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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1
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1answer
90 views

Euclidean geometry applied to Ptolemy geocentric model

I'm looking for a good reference on how Ptolemy used the Euclidean geometry to calculate the planets positions.
1
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0answers
74 views

Very challenging series

Find a closed form for $\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^{2^2}}+\frac{1}{2^{2^{2^2}}}+\cdots $ Since I've never encountered this type of series before I was hoping someone here could help me ...
5
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1answer
85 views

Top 10 math mnemonics

If you study undergraduate medicine, mnemonics are almost indispensable - there is so much factual material to learn. I was never given any mnemonics in my time as a maths undegraduate. But Robert ...
0
votes
0answers
15 views

Problem in complexity class $P$ with highest known degree of a polynomial

Can someone help me find source where is listed complexity of most problems in complexity class $P$, particulary, I would like to know the one with the highest degree found so far. Somewhere I found ...
4
votes
4answers
281 views

Reference for Quantum groups

I would like to know if there are any general references that you would suggest to learn about quantum groups? I have looked at some of the "standard" books, but I am wondering if someone is ...
0
votes
0answers
47 views

Classics on abstract algebra and real analysis

I am going through Apostol's calculus volume 1. What a wonderful creation from Apostol. Even I could not imagine that such a book introducing the basic concepts so informally but easy-to-understand ...
0
votes
2answers
25 views

Examples of dynamical systems over various spaces

Let's define a dynamical system as follow : ‎ A dynamical system is a triple‎ ‎$(T, X, ‎\varphi‎) $‎‎ where T is a time set, X is a state space, and‎ ‎$‎\varphi : T ‎\times X ‎‎\rightarrow X ...
44
votes
4answers
5k views

String Theory: What to do?

This is going to be a relatively broad/open-ended question, so I apologize before hand if it is the wrong place to ask this. Anyways, I'm currently a 3rd year undergraduate starting to more seriously ...
0
votes
1answer
47 views

What is a squashed 3-sphere?

I have found the term "squashed 3-sphere" used in the literature but could not locate a precise definition of it. I suppose it is topologically a 3-sphere with a metric different from the round one. ...
1
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1answer
35 views

Non-separable Hilbert spaces in duals

A topological space $X$ satisfies the countable chain condition if every family of pairwise disjoint open sets in $X$ is countable. I am looking for a reference to the following fact: Suppose that ...
3
votes
1answer
63 views

The periods of the Weierstrass function $\wp(z)$

Is it true that the periods $\omega_1$, $\omega_2$ of $\wp(z)$ are $\omega_1 = 4K$ and $\omega_2 = 4iK'$, respectively? Here, $K = K(k)$ is the complete elliptic integral of the first kind, and $K' = ...
0
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0answers
10 views

Reference for this kind of exercice

I would like to know some reference to practice this kind of exercise with solution. Any (good) book or online resources will be fine. Thanks a lot for any help that can be offered. Algebra ...
1
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0answers
24 views

A Couple Formulas in Besse's “Einstein Manifolds”

In Besse's "Einstein Manifolds," Chapter 6D, there are 2 formulas which I am interested in, which apply to compact Riemannian $4$-manifolds: ...
1
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1answer
56 views

Analog of holomorphic Lefschetz fixed point theorem for smooth algebraic varieties

If $X$ is a compact complex manifold and $f: X \to X$ is a holomorphic map with isolated nondegenerate zeroes. Then there is a version of Lefschetz fixed point formula with traces on Dolbeaut ...
1
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0answers
24 views

Locate proof of Second Fundamental Theorem of Asset Pricing

Where can I find a $\textbf{rigorous}$ proof of the Second Fundamental Theorem of Asset Pricing. That is, A market is complete if and only if it has a unique risk neutral measure. Please do not ...
0
votes
0answers
27 views

What is an open property?

From an academic paper, "the existence of elliptic or hyperbolic 2-periodic orbits is an open property". I have never seen the term "open property" used before, moreover the paper gives no ...
1
vote
0answers
11 views

Definiton of invariant curve

What is the definition(s) of an invariant curve? What book should i read to get a better idea of their use in dynamical systems. Are there any defining features i should be aware of especially with ...
1
vote
0answers
33 views

$C^0$ estimate for solutions of the Neumann problem

I am interested in a reference for (or counterexample to!) a particular $C^0$ estimate for solutions of the Laplace equation with Neumann boundary conditions. More precisely, let $(M,g)$ be a smooth, ...
6
votes
0answers
40 views

Who did first use the concept of “supremum”?

Is there one specific person, who first defined the concept of "supremum"? If so: In which work? In my textbooks or by a quick search on the internet, I did not find an answer to my question.
0
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0answers
33 views

Good coding theory books?

Next week starts my coding theory course and i am really looking forward to it. Can anybody suggest me good coding theory books? I've already taken Cryptography class last semester and i studied it ...
1
vote
1answer
19 views

Loop spaces have the homotopy type of a topological groups

Every based loop space has the homotopy type of a topological group. I would like to understand this fact, and this is what this question is about : why is it true, and how does one prove it? I ...
65
votes
29answers
9k views

What is the single most influential book every mathematician should read?

If you could go back in time and tell yourself to read a specific book at the beginning of your career as a mathematician, which book would it be?
2
votes
2answers
219 views

Hypervolume of expanded $n$-simplex

The hypervolume of the expanded $n$-simplex with side $\sqrt{2}$ appears to be $$\displaystyle\frac{\sqrt{\;n+1\;}\;(2n)!}{n!^3}$$ Does anyone know of a published reference to this result? Or can ...
0
votes
1answer
15 views

Poisson Modeling/ Queue Theory - Reference Material

Can anyone reccomend some practical reference material related to building and implementing queueing theory models. using stochastic (prefferably Poisson) processes? We are looking to build out a few ...
1
vote
3answers
84 views

Defining finite unions of intervals with algebraic endpoints on the reals

I'm currently working a bit on Enderton's logic textbook (2nd ed), and, on the second chapter, he marks the following exercise on definability with an asterisk. Let $(\mathbb{R}; +, \cdot)$ be the ...
2
votes
1answer
40 views

Reference request: modern reference for Cantor's theorems of size of algebraic and transcendental numbers?

Cantor showed that the set of algebraic numbers is countable and the set of transcendental numbers is uncountable. Is there any (modern)book with the proof of these theorems?
0
votes
1answer
30 views

How are the essential upper and lower limits defined?

What means \begin{equation} \operatorname*{ess\,lim\,inf}_{x\to x^*} F(x) \end{equation} and \begin{equation} \operatorname*{ess\,lim\,sup}_{x\to x^*} F(x)? \end{equation} Sorry I also do not know in ...
3
votes
0answers
27 views

Is there anywhere some explicit Bruhat decompositions are written down?

Question in title: most places I see Bruhat decompositions treated they're only briefly mentioned and no examples are given. Also, I calculated the following regarding the Bruhat decomposition of ...
1
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0answers
36 views

Where to find current literature, especially dissertations, on complex analysis?

Is there any public website or any other source which classify written master or doctoral thesis classify with respect to their content? Especially, I am going to make some research about complex ...
2
votes
2answers
109 views

Extending a measurable map $f: G \to \mathbb{R}/\mathbb{Z}$ to a continuous group homomorphism

Let $G$ be a compact abelian metrizable group (where the group operation is written as $+$) and $\mu$ is the Haar measure on $G$. Suppose we have a measurable function $f: G \rightarrow ...
2
votes
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. $K$ ...
6
votes
1answer
154 views

Category Theory textbook (learning through guided discovery Dummit and Foote)

sorry for asking the same question in a slightly different angle, I want a book in Category Theory similar to Dummit and Foote's book in Abstract Algebra. I want it to have tons of examples and ...
1
vote
1answer
40 views

How many points does it take to identify a low-order polynomial in $\mathbb{Z}_N$?

I want to split the Bush's Baked Beans recipe into $M$ parts so that any set of $N<M$ people can reconstruct the recipe, but with the following constraints: Each person knows only a yes or no ...
5
votes
6answers
703 views

Dictionaries and resources for translation of mathematical terminology

Nowadays English seems to be the most frequently used language in mathematics. (Although plenty of papers and books are published in other languages, e.g., Russian, French, German and Chinese.) ...
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votes
5answers
1k views

Book/tutorial recommendations: acquiring math-oriented reading proficiency in German

I'm interested in others' suggestions/recommendations for resources to help me acquire reading proficiency (of current math literature, as well as classic math texts) in German. I realize that ...
1
vote
1answer
49 views

$\sin(x)$ is asymptotically equal to $x+5x^3$

Here is my question: I've never seen before this kind of fact underlined about asymptotic equalities (and why we keep only one term in these equalities) and I'm looking for reference. Here is an ...
5
votes
0answers
105 views

Have these (extremely simple) classes of algebraic structures been considered in the literature? If so, what are they called?

Questions. Have the following kinds algebraic structures been considered in the abstract algebra literature etc.? If so, what are they really called? (I have used made-up terminology for the sake ...
1
vote
1answer
57 views

Book for probability theory

I need a good rigorous book to learn probability theory. So far, I've been suggested Gnedenko’s Theory of Probability, Shiyayev’s Probability and Feller’s An Introduction to Probability Theory and ...
3
votes
2answers
106 views

Motivating mathematics(particularly algebraic number theory) through historical problems.

Most mathematical textbooks start a subject by going backwards, historically. They will define the terms that were invented to solve a problem in their polished form and then use these definitions and ...
5
votes
2answers
117 views

There is no norm in $C^\infty ([a,b])$, which makes it a Banach space.

Does anyone knows a reference, which proves the following: Let $a,b\in \mathbb{R}$ with $a<b$. There is no norm in the space $C^\infty([a,b])$, which makes it a Banach space.
56
votes
1answer
3k views

Theorem that von Neumann proved in five minutes.

In "How To Solve It", George Pólya writes: "There was a seminar for advanced students in Zürich that I was teaching and von Neumann was in the class. I came to a certain theorem, and I said it ...
2
votes
0answers
43 views

Reference request for the proof of the Brodskii–Milman fixed point theroem for isometries

Can any one help me to access the paper M.S Brodskii and D.P Milman, On the center of a convex set, Dokl. Akad. Nauk SSSR 59 (1948) 837–840 in Russian? or to prove the theorem If $K$ is a ...
2
votes
0answers
20 views

Books on prime gaps?

I want to have a book on prime gaps, which includes both the theory of prime gaps and all the results obtained. The conditions may be harsh, but I hope I can have some recommendations that fit at ...
3
votes
2answers
82 views

Is there a theory of lie “rings”?

A Lie group is a group that is a differentiable manifold and addition and inversion are differentiable maps. Is there a theory for rings that are differential manifolds and have differentiable ...
1
vote
3answers
107 views

History of category theory

I am searching some information about the origins of the category theory. Anyone know where can I read about those topics? Thanks!
0
votes
1answer
81 views

Who should I ask for Robin's paper? At any rate, I want to find out if a similar result to his can be achieved with 36 instead of 12.

Robin proved unconditionally that for $\ n \ge 3$ , $$ \sigma(n)<\left(e^\gamma+{\log\log12\left({\frac73}-e^\gamma \log\log12\right)\over (\log \log n)^2}\right)n \log \log n. $$ I need a similar ...
2
votes
2answers
105 views

Example of a proof using the axiom of commensurability

I'm teaching our intro to proofs course (well, one of them) and one of the classic illustrations of an overturned "axiom" is the Greek axiom of commensurability, which stated in geometric terms the ...
5
votes
1answer
215 views

A question about a mathematical analysis book

I am a newcomer to Analysis. All knowledge I know about "Analysis" are differentials,limit and integration (basically, what we have been taught in high school) I am studying Principles of ...
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0answers
19 views

Reference for packing-covering of the sphere.

I suspect the following to be true and well known. I am looking for a reference. About the notations: $d$ is the dimension, $S^{d-1}$ is the unit euclidean sphere in $\mathbb{R}^d$, $d(x,y)$ is the ...
0
votes
0answers
17 views

KAM theory in dynamical systems

What is the best text/lecture notes to read if you want to learn KAM theory in Hamiltonian dynamical systems?