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.

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3
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0answers
25 views

Do any official publications argue that the degree of the zero polynomial should be $0$?

Usually, the degree of the zero polynomial is either left undefined, or else declared to be $-\infty.$ Anyway, I was lying in bed a few minutes ago and suddenly it occurred to me that perhaps $0$ ...
2
votes
0answers
20 views

(Theoretical) Complex Analysis Textbooks

Most books I've seen on complex analysis do not develop it theoretically, which can be somewhat infuriating for the budding pure mathematician. What I am looking for are some comprehensive, rigorous ...
2
votes
0answers
55 views

Fields of Research in Algebra [on hold]

I'm a last-year student in mathematics and I'm looking for a master degree in algebra. So I'm trying to understand what are the most interesting fields of research in algebra all around the world. ...
3
votes
0answers
19 views

On a metric over m-subsets of [n]

Given an integer $n$, denote the set of integers $\{1,2,\dots,n\}$ as $[n]$. For two $m$-subsets $A$ and $B$ of $[n]$, list their elements in the increasing order as $a_1 < a_2 < \dots < a_m$ ...
0
votes
1answer
25 views

Reference for solving linear operator equations

I'm interested in solving an equation of the form $$ Ax = b $$ for some bounded linear operator $A: H_1 \mapsto H_2$ where $H_1, H_2$ are some Hilbert spaces. I've seen in this math.SE post in ...
2
votes
0answers
37 views

Chandrasekhar history [on hold]

I have misplaced an article by Chandrasekhar from the mid 90's in which he drew an analogy between himself and his neat desk and a co-laborer 'down the hall' who was more chaotic with managing his ...
4
votes
0answers
25 views

Shaking a box of rocks (Optimal Packing)

My coworker was telling me that when he plants seeds on his farm, he puts them all in a large container on the tractor and after a period of just driving, the seeds are more densely packed than when ...
3
votes
1answer
36 views

When can you take the limit of a parameter before solving the differential equation?

Short example: consider the differential equation \begin{align*} f'(x)=\frac{k^2}{k^2+k+1}xf(x) \end{align*} where $k$ is a parameter. Wolfram Alpha tells me that the solution to this equation is ...
-4
votes
0answers
79 views

Comments about “Topics in Algebra” by I.N. Herstein and “Abstract Algebra” by Dummit/Foote? [on hold]

Today, I got two gifts from my research mentor: "Topics in Algebra" by I.N. Herstein and "Abstract Algebra" by Dummit/Foote. I am very happy and grateful for his gifts, but I already have been ...
2
votes
0answers
23 views

Reference request: The compactness and compact embedding in Besov Space?

This post has been on MathOverflow for couple of days but receive no response. So I put it here hoping for more attentions. Thank you guys! Let $\Omega\subset \mathbb R^N$ be open bounded with ...
0
votes
0answers
14 views

Reference for General state space Markov chain

What is a good reference for general state space Markov chains? Is there a reference which assumes only familiarity with finite/countable state space Markov chains and then extends the results (e.g., ...
1
vote
1answer
51 views

What are the topics that must be covered in a beginning graph theory course? [on hold]

Good day to everyone. It will be my first time to make a syllabus on elementary graph theory. My question will be: What are the topics that must be covered in a beginning graph theory course? Also ...
0
votes
0answers
15 views

Non-Linear Constrained Optimisation Over Zonotopes: Reference Request

Background I am investigating, numerically, the problem of a chess team attempting to maximise its probability of winning a team match . Each of our N players independently chooses one of two ...
0
votes
1answer
27 views

Automatic way to have a good initial guess for the iterative methods ( newton method) and for high dimensional nonlinear problems

I am solving a variety class of nonlinear systems where I need to reduce in optimal manner the number of iterations of either the newton or modified newton method. For this end I am trying to figure ...
2
votes
1answer
31 views

Reference for differentiation of an integral over variable ball

I am looking for a reference for a 'well-known' formula in $\mathbb{R}^d$: $$ \frac{d}{dr} \int_{\lVert x\rVert\leq r} f(x)dx= \int_{\lVert y\rVert=r} f(y)dS(y), $$ where $dS$ is the Lebesgue surface ...
-4
votes
0answers
57 views

Expansive Mathematical Logic Book [on hold]

I'm going to begin studying mathematical logic and I am looking for a good book, hopefully one that covers a lot (if not the most) material. My school's library has the book by Monk, and the book by ...
1
vote
0answers
19 views

Do complete Hopf algebras have an antipode?

I am reading Quillen's paper on rational homotopy theory. In appendix A of this paper Quillen defines a notion he calls complete Hopf algebras. These are certain cocommutative bialgebra structures ...
0
votes
1answer
100 views

What's the image of $(a, b)$ under a typical $f$: $\mathbb{R}\longrightarrow\mathbb{R}$?

This question is about "typical" or "generic" functions $f$: $\mathbb{R}\longrightarrow\mathbb{R}$, where I leave the two terms undefined, but they are meant to be in the style of "A generic ...
0
votes
0answers
33 views

How to tell complex structures apart

Complex structures are rigid, yet weirdly flexible. For example, the Riemannian mapping theorem says that every non-empty simply connected open subset of $\mathbb{C}$ that is not $\mathbb{C}$ is ...
0
votes
0answers
32 views

I want to ask a favor for integral transform [on hold]

I am helpless. I don't know anything about this topic. And don't have any idea of books. guys please recommend some books on integral transform which are simple, easy to start a new concept. Also ...
2
votes
0answers
46 views
+50

Reference request: fixed point and first-order logics

I'm looking for materials on the relationship between first-order and fixed-point logics, specifically on the condition for a formula in a fixed-point logic to have an equivalent first-order formula. ...
2
votes
1answer
92 views

Proof: $\mathbb{Z}[\zeta_6]$ is a PID.

I am reading through A First Course in Modular Forms. In Proposition 2.2.3 they claim that $\mathbb{Z}[\zeta_6]$ is known to be a principal ideal domain. Does anyone have a reference for the proof of ...
1
vote
2answers
71 views
+50

Modules that have finitely many submodules

Drawing the lattice of submodules of a given module helps me to gain some intuition about the structure of module. Sometimes, however, it is not possible to draw in neat manner; For example vector ...
0
votes
0answers
3 views

Successive divisibility of a sequence? Progressive divisibility? terminology or reference

Perhaps I say that an (infinite) sequence $(r_n)$ of positive integers is progressively divisible iff $r_n \mid r_{n+1}$ for all $n$. Is there some other terminology that is in use for this? I am ...
-1
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0answers
22 views

Solution manual for Modern Differential Geometry for Physicist? [on hold]

Here is the book by Chris J. Isham Anyone has the solution manual of Modern Differential Geometry for Physicist?
10
votes
2answers
264 views

Algebraically flavoured functional analysis book

I'm looking for a book on functional analysis that would suit someone who is more algebraically/geometrically oriented and seeks to learn the subject with the goal of using it later for geometric ...
3
votes
0answers
26 views

Ito's formula and Infinitesmal generator

Consider an Ito process $$ dX_t = \sigma_t dB_t $$ where $\sigma_t$ is a two-state continuous-time Markov chain with state space $\{ \sigma_1, \sigma_2 \}$ that switches state with Poisson ...
0
votes
1answer
27 views

The literature on Chern-Simons theory

Can any one give some literature on Chern-Simsons theory? I can not find any book introducing this theory. Thanks.
-4
votes
0answers
72 views

How to help a postgraduate student to write a book [closed]

How to help a person who has already completed her post-graduation but has also secured a result much weaker than her expected result during the completion of graduation,for writing a higher secondary ...
0
votes
1answer
64 views

Math Literature [closed]

I am a high school math teacher and I am working on implementing literature in my classes. One book we read last year was Driving Mr. Albert: A Trip Across America with Einstein's Brain and they ...
1
vote
0answers
60 views

Best intro to Fundamentals of Mathematics? [closed]

If you like mathematics it's likely that you also want to have the most solid foundations in number theory and analysis possible. I have just finished Elliott Mendelson's book Number Systems and the ...
0
votes
0answers
15 views

Are there any resources on this notion of a “directed” semigroup?

Given two additive semigroups $G$ and $H$, and a semigroup action $ \& : G \times H \to G$, then intuitively $H$ can be thought of as a set of "directions" in which we can move in the space $G$. ...
0
votes
1answer
30 views

Explicit descriptions of the modular curves $Y(5)$ and $Y_1(5)$

The modular curves $Y(5)$ and $Y_1(5)$ associated to the congruence subgroups $\Gamma(5)$ and $\Gamma_1(5)$ are of genus 0. As such, they are nothing but the Riemann sphere $\mathbb P^1$ minus a ...
0
votes
2answers
67 views

Triviality of a vector bundle is an open condition

Is the following statement true (and if not, are there additional assumptions that make it true?) A vector bundle on a variety which is trivial if restricted to a closed subvariety is trivial on ...
-1
votes
0answers
30 views

The exterior Laplace equation

in which case we use the single layer potential and the double layer potential for the Laplace equation ? \begin{eqnarray}\tag{1} \Delta u = 0 \; \mathbb{R}^2\backslash\omega\\ u \to 0 \; at \; ...
0
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0answers
3 views

Is the space of smooth sections of a smooth bundle a Fréchet Manifold?

I'm not very prepared on these concepts and i'm wondering if there're some good references addressing this problem... My aim is to present the problem of linearization for the Euler-Lagrange operator ...
2
votes
0answers
23 views

finding an invariant measure

Are there any methods for finding an (infinite, absolutely continuous with respect to lebesgue measure) invariant measure $d\mu=f(u,v)dudv$ for something like the following? $$ T:Q\to Q, \ ...
0
votes
0answers
26 views

Proof of Sokhotski-Plemelj theorem

Sokhotski-Plemelj theorem states $$ \phi_i(z)=\frac{1}{2\pi i}\mathcal{P}\int_C\frac{\varphi(\zeta) \,d\zeta}{\zeta-z}+\frac{1}{2}\varphi(z), \, \\ \phi_e(z)=\frac{1}{2\pi ...
0
votes
1answer
44 views

Books on multivariable calculus

I'm looking for a book that covers the following subjects: multivariable functions, extremes of multivariable functions, integration, implicit function theorems, functions defined by integrals, vector ...
0
votes
0answers
28 views

Self-intersection number of fibered surface

Let $R$ be a complete discrete valuation ring with residue field $k$ (can assume algebraically closed), $f:X \to \mathrm{Spec}(R)$ a flat, proper family of projective curves (i.e., $f$ is also ...
1
vote
1answer
35 views

Chaikin's Algorithm: Proof of Convergence

Chaikin's algorithm is, in some sense, similar to de Casteljau algorithm in that (in the limit) it produces a curve from a set of control points. There are claims all over the internet that Chaikin's ...
1
vote
0answers
87 views

On a theorem of Akizuki concerning the minimal number of generators of an ideal

I am looking for a theorem of Akizuki I was told by my professor. He said me that Akizuki showed in his paper "Zur Idealtheorie der einartigen Ringbereiche mit dem Teilerkettensatz" (1938) a result ...
2
votes
0answers
40 views

Resources for learning fixed point logic

As the title says, I am looking for resources to learn some fixed point logic, especially partial fixed point logic. I have basic knowledge of propositional calculus and predicate logic, but sadly not ...
1
vote
1answer
46 views

Is this a valid example of a non-euclidean Sierpinski attractor?

I am learning the basic concepts about the Chaos Game (I did a previous question about the same topic here), the method to create fractals elaborated by professor Michael Barnsley. The basic example ...
0
votes
0answers
34 views

Chaos theory in stock market

I am doing an IB Extended Essay on chaos theory and fractals in the consumer stock market. It is a high school level essay (4000 words) and should be understandable for a calculus student. I'm having ...
2
votes
0answers
42 views

Weil: Fibre Spaces in Algebraic Geometry

I have spent a decent amount of time searching for the notes for Weil's Fibre Spaces in Algebraic Geometry, written by A. Wallace, both in print and online. Does anyone have a file of it they'd be ...
1
vote
1answer
24 views

Couple stress tensor reference.

Can someone give me a good mathematical reference for couple stress tensor in its most basic form. Thank you.
7
votes
7answers
823 views

Rudin's equivalent in Linear Algebra

I am looking for a linear algebra book which is as abstract as possible. But not an abstract algebra book. Something that is what Rudin's is for (beginning) analysis, that is, terse, rigorous and with ...
2
votes
3answers
61 views

Brief book on calculus to read before studying the analysis [on hold]

S.E advisers, I am going to start studying the analysis texts (Rudin-PMA, Apostol-MA, Pugh-RMA) on the first week of August. I have a good proof skills through working on Artin's Algebra and ...
0
votes
0answers
33 views

Universal Algebra: partial algebras and homomorphisms

I'm looking for an accessible introductory text on universal algebra, one which discusses homomorphisms in the context of partial algebras. I have been recommended the Grätzer book, "Universal ...