anyone recommend good beginners text book on either?
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0answers
47 views

How to see that diagonal and tranvections matrices generate $GL_n(\mathbb{Z})$?

I'm trying to see how diagonal and transvection matrices generate $GL_n(\mathbb{Z})$. Is there any book that I can find a more detailed description of this problem? Thanks!
0
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0answers
48 views

classification of equilibrium points of 3d systems of ode's

I'm trying to find information about the classification of equilibrium points of 3d systems of differential equations, The qualitative analysis. I wonder if someone could refer me to some book or ...
2
votes
1answer
41 views

Capacity of a set in $\mathbb{R}^n$

The $2$-capacity of a set $\Omega$ sitting inside an open set $V \subset \mathbb{R}^n$ is given by $$\text{cap}_2(\Omega, V) = \inf_{u \in C^\infty_0(V), u|_\Omega \equiv 1} \int_V |\nabla u|^2 dx.$$ ...
2
votes
1answer
36 views

Expected number of duplicates

Suppose I have $m$ bins and throw $n\ll m$ balls into the bins uniformly at random. (In my application $n\sim m/\log m.$) What is the expected number of duplicates? In other words, if there are $k_i$ ...
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0answers
23 views

Implicitization Problem on Graphs?

I learnt the implicitization problem for varieties in introduction course on Algebraic Geometry. I am trying to understand how to formulate a similar implicitization problem on graphs where the ...
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0answers
37 views

Green's formulae, Stokes theorem, Gauss theorem, divergence theorem and Gauss-Green theorem?

I am getting really confused about the Green's formulae, the Divergence theorem and all those related equalities. For example, How is this formula exactly called? $$\int_\Omega \frac{\partial u}{\...
5
votes
1answer
55 views

Partitioning $\mathbb{P}^1(K)$ via the class group

Let $K\subset\mathbb{C}$ be a number field. There is a surjective map $\phi:\mathbb{P}^1(K)\to Cl(K)$ from the field to the class group, sending $[\alpha:\beta]$ to the class of the ideal $(\alpha,\...
0
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0answers
22 views

Any book where Isometric Isomorphisms between Banach Spaces are explained?

When we work in Functional Analysis we usually say things like $(L^p)^*= (L^p)'$ when we want to expres that there exists an isometric isomorphism between these two spaces. All books that deal with ...
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0answers
56 views

What can I do to learn special functions? [closed]

I want to learn special functions but I'm finding the book by Ranjan Roy far too advanced for me. Please help.
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0answers
10 views

Infinite sum of Legendre Polynomials

The infinite sum of a single Legendre Polynomial has a well known expression. Are there any explicit formulas for the infinite sum of the product of two Legendre Polynomials? I'm interested on ...
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0answers
29 views

Coxeter's “Introduction to Geometry” recommendation

What mathematical background does one need for Coxeter's "Introduction to Geometry"? Is the text suitable for self-study?
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0answers
60 views

Surveys in probability? In the current literature sense

I mostly come from an economics background so when I want to find where the current state of knowledge is in specific fields I look for surveys. These are basically primers so that a researcher can be ...
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0answers
32 views

Theorems of euclidean geometry as invariable properties of geometric configurations

Is there some book, or systematic theory, that proves theorems of euclidean geometry by viewing them as invariable properties of certain geometric configurations ? So that from an easy special case, ...
1
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0answers
30 views

Geometry text recommendation (for self-study)

I had taken a first year geometry course over the summer in order to 'skip' it during the school year, and looking back it, I can say that it was one of the worst decisions I've made. Although I did ...
0
votes
1answer
39 views

Book(s) about Affine geometry.

A quick look on Stack Exchange enabled me to discover "Geometry" from Michele Audin which is very close from what I'm expecting but there isn't the correction of the exercices. To be more specific, I'...
2
votes
0answers
12 views

Reference/Literature on Eichler integrals

Has anyone reference or literature advices on Eichler integrals? I want to know what the Eichler integral associated to a modular form is. It should help to understand this, page 65, 4th sentence in ...
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0answers
44 views

What are the prerequsites for this book?

I am considering reading the book Mathematics made Difficult by Carl E Linderholm. PDF: http://i7-dungeon.sourceforge.net/math_hard.pdf . How much math do I need to know in order to benefit from ...
12
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0answers
154 views

How did Hecke come up with Hecke-operators?

I'm currently studying Hecke-operators and I'm curious how Hecke came up with them. The original definition he gave in his paper is $$\left( f \mid T_n\right) (z) = n^{k - 1} \sum_{ad = n, \, b \mod d,...
0
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1answer
47 views

A modern approach to homotopy theory in $\mathbf{SSet}$

I'm currently trying to understand the basics of homotopy theory for simplicial sets. However, my current sources (Peter Mays "Simplicial objects in algebraic topology" and Kans original "on c.s.s. ...
2
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0answers
27 views

Seeking proof to a Hyperbolic polygon conjecture

In the course of writing a(n Honours) thesis, I'm searching for a proof to a conjecture that appears very likely to be true. Many results will rely upon it. My own attempts to prove it have been ...
2
votes
1answer
50 views
+50

Good book on Spherical Trigonometry

Possible approach/content: Modern Practical (Navigation/Geodesy) unifies with Euclidean/Hyperbolic Trigonometry
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1answer
38 views

Book Recommendation Please! [Casella Berger] Statistical Inference

I would appreciate your 2 cent on book recommendation. I have basic exposure to probability theory back in college (e.g. calc, stats, probability undergrad level) but haven't dealt with them for a ...