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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6
votes
0answers
70 views

Has this subset-sum game been studied?

Consider the following game: two players, Yolanda (who always goes first) and Zachary, take turns selecting (not yet chosen) numbers between $1$ and $9$. The first player who can make three of their ...
2
votes
0answers
24 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
28 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
46 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 ...
26
votes
12answers
6k views

Reference book on measure theory

I post this question with some personal specifications. I hope it does not overlap with old posted questions. Recently I strongly feel that I have to review the knowledge of measure theory for the ...
9
votes
2answers
2k views

Is there a solution manual for Royden fourth edition?

I bought the fourth edition of Royden Real Analysis, this book is awesome and is quite different of third edition that has less excersices. I have the solution manual for the third edition. Is there ...
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 ...
1
vote
1answer
47 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 ...
2
votes
1answer
53 views

Reference on Malcev completion

I need a reference for learning Malcev completion, its associated group scheme, and Lie algebra. Thanks!
8
votes
1answer
172 views

The Irreducible Corepresentations of the eight-dimensional Kac-Paljutkin Quantum Group

Question What are the irreducible corepresentations of the eight-dimensional Kac-Paljutkin Quantum Group? The trivial corepresentation is given by $\Delta_{|W}$ where $W$ is just the one dimensional ...
2
votes
2answers
38 views

Unique four-colorings of planar graphs and the like…

I am doing research into a particular graph coloring problem and wonder if someone can direct me to published work that bears on what I’m studying. It is known that planar graphs that are uniquely ...
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
0answers
41 views

Expected distance of biased 1d random walk with 0 drift

There were many question about biased 1d random walks earlier, but as far as I can tell none of these are directly related. Let $p,q>0$ such that $p+q=1$. Let $X_0=0$ and $X_{i+1} = X_i+1$ with ...
0
votes
0answers
38 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
43 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 ...
2
votes
3answers
63 views

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

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 ...
3
votes
1answer
129 views

Studying for analysis- advice

I find that studying for analysis is unlike other math classes that I've taken. I dedicate a lot of time to studying for it, but it seems like no matter how much time I put into it I am not getting ...
0
votes
0answers
34 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 ...
23
votes
10answers
2k views

Mathematics and Music

I have heard that, in recent years, many mathematicians as well as music theorists have applied different branches of mathematics to music. I would like to know about some books/resources relating to ...
20
votes
7answers
3k views

Math and Music theory books

Are there any good books on musical theory from a mathematical standpoint? Is "Music theory and mathematics : chords, collections, and transformations", edited by Jack Douthett, Martha M. Hyde, and ...
3
votes
1answer
51 views

Is there is any analogue of mean value theorem for integral when the range is whole $R$?

Is there is any analogue of mean value theorem for integral of a continuous function when the range of the integral is whole real line? By MVT: if a function $f$ is continuous on the closed interval ...
1
vote
0answers
34 views

Vector calculus vs Vector analysis?

I was just wondering, is vector analysis the same as vector calculus? What about multivariable calculus? Because my multivariable calculus book (which I assume is the same as vector calculus?) covers ...
1
vote
2answers
159 views

On the decomposition of stochastic matrices as convex combinations of zero-one matrices

Let "stochastic" matrix be the matrix whose rows sum to one and deterministic matrix be a stochastic matrix whose all rows consist of a one and zero. For example $\left [ \begin{array}{ccc} 1 & ...
0
votes
1answer
78 views

Questions on CW-complexes

I am trying to proof the following two statements. If $X_1 \subset \dots \subset X_i \subset \dots$ is a infinite sequence of CW-complexes, then $X = \bigcup X_i$ is a CW-complex and each $X_i$ is a ...
5
votes
2answers
306 views

Stochastic geometry, point processes online lecture

Does any of you know where to find online lecture/podcast introducing stochastic geometry and/or point processes? Thank you! Riccardo
2
votes
2answers
61 views

Trying to understand the limit of regular polygons: circle vs apeirogon (vs infinigon?)

In the definition of regular polygon at the Wikipedia, there is this statement about the limit of a n-gon: "In the limit, a sequence of regular polygons with an increasing number of sides becomes ...
6
votes
2answers
110 views

Generalized convex combination over a Banach space

The Question: Is the following true? If not, what further hypotheses do I need? Let $X$ be a Banach space, and let $C \subset X$ be closed and convex. Let $P$ be a probability measure over $D$, ...
1
vote
1answer
30 views

Example of polynomial in dynamics

I am looking for an example of a post-critically finite polynomial $P$ (i.e. all critical points have finite orbit), which has both the following: a critical point on its Julia set (such as the ...
7
votes
4answers
301 views

What can I do with proper classes?

There are standard tricks, constructions and techniques in ZFC when working with proper classes; for instance one can form the cartesian product of a pair of classes without difficulty, or more ...
2
votes
1answer
19 views

what is a spectral function?

My knowledge in spectral theory is very limited, but lately I heard talking about the spectral function of an operator and how it's important. By curiosity I tried to look for a definition and a ...
1
vote
1answer
36 views

Reference for Dynamic Arrays

I'm looking for a reference for the fact that dynamic arrays have random access in constant time and inserting or deleting an element at the end can be done in constant amortized time. What would be a ...
0
votes
0answers
19 views

The basis induced by the nilpotent linear transformation

In Halmos's book, there is a theorem regarding the nilpotent transformation: If $A$ is a nilpotent linear transformation of index $q$ on a finite-dimensional vector space $V$, then there exist ...
4
votes
2answers
59 views

Order Properties on Open Sets

Considering the subset order on the open sets of a topological space, it seems natural to ask what kind of total orders exist as suborders of the subset order. One possibility is that each total order ...
11
votes
1answer
82 views

Continued fraction estimation of error in Leibniz series for $\pi$.

The following arctan formula for $\pi$ is quite well known $$\frac{\pi}{4} = 1 - \frac{1}{3} + \frac{1}{5} - \frac{1}{7} + \cdots\tag{1}$$ and bears the name of Madhava-Gregory-Leibniz series after ...
1
vote
0answers
38 views

On two definitions of the nerve of a simplicial category

Let ${\mathcal C}$ be a simplicial category. Then there are the following two ways of constructing a simplicial set from ${\mathcal C}$: Form the simplicial nerve $\text{N}_\Delta({\mathcal C}) := ...
4
votes
2answers
61 views

Proof: $Y$ stochastically dominates $X$ implies $E[\phi(Y)]\geq E[\phi(X)]$ for increasing $\phi$

Suppose $X$ and $Y$ are real random variables with CDF $F$ and $G$ such that $F(x)\geq G(x)$ (i.e. $Y$ exhibits (first-order) stochastic dominance over $X$). Then, for all increasing function ...
2
votes
0answers
67 views

Inquiry about My Self-Study Plan for Real Analysis (associated with my undergraduate research) [closed]

S.E advisers, I am a college sophomore in US with a major in mathematics and an aspiring mathematician in the computation theory and cryptography. I recently got an undergraduate research in the ...
19
votes
1answer
373 views

What function satisfies $F'(x) = F(2x)$?

The exponential generating function counting the number of graphs on $n$ labeled vertices satisfies (and is defined by) the equations $$ F'(x) = F(2x) \; \; ; \; \; F(0) = 1 $$ Is there some closed ...
3
votes
0answers
56 views

Analogy between Galois groups and fundamental groups

I've heard that there is an analogy between algebraic field extensions and covers (in topology). In this analogy Galois extensions correspond to Galois covers and Galois groups correspond to ...
0
votes
0answers
40 views

On a modified least square.

Given a vector $y \in \mathbb R^n$ and real constants $x_{ij}$ ($i=1,\dots,n$, $j=1,\dots,p$), we consider a vector $\beta = (\beta_0,\dots,\beta_p)$ which minimize ...
5
votes
3answers
292 views

Are all calculus textbooks “the same”?

I'm not satisfied with my calculus textbook,[1] and because of that I have searched for books by other authors. The problem is: all the books I have taken a look at are almost the same, even the ...
3
votes
0answers
35 views

Proving those hard cyclic inequalities

From time to time some user asks for help to prove a cyclic inequality, that is, something like $$f(x,y,z)\le k$$ where $x,y,z$ are usually real positive numbers and $f$ is a 'cyclic function' (I ...
2
votes
1answer
33 views

A general method for solving systems of quadratic equations

For linear systems we have general methods (i.e. Gauss elimination). Is there a general method for solving systems of quadratic equations with many variables? I heard about Groebner bases; is there ...
3
votes
4answers
67 views

Are there any books with lots of questions of “Fill in The holes” type

Does anyone knows books which have lots of questions ,whose format are like fill in the holes type . . Same goes for theorems and exercises . I am looking on pure math especially Real analysis ...
0
votes
0answers
11 views

Reference request for a mixed boundary value problem

Let $\Sigma$ be a compact Riemannian manifold with boundary and assume that $\partial\Sigma=Y_1\sqcup Y_2.$ Let $\Delta$ be the nonnegative Laplacian on $\Sigma.$ I am looking for the reference for ...
1
vote
0answers
31 views

Product of complex numbers $m+in$ with $0 < m,n \leq N$

I am trying to look for a generalization of Stirling's formula to complex numbers. In the integer case: $$ \log n! = \sum_{k = 1}^n \log k \approx \int_1^n \log x \, dx = n \log n - n$$ For the ...
3
votes
1answer
83 views

Looking for a good alternative to 'An introduction to manifolds' by Loring W. Tu

I'm currently studying some basic theory about manifolds from the book 'An introduction to manifolds' by Loring W. Tu. The problem I have with this book is that there are very little exercises, and ...
5
votes
3answers
291 views

What mathematical analysis book should I read (research, Putnam, personal enrichment)? [closed]

S.E advisers, I am a college sophomore in US with a major in mathematics and an aspiring mathematician in the fields of computation theory and cryptography. Recently, it became important matter that ...
1
vote
1answer
32 views

Books and sources concerning the mathematics of Leibniz and the feud with Newton

I am trying to find books and other sources concerning the mathematical history of Leibniz, including the controversy due to the independent discoveries of calculus by both Newton and Leibniz. I can't ...
5
votes
1answer
106 views

Problem book on linear algebra

Please refer a problem book on linear algebra containing the following topics: Vector spaces, linear dependence of vectors, basis, dimension, linear transformations, matrix representation with ...