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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20 views

References on “Measure and Integration: History and Development”

I would like to get references for Measure and Integration", since I want to study the subject from historical perspective. The references could be books, articles or the online resources.
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0answers
18 views

Where can I read about the techniques for computing areas and volumes before calculus?

I've read the following here: The key insight, however, that earned them this credit, was the fundamental theorem of calculus relating differentiation and integration: this rendered obsolete most ...
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3answers
45 views

Bounding a modified Bessel function of the first kind.

Let $I_0$ be the zeroth-order modified Bessel function of the first kind. We know that, asymptotically as $x\to \infty$, $I_0(x) \sim e^x/\sqrt{2\pi x}$. Does anybody have a reference for the maximum ...
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2answers
50 views

Looking for a proof that the diameter of the smallest bounding circle is less than or equal to $\frac{2}{\sqrt{3}}$ times the diameter of the set

This came up while I was attempting to solve an old journal problem. It's not the easiest result to search for so I figured I would ask. Let $E$ be a subset of $\mathbb{R}^2$, then the diameter of ...
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2answers
237 views

What meaning did Riemann assign to $dx$?

Detlef Laugwitz wrote a monumental biography of Riemann. The book was translated into English by Shenitzer. Laugwitz discusses Riemann's fundamental essay Uber die Hypothesen, welche der Geometrie ...
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1answer
43 views

Gromov hyperbolic metric spaces are quasi-convex

I'm aware about the fact stated above, but I'm not able to find some references or proofs besides Gromov's Hyperbolic Groups - Essays in Group Theory. I'll state things precisely. I will consider a ...
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0answers
127 views

Any comments on Lax's “Calculus with Applications, 2e”

There's a new calculus book titled Calculus with Applications by Peter Lax (2nd edition of an old one). I really liked his linear algebra and functional analysis books, and I was wondering if this ...
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0answers
48 views

Any complex analysis book with programming assignment and exercises?

All: I had studied complex analysis long time ago. Now, I would like to review some material, particularly about Analytic function, Riemann zeta and Analytic function. I have been a software ...
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1answer
65 views

Reference-Request: Symmetric Product Schemes

Is there a good reference for the theory of symmetric product schemes? (I only need a few basic things, the construction, etc.) Googling it turned up a lot of papers which use it as if it's common ...
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0answers
32 views

Where can I study the concept of an algebra? [closed]

I am looking for a book about algebras over a field in general. Thanks for the references.
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1answer
8 views

Quadratic Variation of Diffusion Process and Geometric Brownian Motion

I'm looking to find out the stochastic differential equation satisfied by the quadratic variation of Geometric Brownian Motion, Diffusion Process. For example, for a diffusion process that ...
4
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1answer
130 views

Blow Up: Resolution of Singularity

For blow ups, I have worked only in $\mathbb{CP}^2$. Once I locate the base-point, say $[x,y,z]=[0,1,0]$, I go back to $\mathbb{C}^2$ by considering the chart $y=1$. I then proceed to blow up ...
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1answer
2k views

Probability of finding at least k consecutive heads in N coin tosses?

There are quite a few topics on this question already but I couldn't find a well-explained solution. Please point me towards some relevant literature or theory to analyze this problem. $K$ ...
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0answers
56 views

Integrability of 1-forms and Stokes' Theorem

Let $\alpha$ be a $1$-form defined on a manifold $M$ and $\Delta = ker (\alpha)$. The classical theorem of Frobenius says that $\Delta$ is integrable if $\alpha \wedge d\alpha =0$ i.e if $d\alpha$ is ...
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4answers
145 views

A mathematical approach to economics

Are there books or papers where economics is formalized and studied very rigorously? I am very interested in this topic. I would preferably like free online books and/or papers, but that is not ...
1
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1answer
80 views

A tenth grader's starting point on mathematics

This question primarily concerns the elementary books a Canadian high school student could read and work through to gain further insight into mathematics and be attracted to it. My brother, who has ...
3
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1answer
90 views

(translated)Russian mathematics books?

Most russian mathematician(generally) are known to do and teach mathematics in a very original manner,they do in a very intuitive yet rigorous way, with/through wonderful connection to physics. ...
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0answers
17 views

phase portraits of automorphic functions (a la Indra's Pearls)

I would like to make movies of phase portraits of automorphic/kleinian functions with varying traces -- On page 375 of Indra's Pearls there is a phase portrait of an automorphic function/fonction ...
2
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1answer
93 views

Bezout's bound and resultants - reference request

In Terry Tao's blog post about Bezout's inequality, he writes: In our notation*, this theorem states the following: Theorem 1 (Bezout’s theorem) Let $d=m=2$. If $V$ is finite, then it has ...
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1answer
320 views

Bayesian Inference in Measure Theory

What's the deal. How does this work, or can you point me to some references? I tried $\mu(A|B) = \mu(A \cap B) / \mu(B)$ and got stuck on $\mu(B) = 0$. Edit: Sorry for being lazy. My background is ...
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0answers
19 views

Good reference for matrix computation?

I have studied math and I would like to get to know more about matrix computation relatet topics. In particular I am interested in questions of the following kind: eigenvalues perturbed stochastic ...
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0answers
14 views

Looking for specific book/thesis about Ising models

I am looking for a book/thesis I read about Ising models. I'm pretty sure it was done in the 1970 or maybe 1980s, since it was definitely pre-LaTeX (it looked type-written). The book also included ...
4
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1answer
27 views

Generalize logarithmic coincidences

After playing around with logarithms, I've found the following coincidences: $\log_{10}{2} \approx 0.3$, since $2^{10} \approx 10^3$, and $\log_{10}{5} \approx 0.7$, since $5^{1000} \approx ...
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0answers
18 views

Spectral Theory of Differential Operators References?

What are some nice references about spectral theory of differential operators? Some more details: I'm looking for an exposition about linear partial differential operators both with constant and ...
3
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1answer
40 views

Text defining length, area and volume

I am looking for a geometry textbook that axiomatises concepts such as length, area and volume of objects in Euclidean space; for example, the surface area of a 2-sphere in 3-space. Such a text would ...
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2answers
29 views

Logic with finite symbols

What obstructions do you run into if you're trying to develop first order logic when you only have finitely many constant, relation, and function symbols? Are there any cases where you actually need ...
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3answers
78 views

A resource for Trigonometric Inequalities

I'm looking for a good and detailed guide for trigonometric inequalities in pdf if possible. Any recommended resources?
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1answer
66 views

group-like structure texts.

I was reading Dummit and Foote to be ready for my group theory text, but my teacher seems to be paying special attention to things with less structure than groups, for example monoids, semigroups, and ...
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0answers
34 views

References on the relations between Top, Diff and PL

I have heard many times informal statements like "differentiable and pl manifolds are essentially the same for such and such dimensions", but I would like to know what they mean exactly and how such ...
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0answers
26 views

Are there any linkage or transformation between some period transcendental numbers and algebraic irrational numbers?

Are there any linkage or transformation by combination of integral and algebraic function like in the definition of period number between some period transcendental numbers and algebraic irrational ...
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0answers
18 views

What is the definition of period number and any relation between Abelian integral and such a kind of period number

I recall there is a kind of real or complex number called period number which is defined by integral and algebraic function.But now,I search it again and again having gotten no result.Now any one can ...
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0answers
27 views

In regards to metric spaces, does $d^\star$ have an accepted name, or notation? Do any authors use it?

(I write $\omega$ for the set $\{0,1,2,\ldots\}$.) Let $X$ denote a metric space with metric $d$. Define a function $d^{\star} : X^\omega \times X^\omega \rightarrow [0,\infty]^\omega$ by writing ...
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1answer
40 views

What are those functions

what are such functions $$f(x) = \int_{c}^{x} R \left(t, (P(t))^{\frac{1}{n}} \right) \, dt,$$ where $R$ is a rational function of its two arguments, P is a polynomial with no repeated roots, $n \geq ...
5
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1answer
80 views

Category theory for knot theory

Where would I start to learn category theory for its use in knot theory? I have a background in physics and Ive read Adams Knot book. I know nothing about category theory. Eventually I want to learn ...
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1answer
24 views

Books for a beginner (Pseudoconvex Domains)

Can anyone recommend me a book on Pseudoconvex Domains with include definitions, as well as a few examples? I have some course notes on that subject, but it's really abstract and theoretical. I want ...
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0answers
8 views

Reference request: result concerning Leray trace

Let $V$ be a vector space (possibly of infinite dimension). For a linear homomorphism $f\colon V\to V$ define $$N(f)=\bigcup_{n\in\mathbb{N}} \operatorname{ker}(\underbrace{f\circ\ldots\circ ...
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2answers
75 views

Reference Request: Characters of Finite General Linear Groups

I've been looking at J.A. Green's article The Characters of Finite General Linear Groups and it seems that Green in this article comes up with a way of calculating all irreducible characters of a ...
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0answers
24 views

Taking multisets as fundamental

I have heard that it is possible to axiomatize the concept of multisets as a primitive idea. Is there some text where this is actually done?
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0answers
25 views

Examples of elements in the Dirichlet space

By Dirichlet space we mean $\{F\in C_{0}[0,1]:\text{ there exists }f\in L^{2}[0,1]\text{ with }F(t)=\int_0^t f(x) \, dx$, $\forall t\in [0,1]\}$. The more the better. Any famous examples? Using the ...
2
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1answer
45 views

Unit circle can't be covered by one chart

I am hoping that someone can give me a proof showing why the unit circle cannot be covered by one coordinate chart, or a reference where I can find a proof.
2
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0answers
26 views

Research papers of monotone/pseudomonotone operators with applications to PDEs

I have recently been studying how coercive, pseudomonotone operators are used to prove the existence of solutions to elliptic boundary value problems. I have been studying the book "Nonlinear Partial ...
2
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0answers
80 views

K-theory of $\mathbb{RP}^{\infty}$

what are the $K_0$ and $K_1$ group of $\mathbb{RP}^{\infty}$? Any reference would be good enough.
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0answers
34 views

Reference: Fields of characteristic p

I am interested in learning more about fields of characteristic $p\neq 0$. Does anyone know of a good reference that covers the basics of this topic and possibly galois theory over fields of prime ...
1
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1answer
40 views

Generalization for Stirling numbers 2nd kind to negative column-indexes?

The exponential generating functions for the Stirling numbers 2nd kind are the n'th powers of $f(x)=\exp(x)-1$ (where this is understood as formal power series, Abramowitz&Stegun, 26.8.12). ...
2
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1answer
41 views

Global bounded solution of $u_{tt}=\Delta u-mu+h$ in the Hilbert space $X=H_{0}^{1}\left(\Omega\right)\times L^{2}\left(\Omega\right)$

Let $\Omega$ be an open subset of $\mathbb{R^n}$. Consider the linear wave equation $$\begin{cases} \dfrac{\partial^{2}}{\partial t^{2}}u\left(t,x\right)=\Delta ...
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0answers
24 views

Book for asymptotic behavior of an ODE

I want a good book to master the concepts of limit point, equilibrium point, stability (lyapunov, global, local etc.). I am aware of real analysis. Not aware of ODE.
2
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1answer
56 views

Starting with ring theory

Can anyone suggest a book on rings explaining concepts using visual diagrams, similar to the one visual group theory book by Nathan Carter for groups.The problem with me is that after reading that ...
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0answers
10 views

Reading on Laurent Polynomials

I'm interested in reading about Laurent Polynomials. Does anyone know a good resource/book that I can read about Laurent polynomials? Thanks.
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2answers
42 views

Looking for some decent math books and solutions

I am a graduate student in engineering pursuing computational mechanics. I have learned very quickly that the math required to study in this area is very sophisticated and complicated. I need some ...
4
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1answer
446 views

Moment generating functions/ Characteristic functions of $X,Y$ factor implies $X,Y$ independent.

This is solely a reference request. I have heard a few versions of the following theorem: If the joint moment generating function $\mathbb{E}[e^{uX+vY}] = \mathbb{E}[e^{uX}]\mathbb{E}[e^{vY}]$ ...