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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2
votes
2answers
33 views

Good analysis texts

I'm looking for a good introductory text to analysis, or, more specifically, a text that puts calculus on a much more rigorous ground. I've just finished a year of calculus at my local university, ...
0
votes
0answers
15 views

Solutions to Groups and Symmetry by M.A. Armstrong

I am learning group theory (on my own) using the 'Groups and Symmetry' textbook by MA Armstrong. Does anyone know of a book/website where I can find solutions to the Exercises (so I can check my ...
0
votes
0answers
12 views

Good book for self-studying Binary Relations

I am studying economics and I frequently encounter Binary Relations. But without any good knowledge of it, I get confused. Here is some background, if it's helpful: I know calculus(single and ...
7
votes
1answer
60 views

Is there anything “nice” about the set of normal matrices (over $\Bbb R$ and $\Bbb C$?)

Normal matrices are of course useful to any linear algebra buff, not least because of the spectral theorem. However, taken as a whole, they tend to have some not-so-nice properties. For example: ...
0
votes
0answers
15 views

when does bijective map exist for any pair of rational function?

Let me ask kind of different questions than former ones. Given $$\frac{P_1(x_1,x_2,\dots,x_n)}{P_2(x_1,x_2,\dots,x_n)}\text{, and }\frac{P_3(y_1,y_2,\dots,y_n)}{P_4(y_1,y_2,\dots,y_n)}$$ where $P_i$ ...
-5
votes
0answers
36 views

Please vote the mathematical theory or results or methods you are impressed most [on hold]

Please vote the mathematical theory or results or methods you are impressed most. something that are very deep with completely unexpected solutions ( or results), something that you are astonished. ...
1
vote
0answers
25 views

Proof of Minkowski determinant inequality

I wonder where can I find the proof for the Minkowski determinant inequality? ( i.e., given two positive definite n x n symmetric matricies A and B, $det(A+B)^{1/n}\ge det(A)^{1/n}+det(B)^{1/n}$ ) ...
5
votes
0answers
38 views

Indiscernible subsequences

Work in a saturated model $\cal U$ of sufficiently large cardinality. Are there assumptions on $\kappa<|\cal U|$ that guarantee that any sequence $\langle a_i:i<\kappa\rangle$ has an ...
1
vote
0answers
21 views

Any good resources for Lagrangian and Hamiltonian Dynamics? [migrated]

I'm taking a course on Lagrangian and Hamiltonian Dynamics, and I would like to find a good book/resource with lots of practice questions and answers on either or both topics. So far at my university ...
1
vote
0answers
47 views

Does such a polynomial map always exist?

First question: given $$\frac{P_1(x_1,x_2,\dots,x_n)}{P_2(x_1,x_2,\dots,x_n)}=\frac{P_3(f(x_1,x_2,\dots,x_n))}{P_4(f(x_1,x_2,\dots,x_n))}|\det (J(f(x_1,x_2,\dots,x_n)))|$$ where $P_i$ is ...
2
votes
2answers
75 views

Are addition and multiplication on naturals algebraically distinguishable?

Suppose (N, +) and (N, *) are the structures of addition and multiplication on N, the natural numbers with 0. Let S be the set of equational identities that hold in (N, +), and let T be the set of ...
4
votes
2answers
74 views

Bartle vs Rudin, which one is better for real analysis?

I'm in high school and I want to study real analysis, and I can choose between The elements of real analysis by Robert G. Bartle and Principles of mathematical analysis by Walter Rudin, so, from the ...
0
votes
0answers
31 views

Request topics for presentation [on hold]

I'm in need of some interesting topics (in applications of mathematics, like treasure hunt) to present paper. especially I'm looking for topics in applications of Group theory or basic calculus. ...
2
votes
1answer
44 views

What is the importance of Jacobian Conjecture and any progress on it?

What is the importance of Jacobian Conjecture?Are there any important central problem with the conjecture as precondition? and any progress on it?
1
vote
1answer
35 views

Book to self-learn probability

I am reading some lecture notes (completed with exercises and competition-like problems) provided by my college professor, but I would like to study probability from a proper book. Can you suggest one ...
0
votes
2answers
64 views

Best E-books and online-resources for Probability and its applications(especially games of chance)

I am very much interested in studying games of chance and the probabilities related to our daily life instances but I need an online resource or some e-book to study them. I am a self-learner. Can ...
2
votes
0answers
19 views

Ehrhart Polynomials Modulo Prime Integers

Are there any results known about computing Ehrhart Polynomials modulo prime integers?
2
votes
0answers
13 views

Probablistic bound for $\|RR^TM\|$ for uniformly random orthonormal matrix $R$

I am stuck on a finding a probablistic bound on a nonstandard random matrix. I looked around on the internet and couldn't find any results. This could be because I don't know the key words or because ...
1
vote
0answers
34 views

Question regarding advanced calculus textbooks

I'd like to start off by mentioning that I'm gonna begin studying Computer Science at the local polytechnic university. As I found out, the study of mathematics stops after two years. Recently I've ...
2
votes
1answer
87 views

Should I change my Linear Algebra Textbook?

I know there are many questions related to linear algebra, but the textbook I'm using is not that widely used as other books, I guess. My university uses 'Finite-Dimensional Linear Algebra' by Mark ...
0
votes
1answer
23 views

Applications of random walks

I am searching for a clear and interesting exposition of an application of random walks to some physics topics accessible to advanced high school students.
5
votes
3answers
51 views

Where to study $2$-category theory?

Is there any place where I can read about $2$-categories? I am looking for a proper treatment - there is a section in Borceux's Handbook of Categorical Algebra, but it only sketches some parts of the ...
1
vote
1answer
72 views

Relation between the covers by sets of small diameter and the size of uniformly separated sets

Sorry I didn't find a better title. Here is the problem and my solution so far, I'd appreciate if someone could told me if is correct and for the last point, which at first sight seems to be ...
2
votes
2answers
50 views

“Reverse” quotients.

Given a set $A$ and a equivalence relation $\sim$ on $A$, one can construct the quotient $A/{\sim}$. But what about the opposite? More precisely, given a set $X$, is there a way to know whether exists ...
0
votes
0answers
37 views

Are there any general results about the irrationality of $a^{\frac{p}{q}}$?

Are there any general results about the irrationality of $a^{\frac{p}{q}}$ for $a\in\mathbb{Z}^+$, $p,q\in\mathbb{Z}$, $q\neq 0$ and $a\neq 1$?
0
votes
0answers
33 views

What is an easy to read book on category theory including the introduction of some killer apps for the theory? [duplicate]

What is an easy to read book on category theory including the introduction of some killer apps for the theory ?
1
vote
1answer
46 views

Periodicity with irrational numbers

Recently, I invented the following theorem and found a proof, it seems strange since it is very counter-intuitive to me. The proof is long and non-conceptual. Is there a place or a branch of math ...
0
votes
0answers
16 views

Papers related to Tomography and compressive sensing.

Recently I studied about Radon transformation and its applications. I got to know that they are lots of application in tomography and am very much interest after reading that. Now I wanted to read ...
1
vote
0answers
69 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 ...
1
vote
0answers
62 views

Transfinite composition and $\kappa$-categories

I wonder whether the following ideas make sense, and whether something in that direction has been written down somewhere; do you know a reference? The last definition is supposed to be a ...
0
votes
0answers
13 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 ...
0
votes
0answers
19 views

Where can I learn more about the lattice-theoretic account of affine geometry?

Let $A_n$ denote the complete lattice of affine subspaces of $\mathbb{R}^n$. Let $\dim_n$ denote the function that returns the dimension of an affine subspace.$$\dim_n : A_n \rightarrow (\{-\infty\} ...
-2
votes
0answers
97 views

Solutions to do Carmo's Riemannian Geometry [on hold]

I have lot difficult in solving problem in Riemannian Geometry by Manfredo do Carmo. Does anyone know solution book of those? I just want ask if anybody know so! Gracias!
0
votes
0answers
46 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
22 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 ...
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. ...
5
votes
1answer
82 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
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
vote
0answers
22 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
vote
0answers
23 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
26 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, ...
2
votes
0answers
32 views

Representations of knot groups

Recently, I was studying the knot group and I want to learn some more material about it (e.g. its representations). "Knots" by Burde and Zieschang discusses some material but it is not entirely ...
5
votes
0answers
32 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
votes
0answers
31 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
17 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 ...
1
vote
1answer
55 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
vote
1answer
34 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 ...
2
votes
0answers
46 views
+50

Where can I learn more about the Galois connection induced by a graph on its own powerset?

Conventions. Write $\mathcal{P}(X)$ for the powerset of a set $X$, viewed as partially ordered under $\subseteq$. Given a relation $R \subseteq X \times Y$, write $R^\dagger \subseteq Y \times X$ ...