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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Examples for intensional set theories.

The normal set theory of todays mathematics (ZFC) is extensional, i.e. it has the axiom of extensionality $$\forall A \, \forall B \, ( \forall X \, (X \in A \iff X \in B) \Rightarrow A = B)$$ Are ...
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1answer
65 views

First usage of the symbol ∈

Concerning a book [1] I am reading the symbol $\in$ was first used by Giuseppe Peano and is the first letter $\epsilon$ (epsilon) of the word ἐστί (means "is"). Does anyone know in which work of Peano ...
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0answers
7 views

Polytopes generated as the convex hull of the orbit of a finite reflection group acting on a given vector

Consider a finite reflection group acting on $\mathbb{R}^N$. Pick a vector $x \in \mathbb{R}^N$ and look at the convex hull of its orbit. This is a polytope. There are some interesting particular ...
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1answer
28 views

Request for online reference to Hamilton's “The Ricci Flow on Surfaces”

Does anyone know of an online source for Richard Hamilton's paper "The Ricci Flow on Surfaces?" I've searched Google for it and it doesn't seem to give any results.
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2answers
23 views

What are the roots of unity quadratic integers?

The article of Roots of unity in wikipedia implies that the following roots of unity are quadratic numbers: $$ \{\pm 1\}, \{\pm 1,\pm i\}, \{\pm 1,\pm \zeta,\pm \zeta^2\}. $$ where $\zeta=\exp(2\pi ...
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0answers
12 views

Got stuck with this $L^2(-1, 1)$ optimization problem. Any ideas where it comes from?

Statement Let $u(x) \in L^2(-1, 1)$. Solve the following optimization problem: $$ \begin{cases} J(u) = 4 \int_{-1}^{1} \sqrt{|x| (1 - |x|)} u(x) dx + \left(\int_{-1}^1 \sin(3\pi x) u(x) dx\right)^2 ...
0
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1answer
17 views

Sylvester domains

I'm an undergrad mathematics student and I'd like to request some books about Sylvester domains. Specifically I'd like to understand the fact that not all modules are Sylvester domains. I just proved ...
1
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1answer
33 views

Primitive elements for $K=\Bbb{Q}(\sqrt{2},\sqrt{3})$

The key lemma for proving the primitive Element Theorem (for finite extension of a field $F$ with characteristic $0$) in Artin's Algebra (2nd edition) is the following: Suppose $char F=0$ and ...
2
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0answers
36 views

A few identities on differential forms

I just started studying differentiable manifolds, and I've encountered a few allegedly simple questions that aren't really simple to me. If possible, I'd be very happy to see full proofs (without ...
0
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0answers
9 views

what does well posdeness results tells us concerning non linear evolution equations?

Consider a nonlinear Shr\"odinger equation, $$iu_{t}+\bigtriangleup u + f(u)= 0, u(0)= u_{0}$$ where $u(t, x)$ is complex valued function of $(t,x) \in \mathbb R \times \mathbb R^{n}$, $i=\sqrt{-1}, ...
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0answers
5 views

deterministic limit of gaussian distribution

Let $a$ be a random variable over some set $A$, and let $\mathcal A \subseteq A$ be an event. Let $\mathcal E \subset \mathbb R^n$ be another event, and let $x_1, \dots, x_n$ be several Gaussian ...
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1answer
81 views

Which textbook of differential geometry will introduce conformal transformation?

Which textbook of differerntial geometry will have these formulas about conformal transformation? $$\tilde g_{ij} = e^{2\varphi}g_{ij}$$ $$\tilde \Gamma^k{}_{ij} = \Gamma^k{}_{ij}+ ...
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0answers
17 views

Basic questions about descriptive complexity

I'm trying to learn descriptive complexity, and I'm having trouble on a basic level wrapping my head around what it means for a logical formula to define a computational language. I've tried and ...
5
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9answers
348 views

Good Textbooks for Real Analysis and Topology.

I'm currently in my 3rd year of my undergrad in Mathematics and moving onto my 4th year next year. I took a course in Real Analysis I, but the professor was very confusing and we didn't use a textbook ...
7
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1answer
85 views

How to learn inequalities and become good at proving them?

I am taking a real analysis course next year and I want to start slowly preparing for that class now, so I hope you can help me. The class is quite challenging and the fail rate is relatively high. ...
0
votes
0answers
18 views

Nonorientable surfaces: genus or demigenus?

The genus $g$ of a closed, orientable surface is the maximum number of disjoint simple closed curves that can be drawn on the surface without disconnecting it. In terms of the Euler characteristic, ...
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0answers
21 views

Video lectures and reference book Multivariable calculus

I am in a particular situation that I am doing Master's in a Computer Science related degree, and I would like to take the course on Convex Optimisation which is taught by the Machine Learning ...
0
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0answers
11 views

Book recommendation for introductory algebraic combinatorics?

Preferably: It should have plenty of motivation (as I am self-learning). It should not be skimpy on proofs (as I am self-learning), but perhaps I can make do since I can ask questions elsewhere. It ...
2
votes
1answer
57 views

Easy to read books on Graph Theory

I was asked to read about Graph Theory. First got the book "Graph Theory with Applications" by Bondy and Murty. As a Computer Science student its becoming difficult to read and understand. Then I ...
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0answers
28 views

Generalizations of results on the sum of divisors function over $\mathbb{Q}$ to number fields

Consider the sum of divisor function $$ \sigma_0(n) = \sum_{d\mid n} 1. $$ This is known to satisfy $\sum_{n\leq x} \sigma_0(n) = (x\log x)+2\gamma x+\mathcal{O}(\sqrt{x})$. If, instead, we shift the ...
2
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1answer
49 views

What sort of algebra is this?

Let us say that I have a set of symbols, $S$. The symbols can be operated on by a set of $n$-ary operators, $O$. Importantly, some of these operators are in the set of symbols, i.e. $S \cap O \neq ...
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0answers
33 views

Enlightening books giving a guided tour of mathematics, in a style that Gian-Carlo Rota would not mind?

I am currently reading Gian-Carlo Rota's Indiscrete Thoughts. What more can I say apart from "the man can write"? (In other words, you should really read it if you are interested in mathematics.) I ...
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5answers
139 views

Book recommendation for Linear algebra.

I am looking for suggestions, it has to be a self study book and should be able to relate to applications to real world problems. If it is more computer science oriented , that would be great.
4
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7answers
463 views

Interesting calculus problem advice [on hold]

Can someone suggest a really hard calculus problem that can be solved with the knowledge of a high school student ? I would really like to work my brains on something interesting . Thanks a lot !
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0answers
24 views

Introductory material on discrepancy theory

I'm interested in learning about discrepancy theory. By this I mean material such as http://math.mit.edu/classes/18.095/lect6/notes.pdf . However, I've been unable to get much from "Chazelle, ...
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0answers
28 views

Nagata Smirnov Metrization Theorem

I am looking for a proof for Nagata-Smirnov Metrization Theorem, but I couldn't find one that is readable. I found the paper by Nagata written in 1954 but it is unreadable and uses old notation. ...
2
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5answers
125 views

Reference Book on Special Functions

Now I'm studying the topic that uses the special functions frequently, so I find myself in need for some good reference book on the properties and equalities of the special functions. The optimal one ...
1
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1answer
17 views

How to solve this problem? Distributed Game theory?

I have this problem: We dispose of some resources, say $\{f_1, f_2, \dotsc, f_m\}$; We have some agents or players, say $\{\mathrm{p}_1, \mathrm{p}_2, \dotsc, \mathrm{p}_n\}$; Every player has some ...
3
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0answers
52 views

Saddle point method: a rigorous proof?

I am trying to prove in a fully rigorous way the Saddle Point method for holomorphic functions of 1 complex variable. In books I find only complicated general statements or non-rigorous proofs. Hence ...
0
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0answers
43 views
+50

Book suggestions on projective geometry

I want to be acquainted with projective geometry, so I'm asking for a reference. I need some words to explain my specific background and motivation. There are many things I learnt related to ...
3
votes
2answers
105 views
+50

A conjecture relating Multiple Zeta Values and the Polya Enumeration Theorem

Let me state my motivation. I believe that the Polya Enumeration Theorem and Multiple Zeta Values (the classic being the Basel problem and the values of the Riemann zeta function at the even ...
0
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1answer
32 views

Recommend resources on dynamical systems and singularities

I'm looking for resources on bifurcation theory and systems of non-linear differential equations, but am very particular about the way it is taught/explained. I would like the approach to be based on ...
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6answers
825 views

Mathematics needed in the study of Quantum Physics

As a 12th grade student , I'm currently acquainted with single variable calculus, algebra, and geometry, obviously on a high school level. I tried taking a Quantum Physics course on coursera.com, but ...
3
votes
2answers
74 views

Can the dimension of the Zariski tangent space of a complex curve at a singular point be arbitrarily big?

Can the dimension of the Zariski tangent space of a complex curve at a singular point be arbitrarily big ? Is there a formula relating the dimension of the Zariski tangent space and the order of ...
0
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0answers
4 views

What are some good introductory textbooks on Sieve Theory?

I fail to find a duplicate. If it exists, please give me the link and close the question accordingly. As the title suggests, I am looking for recommendations on introductory books to Sieve Theory. ...
2
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1answer
24 views

Category , lie algebras …

I want a reference book about Lie algebras that have the definition of universal enveloping algebra by the categorical point of view. All references that i found use the construction by the quotient ...
2
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0answers
25 views

Revise high school material

Can you suggest me a comprehensive book to revise high school mathematics (up to besic calculus)? It should be extremely clear and complete and "scientific" (not like most high school books). Thank ...
3
votes
3answers
53 views

Online pronunciation of mathematicians names

I self study mathematics. Since I don't attend lectures and learn by reading books, it happens frequently that I read names of mathematicians that I am not sure of how they should be pronounced. Is ...
2
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0answers
20 views

Relationship between eigenvalues of differential operator and eigenvalues of its adjoint operator.

I am considering $L\phi = -\triangle \phi + u \cdot \nabla \phi$ and its "adjoint" operator $L^* \phi = -\triangle \phi - \nabla \cdot (\phi u)$ on a bounded domain $\Omega \subseteq \mathbb{R}^n$. ...
0
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1answer
18 views

What are good resources for learning Numerical methods for Partial Differential Equations?

I'm having an undergraduate course on Numerical Solutions to Ordinary and Partial Differential Equations. I need online resources to supplement my study preferably videos and books. I want to build a ...
2
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1answer
35 views

Math literature for teaching kids

If you were going to teach you kids programming and asked me what book to use as a guide, I would recommend you either Java programming for kids or Python for kids. But what if I want to teach kids ...
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1answer
40 views

Is there any prize for proving conjecture on Fermat's prime ?-+

I know this site is for mathematical questions and answer places, but I need a little help from you in some other aspect. I have searched in google but didn't get any satisfactory answer for it. This ...
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0answers
43 views

General question: what happens if we replace the regularity stipulation in GCH with other conditions?

I went to bed last night pondering the following. We can formulate both a weak and a strong generalized continuum hypothesis. GCH0. If $\kappa$ is an infinite cardinal number, then $2^\kappa$ is ...
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0answers
21 views

Markov Chain Ergodic Theorem (Proof references)

Where can I find a proof of the erogidc theorem for Markov chains that doesn't use Birkhoff? The theorem states the following : Let $(X_n)_{n\in \mathbb{N}}$ be an irreducible and positively ...
3
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0answers
19 views

Is there a name for this partial order between metrics?

Suppose we have a set $X$ and two metrics $d_1,d_2$ on it (which may or may not attain $\infty$). Assume furthermore that $d_1,d_2$ have the same metric components (where a metric comoponent is a ...
0
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1answer
11 views

book info needed about game theory

can you suggest me a good book on game theory undergrad/grad course,that may provide insight instead of preaching about computation?it would be better if the works of Neumann & Nash are explicitly ...
0
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0answers
67 views

A book suggestion - Algebraic geometry. (Arf rings and Hilbert functions)

I am studying algebraic geometry and I need to learn Arf rings and Hilbert functions. Please suggest me books / lecture notes... etc that explains this topic in detail. Thank you.
0
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1answer
29 views

Why all games are not Potential?

A definition given in wikipedia of an exact potential game as follow: A game $G=(N,A=A_{1}\times\ldots\times A_{N}, u: A \rightarrow \mathbb{R}^N)$ is: an exact potential game if there is a ...
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0answers
14 views

Original publication of P.A.M. Dirac

For an article I am looking for the original publication of P.A.M. Dirac where he explained the difference between a $2\pi$ and $4\pi$ rotation by using a model with strings. This is sometimes called ...
0
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0answers
54 views

Real Analysis and dynamics

I am looking for a textbook or similar resource that addresses the content in a rigorous graduate course in real analysis(at the level of Rudin/Royden) with the following criteria: No hand waving - ...