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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2
votes
1answer
100 views

Reference request: Newton-Kantorovich hypothesis for polynomials of integral coefficients

Kantorovich's theorem states that the Newton method for finding the roots of a nonlinear function is guaranteed to converge if a parameter $h$, determined by the values of the function and its ...
7
votes
5answers
1k views

discrete math book suitable for younger person?

When I took discrete math as an adult I realized that this was a subject I would have enjoyed and done well at much earlier in life, even in my early teens. Does anyone know if there are good books, ...
3
votes
3answers
270 views

Any good books on Mathematics and Programming?

I've been on google for a while now searching for a good book on mathematics combined with programming, but either the level of math they're starting at is too high or the level of programming is too ...
6
votes
1answer
386 views

what textbook would be good as a precursor to discrete mathematics?

I'm about to start a Masters in Software Engineering at university and have not studied/used-intensely anything mathematical for 6 years. I know that computing science makes use of discrete ...
-2
votes
1answer
24 views

Recommend a software for solving math.

I am working with long geometry equation having long chains of other equations in each equation. So recommend a math solving software that may help me solve those long equations and save my time.
1
vote
0answers
27 views

Recommend resources of Abstract Algebra which contain more historical development

I read the Wikipedia page about Abstract Algebra. There is a sentence that says Numerous textbooks in abstract algebra start with axiomatic definitions of various algebraic structures and then ...
1
vote
0answers
21 views

Reference for a couple of terms, $\underline{\operatorname{Hom}}_X(-,-)$ and $\boxtimes$

I have a couple of questions on symbols. What are the names for $\underline{\operatorname{Hom}}_X( \mathscr{F},\mathscr{G})$ for sheaves on a scheme $X$, and $\boxtimes$? And what would be a ...
1
vote
1answer
22 views

Lusin property (N) for functions of several variables

I just read in a paper by Martio and Zeimer$^1$ that smooth functions ($C^1$) of several real variables have the have the Lusin property (N). I have two questions. First, could someone give me a ...
2
votes
0answers
33 views

What calculus material can prepare me for MCMC?

I am looking to revise calculus from scratch to move on to Monte Carlo Markov Chain Methods and Quasi Monte Carlo Methods. I studied calculus properly a couple of years ago however it was back in high ...
6
votes
5answers
2k views

Music — Is the diatonic scale optimal in some sense?

I have recently found a mathematically-sound "proof" that the twelve-tone musical scale is optimal. I am looking for a similar explanation proving that the diatonic scale is optimal in some sense. ...
8
votes
6answers
8k views

Great Book on Probability and Statistics (for Computer Scientists)

I'm a Computer Science sophomore and we're studying Probability and Statistics (fundamentals and all). The teacher recommends a book which I don't like since it does not even try and explain ...
5
votes
3answers
113 views

reference for linear algebra books that teach reverse Hermite method for symmetric matrices

The method I mean is useful for symmetric matrices with integer, or at least rational entries. It diagonalizes but does NOT orthogonally diagonalize. The direction I do it, I usually call it Hermite ...
2
votes
0answers
13 views

Solutions to Dirichlet problem on manifolds with boundary

I am looking for a reference for the following assertion: Let $M$ be a Riemannian manifold with boundary, and $f:\partial M \rightarrow \mathbb{R}$ be smooth. Then there exists a unique smooth ...
2
votes
2answers
183 views

Why Study Homological Algebra?

I'm very interested in learning Homological Algebra. But I'm not sure about the prerequisites for learning this. My current knowledge in algebra consists of Abstract Algebra (Group,Rings,Fields), ...
-2
votes
0answers
24 views

Recommend a book for complex analysis. [duplicate]

I am going to have an introductory course in complex analysis. So please recommend me a book in complex analysis.
31
votes
12answers
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?
4
votes
1answer
53 views

Is there an English version of Johann Bernoulli's integral calculus lectures?

The name of lectures of integral calculus written by Johann or Jeans Bernoulli (he is called by both names as far as I know) might be " lecciones mathematicæ de calculo integral"; I must mention that, ...
4
votes
1answer
73 views

2011 USAMO Problem 3, Hexagons.

In hexagon $ABCDEF$, which is nonconvex but not self-intersecting, no pair of opposite sides are parallel. The internal angles satisfy $\angle A = 3\angle D$, $\angle C = 3 \angle F$, and $\angle E ...
10
votes
1answer
123 views

Is anyone talking about “ball bundles” of metric spaces?

In differential geometry: Each smooth manifold $M$ is equipped with a tangent bundle $TM,$ which is a manifold equipped with a projection back to $M$ Given a smooth map $f : M \rightarrow N$ between ...
0
votes
1answer
25 views

Continuum hypothesis and non measurable set

This is from Chap 8 of Real and Complex analysis of Rudin. The author does not present a proof (using the continuum hypothesis) for the existence of the function $j$. Where can I find such a ...
15
votes
1answer
436 views

Is there an axiomatic approach to ordinal arithmetic?

I've always wondered, is there an axiomatic approach to the arithmetic of ordinal numbers? If so, I imagine it would be on par with set theory in terms of its proof-theoretic strength.
3
votes
0answers
52 views

The form of the zeta function of an elliptic curve over a finite field

I seek a (very) elementary proof that the zeta function of an elliptic curve $E$ over $\mathbb{F}_q$ has the form $$Z(T)=\frac{1-aT+qT^2}{(1-T)(1-qT)}.$$ Something tedious and computational making use ...
0
votes
0answers
45 views

Vector bundles on Hirzebruch surface $\mathbb{F}_2$

I would like to know a classification for all holomorphic vector bundles on the second Hirzebruch surface $\mathbb{F}_2$. Is this known? What is known? In particular, I'm looking for holomorphic ...
1
vote
1answer
33 views

References about moduli space of abelian varieties with level structure

In the course of one of my research project, I have been advised to try to have a look to "Moduli Space of Abelian Varieties with Level Structure". I am interested in references where this topic is ...
2
votes
0answers
47 views

Constructing $\text{Hilb}_P(X/S)$ as a locally closed subscheme of $\text{Hilb}_P(\mathbb{P}^n/S)$?

For a projective scheme $X/S$, how do I construct $\text{Hilb}_P(X/S)$ as a locally closed subscheme of $\text{Hilb}_P(\mathbb{P}^n/S)$? ($P$ is Hilbert polynomial.) Can I get a reference to this ...
2
votes
1answer
33 views

Orbit closures of real symmetric bilinear form

Let $\alpha$ and $\beta$ be two real symmetric bilinear forms in $\operatorname{sym}(\mathbb{R}^n)$, with signatures $(p_{\alpha},n_{\alpha},z_{\alpha})$ and $(p_{\beta},n_{\beta},z_{\beta})$. I ...
0
votes
1answer
23 views

Fourier Series Relation Time - Frequency

I want to study and understand the relation between time and frequency with the help of Fourier Series. Can you indicate me some papers, or some example?
5
votes
2answers
320 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
1
vote
2answers
252 views

Introductory Level Books for Graph Theory

Can anybody please suggest some good introductory level text books on Graph Theory ? Preferably those which don't really require a great pre-requisite background on discrete mathematics, but rather ...
0
votes
0answers
11 views

Metropolis Markov Chain and Mixing Time

I have a statistical mechanical system, which I would like to sample with the Gibbs distribution using a Metropolis-Markov chain. I think the following are standard questions, but I am not sure what ...
48
votes
0answers
2k views

Continuous projections in $\ell_1$ with norm $>1$

I was trying to find papers and articles about non-contractive continuous projections in $\ell_1(S)$ where $S$ is an arbitrary set. If it is not studied yet, I would like to know results for the case ...
0
votes
0answers
14 views

Reductions of structure groups and sections of coset bundles

I'm looking for a reference for the following proposition: Let $G$ be a Lie group and $H$ a (closed) Lie subgroup of $G$. Let $E \to B$ be a principal $G$-bundle. Then reductions of the ...
3
votes
1answer
56 views

High School Geometry Text?

This year I will be teaching 8 hard-working home-educated teens a Geometry course. Back in 1994-1999 I worked full time as a High School educator, taking a turn teaching everything from Pre Algebra ...
0
votes
2answers
52 views

Reference request for Heine-Borel theorem

I would like to know a nice reference for the Heine-Borel theorem. In a text, I have the compactness argument for the following two sets. The reference should be able to cover these two cases. ...
2
votes
2answers
184 views

Problem-solving

I just finished my second year as a mathematics student at university. At university, we learn about advanced mathematics and problems. However, I'm also interested in some problems that doesn't ...
1
vote
0answers
19 views

Generalized Hyperbolic and Circular Functions

I have recently posted a couple of questions in regards to Generalized Hyperbolic and Circular Functions and I was hoping to find a couple more papers available on the particular subject. The papers ...
2
votes
1answer
20 views

Textbook recommendation for Complexity?

I'm interested to learn more about complexity and would like a textbook recommendation. In my undergraduate degree I've done a couple of modules on relevant topics in computational complexity. I do ...
1
vote
1answer
32 views

Where can I find “On the significance of the principle of excluded middle in mathematics, especially in function theory”?

I'm looking for L.E.J. Brouwer's article "On the significance of the principle of excluded middle in mathematics, especially in function theory". I've searched my university catalogues and every open ...
17
votes
10answers
2k views

Entering math through the side door [duplicate]

I am not really good at math, I'd say I'm a lot worse than good when it comes to math but I am a programmer so I have to learn to get over that fact. A lot of times if I want to implement some code I ...
0
votes
2answers
26 views

Reference Request: Soft handed text on duality theory?

Can anyone recommend a text on duality theory which includes basic formulation of the primal and dual formulation and some introduction to minimax problems? Preferably having some computation in ...
5
votes
1answer
139 views

The locker puzzle - predetermined strategy

The question is related to the famous locker puzzle: The director of a prison offers 100 prisoners on death row, which are numbered from 1 to 100, a last chance. In a room there is a cupboard with ...
1
vote
0answers
84 views

First examples in triangulations

I am starting to study about triangulations in my algebraic topology course. We have seen the triangulation of the sphere, the closed disc and so on. Intuitively it's ok, however I couldn't find any ...
0
votes
0answers
19 views

Orbit closures of symmetric bilinear form

Let $A$ and $B$ be two real symmetric matrices in $M_n(\mathbb{R})$. I would like to learn about necessary and sufficient conditions for knowing when $B \in \overline{GL_n(\mathbb{R})\cdot A}$; where: ...
2
votes
0answers
32 views

$\Delta$-Complexes Are Hausdorff

I am using the definition of a $\Delta$-complex as given in Hatcher's book here on pg 103. Now on pg. 104, just before the section on Simplicial Homology, Hatcher remarks that if $X$ has a ...
1
vote
1answer
24 views

Lower semicontinuous integer valued function

I remember reading in some book a characterization of lower semicontinuous functions that are integer valued (for example, rank of a matrix), along the lines that it can either not jump abruptly or ...
0
votes
1answer
159 views

Book for differential equations

I generally use Rudin's book to prepare for my analysis lectures, however, we started doing Lagrange multipliers and differential equations (e.g. Picard-Lindelöf Theorem) which unfortunately isn't ...
2
votes
1answer
58 views

Good book about differential forms

I'm a looking for a good book to self-study differential forms. Particularly, I'm looking for a book that is as similar as possible to Bert Mendelson's "Introduction to topology" (i.e. a book that ...
16
votes
4answers
2k views

Status of The Triangle Book

I am interested in finding out about the current status of the planned book: The Triangle Book by John H. Conway and Steve Sigur. I understand that Steve Sigur died some time back. I got no reply from ...
1
vote
3answers
37 views

Is convergence in probability sometimes equivalent to almost sure convergence?

I was reading on sufficient and necessary conditions for the strong law of large numbers on this encyclopedia of math page, and I came across the following curious passage: The existence of such ...
0
votes
0answers
13 views

Sufficient conditions for integration by parts in higher dimensions

If $\Omega\subset {\mathbb R}^n$ is a bounded open set with $C^1$ boundary and $\nu$ denotes the outward unit normal to $\partial \Omega$, then the following formula holds for every pair of $C^1$ ...