Stack Exchange Network

Stack Exchange network consists of 175 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Visit Stack Exchange

Questions tagged [reference-request]

This tag is for questions seeking external references (books, articles, etc.) about a particular subject. Please do not use this as the only tag for a question.

3
votes
0answers
58 views

MacLane Birkhoff $\textit{ Algebra }$ vs Jacobson $\textit{ Basic Algebra I,II }$ vs Lang $\textit{ Algebra }$

I'm searching for an apt textbook(s) on Abstract Algebra - in particular I'm trying to get a review/comparison of the aforementioned books. I would be grateful for any help in this direction. $$$$ A ...
4
votes
3answers
110 views

Books that leaves proofs for the reader [on hold]

What are some good introductory books that leave many proofs as exercises? I have been self studying analysis by reading Tao's two fantastic books which eventually leaves most of the (easier) proofs ...
3
votes
2answers
72 views

Mathematically rigorous Quantum Mechanics

I am a student of mathematics attending a course in Quantum Mechanics. This course is held by a physicist, and it is really confusing for me to follow his reasonments. With this, I do not mean to be ...
0
votes
1answer
20 views

Reference request: Construction of torsion pair from a class closed under quotients, extensions and coproducts.

The category I'm working in is $\operatorname{Mod}A$ for some unitary ring $A$. I'm looking for a reference on when certain subcategories of $\operatorname{Mod}A$ give rise to torsion pairs. Let $\...
0
votes
0answers
20 views

Study for Ternary and N-ary relations: books and practice material recommendations?

I have learnt the topic binary relations and its types and i am curious about ternary and N-ary relations and i want to learn about there properties. So please can I be recommended books and online ...
0
votes
0answers
10 views

Large Deviation, Optimal Transport and Machine Learning Reference

I am looking for references (books/sites/articles) on the following three subjects: Large Deviation, Optimal Transport and Machine Learning References. I would like works which involve any of them ...
3
votes
0answers
19 views

Reference Request: Jimbo's Proof of Quantum Schur-Weyl Duality

In his seminal 1986 paper "A $q$-analogue of $U(\mathfrak{gl}(N+1))$, Hecke Algebra, and the Yang-Baxter Equation", Jimbo asserted (Proposition 3) that the quantum group associated to $\mathfrak{gl}_n$...
0
votes
0answers
19 views

References for cryptography on elliptic curves? [duplicate]

What are good books to learn cryptography on elliptic curves? I'd like a mathematician oriented book. Thanks.
4
votes
0answers
60 views

Monad terminology/reference request

I am looking at a category $C$ equipped with an exponential, and a monad $T : C \to C$ equipped with a natural transformation $\nu : F \to G$ from the bifunctor $F : (X, Y) \mapsto T(Y^X)$ to the ...
1
vote
1answer
22 views

Is the Drinfeld center of an abelian monoidal category still abelian?

I am interested in knowing if the category $^H_H\mathcal{YD}$ of left-left Yetter-Drinfeld modules over an infinite dimensional Hopf algebra $H$ is an abelian category or not. The answer is ...
0
votes
2answers
42 views

Were the classic “high school” trigonometric formulae known and derived before Fourier transforms?

We all probably learn the famous trigonometric formulae: $$\sin(\alpha+\beta) = \sin(\alpha)\cos(\beta) + \sin(\beta)\cos(\alpha)\\\cos(\alpha+\beta) = \cos(\alpha)\cos(\beta) - \sin(\alpha) \sin(\...
0
votes
0answers
19 views

Haar measure on Homogeneus groups

I would like to have a reference where it is proved that the haar measure of a Homogeneus group is the push forward of the lebesgue measure on the lie algebra through the exponential map. I have some ...
1
vote
2answers
46 views

Geometric-like Sum over Primes

Is there a known way to evaluate sums of the form $$\sum_{p\text{ prime}} x^{p},$$ and are there any restrictions on the value of $x$ (e.g., $|x|<1$ for typical geometric series)? EDIT: The ...
1
vote
0answers
20 views

Reference for a (non-standard) table of characteristic functions

I am searching for a table of characteristic functions of probability distributions with more than the standard distributions. At a pinch a table of fourier transforms will do it too. But I computed ...
1
vote
0answers
63 views

Roots of a polynomial of degree 5 in finite field

I have a polynomial $p(u,v) \in F_q[u,v]$ which is symmetric. In case $q \equiv −1\pmod{10}$, by experiment, I understood that $p(u,v)$ is irreducible. But for every $u \in F_q$, $p_u(v)$ is product ...
1
vote
0answers
31 views

Matrix Calculus Reference Request

Looking for a good book on matrix calculus. I have seen the matrix cook book but it is mostly identities/equations without any proofs or work. I want a thorough treatment of the topic.
1
vote
0answers
18 views

Reference request: applications of topological quantum field theory to continuous-time dynamical systems.

From wikipedia: In dynamics, all continuous time dynamical systems, with and without noise, are Witten-type TQFTs and the phenomenon of the spontaneous breakdown of the corresponding topological ...
0
votes
1answer
20 views

Expression of the dirichlet coefficient of an L-series in terms of the Satake parameters

Last year, I had found a pdf where the expression of the Dirichlet coefficient $\lambda_{\pi}(p^{\nu})$ in terms of the Satake parameters $\alpha_{p,i}(\pi)$ was given. Unfortunately I don't remember ...
0
votes
0answers
17 views

$s$-convexity implies $p$-convexity in Banach lattices

If $1<p<s<\infty$ and $E$ is a Banach lattice which is $s$-convex, is it also $p$-convex? If so, what would be a good reference for this?
0
votes
0answers
14 views

Parametric representation of the real branches $\operatorname{W_{0}},\operatorname{W_{-1}}$ of the Lambert W function

$\require{begingroup} \begingroup$ $\def\a{\alpha}\def\la{\ln{\a}}\def\e{\mathrm{e}}\def\W{\operatorname{W}}$ $\def\Wp{\operatorname{W_0}}\def\Wm{\operatorname{W_{-1}}}$ For $x\in(-\tfrac1{\mathrm{e}...
2
votes
0answers
20 views

LASSO's (or BPDN) parameter tuning

We have to solve the following problem : $$\min_x \|x\|_1 \text{ s.t. } \|Ax-y\| \le \sigma,$$ with $\sigma$ some positive real number, $A$ a complex rectangular matrix and $x,y$ complex vectors. ...
0
votes
0answers
54 views

Is there a reasonable one hour summary of Game Theory?

In his Topology and Geometry course on Youtube (http://www.youtube.com/watch?v=QzfZS3iopR0&t=10m7s), Tadashi Tokieda claims he can teach all of game theory in an hour. He seemed very sincere and ...
7
votes
1answer
100 views

Beach-ball like differential operators of a two-dimensional function

I'm looking for references, known names of, and other useful pointers and insight about (pairs of) differential operators that are "beach-ball like" because they sample a 2-dimensional function in ...
0
votes
0answers
14 views

Reference request for convergence question in probability and statistics

Recently I have asked question here on math.se Regression covergence No one answered it so I decided to try to solve it on my own, however I don't know where to start. I had undergraduate courses in ...
2
votes
1answer
30 views

It would be possible to define an uniform distribution on $\Bbb N$ using infinitesimals?

In standard analysis it is clear that it is impossible to define an uniform probability distribution on $\Bbb N$ because there is no constant $c\in\Bbb R$ such that $\sum_{k=1}^\infty c=1$. Using ...
1
vote
0answers
22 views

Reference request: Density of testfunctions in sobolev space $ W^{1}_{0}$

can someone help me out and name a good source where the following statement ist proven? $C^\infty_0(\Omega)$ is dense in $W^{1,p}_0(\Omega)$ with $\Omega \subset \mathbb{R}^n$ being an open, bounded ...
0
votes
1answer
28 views

Reference for homology of real projective space in a field.

I need a reference in a book for the computation of the homology of real projective space with coefficients in an arbitrary field. I do know how to do the computation, and I also found an online ...
3
votes
1answer
61 views

Categorical general topology — reference request

I am looking for literature describing general topology in terms of category theory. I would prefer literature which does not assume too much familiarity with category theory, but would appreciate any ...
2
votes
1answer
107 views
+100

Propagation of regularity for the heat equation

Let $\Omega$ be an open bounded subset of $\mathbb R^N$. Let $u_0 \in L^\infty(\Omega)$ and $f \in L^\infty((0,T)\times\Omega)$ and consider the following boundary value problem for the heat equation:...
0
votes
0answers
29 views

On the preimage of injective holomorphic map

I am hoping the following is true. Mention of related ideas/topics are appreciated. Suppose $F:\mathbb{C}^n \to \mathbb{C}^n$ is a injective holomorphic mapping such that $F(0)=0$ and $dF(0) = I_n$ ...
1
vote
0answers
60 views

References on Kähler Differentials

I'm working on an independent study project on Kähler differentials for my commutative algebra class. I'm looking for any references on these that might help me out. Any references to their use in ...
1
vote
2answers
26 views

Polytopes with equal facets

My question is very simple though I was not able to find any related information. Is it true that if a convex polytope has combinatorially isomorphic facets then it is combinatorially isomorphic to ...
1
vote
1answer
33 views

Values of some “natural” sums over multiindices with a given absolut value

I'd like to know if there is a nice closed expression in terms of $j$ and $k$ of the sum $$ S_{j,k}:=\sum_{(i_1,\ldots,i_k)\in \mathbb{N}^k_0:\\i_1+\cdots+i_k=j}\frac{1}{i_1!\cdots i_k!}. $$ ...
2
votes
1answer
55 views

Tips for a dum-dum : Introduction to Analysis 1 and 2

First off let me say that math and I don’t get along. I want to be it’s friend, but it certainly doesn’t want to be mine. I have been out of high school for some time (decades) and recently returned ...
0
votes
0answers
22 views

Reference for elementary substructures of the standard model of analysis

Is there was any resource discussing or categorizing elementary substructures of the intended model of analysis? Analysis in this context is also known as second-order arithmetic. They will of course ...
0
votes
0answers
22 views

Answer sheet of Probability by Shiryaev, Albert N.

Do any of you have answer sheet for the questions of book "Probability" by Shiryaev ? I actually bought Probability-1 one of his newest books and questions seem similar to his older book Probability. ...
0
votes
0answers
31 views

Require guidance to proceed further in learning statistics

In my undergraduate course I learnt introductory level statistics and I really enjoyed it. With that background I decided to follow predictive analysis further and decided to take up this book . But I ...
0
votes
0answers
15 views

Reading material for Kähler geometry

I'd like to read and understand this paper on Kähler geometry. The most advanced math I've done is a read through Rudin's Principles of Mathematical Analysis which teaches analysis up to differential ...
0
votes
0answers
17 views

I need resources for elementary Number Theory, Theory of Equations (For KVPY exam), (details in post) [closed]

So I am currently starting 11th grade (in India). There's this KVPY scholarship exam that I am preparing for, and it needs pretty advanced concepts, like number theory (congruence modulo), theory of ...
3
votes
1answer
22 views

The derivative of the Delta function times another function

Good evening! I can't understand how to prove that $$\alpha(x)\delta'(x)=-\alpha'(0)\delta(x)+\alpha(0)\delta'(x).$$ I tried to use $$(Df,\phi)=-(f, D\phi),$$ also I used that $$(D(hf),\phi)=(h'f+hf',\...
1
vote
0answers
46 views

Proof that the merit of a prime gap can become arbitary large?

If $p_n$ denotes the $n$-th prime number, we can define $$g_n:=p_{n+1}-p_n$$ as the gap after the $n$-th prime number. The merit of a prime gap is defined as $$m(p_n):=\frac{g_n}{\ln(p_n)}$$ It is ...
2
votes
0answers
20 views

If the frontier is a union of the orbits of a autonomous ODE then the set is invariant

I'm looking for a proof or reference proving this theorem which was written in my ODE class: Let $D \subseteq \mathbb{R}^d$ be open and $f:D \to \mathbb{R}^d$ continuous such that each IVP has a ...
2
votes
0answers
30 views

Exhibition where children were playing Tic Tac Toe against their parents

I recall that there was an exhibition, in some place in the US I believe, where children could play tic tac toe against their parents. The catch was the following: both were sitting in front of a ...
4
votes
0answers
76 views

Classifying the chains of orderable sets' power sets up to isomorphism

Recently, while trying to understand another result, I began to wonder about the following question: Given some orderable set $A,$ what (if anything) can we conclude about the order type or ...
0
votes
0answers
17 views

reference on min/max rules

I am looking for some references to the basic algebra involving $\max()$ and $\min()$ functions. e.g: $$\max(x,y) = -\min(-x,-y)$$ $$\max(x-a,0)-\max(y-b,0) \le \max(x-y - (a-b), 0)$$ and the like....
1
vote
1answer
29 views

References on the Hugoniot locus of hyperbolic systems

I would like to get a good reference to study Hugoniot Locus in conservation laws, maybe videos or PDF's. Many thanks.
3
votes
0answers
19 views

Reference Request: Proof of $\mathrm{H}(\mathrm{Prim}\,\mathcal{H}) \cong \mathrm{Prim}\,\mathrm{H}(\mathcal{H})$ for cocommutative dg-Hopf algebras

In Loday’s book Cyclic Homology the following theorem appears: A.9 Theorem. On a cocommutative differential graded Hopf algebra $\mathcal{H}$ over a characteristic zero field $k$ the homology and ...
4
votes
0answers
49 views

What are some of the best textbooks on multi-objective optimization?

I am looking for textbooks on non-linear multi-objective optimization that are rigorous. For instance, I am most comfortable with Arkadi Nemirovski style. I am looking for a book on nonlinear multi-...
3
votes
1answer
88 views

Difference between several books on complex geometry

I would like to learn some complex geometry, especially the interaction between algebraic geometry and complex geometry. I found that there are several famous books: Huybrechts, Complex Geometry; ...
2
votes
0answers
54 views

A surprisingly simple smooth function, is it used as a sigmoid?

Consider the function $$f(x) = \frac{x}{1+|x|}$$ For what we can prove about it's derivative, it exists everywhere, is maximal at $x=0$ ($f'(0)=1$) and we can verify $$\forall x\in \mathbb R : f(x)\...