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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1answer
16 views

Connections between SDE and PDE

I have encountered a number of situations where the solution of a PDE and a certain expectation associated to a Markov process are equal. Two examples include: The heat equation $u_t = \Delta u$ ...
1
vote
1answer
32 views

How did Fourier series lead to the development of rigorous analysis?

Once I've heard that the studies of Fourier series have lead to rigorous definitions of such concepts as function, convergence, integral, limit. And also that Cantor's study of Fourier series led him ...
4
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0answers
28 views

What's a good text to read before Coxeter's Geometry Revisited?

I am interested in reading Coxeter's famous text Geometry Revisited. It's not clear to me what the prerequisites for this text are, however. I'm sure I have enough mathematical maturity: I know ...
0
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0answers
30 views

Who invented complex geometry?

Same as title: What is the first ever major book on complex geometry in its modern form? (People who string together previous results into one comprehensive work)
0
votes
1answer
16 views

Reference request: functional analysis results used in Taubes paper (1980)

I'm studying Taubes paper 'Arbitrary N-vortex solutions to the first order Ginzburg-Landau equations'. I'm looking for a reference of three following theorems: Let $f(x)$ be a convex funtional ...
3
votes
3answers
49 views

Books that follow axiomatic approach?

What are some maths textbooks that follow the "axiomatic approach"? (I would call it "theorem-proof" approach, but I'm more after books that start from the complete basics in a branch of math) What I ...
3
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2answers
61 views

Formal notion of computational content

In constructive mathematics we often hear expressions such as "extracting computational content from proofs", "the constructivity of mathematics lies in its computational content", "realizability ...
0
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0answers
17 views

What are such pairs of monotone mappings?

Let $P, P'$ be some partial orders and $f$ and $g$ two monotone mappings of type $P \to P'$. Consider the property $g(f(x)) \leq f(x)$, for all $x \in P$. My questions: Have you encountered such ...
1
vote
0answers
18 views

Generating Function for 2-Associated Stirling Numbers of the Second Kind

I am looking for a paper which explicitly defines a power series for 2-associated Stirling Numbers of the Second Kind. The paper defines the generating function as follows: Let $S_2(n,k)=b(n,k)$ be ...
0
votes
1answer
28 views

Need a reference book on stokes theorem other than rudin

As the title suggests, I am looking for a book (other than Rudin's Mathematical Analysis) that covers differential forms, simplexes, chains, stokes theorem. Actually I am not familiar with tensor ...
3
votes
1answer
33 views

question on subgroup of compact group

Suppose $G$ is a compact metrizable abelian group, is it true that $G$ has no finite index subgroups iff $G$ is connected? Any reference or help is appreciated. Thanks in advance! Here are my ...
2
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0answers
24 views

Reference request regarding calculus exam

I'm currently a first year computer science student and I'm deeply interested in calculus . That being said, what we studied so far consists of: Cantor sets, sequences and a brief introduction to ...
0
votes
0answers
25 views

Maturity and Proficiency in calculus, linear algebra for successful research

Will the high level maturity and proficiency in basic calculus, linear algebra (both calculation and theorem aspects) be required or recommended as an important factor to be successful in mathematical ...
1
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0answers
13 views

Multiple regression equation

Can someone please recommend me a good book to understand multiple regression? I need to know how to calculate the equation of multiple regression with two independent variables The one I have does ...
2
votes
0answers
49 views

What is known about$\sum\limits_{p\text{ prime}} \frac{1}{p^2-1}$?

Are there some known results for $\sum\limits_{p\text{ prime}} \dfrac{1}{p^2-1}$? I wasn't able to find anything about this sum in the internet or in my books!
1
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0answers
17 views

Mapping graphs to themselves, e.g. the meta-graph

I'm looking for any prior work on a (for lack of a better word) meta-graph. Let $M=(V,E)$ be a a meta-graph with vertex and edge set $V,E$. The meta-graph is formed by mapping a set of graphs $G = ...
0
votes
0answers
26 views

Translation of an old proof

I have an old paper, Frobenius, G. (1902). Uber primitive Gruppen des Grades n und der Klasse n - 1. S. B. Akad. Berlin 1902, 455-459. in the Germany language. Is their a way to access a translation ...
2
votes
0answers
151 views

How can I have a copy of this old paper? [on hold]

How can I have a copy of this old paper and a translation of it? Frobenius, G. (1902). Uber primitive Gruppen des Grades n und der Klasse n - 1. S. B. Akad. Berlin 1902, 455-459.
1
vote
1answer
27 views

How to calculate $\mathbb{P}[Y\in F|X]_{\omega}$

Here I have an exercise of book: Probability and Measure of PATRICK BILLINGSLEY of conditional probability in the page 442, exercice 33.4 (b): Let $(\Omega, \mathcal{F}, \mathbb{P})$ be a probability ...
1
vote
2answers
37 views

Why is the expected value of $|X|^p$ equal to $p\int_{0}^{\infty}y^{p-1}\mathbb{P}(|X|>y) dy$?

I'm trying to understand a passage from the book: A Basic Course in Probability Theory, Rabi Bhattacharya Edward C. Waymire, in the page 21. The calculation is the following: If $X$ is a random ...
4
votes
2answers
107 views

Are all calculus textbooks “the same”?

I'm not satisfied with my calculus textbook,[1] and because of that I have searched for books by other authors. The problem is: all the books I have taken a look at are almost the same, even the ...
0
votes
1answer
13 views

Any books on Trigonometrical Sums (for the Theory of Numbers )?

All: Can anyone recommend good books on Trigonometrical Sums ? The only book I found is Vinogradov's book: Method of Trigonometrical Sums in the Theory of Numbers. but it is really old. I am ...
1
vote
0answers
23 views

Fundamental solution of Laplacian on manifold

I'm looking for a reference for the result that there exists a fundamental solution for the Laplacian on a flat torus $$\Delta \Gamma(x-y) = \delta(x-y), \quad x,y \in \mathbb T^2.$$ and that, ...
2
votes
1answer
29 views

Other Useful Series Tests

So after taking calculus II, or maybe a first course in analysis, everyone learns a few series tests. They learn 1) Divergence Tests 2) Integral Test (from which we deduce things like $p$-series. ...
4
votes
1answer
69 views

Proof of $p_n<n^2$ by Elementary Means

Is there any proof of the inequality $p_n<n^2$ (for all sufficiently large $n$) by elementary means and without using Prime Number Theorem? I searched in google but in vain. The results that I ...
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0answers
13 views

A formalization of the soft sciences

Branches of physics have been formalized in mathematical language. Have there been texts where the same has been done for chemistry, biology, neuroscience, sociology, and astronomy? I would love to ...
2
votes
1answer
44 views

Convert one proof into another

For a long time I have been investigating this question on my own, but it seems impenetrable. The question is this: To find a method whereby it becomes possible to convert proof A into proof B, where ...
2
votes
1answer
47 views

Fermat solved $x^2+2=y^3$ by infinite descent?

In a letter to Christiaan Huygens entitled "on problems in the theory of numbers: a letter to Christiaan Huygens", Fermat claism that he solved the diophantine $x^2+2=y^3$ using infinite descent. Here ...
4
votes
0answers
64 views

Looking for a paper by Y. Morita

Does someone have access to the following paper? Y. Morita, Elementary proofs of the commutativity of rings satisfying $x^n=x$, Memoirs Def. Acad. Jap. XVIII (1978), 1-23. MR-Link ...
0
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0answers
30 views

Textbooks to complete concurrently - Self learning empowerment

A user is completing some year challenge that takes them through $9$ textbooks and they are alternating in author. Algebra - Cohn Analysis - Rudin Topology - Lee Repeat three times. I would like ...
0
votes
0answers
28 views

A linear algebra textbook that is advanced enough as a prerequisite to read time series and econometric textbook?

A linear algebra textbook that is advanced and comprehensive enough as a prerequisite to read time series by Hamiliton and econometric by Hayashi? If possible, please also answer on which statistics ...
0
votes
0answers
5 views

Exercise needed for weak solution of elliptic equations

I'm trying to find more exercise for weak theorem for 2nd order elliptic PDEs, like the exercise in chapter 6 on Evans's PDE book. Any suggestions other than Evans or Gilbarg-Trudinger? Thx!
5
votes
3answers
128 views

Proof of Nesbitt's Inequality?

I just thought of this proof but I can't seem to get it to work. Let $a,b,c>0$, prove that $$\frac{a}{b+c}+\frac{b}{c+a}+\frac{c}{a+b}\ge \frac{3}{2}$$ Proof: Since the inequality is homogeneous, ...
1
vote
0answers
10 views

Fundamental domain for a $C_2$-action on a Stone space

The following result seems to be true (I can prove it, only quite indirectly): Let $X$ be a Stone space (i.e. a compact totally disconnected Hausdorff space) and $\sigma : X \to X$ be a ...
3
votes
0answers
53 views
+50

Pre-requisites and references for $K3$ surfaces

I would like to know the "roadmap" to study $K3$ surfaces. Perhaps, my background might be helpful: I am an undergraduate student, who knows the basics of Differential Geometry, Topology, Complex ...
1
vote
1answer
25 views

Connections between loops (algebraic structure) and graphs

I would like to know whether there are known constructions which provide a bijection between loops (isomorphism classes) and (possibly directed) graphs. Any reference to a useful paper in this ...
10
votes
1answer
105 views
+50

Value in retracing mathematicians' steps (specifically Galois)?

So I'd like to learn Galois Theory, which I am probably not "qualified" for in an ordinary sense (I've never done abstract algebra, and I'm just now learning linear algebra in my vector calculus ...
3
votes
5answers
116 views
+50

Mathematicians' manual of style

I know that there are many styles to write citations and footnotes and that they are all equally good (as long as the reference is complete), but I would like to know if mathematicians follow some ...
0
votes
1answer
26 views

Reference Request for a book on Field Theory

Please recommend me a book on Field theory which has in-depth proofs and intution would by a plus point. Lately i've been having a hard time with it. Thanks. :) I've tried Basic Algebra by P.M. Cohn ...
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0answers
55 views

Mathematics only with physics? What about biology and chemistry?

In The Mathematical Mechanic, the author "reveals how physics can simplify proofs and lead to quicker solutions and new theorems, and how physical solutions can illustrate why results are true in ways ...
4
votes
0answers
70 views
+50

Concerning the classical normalized Eisenstein series

Earlier I asked this question. As of today, it has not been answered. Yet still, I have a follow-up question: In general, how does one express $E_4(\tau)$ and $E_6(\tau)$ in closed form for special ...
3
votes
1answer
42 views
+50

How to define a taxonomy of non associative operations?

Let $A$ be a set, and let $a,b,c\in A$. Let also $\circ: A\times A\rightarrow A$ be a binary operation on $A$. We agree as usual to write $a\circ b$ to mean $\circ(a,b)$. We say that $\circ$ is ...
1
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2answers
157 views

Friends and Enemies of Infinities [on hold]

Infinity is a dividing line in the community of mathematicians. There is a long standing contest between those who believe in rich theory of infinite mathematics and large infinite numbers and those ...
-1
votes
0answers
75 views

Big list of books that focus on intuitive explanations [on hold]

Sometimes, it happens that I come across books that at times give some intuitive explanations of ideas and concepts. But now I would like to ask if you can make a list of books that focus on giving ...
1
vote
2answers
35 views

Trigonometry textbook or tutorial

Is there an actual textbook or online resource that has a tutorial to solve $a\sin x+b\cos x=c$ for $a, b, c$ being either positive or negative? I tried to find these types of equations/functions in ...
15
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7answers
2k views

Why do we stop at exponentiation stage in arithmetic of natural numbers?

In natural numbers the unary successor operator $S$ is the most natural function which maps each number to the next one. Furthermore we may consider the binary relation $+$ as an iteration of $S$. ...
31
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17answers
2k views

Suggestion for Math Movies [closed]

I am interested in Math movies which inspire and motivate. I know about A Beautiful Mind, Good Will Hunting, and Pi. Are there any others someone can suggest?
1
vote
1answer
15 views

Piecewise homogeneous Poisson process

Is there a name for a Poisson process which is piecewise homogeneous? I.e. time-homogeneous but with a parameter change each increment. Any references appreciated.
0
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0answers
19 views

Numerical method of lines for solving PDEs

Could you please advise some literature about the numerical method of lines (MOL) for parabolic PDEs? It is a method of solving PDEs with discretizing only by space but not by time. A system of ODEs ...
2
votes
0answers
60 views
+50

The math and logic of video games

Is there a paper or text somewhere where someone axiomatizes the concept of video or computer games and makes definitions and proves theorems? I would love to see such a text. It would be quite ...