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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12 views

Harold Jacob's Geometry Vs. Jo Greig's Tutor in a Book's Geometry?

I was wondering which one of these books would you highly recommend, or if there are better suggestions....a book with profs and number problems? I took Essentials of Geometry (in my Community ...
4
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1answer
52 views

Rigorous mathematical treatments of engineering topics

I started out as an engineering student and got interested in mathematics. So after some point (Rigorous analysis and linear algebra, some real analysis, basic measure theory and topology etc.) I ...
6
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1answer
63 views

Derivation of Schrödinger's equation

I recall a famous quote of the late physicist Richard Feynman: Where did we get that from? It's not possible to derive it from anything you know. It came out of the mind of Schrödinger. This ...
3
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0answers
19 views

Where can I find some articles of Weil.

Where can I find the articles of Weil: Variétés abéliennes et courbes algébriques Sur les courbes algébriques et les variétés qui s'en déduisent. on Internet?
0
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1answer
24 views

Restriction of an operator on a Banach space

Let $X$ be a Banach space and $A:D(A)\to X$ be an unbounded linear operator such that for all $\lambda>c$ ($c$ some constant), $(\lambda I-A)^{-1}$ exists and is a bounded operator which satisfies: ...
1
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1answer
71 views

Measure Theory Book

What book should I use for measure theory?I have solved Rudin's Principle Of mathematical analysis up to chapter 7.Some people advised me to use Real and complex analysis by Rudin, while other said it ...
1
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0answers
28 views

When is every open set a $F_\sigma$?

My question concerns the $F_\sigma$ property of a topological space $X$. I want to know if there is a particular name for those spaces in which every open set is $F_\sigma$. Moreover, if $X$ is a ...
2
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0answers
22 views

Have any authors suggested mathematics-wide prefixes for “missing a quotient” and/or “missing an identity”?

The prefixes in the following terms both mean: "missing the obvious quotient by the obvious equivalence relation." seminorm pseudometric Similarly, the prefixes in the following terms both mean: ...
2
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0answers
22 views

Properties shared by equivalent norms.

I am interested in knowing about "geometric" properties shared by equivalent norms on a Banach space. Here I mean "geometric" as opposed to topological, and probably in particular with reference to ...
2
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0answers
49 views

Interesting examples of switching limit and integral

We learn many theorems regarding the relationship of limit and integral (Dominated/ Monotone Convergence, Fatou, Semicontinuity of norms, etc...). As I'm working on my research, I find that I often ...
3
votes
1answer
23 views

Regularity for a parabolic problem with nonsmooth coefficients

I'm looking for references on the regularity of the (weak) solution to the parabolic problem with nonsmooth coefficients. In most literature, like Evans, the coefficients are often assumed to be ...
0
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0answers
24 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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0answers
21 views

Finite Blaschke product [on hold]

I want to do my research in Finite Blaschke products. Also, I want to enter graduate school in the US. I'm a final year mathematics student in Sri Lanka.
1
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1answer
27 views

Characterization of solvable groups in terms of subgroups of certain orders?

In this question, the OP mentions the following result: a finite group $G$ is solvable if and only if $$\text{for all $n$ dividing $|G|$ such that $\gcd(\frac{|G|}{n},n)=1$, $G$ has a subroup order ...
0
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0answers
49 views

Alternatives to the notation $\|x\|$ for the norm of $x$?

For aesthetic reasons, I don't like the notation $\|x\|$ for the norm of $x$. Have any alternatives been proposed?
0
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0answers
14 views

Reference for p-capacitary functions

Consider $\Omega_1 $ and $\Omega_2$ two open bounded and convex sets in $R^n$with $\Omega_1 \supset \overline{\Omega}_2$. The unique weak solution of the problem $$ \begin{cases} \Delta_p u = 0 ...
1
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1answer
60 views

Is $\{1,1,2,3,4,5,\cdots,i,\cdots \} $ the simple continued fraction algebraic or transcendental?

Is $$1+\cfrac{1}{1+\cfrac{1}{2+\cdots}} $$ or$\{1,1,2,3,4,5,\cdots,i,\cdots \} , i\in \mathbb{N}$ the simple continued fraction algebraic or transcendental? Any reference is appreciated EDIT and ...
3
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0answers
38 views

Best algebra text for Model Theory

I'm looking for an algebra book that is tailored towards some of the ideas in Model Theory, I'm currently slogging through Hodges' Model Theory. I'm a bit rusty with my algebra and was curious if ...
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0answers
26 views

A book on analytic geometry

It's easy to find good recommendation for books here for any subject other than analytic geometry ,therefore I'd like to ask for any suggestion of analytic geometry books ,the only charactrestic I'm ...
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1answer
30 views

Books to get started on mathematics

I'm studying grammar and I feel a based mathematics would help me. What you recommend to start considering I'm not familiar with well developed therms and etc?
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0answers
28 views

A reference on Kodaira-Spencer deformation theory

I am looking for an introduction to Kodaira-Spencer deformation theory. I have a background in Teichmüller theory, but I know almost nothing of (and am not so interested in) algebraic geometry. Do ...
0
votes
1answer
20 views

Any upper bound for $a_i$ in $\gamma =\{a_0,a_1,\dots,a_i,\dots\}$ the simple continued fraction expansion of real positive algebraic numbers?

Are there any upper bound for $a_i$ in $\gamma =\{a_0,a_1,\dots,a_i,\dots\}$ the simple continued fraction expansion of real positive algebraic numbers?
1
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1answer
29 views

Localization of the Integer Ring

Let $\mathbb{Z}$ be the ring of integers and let $p$ be a prime, then the $p$-localization of $\mathbb{Z}$ is defined as $\mathbb{Z}_{(p)}=\{\displaystyle\frac{a}{b}|a,b\in\mathbb{Z},p\nmid b\}$. I ...
0
votes
1answer
25 views

Reference request: About Weil book

In "Standard conjectures on algebraic cycles" of Grothendieck and "Algebraic cycles and the Weil conjectures" of Kleiman they say in their references: A. Weil: Variétés Kählériennes, Hermann, ...
4
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0answers
57 views

Are multi-valued functions a rigorous concept or simply a conversational shorthand?

In Brown and Churchill's book, the concept of multivalued functions is not discussed in a very rigorous way (if at all). But I can see that branch cuts have importance in complex analysis, so I want ...
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0answers
49 views

Are there axiomatizations of first order logic or set theory defined in first order logic or set theory?

There are several axiomatizations for number theory, group theory, and other theories represented in first order logic. Further, these theories are also representable in set theory such as $\sf ZFC$ ...
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0answers
10 views

Is every frame homomorphism induced by a measurable function?

Let $M$ be the Lebesgue measure algebra of the unit interval $[0,1]$, i.e. equivalence classes of Lebesgue measurable sets modulo sets of measure $0$. This is a complete Boolean algebra, hence in ...
1
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1answer
39 views

Clustering analysis of a weighted graph

My data consists of a large weighted undirected graph of $n$ nodes. I need to group the nodes into $m$ clusters ($m < n$), such that nodes in a cluster are connected with heavy weights. What ...
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0answers
23 views

Positive definite functions generated by irreducible representations — what do people call them?

Let $G$ be a group and $\pi:G\to B(H)$ be its irreducible unitary representation (one can endow $G$ with topology and claim that $\pi$ is continuous in some sense, this doesn't matter). For a given ...
0
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0answers
25 views

Di Perna-Lions theory

I'm reading the paper of Di Perna and Lions "Ordinary differential equations, transport theory and Sobolev spaces". I'm not understanding the proof of corollary II.2; in particular I don't understand ...
-1
votes
1answer
34 views

Counterexamples in measure theory

Can you suggest me a book which primarily deals with counter-examples in measure theory? Thank You in advance!
5
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0answers
36 views

Reference for the fact that a smooth function analytic on every line is itself analytic

Let $f \in \mathcal C^\infty(\mathbb R^p)$ ($p \geq 2$) be a smooth function such that the functions $g_d(t) := f(td)$ are all analytic for all $t \in \mathbb R$ and all $d \in \mathbb R^p.$ (i.e. $f$ ...
1
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1answer
27 views

Absolute value of a cubic Gauss sum (over Field $\mathbb{F}_p$ )

I'm interested in the quantity $|\sum_{x \in \mathbb{F}_p} \omega^{ax^3+bx^2+cx}|$ where $a \in \mathbb{F}_p^*,b,c \in \mathbb{F}_p$ and $\omega$ is a primitive $p$-th root of unity i.e. ...
3
votes
1answer
58 views

Integral of products of cosines

Given $m+1$ integers $\alpha_0,\ldots,\alpha_m\geq 1$, I was trying to get a nice closed formula for the integral $$ \int_0^\pi\cos(\alpha_1\theta)\cdots\cos(\alpha_m\theta)d\theta. $$ More precisely, ...
4
votes
2answers
55 views

module over a quotient of a principal ideal domain

The Statement I suspect the following proposition is well known, but I found no reference. Proposition If $A$ is a principal ideal domain, if $I$ is a nonzero ideal of $A$, and if $M$ is an ...
1
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1answer
29 views

winding number in several complex variables

Is there any analogue of the concept of winding numbers in the theory of several complex variables? If so, can anyone provide me references for studying it?
1
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0answers
11 views

What to study to learn descriptive complexity?

I have an assignment to study the descriptive complexity of a given device that is described with some algebra and informal statements. I have a background in computer engineering but I haven't ...
-1
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1answer
73 views

mathematics books written in French and not yet translated in English [closed]

Could you suggest any good mathematics books written in French and not yet translated in English?
1
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1answer
45 views

Name for the embedding property

There is an exercise in Burris and Sankappanavar's "A Course in Universal Algebra": Problem: Find two algebras $\mathbf{A}_1$, $\mathbf{A}_2$ such that neither can be embedded in $\mathbf{A}_1 \times ...
3
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0answers
30 views

Arithmetic properties of the partition function

Ramanujan mentioned in his paper in 1920 that "it appears that there are no equally simple properties for any moduli involving primes other than these three" $p(5n+4)\equiv0 \mod 5$ $p(7n+5)\equiv0 ...
4
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1answer
57 views

Where can I find the proof of this Ramanujan result?

I'm searching for a proof of one impressive Ramanujan result. Not one in particular, the only request I have is to be really impressive. For example $$ ...
-5
votes
1answer
55 views

Attitude toward risk taking and the exponential utility function [closed]

I want to know some reference/book on the following topic: "Attitude toward risk taking and the exponential utility function". Thanks in advance.
1
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3answers
64 views

May directed graph be embedded into manifold?

May directed graph be embedded into manifold?How ?and what is the condition?
4
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2answers
225 views

Is there any similar math limerick?

I found this one $$\frac{(12+144+20)+\left(3 \cdot \sqrt{4}\right)}{7}+(5 \cdot 11)=9^2+0.$$ Which is : ...
3
votes
1answer
171 views

Mathematician who talked about the probability of a “good” graph?

In my undergraduate years, one of my professors always talked about this one mathematician who was talking about "good" graphs and wondered about the existence of such a graph. Apparently this ...
3
votes
0answers
127 views
+50

Video lectures of algebraic geometry (Hartshorne, Shafarevich, … )

I am a commutative algebra student. I wonder if there is some video lectures of algebraic geometry courses available online for free? I'd like the lectures to cover main topics of the books ...
2
votes
0answers
18 views

Reference for Envelope, Evolute and involute

I have to give a lecture on Envelopes, Evolute and Involute to I year undergraduate students. Please suggest me some books which explain these concepts with examples geometrically. Already I have seen ...
2
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1answer
38 views

Definition of the shapes of the English letters

Has anyone ever defined the precise shapes of the upper and lowercase letters of the English alphabet in a precise, mathematical, geometric way? For instance, the letter "A" could be defined as two ...
1
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2answers
68 views

Books that integrate physical reasoning with mathematical reasoning? mathematicians?

As the title says, can anyone help me to find any book that shows how physical reasoning using concepts from classical/quantum mechanics and physics in general can enlighten us about mathematical ...
10
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2answers
162 views

Applications of Algebra in Physics

Often I have heard about the link between Algebra (in particular Representations of Groups and Algebras) and some "indefinite" field of Physics. I have a good preparation in Algebra and ...