# Questions tagged [reference-request]

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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### What is Fredholm psuedo-inverse?

Background In 1903, Fredholm invented the concept of pseudo inverse for integral operators, then around half a decade later mathematicians came up with the idea of pseudo inverse for matrix. On the ...
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### Book on sufficient conditions for central limit theorem?

A few years ago, I took an advanced statics course where the Professor explained the the independent and identically distributed conditions are not necessairy for the Central limit theorem to hold. He ...
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### Is $H_m - H_n$ a surjection onto $\mathbb{Q}^+$?

I was wondering whether, for each rational $q$, we may always write $$q = \sum_{k=a}^b \frac 1k$$ For some positive integers $a \leq b$. I get the feeling that this is not true (although an ...
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### sufficient amount of computer science a pure mathematics student would need to know

I am a master’s pure mathematics student. Recently I have been studying just a bit of discrete geometry (e.g. configurations of points) and I seem to be enjoying it in that its ideas are simply ...
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### Textbooks in which determinant is defined as an alternating multilinear map

I'm interested in this abstract definition of determinant, i.e. determinant is defined as an alternating multilinear map. Could you please suggest me some Linear Algebra textbooks that define ...
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### Reference request for ISI Mtech QROR entrance exam

I like to ask you for any references, books, pdf etc. that comprises of a lot problems with the level of this exam. Entire syllabus for MMA(objective one): Analytical Reasoning: Algebra: Arithmetic,...
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### How to utilize the special feature of this recursive problem to reduce computational complexity?

Assume $A$ is a $n \times n$ matrix of non-negative numbers. $A_i$ is the $i$-th row of $A$. $(a_1, \ldots, a_n)$ and $(b_1, \ldots, b_n)$ belong to $\mathbb R_+^n$. $X= [x_1, \ldots, x_n]^\intercal$ ...
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### Linear Algebra Textbook for Reference?

Just want a good linear algebra textbook for reference. I know that there is a lot of good ones, but I am not a mathematician and I don't want anything way too abstract like Axler, Curtis, Hoffman&...
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### Introduction to non linear parabolic differential equations.

I would like to know what the basic references to study non-linear parabolic problems, specifically problems of the type \begin{equation*} \frac{\partial u}{\partial t} - \Delta u = f(x,u), \end{...
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### Reference for $p$-adic Haar integral

I have stumbled upon the notion of a $K$-valued Haar integral on a locally compact group, where $K$ is a non-Archimedean field, as well as the $K$-valued modular function, in an article of Schikhof. ...
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### Textbooks on Stochastic Numerical Analysis

I'm trying to find a nice textbook from which to improve my knowledge on numerical analysis for stochastic differential equations, with a particular focus on intuitive derivations of different ...
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### Any reference(a book) that defines the $n$-dimensional rotation matrix?

I want to refer to a mathematics book that explains the n-dimensional rotation matrix or rotation transformation. Wikipedia concentrates most on 2D or 3D. There are things that one can say definition ...
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### Motivation For Weight Choice In Pooled Variance

In the formula for pooled variance, the estimated variance of each population of size $n_i$ is weighted by $n_i-1$. Is there a good motivation for this? I would assume the formula is always unbiased,...
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### Function field analogy

I am rephrasing the previous question: Can I get good and accessible references to read to understand this particular statement in Wikipedia: "The function field analogy states that almost all ...
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### References for Learning Inverse Limits (for Profinite Groups)

I'm doing some independent study on Profinite Groups this summer and, as I understand it, it is important to be familiar with the notion of an inverse limit before doing so. The trouble for me is that ...
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### Why are the $p$-oldforms $f(z)$ and $f(pz)$ linearly independent at level $\Gamma_0(pN)$?

Let $f$ be a newform (normalized eigenform) of weight $k$ and level $\Gamma_0(N)$. Fix $p$ not dividing $N$ and set $f_p(z)=f(pz)$. Viewing $f$ and $f_p$ at level $\Gamma_0(pN)$, why are they ...
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### Proof of the classifying space cohomology isomorphism for local coefficients

There are many references which will show that for (say) a finite discrete group $G$, you can construct the classifying space $BG$ which $G$ as its fundamental group and the same cohomology groups, ...
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### Reducing the strength of a category theoretic proof

The motivation for this question is the following: Say we have a formula $\phi$ in peano arithmetic, and we have proof $\pi$ of $\phi$ using possibly higher order arithmetic or category theory (that ...
### Approximating $t\to f(t) = \sqrt{t}$ by polynomial and bitwise refinement, how fast will it be?
Say that we want to approximate the function $$t\to f(t) = \sqrt{t}$$ on the interval $t\in [0,1]$. We know that polynomial approximation close to $0$ is very bad so we want to avoid that. Instead ...