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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9 views

How to formulate and analyze systems of stochastic differential equations?

I'm having trouble finding reference material on how to deal with systems of stochastic differential equations. Specifically, I'm interested in ecological models. For example, consider the standard ...
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1answer
56 views

Can I ask about copyright here? [closed]

I don't know it is okay if I post about copyright here. If there is any problem, please leave a comment. I will delete this post. Thank you. I am a graduate student studying engineering and ...
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0answers
31 views

An identity for $q-$Fibonacci numbers if $q$ is a root of unity.

In his proof of the Rogers-Ramanujan identities I. Schur introduced two $q-$analogues of the Fibonacci numbers ${F_n}({q})$ and ${G_n}({q})$, which satisfy ${F_0}({q})=0$, ${F_1}({q})=1$ and ...
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1answer
35 views

Bernstein Inequality (wiki correction?!)

I am having trouble with one of the statements made on this wikipedia page, in particular the second Bernstein Inequality on: https://en.wikipedia.org/wiki/Bernstein_inequalities_(probability_theory) ...
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1answer
61 views

Short exact sequences from the Euler sequence.

I was reading an article in which the author said that the sequence $\require{AMScd}$ \begin{CD} 0 @>>>\Omega ^1_{\mathbb{P}^n} @>>> \mathcal{O}_{\mathbb{P}^n}(-1)^{\oplus n} ...
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0answers
30 views

Good problems to do while reading Hardy's book on divergent series?

I am reading Hardy's text on divergent series and to my great dissapointment it has no exercises. I wonder if anybody among you know of some suitable references with problems to read simultaneously ...
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1answer
20 views

Good book on combinatorics for beginners in statistical mechanics

Im studying stat mech and i want to have a better understanding on counting microstates. What book in combinatorics do you guys recommend for beginners like me? Thanks in advance
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1answer
68 views

Does anyone know a book on sketching surfaces?

Is anyone aware of books or sources dedicated to sketching surfaces? Sort of like Forst's An Elementary Treatise on Curve Tracing, but on surfaces; or a book that has a fair few chapters dedicated to ...
2
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2answers
894 views

What does it mean by piecewise smooth boundary?

I will be highly obliged if anyone can give me any reference where i can get the definition of domain (in $\mathbb{R^n}$) with piecewise smooth boundary. My question is when a domain in ...
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1answer
40 views

Good introductory book in geometric probability

I recently came across the proof of the Buffon theorem and I was fascinated by geometric probability. Could someone indicate me a good introductory book? Maybe with many exercises?
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1answer
41 views

Does equivalence of algebraic categories imply bi-interpratibility of their theories?

By an algebraic theory $\mathcal{T}$ I mean any category with finite products such that the objects are given by all finite powers of some object $X$. Let $Alg\mathcal{T}$ be the concrete category of ...
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1answer
36 views

rigorous statistics book recommendations

I am learning statistical inference by myself, I have skim through a few books like Casella Hoggs and I find it omitted lots of details, for example, they didn't introduce the conditional expectation, ...
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1answer
64 views

Errata for Mathematics: Its Content, Methods and Meaning?

I'm new here, so I hope this is the right place to post this! I am currently reading through the Dover edition of the textbook Mathematics: Its Content, Methods and Meaning, by Aleksandrov, ...
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0answers
51 views

Finding a problem book in algebraic topology

I simply need book with problems solved with greatest explanation possible. I know about Hatcher and have a great lecturer, so I do not need theory. I need problems solved in detail.
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0answers
11 views

reference for convex function results

Here is a simple property of a concave function from $\mathbb{R}$ to $\mathbb{R}$, Given $x,x'\in \mathbb{R}$ with $x'>x$, if $\exists \kappa'\in (0,1)$ such that ...
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5answers
874 views

A good book on inverse problems for engineers

I'm looking for a book on inverse problems which is suitable for engineers; both introduction and practical applications are required. Currently I'm looking to Parameter Estimation and Inverse ...
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0answers
20 views

Looking for concrete examples of semigroups, with explicit computations done to help make the theory more understandable.

I would appreciate if someone can help me find a resource which has a bunch of worked out examples showing how to find, for example, the smallest congruence containing a relation on the semi groups, ...
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0answers
33 views

I'm looking for a good book on FOL and set theory.

I finally decided to really learn some axiomatic set theory, at least the basics. I've studied a bit of FOL, but a review would be nice. In short, I'm looking for a book that focuses on $\sf ZFC$ or ...
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1answer
23 views

Sum greater than 1; minimization for non-strict inequalities

I want to show that if $x_k>0$ for $k=1,2,...,n$ and $\sum_{k=1}^n x_k=1$, then $\sum \frac{x_k^2}{y_k}\ge 1$ for any $y_1, y_2,...,y_n>0$ so that $\sum_{k=1}^n y_k=1$. I tried solving the ...
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1answer
52 views

Any good books for Infinite Series?

I wanted to know about some good or even free books on Infinite Series. Being Poor plz tell me books tht are rather cheap but good books.
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0answers
31 views

How useful is Prentice Hall Algebra 2?

I am currently a sophmore in highschool, and I wish to continue learning mathematics over the summer. My school laptop has a copy of Algebra 2 published by Prentice Hall. I have so far been unable to ...
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0answers
40 views

Knot theory and homology

What is the best way to learn about homology in knot theory? I am looking for a introductory book or resource, I dont know any homology, would I need to read a book about this first? If so, which?
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1answer
105 views

Defining homology groups directly from the topology

Both simplicial and singular homology theories rely on 'model objects', simplexes or simplicial complexes, to define the homology groups of a topological space. I was wondering if there is a way to ...
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1answer
77 views

Does “the functions agree at infinity” mean anything?

I want a way to describe how two continuous functions $f,g \colon (X-x) \to Y$ might "share a limit" at the point $x$ when unfortunately neither of $\displaystyle \lim _{y \to x}f(x)$ or ...
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0answers
67 views

Infinitely generated torsion free modules over PID

Let $R$ be a PID and $\mathbf{V}$ a torsion-free $R$-module, not necessarily finitely generated. If I understand it correctly, every rank 1 submodule of $\mathbf{V}$ is isomorphic to a submodule of ...
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0answers
23 views

Brill-Noether theory- reference request

I need some reference, some books or something suitable for a begginer. I found some .pdf's on google, that have interesting introduction, but couldn't find any book.
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2answers
1k views

Joseph Kitchen's Calculus (reference)

I'm asking about one textbook: Kitchen's Calculus. I tried to get a copy in different libraries but nothing. I tried buying it and I cannot find it wherever I've been. I've heard that is an ...
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1answer
24 views

Good reference to study Free Algebras

I am interested in studying free algebras as Free Pre-Lie Algebras, Free Dendriform Algebras etc. But I dont know what a free algebra is in general. I found this definition on Wikipedia but it does ...
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1answer
31 views

Any good books for studying Continued Fraction?

Does anyone have recommendations for cheap books on Continued Fractions? I do not have much money and so it needs to be a cheap book.
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6answers
83 views

What are some good books on algebraic inequalities?

By algebraic inequalities I mean inequalities like Cauchy's inequality, the AM-GM inequality etc. I need it for the International Mathematics Olympiad (IMO), so I hope I can find some books that ...
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1answer
99 views

create interest in Maths to my son [closed]

I hope this is the right place to ask this question : my children are presently studying in Class 8 & Class 4. Elder child studying in Class 8 says he likes Physics, Chemistry, Astronomy but does ...
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0answers
32 views

Some sort of matrix.

How do you call this sort of algebraic entity as: \begin{bmatrix} a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} \end{bmatrix} I mean it's not a matrix as in a $m\times n$ array, ...
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1answer
30 views

Exercise with solution in Algebric topology

Can anyone suggest a collection of (solved) exercises in Algebric topology? Undergrad level, as I want to study on my own and take an exam, I found some lecturenote but I need to see some example or ...
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0answers
19 views

Can you find an interpretation of the following arithmetical function?

For integers $n\geq 1$, taking $k\geq 1$ for $$z_k:=\mu(k)+i,$$ where $\mu(k)$ is the Möbius function and $i=\sqrt{-1}$ the complex imaginay unit, then we define the (real) arithmetical function ...
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0answers
32 views

Recommend guide book of algebraic geometry [duplicate]

I have a little knowledge about geometry and algebraic topology . I want to learn some basic conception and thought of algebraic geometry. Besides , I want to know main of theory of sheaves. What book ...
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0answers
24 views

Analytic solutions

In a book about differential equantions I have read that if the function $f$ in analytic, then a solution of $y'=f(x,y)$ is analytic. Is there a good book that prove this claim?
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9 views

Strong maximum principle for heat equation

Let $M$ be a closed Riemannian manifold. If $u \in H^1(0,T;L^2) \cap L^2(0,T;H^1)$ is a weak solution of $$u_t - \Delta u = f$$ $$u(0) =u_0$$ where $f \in L^2(0,T;L^2)$ with $f(t,x) \geq 0$ a.e. and ...
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1answer
159 views

Name of the class of graphs obtained by deleting $\mathcal{Q}_d$ from $\mathcal{Q}_n$

Let $\mathcal{Q}_n$ denote the $n$-cube graph. I would like to know if there is a name for the class of graphs obtained by deleting a ${\bf single}$ arbitrary copy of $\mathcal{Q}_d$ from ...
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1answer
27 views

What area of statistics deals with such kind of problems?

Consider $2$ samples from the starting normal distribution with parameters $\mu=0, \sigma = 1$ with size $N$. Find the variance of the random variable $\xi$ equal to average sum of $1$st sample - ...
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1answer
19 views

$2$-capacity of a set in $\mathbb{R}^n$

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 $\Omega \subset \mathbb{R}^n$ such that $F \subset \Omega$, define ...
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0answers
48 views

Reference request for Grothendieck's work on “Integration with values in a topological group”

Recently I was reading the available part of the second part of W. Scharlau's book on Alexandre Grothendieck (see here). There I found, An anecdote survives about Grothendieck's arrival in Nancy: ...
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4answers
852 views

Video lectures on Partial Differential Equations

Would anyone happen to know any introductory video lectures / courses on partial differential equations? I have tried to find it without success (I found, however, on ODEs). It does not have to be ...
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0answers
42 views

What's about $\sum_{n=1}^\infty e^{-p_n u}$, where $p_n$ is the nth-prime number?

I am assuming that the following function, for which I am asking as reference request, should be known in the literature, since Glaisher studied the Prime Zeta Function, and my computation is the ...
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0answers
52 views

Convergence of the Euler product

Suppose that the Riemann Hypothesis is true. It is well known that then the Dirichlet series $$\sum_{n=1}^\infty\frac{\mu(n)}{n^s}$$ converges in the half-plane ${\rm {Re}}\, s>\frac{1}{2}$. Does ...
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1answer
37 views

Cohomology groups of a non-degenerate algebraic variety.

Let $X\subset\mathbb{P}^{n}$ be an algebraic variety. Let us suppose that $X$ is non-degenerate (it is not contained in any hyperplane of $\mathbb{P}^{n}$). I have read that (at least for curves) the ...
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0answers
23 views

Very Basic Numerical Methods Book for Freshman students

To cut a long story short; the nature of this degree (it's not a college degree) is such that numerical methods is treated shortly after Calc I (single-var) and linear algebra, but before multi-var ...
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58 views

Capacity vs measure of a set - intuitive understanding

There is a concept of measure of "largeness" of a set, called capacity. The intuition is, instead of physical largeness (measured by Hausdorff or Lebesgue measure), capacity measures how good a given ...
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1answer
81 views

Rings that cannot be representations rings

Given a monoidal category $\mathcal{C}$ one can define the Green ring (or representation ring) $r(\mathcal{C})$ as the abelian group generated by the isomorphism classes $[V]$ of $\mathcal{C}$ modulo ...
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0answers
77 views

How to relearn undergrad and tackle grad mathematics? Want to become a better mathematician!

I am a student who has just completed their degree in pure math. Unfortunately, my undergrad was a very... Unpleasant time for me due to personal reasons. Although math is accepted as a very ...
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3answers
91 views

Help finding specific book

I'm studying Engineering and I'm in my second year, studying Multivariable Calculus, but my University is kind of hard teaching me fresh calculus with topology and analysis, and is kind of hard, so I ...