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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1answer
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Out of plane cross section evolution of surfaces based on local geometry information

With this question I would like to kindly ask for feedback or general pointers to even remotely related works in regards to a challenge I face. Given a smooth surface $S$ $:\mathbb{R}^2\rightarrow ...
2
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0answers
62 views

Deep questions in number theory not accessible by combinatorial results

Number theory and arithmetic geometry were invented to solve many questions about properties of numbers. What are the some of the foundational results or estimates that are accessible to powerful ...
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1answer
67 views

Discrete Mathematics in KhanAcademy [closed]

Where is a section of discrete mathematics in KhanAcademy? https://www.khanacademy.org/
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1answer
14 views

Texts on Coxeter groups

I'm looking for an introductory text on Coxeter groups. It can assume undegraduate knowledge of Algebra (Groups up to and including the Sylow theorems in Fraleigh, elementary knowledge of rings, ...
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0answers
20 views

How to search the set of papers whose references contain a given preprint?

I am reading a preprint titled Combinatorial Group Theory In Homotopy Theory I by Fred Cohen (available at Cohen's web page) Now I need to find all papers whose references contain this preprint. Is ...
2
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2answers
39 views

Reference request: Introduction to Applied Differential Geometry for Physicists and Engineers

I'm looking for a book on differential geometry or differential topology that is comprehensive and reads at the level of someone with engineering background (i.e. Boyce's ODE, Stewart's Calculus, ...
0
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1answer
35 views

Books for these topics.

I have an lecturership exam in India and in the syllabus there are few topics under the tags "Calculus of variations" and "Linear integral equations", and if please if someone could tell me which ...
1
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1answer
38 views

References for Algebraic number theory

I am doing algebraic number theory first time. I have done all ring theory and field theory. I am interested in algebra , so also pretty much excited about algebraic number theory. I have a month's ...
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0answers
28 views

Rreferences for free groups

I have done free groups. I studied it from Rotman two semesters back. But this semester I am doing combinatorial group theory and obviously it starts with free groups. I have to revise Free groups but ...
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0answers
36 views

any online video course for analytic number theory or elementary number theory?

All: I am looking for online video course on analytic number theory for self-study. On Youtube, there are a few seminars, but no complete course for a semester or a year. Can anyone point out if ...
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3answers
89 views

A good introductory book on Ring and Field theory with a view towards Number Theory ?

Please suggest some good introductory books on Rings&Fields with a view towards Number Theory ?
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0answers
28 views

Basic question: degree of normal bundle is not self-intersection number

For $C$ a (possibly singular) curve on a nonsingular projective surface $X$, let's define $C^2=deg_C(\mathcal{O}_X(C))$. Why is it not the same as $deg_C(N_{X|C})$ when $C$ is singular? Why do ...
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1answer
215 views

Does anyone know about Ramanujan's method of solving the quartic? [closed]

I have read (probably) in Kanigel's book The Man Who Knew Infinity that S. Ramanujan devised his own method of solving the Quartic Equation after he learnt to solve the Cubic Equation. Does anyone ...
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0answers
7 views

Can you give some information for rothe method

I want to learn a numerical method for PDEs other than finite difference method. After some research on internet i have found Rothe method and it looks interesting to me. Unfortunately, i couldn't ...
0
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0answers
13 views

What are the good books for learning Integral equations

I mainly study statistics. But I am interested in learning Integral equations. So what are the good books for learning Integral equations. I have no expertise in this topic. Any good lecture notes ...
2
votes
2answers
85 views

Closed orbits of vector fields under perturbation

Consider a vector field $V$ on an annulus $U$, say. Also, assume that the vector field $V$ has a closed orbit. I am looking for a reference that gives stability results of the following type: If the ...
3
votes
1answer
58 views

Multilinear form as scalar multiple of determinant function

While going through Hungerford's $\textit{Algebra}$, there is a theorem of linear algebra which states that every alternating $R$-multilinear form $f$ on $M_n(R), R$ a commutative ring, is a unique ...
2
votes
1answer
29 views

What is a minimal fiber of a Riemannian submersion

I am reading "Spectral Geometry, Riemannian Submersions and the Gromov-Lawson conjecture" by Gilkey, Leahy and Park, and I'm having some trouble with some of the terms they introduce without ...
3
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0answers
35 views

Sources on flat bundles

I am looking for the most complete source on Cheeger-Chern-Simons invariants, Deligne cohomology and other "cohomological" topics, associated with the theory of flat bundles. I would also like to know ...
7
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1answer
128 views

Nonlinear partial differential equations with applications

Has anyone studied the book 'Nonlinear Partial differential equations with applications' by Tomas Roubicek? I am interested in discussing a point of interest in this book. Specifically, on page 52, ...
2
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1answer
67 views

Galois theory on curves

Context: Let $\mathbb{F}$ be the algebraic closure of $\mathbb{F}_q$ for $q$ prime. We know that $\mathbb{F}(t)$ for $t$ transcendental is the function field of the projective line ...
2
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0answers
61 views

Basic Fourier analysis explanation needed wrt a function $f$ and a finite Borel measure $\mu$

An extract from Chapter 12 of Matilla's Geometry of Sets and Measure on Euclidean Spaces I do not believe that formulas (12.1-12.3) are easily seen to be valid. I do not understand what ...
2
votes
2answers
80 views

Good references on Riemannian Geometry

I'd like a textbook that covers do Carmo's contents (can be more), but that isn't do Carmo. I did not like his writting style. That being said, I particularly like the styles of: Walter Rudin ...
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0answers
40 views

Applications of resolution of singularities

I would to know applications of Resolution of Singularities, this means what is profits of having a resolution of singularities of a variety both in and out of mathematics and both in positive and ...
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0answers
20 views

Method's name/Theory: Equivalence of complex and real matrices of double dimension

I remember reading a document where it was explained, how complex matrices are equivalent to real matrices of double size, according (as far as I remember): Let $C$ be a complex matrix, then $D = ...
2
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1answer
26 views

Toeplitz Operator is compact if and only if it has finite rank

A referee has pointed out to me that it is "well known that a Toeplitz operator is compact if and only if it has finite rank" and pointed me to R. Douglas: Banach algebra techniques in the ...
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0answers
39 views

Sylow's Theorem and Wielandt's Proof

I came up with following questions, while reading Wielandt's paper "Ein Beweis fur die Existenz der Sylowgruppen". (I know the ideas of the proof, but my questions are related to some statements or ...
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0answers
19 views

References for Hilbert symbols on $p$-adic fields

Can somebody give me some reference (Please not Serre, as it is too tough for me now) any reference for the basics and concepts on $p$-adic rings and fields and then gradually relating them to ...
1
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1answer
54 views

Subsets of a monoid closed under left-multiplication by elements of a submonoid

Let $M, T$ be monoids (or, semigroups) with $M \subset T$. Then we can consider subsets $S$ of $T$ that are closed under left-multiplication by something in $M$, i.e. $$ a \in S, m \in M \implies ma ...
3
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1answer
56 views

Solving Kepler's second law

Kepler's second law, about equal areas in equal times, is a differential equation: it gives velocity as a function of location. Where are the best expository accounts of the process of solving this ...
3
votes
1answer
79 views

Studying for analysis- advice

I find that studying for analysis is unlike other math classes that I've taken. I dedicate a lot of time to studying for it, but it seems like no matter how much time I put into it I am not getting ...
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0answers
36 views

Heat Equation on Manifold

Laplacian operator is defined well on Riemannian manifold, denoted by $\Delta$. Therefore people can study PDE $\Delta f=0$ on manifold. So is there any analogy to heat equation or wave equation on ...
2
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0answers
36 views

Modular property of Weierstrass $\wp$ function

For $\tau\in \mathbb H=\{ x+iy\in \mathbb C \lvert x,y\in \mathbb R, \, y>0\}$ and $z\in \mathbb C$, let us define $$ \wp=\wp(\cdot,\tau): \mathbb C \rightarrow \mathbb P^1\, , \quad z\mapsto ...
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0answers
19 views

Primes Representable as Quadratic Form - Specifically Norm of an Imaginary Quadratic Field with Class # 1

Could someone point me towards the result that states that a prime is expressible as a norm of an imaginary quadratic field with class number 1 iff $\left(\frac{p}{D}\right)=1$.
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2answers
32 views

Looking a good book about Fourier Series

I'm studying Rudin's Mathematical Analysis, but I'd like to study another book (specially the Fourier Series topics) to improve my knowledge. Could you give any suggestions? Thanks so much!
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0answers
46 views

References on filter quantifiers

This post is primarily a reference request. In combinatorics and other areas, we use filter quantifiers to simplify the statements of various definitions, theorems and proofs. The general idea is ...
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9answers
2k views

“Honest” introductory real analysis book

I was asked if I could suggest an "honest" introductory real analysis book, where "honest" means: with every single theorem proved (that is, no "left to the reader" or "you can easily see"); with ...
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1answer
40 views

Reference for a nice formula

In this post, $no identity$ gives a nice formula for the distance of a vector to a subspace: $d^2(p,L)=\frac{G(v_1,\ldots,v_m,p)}{G(v_1,\ldots,v_m)}\tag{1}$ Can anyone give me reference where I can ...
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0answers
38 views

Component-wise connected sum of links

Given two links $K = K_1 \cup \dotsb \cup K_n$ and $L = L_1 \cup \dotsb \cup L_n$, where each $K_i$ and $L_j$ are oriented knots, can we define the connected sum $K\#L$ by taking the connected sum of ...
7
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1answer
135 views

What branches are these (contest) maths questions from?

The OP is studying for his local math competition (Australian), and when running through past papers I found some questions subtle to handle. I decide to buy some books to aid my study, but there are ...
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0answers
28 views

Some basic questions about fibered surfaces

I get stuck at the section 8.3 Fibered Surfaces of Qing Liu's book Liu: Algebraic Geometry and Arithmetic Curves and I feel strange that it is not easy to find many other books or papers discussing ...
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0answers
32 views

prime case function?

Does there exist a name (or assigned to a mathemtician) for a case function $f(x)$ in literature, such that it twould take the value $1$ when $x$ primes, and zero otherwise? I am just looking for a ...
0
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2answers
37 views

Questions about elipse

Given the center of an elipse and three of its points, is this elipse completely determined? What is the easiest way to show that five points of an elipse are enough to determine the elipse?
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0answers
44 views

Where can I get full list of giuga numbers discovered so far?

I want full list of giuga numbers discovered so far , on googling i found this list. But it is not a complete list? Where can I get them ? Or is there any non-brute force generating algorithm for ...
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1answer
128 views

The distance from the center of a circle, which is tangent to a ellipse $x^2/a^2+y^2/b^2=1$ and two parallel tangent lines of the ellipse is $a+b$

Consider the following problem: Let $E$ be the ellipse $x^2/a^2+y^2/b^2=1$ with $a>b$. Consider two tangent lines on $E$ which are parallel, say, $r$ and $s$. Let $C$ be a circle, which is ...
6
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0answers
78 views

Duals of representations of affine group schemes, in particular $\mathrm{GL}_n$

Duals of representations of affine group schemes Let $R$ be a commutative ring. If $G$ is a group and $V$ is a dualizable i.e. finitely generated projective $R$-module on which $G$ acts, then it is ...
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2answers
138 views

Hardy–Littlewood-Sobolev inequality without Marcinkiewicz interpolation?

Here is the statement of the Hardy–Littlewood–Sobolev theorem. Let $0< \alpha< n$, $1 < p < q < \infty$ and $\frac{1}{q}=\frac{1}{p}-\frac{\alpha}{n}$. Then: $$ \left \| ...
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0answers
51 views

Differential Geometry for Computer Science

I am looking for a good book or other resources on Differential Geometry for Computer Sciences or more specifically Differential Geometry used in Computer Graphics, Geometric Modelling and Mesh ...
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0answers
35 views

International Awards for Roger Apery?

Roger Apery stunned the math community when he proved that $\zeta(3)$ is irrational, in a truly elementary fashion. I wonder if he received any international awards specifically for this achievement. ...
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2answers
131 views

What is the function $f(x)=x^x$ called? How do you integrate it?

For real numbers $x > 0$, the function $f(x)=x^x$ seems pretty cool. Is there a name for this function? It's obviously been studied before. It grows faster than exponential functions and ...