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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2
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0answers
6 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.
0
votes
1answer
18 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
0answers
18 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
22 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
96 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 ...
-1
votes
0answers
45 views

Paper pen algorithms [on hold]

I want all paper and pen algorithms from addition to fields medal problems. Where do I go? I've searched the web, I've even bought a book, but without any luck.
2
votes
0answers
28 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 ...
3
votes
0answers
48 views

How to approach real analaysis

I'm just starting first year in university in Europe and here there there is no Calculus, instead you jump right into Analysis. The trouble is, for some time I self-studied through US style books and ...
2
votes
1answer
78 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 ...
9
votes
6answers
342 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? ...
0
votes
1answer
16 views

If $R\rightarrow S$ is faithfully flat then show that it is pure, and reference for purity

I was reading about $F$-purity and $F$-splittings, when I came across then following statement which I can't proof: Definition: Let $R$ be a commutative ring with identity, and $M,N$ be $R$-modules. ...
0
votes
0answers
44 views

Has this partition a name?

The decomposition in disjoint cycles in $S_n$ was inspiring for this question. I found out (if I did nothing wrong) that more generally a bijection $f:X\rightarrow X$ induces a partition of $X$ ...
0
votes
3answers
42 views

A proof of compactness, connectedness of real projective space

I need a reference for a complete proof of the below theorem: Let $RP^n$ be $n$-dimensional real projective space. Then $RP^n$ is a compact, connected manifold. (Consider the standard topology over ...
2
votes
0answers
27 views

Besov spaces---concrete description of spatial inhomogeneity

Some very pedestrian questions about Besov spaces. Just to fix notation: 1.Let $f \in \mathcal{S}'$, the space of tempered distributions. 2.$\Psi, \{ \Phi_n \}_{n \geq 0} \subset \mathcal{S}$ such ...
0
votes
2answers
40 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
1
vote
1answer
19 views

Canonical form for orthogonal similarity classes

Could someone point me to a reference re canonical forms for classes of matrices in $M_n(\mathbb{C})$ which are unitarily similar? That is, canonical representatives for the equivalence class defined ...
0
votes
0answers
18 views

Mathematics Subject GRE Apps [on hold]

I was wondering if anybody could recommend any smartphone apps which would be helpful for the Mathematics Specific Subject GRE exam. Most of the resources I have found are for the general GRE. ...
2
votes
2answers
81 views

Example of a proof using the axiom of commensurability

I'm teaching our intro to proofs course (well, one of them) and one of the classic illustrations of an overturned "axiom" is the Greek axiom of commensurability, which stated in geometric terms the ...
2
votes
1answer
46 views

Generalized Logarithmic Integral - reference request

This page at I&S forum defines the Generalized Logarithmic Integral as $$L\left[ \begin{matrix} a,b,c \\ d,e,f \end{matrix};z\right] =\int_0^z \frac{\log^a x \log^b(1-x)\log^c(1+x)}{x^d (1-x)^e ...
2
votes
1answer
52 views

Combinatorics of a game

Suppose there are $n$ people sitting in a circle, with $n$ odd. The game is played in rounds until one player is left. Each round the remaining players point either to the person on their right or ...
1
vote
0answers
39 views

Linear programming - Textbook recommendations

Next term, I will attend a course on linear programming. Due to the assignments, we will have to write many thorough proofs. I anticipate that we will be supposed to cope with in-depth background ...
0
votes
0answers
38 views

An explict description of the integral closure of $A=k[x,y]/\langle x^3-y^2\rangle$.

Let $k=\mathbb C$ and $A=k[x,y]/\langle x^3-y^2\rangle$. Denote by $X$ and $Y$ the cosets of $x$ and $y$ in $A$. Question: How do we see that the integral closure $A'$ of $A$ is $k[Y/X]$? Since ...
-2
votes
0answers
49 views

Solutions to Topology by Munkres [on hold]

I was searching for solution to chapters 1, 2 & 3 of the book 'Topology' by James Munkres. Any suggestions where it can be available.
1
vote
0answers
33 views
+150

Alternative proof of Girard's theorem

I am looking for an alternative proof of Girard's theorem. The standard proof, which is almost trivial, relies too much on visualizing spherical triangles on the sphere. Is there a more algebraic ...
0
votes
0answers
23 views
+50

Changing a queueing processes

I am wondering if there are any general results related to how queue behavior changes if one is allowed to repeatedly make one-off behavior changes. Situation Consider a general queueing system ...
1
vote
0answers
19 views

English translation of Minkowski's Geometry of Numbers

Is there an English translation of Minkowski's Geometry of Numbers? I have searched it but have found nothing.
2
votes
0answers
39 views

What is the relation between the length of period of simple continued fraction expansion of quadratic algebraic numbers and the integer

As we know,$\sqrt{2} = [1;2,2,2,2,…]$; while $\sqrt{14}= [3;1,2,1,6,1,2,1,6…]$,let $L$ the length of period of simple continued fraction expansion of quadratic algebraic numbers be the number of ...
5
votes
0answers
43 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
0answers
35 views

Reference for understanding coalgebra

I am trying to read this paper, but I have no knowledge of coalgebra and have just started to learn Category Theory so I am struggling to understand it. Are there any references that can explain ...
0
votes
3answers
41 views

Collected works of David Hilbert?

1) Is there a collected works of D. Hilbert? 2) If 1) is affirmative, is there an English translation of the collected works of D. Hilbert?
0
votes
0answers
32 views

Solutions to problems in the ODE book by Gerald Teschl

I am self learning ODE by the book: Ordinary Differential Equations and Dynamical Systems by Gerald Teschl. Anyone knows where I can solutions to the problems given in this book? Thank you.
2
votes
2answers
68 views

Which book is appropriate for a Chemistry student that needs to learn basics about integrals?

A friend of me who is not studying mathematics now needs to deal with integrals, double integrals and triple integrals within his study of chemistry. He asked me to give him a suggestion for a basic ...
0
votes
0answers
28 views

Updating the LU Factorization

I am looking for a way to update the $LU$ factorization of a general $m \times n$ matrix after adding a column to the matrix. I have to iterate this procedure so I will begin with a matrix that is $m ...
6
votes
2answers
117 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 ...
2
votes
0answers
19 views

Relations between Eisenstein series and 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 - ...
0
votes
0answers
7 views

about a barrier argument involving p-harmonic functios

Consider the lemma 2.2 and lemma 2.3 of this paper : http://www.ams.org/journals/tran/2002-354-06/S0002-9947-02-02892-1/S0002-9947-02-02892-1.pdf Lemma2.2: Let $D $ a convex domain in $R^n$ and ...
1
vote
0answers
6 views

References to papers/books that uses a kernel to smooth a discrete distribution

Since a kernel, such as Gaussian, is often used to smooth out the distribution of discrete points in 1D, 2D or 3D, I believe there must be some study materials or research work that have used this, ...
0
votes
0answers
16 views

References to papers/books that uses a kernel to smooth a discrete distribution

Since a kernel, such as Gaussian, is often used to smooth out the distribution of discrete points in 1D, 2D or 3D, I believe there must be some study materials or research work that have used this, ...
7
votes
1answer
532 views

If I know the probability of something happening after n trials is X, how can I estimate the probability of it happening for each individual trial.

This is assuming each trial has an independent probability. In other words, lets say that I perform $50$ trials a $100$ times. I know that the event happened only in $5\%$ of those hundred $50$-trial ...
1
vote
0answers
18 views

3-Point Shoot using Quadratic Equation [on hold]

This is my assignment. The question is "In what part of the three-point line can a player do best the three-point shoot to gain 3 point but using quadratic equation." There are no data given but we ...
1
vote
0answers
39 views

Absolute continuity and convolution

Suppose that $\mu$ is a finite Borel measure on the real line, $f, g\in L^1(\mu)$. Define $\nu=\mu\ast\mu$. Do I understand correctly that the convolution $f\mu\ast g\mu$ is absolutely continuous wrt ...
0
votes
1answer
30 views

Main theorem of Pythagorean plane

The theorem states: Any Pythagorean plane is isomorphic to the Cartesian plane $F^2$ over its field $F$ of segments. Can anyone give me a reference for this theorem?
4
votes
2answers
91 views

How to prove that all smooth vector bundles on a given vector bundle are the pull back of a vector bundle on the base

Recently, during a conversation, I heard about the result (previously mentioned also here on MO), whose statement is reported below. Not having the specific background necessary to reconstruct a proof ...
0
votes
0answers
21 views

Hölder continuity for parabolic equations

What is a good and modern reference for hölder regularity for non-degenerate parabolic equations? To be a bit more precise, I have a degenerate parabolic equation, exhibiting two degeneracies, and can ...
0
votes
0answers
14 views

Geometric dual graph

It is well known the notion of geometric dual graph. Let $G^*$ be the geometric dual of a planar graph $G$. I need the proof that $(G^*)^* \cong G$ , where can I find it ?
1
vote
0answers
35 views

Building a function $p : \mathcal{D} \rightarrow \mathbf{Ord}$ from a faithful functor $U : \mathcal{C} \rightarrow \mathcal{D}.$

For simplicity, I will ignore size issues in this question. Let $\mathcal{D}$ and $\mathcal{O}$ denote categories. By a function $\mathcal{D} \rightarrow \mathcal{O},$ let us mean a functor from the ...
5
votes
2answers
121 views
+100

Which statements are equivalent to the parallel postulate?

I would like to have a long-ish list of statements that are equivalent to the parallel postulate. If a line segment intersects two straight lines forming two interior angles on the same side that ...
0
votes
0answers
17 views

Non-standard extensions of $p$-adic fields

Does there exist a non-standard extension of a non-Archimedean field (such as the construction $*\mathbb{R}$ out of $\mathbb{R}$ or the surreals $\mathbb{S}_\mathbb{R}$, not to mention their ...
0
votes
0answers
86 views

Proof that $G(3)\le 7$

Let $G(k)$ be the minimal $n$ s.t. every sufficiently large integer is the sum of $n$ nonnegative $k$th powers. Does anybody know where I can find Vaughan's proof that $G(3)\le 7$? I can't find a ...
2
votes
1answer
41 views

Reference for $F$-algebras and induction?

I've been learning about $F$-coalgebras and coinduction from this fantastic paper, which has really helped me get a feel with its many examples. I'm starting to struggle with reconciling the ...