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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0
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0answers
11 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
35 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
0answers
28 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
43 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
20 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
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0answers
13 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
4 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!
0
votes
0answers
13 views

Reference for symplectic quotients

Where can I find a good reference to get started on symplectic quotients (also called Marsden–Weinstein quotients)? I have found a couple around, but I wouldn't know which ones are the best ones, and ...
5
votes
3answers
121 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
9 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
33 views

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 ...
6
votes
0answers
50 views

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 ...
1
vote
2answers
51 views

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
25 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 ...
0
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0answers
52 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 ...
0
votes
0answers
11 views

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 ...
2
votes
1answer
16 views

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 ...
2
votes
2answers
134 views

Friends and Enemies of Infinities

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
73 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
34 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 ...
14
votes
7answers
1k 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 [on hold]

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
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1answer
13 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
votes
0answers
17 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
45 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 ...
0
votes
0answers
11 views

Special values of the Dedekind eta function

Does anyone know of an article or a book which contains a comprehensive list of some known explicit values of the Dedekind eta function $\eta(\tau)$?
0
votes
0answers
58 views

Is the notion of “small cardinal” well definable?

When we talk about large cardinals, at least for many of them, we usually isolate a particular property expressing their "relative largeness with respect to cardinals below them". For example being ...
4
votes
0answers
31 views

$\sum_{a^2<p\leq (a+1)^2}p$ Summation of primes

$$\sum_{a^2<p\leq (a+1)^2}p$$ where p is prime. Are there some known bounds for this sum?
1
vote
0answers
20 views

Special values of the classical normalized Eisenstein series

I am looking for a comprehensive list of some known special values of the classical normalized Eisenstein series $E_4(\tau)$ and $E_6(\tau)$. Does anyone know where I can find a table of some known ...
0
votes
0answers
16 views

Minkowski functional application [on hold]

How minkowski functional are applicable in the study of contact angle over irregular surfaces. Please help me by sharing some references if you have.
-4
votes
1answer
67 views

Past Papers Of multivariable calculus OF MIT,Princeton or harvard [on hold]

Does anybody know from where to get the past 10 years of papers finals?
2
votes
1answer
29 views

Generators of $\text{GL}_{2}(\mathbb{Z})$ group, good reference book?

Does anyone know, where I can find a reference (preferably a book) which says that the general linear group $\text{GL}_{2}(\mathbb{Z})$ is generated by the set $$\left\{\begin{bmatrix} ...
3
votes
2answers
58 views

Formal theories dealing with non-commutattive and non-transitive notion of equality

This question is inspired by a philosophical discussion which I don't want to bother you with. As far as I know when we use (or define) the statement "$x$ is equal to $y$" in logic and ordinary ...
1
vote
1answer
41 views

Differential-geometry textbook with solved problems

I'm looking for a textbook in differential geometry which inside has exercises with (at least) final answers. Since it's my first course in differential geometry it doesn't have to cover material (we ...
2
votes
1answer
23 views

Reference for Topological Groups

Topological groups were a topic that were covered minimally at my undergraduate institution but it's a topic that I'm finding a need quite a bit in the number theory I'm reading (class field theory). ...
1
vote
0answers
27 views

Reference request: Galois descent

What is a classic (perhaps even original) reference for Galois descent? I know that it can be seen as a special case of faithfully flat descent (for which FGA and SGA I is the usual reference) and ...
4
votes
2answers
27 views

Conservative Measures under a group action (reference request)

I was reading a paper and the author define the concept of conservative measure: Let $(X,\mathcal{B})$ a measurable space and $G$ a group that acts on $X$ by $$G\times X:(g,x)\mapsto T_g(x)$$ where ...
1
vote
1answer
31 views

Fundamental domains of Dihedral groups

Let $D_n$ be dihedral group of order $2n$, it acts on plane $\mathbb{R}^2$ in a standard way, by rotations and reflections. How one can find fundamental domains for such action?
0
votes
0answers
60 views
+150

Functions $h$ such that $h(x*x') = f(x) * g(x').$

Definition 0. Call a magma $X$ surjective iff the distinguished binary operation of $X$ induces a surjective function $X \times X \rightarrow X$. Now for the main idea: Definition 1. Let: ...
3
votes
0answers
30 views

Sharkovskii's theorem in two dimensions?

Question A weak form of Sharkovskii's theorem in $1$D dynamical systems states that, if a continuous function $f:I\to I$ does not include a periodic point of least period $2$ on $I$, then ...
0
votes
0answers
14 views

Every Hilbert Space has an orthonormal basis [duplicate]

I'd be really grateful if someone could tell me what steps I should take (ie. what books to read) before I can prove the statement in the title. I currently have taken rigorous courses in Linear ...
1
vote
0answers
63 views

(locally) “almost convex” property of the distance function in a general Riemannian manifold

Given two constant-speed geodesics $\gamma_1$ and $\gamma_2$ in an euclidean space $\mathbb E^n$, it is possibile to see that: $$ t \mapsto d(\gamma_1(t), \gamma_2(t)) $$ is a convex function. The ...
1
vote
0answers
38 views

A good (and possibly seminal) book on Multimodal Logic?

I'd like to study Multimodal Logics (in the sense of Catach's Normal Multimodal Logics for instance). Some suggestions? Thank you.
0
votes
0answers
10 views

Superpositions of renewal processes

Consider a small number of independent renewal processes, with their events superposed to create a single point process from the union of their outputs. What techniques could I use to characterise the ...
2
votes
0answers
21 views

Base change is exact for algebraic groups

I need a reference for the following fact: let $1 \to G' \to G \to G'' \to 1$ be a ses of algebraic groups over $S$. Let $S' \to S$ be a base change. Then $1 \to G'_{S'} \to G_{S'} \to G''_{S'} \to ...
-1
votes
0answers
58 views

Do you know of a book about all the rules of mathematics? [closed]

Currently studying mathematics and a book about all the rules of mathematics would really help me. for example: from basic things as negative times negative makes positive, and all the way to advanced ...
6
votes
1answer
140 views

Searching for a thesis.

In several articles about curves, etc, in Minkowski spaces $\Bbb L^3$ and $\Bbb L^4$, there is Walrave, J., Curves and surfaces in Minkowski space. Doctoral Thesis, K.U. Leuven, Fac. of ...
6
votes
0answers
48 views

duality for (co)homology of Lie algebras

Let $R$ be a commutative ring and $\mathfrak{g}$ a Lie $R$-algebra that has an $R$-module basis with $n$ elements. What is the relationship between $H_k(\mathfrak{g};R)$, $H_{n-k}(\mathfrak{g};R)$, ...
1
vote
0answers
33 views

Cohomology and Base Change - Degree 0 Sanity Check

Both Vakil and Hartshorne describe Cohomology and Base Change in the following way: Suppose $f:X \rightarrow Y$ is a projective (in Vakil, proper) morphism of Noetherian schemes, $F$ a coherent ...