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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1
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1answer
25 views

Limit(s) of a Sequence from the decimal expansion of $\pi$

I found a statement in a book concerning the decimal expansion of $\pi$ that I do not really understand. The statement is my problem number 2, where problem number 1 really looks like a reference ...
0
votes
0answers
33 views

Difference between Calculus $4$th edition and Calculus $3$rd edition by Michael Spivak?

I currently possess Calculus $3$rd edition by Michael Spivak in it's electronic form. However, I am considering buying a hard copy and have the option of buying either a used $3$rd edition or a new ...
0
votes
0answers
6 views

Table or diagram that classifies stochastic processes and summarizes their relationship?

I am looking for a diagram, table, graph, or something along those lines that classifies stochastic processes and summarizes how they relate to each other. Just to give an idea, I am interested in a ...
0
votes
1answer
13 views

How can I conclude this “gluing property” for these Sobolev functions?

Let $u \in W^{1,2}(\Omega) \cap C(\Omega)$, where $\Omega$ is an open bounded domain in $R^n$ with smooth boundary.Let $B(x,R) \subset \overline{B(x,R)} \subset \Omega $ a ball. Consider $u^{\star} ...
7
votes
7answers
442 views

Enjoyable book to learn Topology.

I believe Visual Group Theory - Nathan Carter is the best book for a non-mathematician (with high school math) to learn Group Theory. Could someone please recommend me a similar book (if there is) to ...
5
votes
2answers
292 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
0
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0answers
30 views

Set Theory text with solutions to exercises [duplicate]

I'm looking for a set theory text that has solutions to the exercises. I will be studying on my own and want to be able to check my understanding. Thanks for the suggestions.
2
votes
0answers
21 views

Generalization of a Result Concerning Projective Planes

Let $\mathcal P$ denote the set of all possible orders of projective planes. For $q\in\mathcal P$, let $PG_2(q)$ denote the projective plane of order $q$. There is a theorem due to James Singler ...
1
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2answers
71 views

Non-English-language graduate-level textbooks on differential geometry

I'm looking for modern graduate-level non-English-language differential geometry textbooks. I'm interested in original works by non-English-language speakers in their native languages, not ...
0
votes
0answers
12 views

$k$-vertex connected minimal Steiner network problem

Could any one suggest to me a paper related to the $k$-vertex connected minimal Steiner network problem? $k$-vertex connected minimal Steiner network problem is defined as: For an undirected and ...
19
votes
3answers
971 views

The most active fields of mathematics? [closed]

Which fields of mathematics are the most active at this time -- by number of papers published, grant money, people working in them or by any other measure? Any trends in this regard?
2
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0answers
19 views

Dimension of curves admitting a $g_d^r$ in $\mathcal{M}_g$

Let $\mathcal{M}_g$ be the moduli space of genus $g$ curves and $\mathcal{M}_{g,d}^r = \{[C] \in \mathcal{M}_g| \text{ C carries a } g_d^r \}$ the locus of genus $g$ curves carrying a linear system of ...
31
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11answers
14k views

Good books on mathematical logic?

I just started to learn mathematical logic. I'm a graduate student. I need a book with relatively more examples. Any recommendation?
1
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1answer
27 views

Permutation representations of finite abelian groups [closed]

What is a good source to study from about permutation representations of finite abelian groups, specifically $\mathbb{Z}_{p}$? If reference for the specific topic is not available, I would like to ...
2
votes
0answers
46 views

Find motivation for calculating $\int_{2}^{X} A^2(t) A(\alpha t)dt$

I read a thesis of Kong Kar Lun (student of Tsang K.M) about the some mean value theorems for certain errors terms in analytic number theory and in which he gave the asymptotic formulas of the ...
1
vote
1answer
34 views

Is the Fourier Transform of the limit the limit of the Fourier Transform?

Assume you want to compute the Fourier transform of a function $f_\epsilon(x)$ given by \begin{align} \mathcal{F}(f_\epsilon)(k) = \int f_\epsilon(x) e^{-ikx}\, dx \end{align} Further assume, that ...
4
votes
1answer
37 views

Fractional powers of positive self-adjoint operators

Consider two positive unbounded operators $A$ and $B$ densely defined on a Hilbert space $H$ self-adjoint on a domain $\mathcal{D}(A) = \mathcal{D}(B) = H_1$. By the spectral theorem, we can define ...
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7answers
463 views

Good Pre-Calculus book?

I was reading this article and the author mentioned I should come here and get some advice. I'm 17, currently taking Pre-Calc in high schooling doing really good, but I feel like I'm not getting the ...
1
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0answers
53 views

Ph.D thesis by Whitcomb

Does somebody has a link to Ph.D thesis by Whitcomb titled "The group ring problem" University of Chicago 1968. It was referred in a paper and I have some things to look up in that. I could not find ...
2
votes
1answer
44 views

Integral of the exponential of a homogeneous quartic - reference request

For a calculation I am doing, I have to calculate an integral of the form $$ I = \int_{\mathbf{R}^n} \exp[-Q(\mathbf{x})] d^n\mathbf{x} \text,$$ where $Q(\mathbf{x})$ is a homogenous, degree-4 ...
0
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0answers
19 views

References for Dirichlet characters and L-functions

I am working on some exercises from my Analytic Number Theory course regarding Dirichlet characters, and I was wondering if someone could provide some references for this. Here's a problem that I'm ...
0
votes
1answer
28 views

Prerequisites for Random Graph Theory

I would dearly love to know the prerequisites for self-studying Random Graph Theory and Percolation Theory in Probability. My knowledge currently involves: Basic probability concepts: the axioms, ...
3
votes
0answers
24 views

What can be said about the space of vector fields for which a given, say $C^1$, function is a Lyapunov function?

I am learning Morse homology and I have been thinking about the following observation. One way of doing, say finite-dimensional, Morse theory is by fixing a Morse function $f\in C^{\infty}(M)$, where ...
3
votes
1answer
45 views

Multivariable calculus chain rule for weak derivatives

Let $g:(0,1) \rightarrow \mathbb R^n$ be absolutely continuous, $F \in W^{1,2} (\mathbb R^n).$ Is it true that a.e. it holds $$ \dfrac{dF(g(t))}{dt} = \nabla F(g(t)) \cdot g'(t) \quad ? $$ What I ...
1
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0answers
35 views

What is the connection between game theory and (modal) logic?

I'm interested in dynamic epistemic logic lately (reasoning about information and change in multi-agent systems). I also like game theory. I'm looking for some good resources about the connection ...
2
votes
1answer
32 views

Is there a theory of induced representations for semigroups?

Given a semigroup $G$, a subgroup $H\subseteq G$ (not merely a subsemigroup) and a representation $\rho: H\rightarrow GL(V)$ for some vector space $V$, is there a canonical definition of an induced ...
4
votes
1answer
70 views

Introductions to Ehresmann connections and Chern-Simons forms

I am looking for introductory texts on Ehresmann connections and Chern-Simons forms. I seek detailed, hands-on presentation. Please, recommend sources that employ a differential forms approach rather ...
1
vote
1answer
75 views

Path to understand the maths behind contemporary Physics.

I am a physicist but I do really love maths and I would like to learn and have a deep understanding of the maths used in theoretical physics, just for leisure, in my free time. I know there is a ...
20
votes
2answers
346 views

How to ask dumb questions [closed]

I am having trouble asking questions in seminars, conferences, and public talks. As a graduate student I often fail to keep up with the speaker and more mature members of the audience at research ...
3
votes
1answer
56 views

Visual approach to abstract algebra

I'm currently finding abstract algebra to be very fascinating. However, one of the things that pulls me back is that I sometimes find it hard to understand something visually. For example, one could ...
3
votes
1answer
43 views

Differential Equations Lectures or books from a theoretical perspective?

I am looking for some differential equation lectures from a theoretical perspective, not a strictly computational one. I found the MIT 18.03 lectures which (as the professor says towards the end of ...
37
votes
10answers
3k views

Mathematical literature to lose yourself in

H.M. Edwards in the preface to his book on the Riemann Zeta Function, summarises his philosophy on learning Mathematics: ...I have tried to say to students of mathematics that they should read the ...
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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
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0answers
14 views

Reference request: 2nd order Taylor expansion for functions between finite dimensional normed vector spaces using Fréchet derivatives

I'm looking for a reference of 2nd order Taylor expansion for functions between finite dimensional normed vector spaces using Fréchet derivatives. If this can't be found I think it would suffice for ...
2
votes
2answers
176 views

Is the zero ring a domain?

Is the zero ring usually considered a domain or not? Wikipedia says: The zero ring is not an integral domain; this agrees with the fact that its zero ideal is not prime. Whether the zero ring ...
4
votes
0answers
77 views

Where can I learn more about the concept that is dual to “relation”?

Let $X$ and $Y$ denote sets. Then a relation $X \rightarrow Y$ is, by definition, a subset of $X \times Y$. Dually, we can define that a "corelation" $X \rightarrow Y$ is a partitioning of $X \uplus ...
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0answers
38 views

The following ODE global existence theorem reference?

There is an ODE existence theorem of the form: Let $f:[a,b]\times \mathbb{R}^n \to \mathbb{R}^n$ be a Caratheodory function. Suppose that there is a constant $c$ such that if $y$ is a ...
1
vote
1answer
37 views

Labeled commutative diagram

Consider a commutative diagram. For example the following diagram in $\mathbf{Set}$: $$ \begin{array}{ccc} & \overset{+1}{\longrightarrow} &\\ \mathbb{Z} & & \mathbb{Z} \\ & ...
2
votes
0answers
58 views

Biography of L. Euler [migrated]

Could you recommend a historically rigorous biography of L. Euler (if possible with discussions and examples of the mathematics he was doing)? Edit: I'd rather prefer a book (not necessarily about ...
20
votes
10answers
459 views

What are the theorems in mathematics which can be proved using completely different ideas?

I would like to know about theorems which can give different proofs using completely different techniques. For example: When I read from the book Proof from the Book, I saw there were ...
3
votes
1answer
91 views

A Generalized version of Inclusion-Exclusion Principle?

I recently read Doron Zeilberger's paper on Inclusion-Exclusion Principle. Let's say there are $n$ properties which are numbered $1,\cdots,n$. And let $A$ be a set of elements which has some of ...
0
votes
0answers
21 views

Functions equal in Sobolev spaces

Consider the Sobolev space $H^k(\mathbb{R}^n)$, where $k, n \geq 1$ are integers. Also, consider $u, v \in H^k(\mathbb{R}^n)$ such that $u$ and $v$ are equal almost everywhere in the Lebesgue measure ...
2
votes
1answer
68 views

Reference Request concerning Jet Bundles..

can anyone recommend me a nice reference concerning jet bundles? I've been looking for one for a long time but I couldn't find it...Thanks..
1
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0answers
22 views

Elliptic regularity of second order pseudos

Let $M$ be a compact manifold. Choose a point $q \in M$. Let $P$ be a second order positive self-adjoint pseudodifferential operator such that $\text{Spec}(P) \subset (0, \infty)$. Also, we know that ...
0
votes
1answer
22 views

Request book contains all functions with their series representations

Is there any book that contains all functions with their series representations like this site http://functions.wolfram.com/ElementaryFunctions/Log/06/ShowAll.html?
0
votes
1answer
32 views

Riemann surfaces from a number theoretic point of view

I need to learn the basic theory of Riemann surfaces and would like to pick a book which is most relevant to algebraic number theory. I have a good understanding of all underdraduate algebra and the ...
1
vote
0answers
21 views

Is there a polynomial time algorithm for Poly-trees (oriented trees) isomorphism?

In terms of graph isomorphism complexity classes Trees have a polynomial time algorithm and Directed Acyclic Graphs (DAG's) do not (so far). What about Poly-trees (oriented trees)? These are DAG's ...
26
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4answers
6k views

Rudin or Apostol

I have an option to choose between the two books Mathematical Analysis by Tom Apostol and Principles of Mathematical Analysis by Walter Rudin as I was gifted Rudin by a friend and ended up buying the ...
3
votes
2answers
60 views

What are some good reasonably rigorous texts on the mathematics of infinity?

The Infinite Book is too light and not focused enough on the mathematics of infinity, and Everything and More: A Brief History of Infinity has too much focus on the history of infinity instead of the ...
2
votes
0answers
98 views

references for an arithmetic function

I was wondering if anyone is aware of any existing literature on the arithmetic function defined as $$f(n):=2^{\omega(n)}\tau(n).$$ Here $\omega(n)$ is the number of distinct prime divisors of $n$ and ...