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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1
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0answers
48 views

Suggested book for self study.

I have a degree in Financial Risk Management, and did 4 semesters of calculus and analysis(but that was about 10 years back), with most of my other efforts going toward Mathematical Statistics and ...
1
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3answers
100 views

Recommendation on Category theory textbook [duplicate]

I had posted a question about category theory some months ago, and I got answered that there are two ways to study Category Theory. One is to treat Category Theory as a logic system independent from ...
7
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1answer
129 views

Which hot math research fields became insignificant later on?

In history (for last 150 years), which math research fields were hot (popular) at their time , but whose results became insignificant (almost useless) later on? The reason I ask this question is ...
16
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1answer
318 views

Mathematics of Torrenting

It is more or less common knowledge that a bittorrent network has the potential to be much faster than direct downloads, but I have never seen any real math describing why, or any theoretical bounds ...
1
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2answers
25 views

Verification of sequence result

Is it true that if a real sequence $\{x_n\}_1^\infty$ has an infimum but no convergent subsequences then the infimum must be the minimum as well? Secondly, can it be proved that the sequence defined ...
1
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0answers
36 views

Construction of noncommutative torus

In short, how do we get the formula for the NC torus? I find the equations in many places (including here) but I still have no idea for how this comes from the torus. If my understanding is correct, ...
1
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1answer
39 views

Prerequisites for Hilbert Cohn-Vossen's Geometry and the Imagination?

I've not read this book(not really),but I would like to know how much is assumed by the reader. can I recommend this to the layperson? Also ,any more recent similar books? I already know of Courant ...
1
vote
1answer
83 views

Book recommendations for these types of math?

I'm planning to write a math olympiad in a couple of months (4-5), and am just really trying to get the preparation in. I'm a fairly good math student (did ok in math, not an A+, but I got an A so my ...
2
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0answers
129 views

Changing a queueing processes

Situation Consider a general queueing system $\mathscr{S}$, whose customer arrival times are independent, and whose service times are independent; both of these are allowed to have general ...
8
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1answer
355 views

Question regarding the Kolmogorov-Riesz theorem on relatively compact subsets of $L^p(\Omega)$.

Usually, the Kolmogorov-Riesz theorem is quoted for $L^p(\mathbb R^n)$, but I am looking for versions considering spaces over subsets in $\mathbb R^n$. The following is from the book "Sobolev spaces" ...
3
votes
1answer
74 views

Eisenstein-type series

Is the series, $$1 - 24\sum_{n = 1}^\infty \frac{q^{2n}}{(1 - q^{2n})^2}, \quad q = e^{\pi i \tau}, \quad \textbf{I}[\tau] > 0,$$ somehow related to $$E_2(q) = 1 - 24\sum_{n = 1}^\infty ...
0
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1answer
24 views

Singular locus of orientable 3-orbifolds

Any reference (or any hints if the proof is easy) for the proof that the singular locus of a 3-dimensional orientable orbifold is a trivalent graph with each edge labelled by integers $a,b,c>1$ and ...
1
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1answer
61 views

Hilbert Class Field for pure cubic fields

I am new to class field theory, I want to study Hilbert class field for pure cubic fields. Which is the good source? Thank you in advance.
6
votes
2answers
530 views

Organizing types of functions by their calculus-related properties, in diagram form?

Does anyone know of a diagram that displays and organizes categories of functions according to their calculus-related properties (e.g. continuous, $C^\infty$, degrees of differentiability and ...
2
votes
4answers
63 views

Bounding a modified Bessel function of the first kind.

Let $I_0$ be the zeroth-order modified Bessel function of the first kind. We know that, asymptotically as $x\to \infty$, $I_0(x) \sim e^x/\sqrt{2\pi x}$. Does anybody have a reference for the maximum ...
6
votes
2answers
153 views

Push forward of the structure sheaf along covering

Let $f: X \to Y$ be a covering (proper, surjective, finite regular map) of smooth projective varieties of degree $d$. How one can show that in this case $f_* \mathcal{O}_X$ is a locally free sheaf of ...
1
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0answers
36 views

Expected values of continuous and bounded functions are equal then random variables are equal, too.

I have seen several of reasoning based on the following fact: Real random variables $X, Y$ in $\mathbb{R}^n$ are equal almost surely if and only if $\mathbb{E}g(X)f(X) = \mathbb{E} g(X)f(Y)$ for ...
3
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1answer
65 views

Groups of isometries

I recently read the popular scientific book "Symmetry and the Monster" and it emphasizes groups as the sets of symmetries of geometrical objects. So I was wondering, do all groups appear as symmetry ...
1
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0answers
24 views

Weak stochastic integral

I recently encountered the following object, referred to as "weak stochastic integral" in the book of SPDE's by Prévôt/Röckner [PR07]: $$ \int_0^T \langle \Psi \,\mathrm dW(t), \Phi(t)\rangle $$ A ...
2
votes
1answer
36 views

Markov processes on function spaces

Is there any reference on Continuous time Markov process whose state space is infinite dimensional function spaces, such as the space of continuous functions $C(R^d)$? It seems Dirichlet Form is a ...
25
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11answers
4k views

Good books on Philosophy of Mathematics

Where can I learn more about the implications, meta discussions, history and the foundations of mathematics? Is Russell's Introduction to Mathematical Philosophy a good start?
0
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0answers
21 views

Problem supplement for Advanced Calculus (Loomis and Sternberg)

There are too many problems in Loomis and Sternberg's Advanced Calculus for them to be useful. Can someone recommend a collection of problems to supplement this book? A short list of its best problems ...
5
votes
2answers
326 views

Complex and Kähler-manifolds

I was woundering if anyone knows any good references about Kähler and complex manifolds? I'm studying supergravity theories and for the simpelest N=1 supergravity we'll get these. Now in the ...
3
votes
1answer
33 views

Disquisitiones Arithmeticae Chapter 8?

Does anyone know where I can find the posthumously published (I think) chapter 8 of Gauss's Disquisitiones Arithmaticae?
1
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1answer
30 views

How can I solve this set of linear coupled system?

Consider the matrix $A=\begin{bmatrix} -2k & k \\ k & -2k \end{bmatrix}$ .I have to solve this linear coupled system : $X'' = A.X$, where $X= \begin{bmatrix} x_1(t) \\ x_2(t) \end{bmatrix}$ ...
1
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1answer
44 views

Question for recommending a good textbook in representation of quivers

I am taking representation of quivers, and the lecture notes seems not enough. So could you recommend a good textbook for this course. There is a new book "Quiver Representations, by Ralf Schiffler" ...
0
votes
2answers
90 views

defining the group law on elliptic curves in general

Let $k$ be an arbitrary field and $C \subset \mathbb{P}^2(k)$ an elliptic curve. In order to define the group law on $C$ we need to establish some geometric facts first, e.g. Any line intersects $C$ ...
6
votes
1answer
56 views

probability that two randomly selected integers of an imaginary quadratic field of class number 1 are coprime

Given an imaginary quadratic field $\mathbb{Q}(\sqrt{-D})$, where $D$ is a Heegner number (1, 2, 3, 7, 11, 19, 43, 67, 163), what is the probability that two randomly selected elements of that fields' ...
3
votes
1answer
27 views

Statistical Estimation Book Request

I am seeking a clear book for parameter estimation, estimation methods, properties of estimators, minimum variance estimators, asymptotic properties of estimators and interval estimation reducution.
2
votes
2answers
295 views

What are the best texts on undergraduate linear algebra?

I have recently finished a course in 'elementary linear algebra,' which entails basic systems of linear equations, in-depth study on matrices, the basics of vector space, inner product spaces, linear ...
12
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9answers
3k views

A Book for abstract Algebra

I am self learning abstract algebra. I am using the book Algebra by Serge Lang. The book has different definitions for some algebraic structures. (For example, according to that book rings are defined ...
9
votes
6answers
417 views

Reference request for undergraduate complex analysis.

I am a second year student studying electrical engineering. I self-study pure mathematics and want to pursue a career as a mathematician. What are some prerequisites for studying complex analysis? ...
1
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0answers
19 views

Bounds re Asymptotic Formula for the Sum of Largest Prime Factors

I have a reference request related to the result : $\sum_{n=2}^{x} P(n)$ ~ $\frac{\pi^2}{12}\frac{x^{2}}{log(x)}$ as $x \rightarrow \infty$ where $P(n)$ is the largest prime factor of the positive ...
3
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0answers
36 views

Relations between the Eisenstein series and the hypergeometric series

It is known that $$E_4(\tau) = {}_{2}F_{1}\left(\frac{1}{12}, \frac{5}{12}; 1; \frac{1}{J(\tau)}\right)^4$$ and $$E_6(\tau) = {}_{2}F_{1}\left(\frac{1}{12}, \frac{7}{12}; 1; \frac{1}{1 - ...
4
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2answers
80 views

what is the most easy to read Algebraic Geometry book? [duplicate]

All: what is the most easy to read (most accessible) Algebraic Geometry book ? (If possible, I am looking for an introduction book, maybe for undergraduate, and maybe similar to A Friendly ...
1
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1answer
41 views

Examples of divergent series summed by means of the analytic continuation of the corresponding

For my Bachelor's thesis, I am investigating divergent series. This is (yet another) question on this topic. Apparently, a divergent series $$ S = \sum_{n=1}^{\infty} a_{n} $$ can be summed by means ...
3
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1answer
45 views

Gauss Disq. Arithm. Translation Errata?

Note: I apologize if this is the wrong website/section to be posting such questions, but at the same time I hope someone can help me. Hi, this year I finished high school and decided to start reading ...
1
vote
1answer
418 views

Linear algebra and Multivariable calculus prerequisites for Stochastic Calculus

Which topics are considered "graduate-level" for the following subjects: Linear algebra Multivariable calculus On Internet, it is said that you need "graduate level" Linear algebra and ...
20
votes
2answers
478 views

How does one parameterize the surface formed by a *real paper* Möbius strip?

Here is a picture of a Möbius strip, made out of some thick green paper: I want to know either an explicit parametrization, or a description of a process to find the shape formed by this strip, as ...
4
votes
0answers
139 views

Dummit and Foote as a First Text in Abstract Algebra

I'm wondering how Dummit and Foote (3rd ed.) would fair as a first text in Abstract Algebra. I've researched this question on this site, and found a few opinions, which conflicted. Some people said ...
1
vote
1answer
61 views

On Stochastic 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
27 views

Verification of extension result for Lipschitz functions

does anyone know the following result? If it holds in this form and any source which presents it? Thanks a lot. Consider metric space $(X,d_{X})$. Let $f:A \subset (X,d_{X}) \rightarrow \mathbb{R}$ ...
0
votes
1answer
97 views

When is a vector space (over field $K$) also a ring (with subring $K$)?

(Apologies in advance for the very naive question. I'm just learning about all this. Also, for the sake of expedience, below I use the word "ring" when it would more correct for me to use ...
4
votes
3answers
125 views

(translated)Russian mathematics books?

Most russian mathematician(generally) are known to do and teach mathematics in a very original manner,they do in a very intuitive yet rigorous way, with/through wonderful connection to physics. ...
4
votes
6answers
96 views

Book on “Measure and integration” for starters.

This semester I have a course on Measure and Integration. I'd like you to recommend me some books.
0
votes
2answers
57 views

Problem book for abstract linear algebra

Kindly suggest a good book for abstract linear algebra other than finite dimensional vector space by P R Halmos
0
votes
0answers
20 views

Reference request for properties of harmonic polynomials

I am reading this paper, and on page $4$ it takes a non-degenerate quadratic form $q$ on a finite dimensional complex vector space $V$, defines the laplacian assosciated to $q$, $\Delta$, acting on ...
2
votes
1answer
26 views

complexity of solving $n \times n$ rank deficient linear system

I think it is known that given a nonsingular $A \in \mathbb{R}^{n \times n}$ and $b \in \mathbb{R}^n$, solving a linear system $Ax =b$ for $x$ can be done in $O(n^3)$ steps. Now assume $A$ is of rank ...
2
votes
3answers
127 views

Abstract Algebra Book Request

I am looking for a good undergraduate level book on Abstract Algebra. By a 'good book' I mean a book which gives equal importance to both, rigor and the historical perspective of the subject. For ...
2
votes
1answer
84 views

Is there a theory of “rings” with partially defined multiplication?

Consider the abelian group $R [[\mathbb{Z}^d]]$ of all formal Laurent series over a commutative ring $R$ (a typical element has the form $\sum_{v \in \mathbb{Z}^d} \lambda_v \cdot X_1^{v_1} \dots ...