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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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
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 ...
3
votes
5answers
494 views

Recursion theory text, alternative to Soare

I want/need to learn some recursion theory, roughly equivalent to parts A and B of Soare's text. This covers "basic graduate material", up to Post's problem, oracle constructions, and the finite ...
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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 ...
2
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1answer
204 views

Examples of Eilenberg-type Swindles

I am compiling a list of 'swindles' in the style of the Eilenberg-Mazur swindle. I've already got some swindles in K-theory, the Mazur Swindle and the proof of the Cantor–Bernstein–Schroeder theorem. ...
2
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2answers
84 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 ...
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 ...
6
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1answer
128 views

Pre-requisites and references for $K3$ surfaces

I would like to know the "roadmap" to study $K3$ surfaces. Perhaps, my background might be helpful: I am an undergraduate student, who knows the basics of Differential Geometry, Topology, Complex ...
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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 ...
2
votes
3answers
255 views

What is the “Principle of permanence”?

While reading the book "The Number-System of Algebra (2nd edition)." term "Principle of permanence" occurred to me. I remember I had read this in the book "Beginning algebra for college students.". I ...
2
votes
2answers
57 views

Connections between SDE and PDE

I have encountered a number of situations where the solution of a PDE and a certain expectation associated to a Markov process are equal. Two examples include: The heat equation $u_t = \frac{1}{2} ...
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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 ...
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12answers
31k views

What is a good book for learning math from the ground up?

I am wondering which books are recommended for learning math from the ground up-- from rather basic math to advanced math (middle school -> graduate school). I am about to finish my masters of ...
2
votes
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 ...
3
votes
2answers
113 views

Reference Request to Prepare for Hatcher's “Algebraic Topology”

Hatcher himself has an excellent and always generously free set of notes on point- set topology: http://www.math.cornell.edu/~hatcher/Top/TopNotes.pdf It includes up to quotient spaces. It seems ...
2
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0answers
133 views

Note or book on Examples of regular, Gorenstein, Cohen Macaulay, … rings

I need a good note or book with plenty of examples in commutative algebra and algebraic geometry which surveyed being regular, Gorenstein, Cohen Macaulay, .... Can you help? thanks.
2
votes
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 ...
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 ...
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7answers
3k views

List of problem books in undergraduate and graduate mathematics

I would like to know some good problem books in various branches of undergraduate and graduate mathematics like group theory, galois theory, commutative algebra, real analysis, complex analysis, ...
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 ...
5
votes
2answers
156 views

Generating Function for 2-Associated Stirling Numbers of the Second Kind

I am looking for a paper which explicitly defines a power series for 2-associated Stirling Numbers of the Second Kind. The paper defines the generating function as follows: Let $S_2(n,k)=b(n,k)$ be ...
3
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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 = ...
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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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0answers
37 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 ...
4
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2answers
103 views

Ordinal exponentiation identity with natural sum of exponents

This is related to a previous question on How to think about ordinal exponentiation? One possible definition for the natural product $\alpha\otimes\beta$ of ordinals is based on Cantor Normal Forms ...
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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 ...
3
votes
1answer
21 views

Online Encyclopedia of Error-Correcting Codes

Is there some kind person on the internet who is making an exhaustive collection of error-correcting codes? I'm looking for something analogous to the OEIS. I want to ask questions like "what is this ...
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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 ...
7
votes
2answers
137 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 \| ...
3
votes
1answer
77 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 ...
1
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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 ...
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0answers
35 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 $\left(\frac{p}{D}\right)=1$.
4
votes
1answer
513 views

Reference request for the following proof of Euclid's Lemma

I'm looking for a reference containing the following proof of Euclid's Lemma. Recall the statement: Let $a,b$ be positive integers and let $p$ be a prime dividing $ab$. Then $p$ divides $a$ or $b$. ...
7
votes
1answer
134 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 ...
3
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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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5answers
204 views

Book recommend for topics of Integrals in multivariable calculus.

I am an average student and have to study following topics on my own for the exam : The measure of a bounded interval in $\mathbb R^n$ , the Riemann integral of a bounded function defined on a ...
0
votes
2answers
119 views

Best Book or Source for learning Multivariable Calculus!

I urgently need some sources for learning multivariable calculus in an efficient way, without too much intuition. I'd like it to be explained in a clear and concise way and with a number of worked ...
0
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2answers
85 views

Book on calculus of several variables.

I'm an undergraduate student in mathematics and want to study Calculus of several variables currently this semester which involves the use of analysis, vector spaces and linear transformations. Can ...
1
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1answer
107 views

Less Terse alternative to Advanced Calculus by Folland.

I am currently in an advanced calculus class in university. We use Advanced Calculus by Folland. When I try to follow along the book I find that it is not verbose enough, and has too few examples. I ...
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1answer
113 views

Reference books or any sources advice for my advanced calculus course

My course outline: Differentiation of functions of several variables: partial derivatives, differential, differentiability, inverse function theorem, implicit function theorem, free extremum ...
6
votes
5answers
4k views

Multivariable Calculus books similar to “Advanced Calculus of Several Variables” by C.H. Edwards

I am currently trying to teach myself multivariable calculus using C.H. Edwards' "Advanced Calculus of Several Variables", but the text unfortunately doesn't have very many problems with solutions. ...
3
votes
1answer
173 views

Linear algebra and geometric insight: a rigorous approach to vector spaces, matrices, and linear applications

Could you point out some references (undergraduate level) that give a geometric understanding of vector spaces, matrices, and linear applications? As far as I know, many textbooks start with an ...
3
votes
1answer
118 views

euclidean geometry books…

I consider myself poor in plane euclidean geometry. so I need a good geometry book which contains very good theory, and a collection a large number of solved problems, and the end of each part.This ...
36
votes
7answers
1k views

Original works of great mathematicians

In almost every mathematical text there is a line as This was first proved by Gauss or This formula first appeared in a work of Riemann, but for me it's more like My friend told me once that... For ...
6
votes
1answer
840 views

Difference between Gilbert Strang's “Introduction to Linear Algebra” and his “Linear Algebra and Its Applications”?

Could someone please explain the difference between Gilbert Strang's "Introduction to Linear Algebra" and his "Linear Algebra and Its Applications"? Thank you.
3
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0answers
76 views

Reference requests for an opt-cited result in Jennrich (1969)

Lemma 2 on page 637 of Jennrich (1967) states that: Let $Q$ be a real-valued function on $\Theta\times Y$ where $\Theta$ is a compact subset of a Euclidean space and $Y$ is a measurable space. ...
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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 ...
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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 ...