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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3
votes
1answer
39 views

Are there books introducing to Complex Analysis for people with algebraic background?

I'm a third year student who is mostly interested in commutative algebra. In Algebraic Geometry a lot of example come from Complex Analysis. So to deepen my understanding/intuition, I'll finally ...
0
votes
1answer
12 views

Interior ball condition in $C^2$ domains

Why a $C^2$ domain satisfies the interior ball condition? I accept a reference too. Thank you.
1
vote
0answers
15 views

doubt about definition of holomorphic polynomials

In a topic of several complex variable theory (in particular functions on $\mathbb{C}^2$), I came across a term homogeneous holomorphoic polynomial. By the word, I think it is a polynomial in complex ...
2
votes
1answer
49 views

Good book for general topology [duplicate]

I want a book in general topology with many interesting and hard exercises. I mean a book with topics the same as Munkres but with challenging questions to improve my problem solving ability.
0
votes
0answers
14 views

Is there a good introductory complex-analysis text in general setting, namely Riemann sphere?

I have studied first 1~3 chapters of some complex analysis texts (Ahlfors, Conway, Silverman) Well, i specially like Ahlfors in many ways but this text doesn't seem to develop a theory in a general ...
6
votes
6answers
356 views

Book on combinatorial identities

Do you know any good book that deals extensively with identities obtained using combinatorial and/or probabilistic arguments (e.g., by solving the same combinatorial or probability problem in two ...
3
votes
2answers
35 views

Non-empty intersection between a compact and an unbounded connected subset of $\mathbb{R}^d$

I am quoting from MathOverflow, where I have just read it as part of a comment: "If $C$ and $S$ are, resp., a compact and a connected unbounded subset of $\mathbb{R}^d$ such that $C\cap S \ne ...
1
vote
0answers
18 views

Conjugating an operator with a gauge transformation; how is the kernel affected.

For the differential operator $$ D := i I \frac{d}{dx} + A(x) \colon C^\infty_T([0,\beta]),\mathbb{C}^m) \to C^\infty_T ([0,\beta],\mathbb{C}^m) $$ where $A(x)$ is Hermitian and $C^\infty_T ...
0
votes
1answer
31 views

Reference for introductory Lie Groups

I am currently learning about Lie groups,So kindly suggest a reference for Lie groups, which contains lecture on Manifolds as well.
0
votes
0answers
33 views

Reference request: An example of a false conjecture with a very large number as the first counter example

I recall that there was some conjecture, something that I believe involved prime numbers, and was believed to be true (as it was checked up to a relatively large number) until a counter example was ...
2
votes
2answers
47 views

Relationship between mathematics and music

I have a strong mathematical background and I am interested in the relationship between mathematics and music. I have found some introductory material on the web. Do you know any good books that will ...
1
vote
5answers
57 views

Why if $aX+c=bX+d$ then $a=b$ and $c=d$?

There is theorem in linear algebra. I forgot it!! But I remember something from it. Can you please give me a reference? It is related to something like this. If I have two polynomials ...
1
vote
3answers
37 views

Good book for mathematical modeling

Could you recommend/suggest a good book about mathematical modeling (Not advanced) with examples about classical mechanics, dynamics, aerodynamics, chemistry, electronics and etc?
3
votes
2answers
63 views

Universe enlargement and modal logic

In model theory and category theory, we often need to "enlarge" our universe (whatever that means) so that our proper classes become "small" and we can thereby manipulate them in more sophisticated ...
3
votes
1answer
51 views

Geometry textbook

I am planning to take a graduate Geometry course next semester. The preliminary syllabus does not specify any textbook but has the following descriptions: Catalog Course Description: This course ...
2
votes
1answer
105 views

Characterizing a certain set of matrices arising from binary trees

Suppose I have a binary tree, like v1 v4 \ / -------- / \ v2 v3 I can write a matrix for this tree whose $(i,j)$th ...
1
vote
0answers
32 views

Finding the $\log$ of a matrix by contour integration

My teacher presented this way of determining the logarithm of a matrix $\Omega$ in class today: $$\log \Omega = \frac1{2\pi i}\oint_{\Gamma} (\zeta I - \Omega)^{-1} \log \zeta \,d\zeta.$$ Does ...
1
vote
2answers
113 views

Recommendation for Number Theory Textbook

. Greetings, every mathematicians! I'm a foreigner (meaning English is not my first language) and an undergraduate student. I'm currently studying linear algebra, set theory and have already studied ...
0
votes
0answers
24 views

Measure Theory vs. Decision Theory - problem classification

I am having trouble classifying my problem, and I am seeking some guidance on book advice. I don't know if I have measure-theory problem and/or a decision-theory problem (or other field). I want to ...
0
votes
1answer
36 views

Recommend Fourier Analysis Workbook or online examples

I am studying a graduate level course in Fourier Analysis, however my Functional Analysis background is extremely weak, I have also never met Lebesgue Integration and it has been a while since I ...
0
votes
1answer
30 views

Overview of game theory

I have a good high school math background, and I am interested in game theory, so I wanted to know something more about it, but I found very technical things or wikipedia. I am looking for something ...
0
votes
0answers
39 views

Ring $R$ as $R[x]$-module

My professor mentioned some interesting examples of modules, giving as an example the following two: $R$ as an $R[x]$-module, in which multiplication by $x$ was taken to be evaluation under a fixed ...
1
vote
1answer
30 views

What do I need to know to understand Lam's Serre's Problem on projective modules

What do I need to know to understand this book: Lam's Serre's Problem on projective modules? I've already read Hungerford's book and Atiyah and Macdonald's book, however when I started to read the ...
3
votes
4answers
87 views

Is there a shorter path to these results?

I'm a student of Physics, however I usually study mathematics on texts aimed at mathematicians to gain a deeper understanding. Currently I'm studying differential geometry on Spivak's book and one of ...
10
votes
3answers
150 views

Computing $\int_0^\pi \sin(x) \; dx$ using the definition.

A colleague of mine and I, in the course of teaching integral calculus for the umpteenth time, were wondering if we could expand the class of examples that our students are exposed to when computing ...
1
vote
0answers
24 views

Automorphism group of a bipartite regular graph

Showing an automorphism group of complete bipartite graph $K_{n,m}$ is easy. I'm wondering if there is an classification of automorphism groups of bipartite regular graphs. Did anyone heard something ...
2
votes
0answers
29 views

History of Morse theory.

How can I get good references which give many information about history of Morse theory? Now I am interested in how and who found that Hessian have a lot of data. Thank you for your helping!!
4
votes
2answers
67 views

Works on Calculus by Newton and Leibniz (primary sources)

I'm trying to find PDFs or hard copies of the following works from the dawn of calculus. Does anyone know where I could find English translations of them? Newton - De analysi per aequationes numero ...
1
vote
0answers
26 views

Reference needed for the following sobolev inequalties

I'm reading a paper and the authors applied the following sobolev type estimates $$ ||(Dv)^{2}||_{H^{3k-2}(\Omega)}\leq C||v||_{H^{3k-1+\alpha}(\Omega)}^{2} $$ for $\alpha>\frac{1}{4}$, where $v$ ...
0
votes
0answers
19 views

How we compute expectation of a singular random variable?

In probability (or measure) courses, we often see the Cantor distribution that is singular with respect to the Lebesgue measure. Its CDF is increasing but whenever its differentiable, the ...
1
vote
0answers
23 views

Smoothness of solutions to Fredholm integral equation

Let $K(x,y)=k(|x-y|)$ where $k$ is continuous on $(0,1]$, and assume function $f\in L^2[0,1]$ satisfies $f(x)=\int_0^1 f(y)K(x,y)dy$. Is $f$ necessarily $C^\infty $ ? under what condition on kernel ...
0
votes
1answer
56 views

Book for advanced homological algebra

I already read the books: 1.- An introduction to homological algebra - Rotman (the two versions of it) 2.- An introduction to homological algebra - Weibel 3.- A course on homological algebra - ...
1
vote
0answers
40 views

coalgebra/algebra of the identity endfunctor

Let $\mathbb{C}$ be a small/locally small category and let $T:\mathbb{C} \to \mathbb{C}$ be an endofunctor. One can then have $T$-algebras and $T$-coalgebras in the usual way: for $X,Y \in ...
3
votes
3answers
80 views

From groups to groupoids.

Let $\mathcal{G}$ be a groupoid and $p$ an object in $\mathcal{G}.$ It is well known that the set ${\rm Mor}_{\mathcal{G}}(p,p)$ is a group. I would like to know if there is a way to recognize a ...
0
votes
0answers
14 views

Classification of second order PDE

I am trying to understand the classification of second order PDE's from this article. In page 45, line 1 can somebody please explain to me how $\partial^2U \over {\partial x_i\partial x_j} $ was ...
2
votes
1answer
75 views

Book to prepare for university math?

Can you suggest some books to prepare for university math?
1
vote
0answers
37 views

Books explaining differentiation under the integral sign

I've heard that this is a great tool to have in you math toolkit, but I cannot comprehend this method just from the wiki entry and 2 page pdf files. I'm looking for a book which has problems ...
0
votes
1answer
31 views

Reference about the Conley index thoery

I'm reading "Isolated invariant sets and the Morse index" by Charles Conley.But I'm lost in some of the concise description or definition.Could you recommend me some references or textbooks for the ...
3
votes
0answers
61 views

On the weak convergence in reflexive Banach space

Consider the following proposition: Proposition 1. Let $X$ be a reflexive Banach space and suppose that $\{x_n\}$ is a sequence in $X$ that is bounded and has at most one weakly sequentially cluster ...
0
votes
0answers
17 views

Reference for elliptic regularity for $-\triangle \phi + u \cdot \nabla\phi=f$ under minimal assumptions

I have a distributional solution to $-\triangle \phi + u \cdot \nabla \phi= f$ in $U \subseteq \mathbb{R}^n$ and $\phi=0$ on $\partial U$. I have that $U$ is open, bounded, connected, ...
1
vote
4answers
96 views

Nice book on geometry to gift an undergraduate in mathematics

I would like some suggestions on a nice book on geometry to gift an undergraduate. I'm not searching for something that is common: I need something new and exciting. Suggestions?
7
votes
1answer
123 views

What is the Coxeter diagram for?

I understand that Coxeter diagrams are supposed to communicate something about the structure of symmetry groups of polyhedra, but I am baffled about what that something is, or why the Coxeter ...
0
votes
0answers
14 views

algorithm for traversing a fractal in a “maximally ordered” way

consider a multidimensional fractal that can be "traversed" in an arbitrary order. is there an algorithm for traversing a fractal in a "maximally ordered" way? in other words the algorithm has ...
3
votes
3answers
125 views

$1992$ IMO Functional Equation problem

The problem states: Let $\Bbb R$ denote the set of all real numbers. Find all functions $f : \Bbb R \rightarrow \Bbb R$ such that $$f(x^{2}+f(y))=y+(f(x))^{2} \space \space \space \forall x, y \in ...
0
votes
1answer
12 views

about lower semicontinuous functional

Let $X$ a topological space.My book define : A functional $\varphi: X \rightarrow R$ is lower-semicontinuous (l.s.c) if $\varphi^{-1}(a, + \infty)$ is open in $X$ for any $a \in R.$ (1) And the book ...
3
votes
1answer
59 views

Book/Books leading up to the the axiom of choice?

I am familiar with the axioms of ZF set theory and some basic uses of them to completely formally construct more complex objects such as natural numbers etc. However I have pretty much no background ...
10
votes
0answers
69 views

Statistics Primer for the Unwary Mathematician

I have a new position in a biology department (after being housed in a maths department) working on cognitive and population modeling. People in my lab are asking for help with applying statistical ...
5
votes
2answers
169 views

Interaction of completeness and second incompleteness theorems

So I was reading the Wikipedia article on Godel's completeness theorem, the section on its relation to completeness. It says that completeness gives the existence of a model of arithmetic $\mathcal M ...
1
vote
1answer
54 views

Recreational Mathematics title search

I once read part of a book on recreational mathematics that told a variety of stories. A central part of each story was a piece of non-trivial, and very interesting mathematics: the sofa moving ...
1
vote
0answers
17 views

Non-Intersecting up-right lattice paths and standard Young Tableaux

Consider the Lattice $\mathbb{Z}^2$ and an initial set of points with coordinates $(0,u_1)$, $(0,u_2)$, $\cdots$ $(0,u_n)$, final set of points $(m,v_1),(m,v_2),\cdots,(m,v_n)$, where $v_i,u_i$ are ...