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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0
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2answers
74 views

Positive operators in Hilbert spaces

Let $H$ be a Hilbert space. I am just asking if there's some reference which studies operators $A$ with this property: $$\left\langle Ax,x\right\rangle \geq0,$$ for all $x\in H$. And $Ax=0$ whenever ...
1
vote
0answers
47 views

what is the origin of the proof via peaks?

What is the history of the proof of the existence of a monotone subsequence via peaks as found for example here as well as in problem 6, page 4 here (where they are called "giants" instead of ...
1
vote
0answers
9 views

Reference requests on SP -graphs to outline its research areas

I want to understand SP graphs (series-parallel graphs) deeper for more elegant computation. I want to understand which area to research to understand sp-graph deeper: logical formalism? ...
4
votes
1answer
144 views

Book in which Calculus is explained in the form of a Teacher-Student Conversation

I remember reading the preface of a Physics textbook in which the author mentions a book on Introductory Calculus in which the matter is explained in the form of an innovative conversation between a ...
6
votes
4answers
450 views

University-level books focusing on intuition?

I help some students with difficulties in Mathematics and Physics (especially math, physics, and engineering majors). While in high school they usually don't study, or are not interested, etc., in ...
2
votes
2answers
121 views

Trigonometry book which develops geometric intuition.

I'm looking for a trigonometry text that helps develop a lot of geometric intuition and goes deep into the subject. Also some geometry problems which actually require thinking about would be in order. ...
35
votes
4answers
3k views

What's between the finite and the infinite?

I'm wondering if there are any non-standard theories (built upon ZFC with some axioms weakened or replaced) that make formal sense of hypothetical set-like objects whose "cardinality" is "in between" ...
1
vote
2answers
2k views

What is a third proportional?

I searched online, couldn't find anything clear. If I had two numbers, $a,b$, what is their third proportional? Apparently it can be either $c$ such that $a/b=b/c$ or $b/a=a/c$, but obviously these ...
5
votes
1answer
47 views

Components of the space of immersions 2-manifold into $\mathbb R^3$

Let $M$ be a $2$-sphere with $g$ handles. Consider the space of maps $M\to \mathbb R^3$, which are immersions [i.e. smooth maps with nondegenerate differential in each point $x\in M$], with ...
1
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3answers
69 views

Resources on Mathematics for the Educated non-Mathematician

I was wondering what the best books are for giving an educated non-mathematician the gist of real mathematics. Not to say that I am by any means a real mathematician, but it is one of my goals to ...
0
votes
1answer
28 views

Treatments of Lie theory and Noether theorems in tensor notation

I am looking for a conceptual treatment of Lie theory and Noether theorems that uses tensors calculus rather than exterior calculus. I know that tensor calculus is not optimal for these subjects, ...
2
votes
0answers
48 views

Reference request: Do any papers on odd perfect numbers approach the problem using the following equation?

(Note: This question has been cross-posted to MO.) Do any papers on odd perfect numbers approach the problem using the following equation? $$N - (q^k + n^2) + 1 = ...
8
votes
4answers
325 views

Is “Linear Algebra Done Right 3rd edition” good for a beginner?

Amazon book reviews say it takes unorthodox approach and is for a second exposure to linear algebra. I didn't have a first exposure to linear algebra. Is this book going to be bad for me, then? Or, ...
2
votes
2answers
69 views

Reference Request for Fibre Bundle Theory from the Smooth Manifold Point of View

I am looking for a book, or a set of notes, which discusses some basic theory of fibre bundles. I am interested more in the geometric aspect (smooth manifolds) rather than topological aspect. I found ...
12
votes
6answers
6k views

Geometry Book Recommendation?

Can someone recommend a good basic book on Geometry? Let me be more specific on what I am looking for. I'd like a book that starts with Euclid's definitions and postulates and goes on from there to ...
1
vote
2answers
103 views

Introductory Linear Algebra Book Recommendation

I am looking for an introductory book on Linear Algebra. But the posts that I have found related to this question (for example this one) doesn't meet (neither address) my specific requirements. So I ...
0
votes
0answers
43 views

Text book on solid geometry/stereometry, without involving analytic geometry

As the title says I'm searching for a textbook, about solid geometry, without involving analytic geometry. The material which the book should cover is the stereometry learned in the eastern bloc. An ...
10
votes
11answers
862 views

Text suggestion for linear algebra and geometry

I want to study more linear algebra over the summer, specifically relating it to geometry. I was originally going to read Shafarevich's Linear Algebra & Geometry, after a recommendation, but it ...
6
votes
1answer
2k views

What's a good book on advanced linear algebra?

I'm taking an advanced linear algebra course and I'm a little confused about books. The teacher said we could use any book we wanted to, but he recomended just Hoffman and Kunze and also Kostrikin, ...
2
votes
1answer
124 views

Develop good understanding of Linear Algebra

I am self studying Linear Algebra from book by Kenneth Hoffman and Ray Kunze, and currently I'm on 2nd Chapter of vector spaces, though the text is easy to follow, specially the exercises that follow ...
2
votes
1answer
42 views

Question on syzygies

It is hard to formulate a question, but I want to ask about a reference/recipe for computing syzygies in general. For example, on $\mathbb{P}^1_{(x:y)}$ there is an exact sequence $0\longrightarrow ...
1
vote
0answers
55 views

Books with similar coverage to Linear Algebra Done Wrong

Axler's book is great, but for my immediate purposes, it isn't suitable. I've been looking at the Table of Contents of Linear Algebra Done Wrong by Treil starting at p. 5 of this document but there's ...
0
votes
2answers
52 views

Is $x_1^d + x_2^d + x_3^d + x_4^d + x_5^d= 0$ a geometrically integral hypersurface in $\mathbb{P}^4$?

Let $d>2. $Let $X$ be a surface defined by $x_1^d + x_2^d + x_3^d + x_4^d + x_5^d= 0$ in $\mathbb{P}^4_{\mathbb{Q}}$? I am interested in finding out if this is a geometrically integral hypersurface ...
2
votes
0answers
21 views

Website for sharing solutions/proof verification?

Is there a website for sharing solutions to exercises in math books? I'm self-studying math and I find solution manuals like this very helpful. When I do an exercise, I usually scribble down a few ...
3
votes
0answers
49 views

Short exact sequence on $\mathbb{P}^1$

Let F be a torsion free sheaf of rank $n+4$ over $\mathbb{P}^1$ which fits in the SES $0\longrightarrow\mathcal{O}_\mathbb{P^1}(-3)^{n+2}\longrightarrow ...
1
vote
0answers
25 views

Hilbert's inequality for $\left|\sum_{n\neq m}\frac{a_n \bar{a}_m}{\left(n-m\right)^\lambda}\right|$.

We know that, the Hilbert's inequality for double series states $$\left|\sum_{n\neq m}\frac{a_n \bar{a}_m}{n-m}\right|\leq\pi \sum_n |a_n|^2$$ for $a_n\in\mathbb C$. I'd like to know if inequalities ...
2
votes
1answer
483 views

Centre of symmetric group algebra

I'd like to know a reference for a simple proof that $\{c_\mu\mid \mu\vdash n\}$ is a basis for the centre of the symmetric group algebra $\mathbb{C}\mathfrak{S}_n$, where $c_\mu$ is the sum of all ...
23
votes
2answers
342 views

A diophantine equation with only “titanic” solutions

I made a note some time ago that I had read in some book that the equation $$313(x^3+y^3)=t^3$$ has positive integer solutions, but that these are so large that it would be absolutely hopeless to ...
5
votes
3answers
315 views

CINEMA : Mathematicians

I know that a similar question has been asked about mathematics documentaries in general, but I would like some recommendations on films specifically about various mathematicians (male and or female). ...
4
votes
1answer
1k views

Dual and adjoint operator

Let $X$ be a Hilbert space with associated canonical isomorphism $I:X\rightarrow X^\ast$ (by the Riesz representation theorem). If $A:X\rightarrow X$ is a linear operator on $X$, then its dual ...
2
votes
0answers
38 views

Construction of Tate curve and formal schemes

In the notes websites.math.leidenuniv.nl/geom/tate.ps (and probably in other places), there is a construction of the Tate curve, where the steps are summarized below. 1) Take ...
3
votes
0answers
80 views

Symmetry and trivial solutions to Pell equations

Below is a representation of the solutions to the equation $x^2-Dy^2=1$ for $6(6-1)\leq D \leq 6(6+1)$: \begin{array}{c} & 30 & 31 & 32 & 33 & 34 & 35 & 36 & 37 & ...
1
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0answers
24 views

Reference request: correlation and spectral analysis of stochastic processes

I'm wondering if anyone knows of a reasonably rigorous text on stochastic processes that discusses specifically things like the autocorrelation, spectral density, and other "correlation and spectral" ...
6
votes
1answer
113 views

name of the unit of adjunction between $-\times C$ and $\cdot^C$

Answers to a earlier question about the categorical interpretation of first-order quantification led me to learn more about adjoints. Now, I understand that a category $\mathscr{C}$ with products has ...
2
votes
1answer
35 views

Geodesics are minimizing in a simply connected manifold without conjugate points?

Let $\tilde M$ be a compact Riemannian manifold, without conjugate points. Denote by $M$ its universal cover. Then in this paper, it is claimed that every geodesic is globally length minimizing. Why ...
1
vote
2answers
64 views

No Galois Theory in Godement's Cours d'Algebre?

I just procured an English translation of Godement's Cours d'Algebre and was interested in reading the treatment of Galois Theory. I started to look for the relevant chapter in the ToC, but to my ...
0
votes
0answers
17 views

Decidability of the theory $(\mathbb{R},+,*,\max,\leq)$

I know that the theory $(\mathbb{R},+,*,\leq)$ is decidable (Tarski 51) and I was wondering wether the decidability status is known when extending this theory with the $\max$ operator. Do you have ...
1
vote
2answers
46 views

how to find null space basis directly by matrix calculation

The problem of finding the basis for the null space of an $m \times n$ matrix $A$ is a well-known problem of linear algebra. We solve $Ax=0$ by Gaussian elimination. Either the solution is unique and ...
23
votes
3answers
528 views

List of old books that modern masters recommend

This is a fairly unambigious question but it hasn't been asked before so I thought I would ask it myself: Which old books do the modern masters recommend? There are old books where the mathematical ...
1
vote
1answer
44 views

Does this function have a name? What other properties does it have?

Let $x < y$ be real numbers and let $ a$ satisfy $0<a<1$, Does the function $ z = a y +(1-a)x$ have a name? What properties does this function have? This particular function has come up a ...
0
votes
0answers
40 views

Quick question about number of positive summands in a sum of $p$-adic integers

I've started reading recently on $p$-adic numbers online. Forgive me if the question is silly. Let $\mathbb{Z}_p$ be the ring of $p$-adic integers and let $a_1, \ldots, a_k \in \mathbb{Z}_p$. If ...
0
votes
0answers
33 views

Prove that The set of Sentences over a theory $T$ is a Cartesian Closed Category

i am sorry to bother but, I have doubts with this problem: In some elementary theory $\;$ $T$ $\;$ consider the set $S=\{p,q,\ldots \}$ of sentences of $T$ as a preorder, with $p\leq q$ meaning "$p$ ...
0
votes
2answers
55 views

Reference request on complex projective algebraic geometry

I am looking for a reference on complex algebraic projective geometry. Specifically, I would like to become more acquainted with notions like the dimension and the degree of a projective algebraic ...
4
votes
3answers
956 views

Lack of rigour in Spivak's Calculus book?

I logged on today with this exact question: Ellipse definition I found it disconcerting for him to say that it was clear that $a > c$ when $a$ could be equal to $c$ (a straight line) or maybe even ...
0
votes
1answer
20 views

Convergence of the Ratio of Consecutive Terms of Positive Recurrence Sequences (Reference Request)

I would like to locate a source that shows (or gets pretty close to) the following. Let $S$ be a positive (integer) recurrence sequence $S_n=S_{n-1}+S_{n-k}$ for some $k>1$. Then, ...
6
votes
2answers
424 views

Prove that hyperspherical coordinates are a diffeomorphism, derive Jacobian

The explicit form for the transformation into hyperspherical coordinates is $$x_1 = r\sin\theta_1 \sin\theta_2 \dotsb \sin \theta_{n-1} \\ x_2 = r\sin\theta_1 \sin\theta_2 \dotsb \cos \theta_{n-1} \\ ...
0
votes
0answers
14 views

Exercise 2.1.5 in An Introduction to Random Matrices by Zeitouni et al.

I have a question regarding exercise 2.1.5 on page 19 in this book: http://www.wisdom.weizmann.ac.il/~zeitouni/cupbook.pdf I would like a reference or help on this exercise. The exercise asks the ...
0
votes
0answers
16 views

Reference request: Inverse problem with stochastic error term

In many inverse problems there is an an error term resp. disturbance like $\|{y_\delta} - y \| \le \delta$ with noise level $\delta$, because only noisy data $y_\delta$ are known. Now I'm interested ...
0
votes
0answers
75 views

What variant of exponential smoothing is used in the VEGAS numerical integration algorithm?

The VEGAS numerical integration algorithm uses the following procedure to update a vector x of length n: ...
5
votes
6answers
828 views

Rigorous Textbook for Introduction to Complex Numbers/Analysis?

Does anybody know where I can find a rigorous textbook on developing complex numbers/analysis? I'm currently working through Needham's Visual Complex Analysis, which is interesting but non-rigorous. ...