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Questions asking for recommendations of textbooks on some subject. It can be helpful to indicate whether the request is for self-study, for use in a course one teaches, for use accompanying a course one takes etc., and to give some additional details on the context. Typically, additional tags are ...

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85 views

Quantum ergodicity of Eigenfunctions on PSL2(Z)/H 2

I am trying to read this paper. But any line of it is impossible to read! I have studied Graduate Algebra books, Multiplicative Number Theory, Graduate Real and Complex Analysis, R Zeta fn , ...
1
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1answer
484 views

State-of-the-art geometry book? [closed]

For my best friend's birthday, I am looking for a geometry book. He's currently doing his math PhD and is really fond of geometry, especially hyperbolic or higher-dimensional ones, also interested in (...
10
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2answers
450 views

Good introductory references on moduli (stacks), for arithmetic objects

I've studied some fundation of algebraic geometry, such as Hartshorne's "Algebraic Geometry", Liu's "Algebraic Geometry and Arithmetic Curves", Silverman's "The Arithmetic of Elliptic Curves", and ...
8
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2answers
663 views

The Stacks project

I have a question concerning the admirable Stacks Project. Which comparable projects are there: approach-wise: "an open source textbook on algebraic stacks and the algebraic geometry that ...
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0answers
44 views

Resource request: Moyal $\star$-product based calculations

I already asked two questions about the Moyal $\star$-product here and here but I think I'll have a lot more similar questions, so I'm wondering if anyone can help me with finding some good resources. ...
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2answers
623 views

Design principles for good undergraduate textbooks to enhance student understanding

I am writing an ODEs textbook for second year students and I would like to get inspirations on general good designs on undergraduate textbooks taught in the first two years (i.e. calculus, linear ...
2
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1answer
145 views

Rigorous multivariate differentiation of integral with moving boundaries (Leibniz integral rule)

The Leibniz integral rule, in its multivariate form, deals with differentiation of the following sort: $$ \frac{\partial}{\partial t} \int_{D(t)} F({\bf x}, t) \, d{\bf x} \, , \qquad D(t)\in \mathbb{...
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2answers
396 views

Books building up to the Gross-Zagier formula

I am an undergrad extremely interested in some applications of the Gross-Zagier formula for elliptic curves. I have a strong foundation in group theory and abstract algebra, and an understanding of ...
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3answers
622 views

What are good Morse Theory lecture notes and books?

Searching on the net I couldnt find any recent lecture/course notes on Morse Theory. I found an old set of notes (http://www.math.toronto.edu/mgualt/Morse%20Theory/mfp.pdf) by Mike Hutchings and these ...
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1answer
129 views

Syzygies of projective varieties

I want to see some examples of syzygies of projective varieties, if possible not from Eisenbud, because I know those.
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0answers
33 views

Comprehensive reference for lumped or projected markov chains

Consider a Markov chain $X_n$ taking values in finite countable set $\mathcal{X}$ with transition matrix $P$. Consider a function $f:\mathcal{X}\to\mathcal{Y}$ inducing a partition $\mathcal{Y}=\{\...
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5answers
879 views

Topological vector space textbook with enough applications

(Sorry for my bad English.) For "applications", I mean applications in math, not real-life. There are many textbooks about topological vector space, for example, GTM269 by Osborne, Modern Methods in ...
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0answers
161 views

Rigorous book for curvature and Riemannian manifolds

I am looking for a rigorous book on Riemannain manifolds with an emphasis on curvature and how it affects the global geometry of the manifold. I have had elementary courses on differential geometry ...
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3answers
284 views

Good books on the divisor sum function $\sigma(n)$?

I would like gain detailed knowledge about properties of the divisor sum function $\sigma(n)$, special equation that have been studied (e.g. $\sigma(n) = 2n$ perfect numbers, ...) and progress that ...
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0answers
172 views

Literature about most basic existence proofs in graph theory

I'm writing a MIZAR article about foundations in graph theory e.g. constructing a supergraph from a given graph by adding a vertex to it. The main theorem of the article will be that any graph ...
2
votes
0answers
263 views

Textbooks in differential geometry that treat $C^k$ manifolds

I am looking for textbooks in differential geometry that treat $C^k$ manifolds right from the start. Ideally, the textbook should maintain this general point of view through all chapters and ...
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2answers
635 views

Reference request for Functional Analysis

Does anyone know a book that motivates the beginning of functional analysis in a clear way? By "clear," I mean that it shows why one would want to define Hilbert spaces and why the theorems are ...
3
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0answers
154 views

Applications of logic in theoretical and practical Computer Science [closed]

Can anyone suggest theoretical and/or practical applications of logic (modal, dynamic, Lukasiewici etc.) in Computer Science (like Markov Chains for linear algebra), as well as some open-source books ...
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4answers
1k views

Good book for measure theory and functional analysis

I have taken advanced courses both in measure theory and also in functional analysis (Banach and Hilbert spaces, spectral theory of bounded and unbounded operators, etc.) The connections between the ...
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6answers
2k views

Russian Equivalent of Big Rudin

Is there any Russian-authored textbook on Analysis equivalent to Big Rudin (Real and Complex Analysis)? I like Russian math textbooks a lot. I am looking for Russian textbooks (either in English or ...
7
votes
1answer
195 views

KPZ-NLS-Burgers relationship

The Burger's equation $$y_t (t,x) + y\cdot y_x - y_{xx} =0 \, \, ,$$ can be obtained as a limit of the one-dimensional cubic Nonlinear Schrodinger equation (NLS) $$ i\psi _t (t,x) + \psi _{xx} +|\...
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1answer
83 views

Examples of the time-dependent linear wave equation

I am looking for examples of the non-autonomous linear wave equation that have some relevant applications. What articles and sources (maybe, some catalogue like Handbook of Nonlinear Partial ...
4
votes
4answers
292 views

fractional laplacian on $\mathbb{R}.$

Is there a book on fractional operator $(-\frac{d^2}{dx^2})^{s}$ with $s\in (0, \frac{1}{2}]$. The textbook should ideally contain estimates and properties of all kinds, and Schauder to Moser theory.
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1answer
86 views

Literature on the total variation of fractal graphs/fractal Brownian motion?

I know that for standard Brownian motion, the total variation sampled at intervals of length $\Delta$ converges to $V(\Delta) = C \Delta^{-1/2}$ for some constant $C$. I wish to use this fact to study ...
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1answer
96 views

Critical gKdV - tutorial

I'm looking for a good introduction to the critical generelized KdV equation $$u_t +u_{xxx}+5u^4u_x = 0 \, , $$ $$ u(t=0,x) = u_0 (x) \, , \qquad x\in \mathbb{R} \, ,$$ and its blowup solutions. There ...
3
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1answer
129 views

Semi-elliptic pdes reference

The pde $$ Pf(x)=\sum _{i,j=1}^{n}a_{ij}(x){\frac {\partial ^{2}f}{\partial x_{i}\,\partial x_{j}}}(x)+\sum _{i=1}^{n}b_{i}(x){\frac {\partial f}{\partial x_{i}}}(x)+c(x)f(x),$$ is said to be semi-...
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0answers
537 views

Books on von Neumann algebras

I am interested in non-commutative $L^p$ spaces. I have a very basic background on von Neumann algebras. But all the papers appearing now a days really requires very deep knowledge of von Neumann ...
4
votes
1answer
136 views

Graduate-level reference on temporal point processes

I am looking for a modern, graduate level, rigorous book on temporal point processes which also treats self-correcting point processes, and self-exciting point processes. It would be even more ...
16
votes
1answer
996 views

A book on elliptic curves using scheme theory?

I'm interested in learning some stuff about elliptic curves. I've been learning scheme theory, and I'm interested in seeing these tools "in action". It seems that the standard introduction to elliptic ...
65
votes
7answers
6k views

Books on music theory intended for mathematicians

Some time ago I attended a colloquium given by Princeton music theorist Dmitri Tymoczko, where he gave a fascinating talk on the connection between music composition and certain geometric objects (as ...
6
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0answers
411 views

Are French, original editions of Grothendieck's EGA&SGA out of sales?

I have been desperately searching for the hardcopies of Grothendieck's EGA and SGA trilogy, but I could not find available sales except for some used books at Amazon with ridiculously expensive prices....
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2answers
110 views

Distributional equations: reference request [closed]

I'm really having a hard time finding a book that covers distributional equations such as $xT = \delta(x)$ or distributional differential equations. Any suggestions?
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0answers
223 views

Copylefted introduction to topology

Is there a textbook in topology with a copyleft license? $$ $$
4
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2answers
258 views

Monograph on harmonic analysis with applications to PDEs

"There are two ways to teach mathematics, namely the systematic way and the application-oriented way"- E. Zeidler I'm a fresh researcher on PDEs, especially interested in evolution equations in ...
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2answers
449 views

Alternative or reprint of Carter's “Finite Groups of Lie Type: Conjugacy Classes and Complex Characters”

I would like to learn about character theory of finite groups of Lie type and some Deligne-Lusztig theory. The classic textbook on the subject seems to be Roger W. Carter's Finite Groups of Lie Type: ...
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0answers
833 views

Geometry of schemes by Eisenbud and Harris

I have some background of algebraic geometry. I am now trying to study schemes from book Geometry of schemes by Eisenbud and Harris. I was checking recommendations for books on algebraic geometry ...
2
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3answers
875 views

Books for (Complex) Algebraic Curves

I would like to suggest me some good books on (Complex) Algebraic Curves. I am searching a book for Undergraduate-Begginer Level in this part of mathematics, the algebraic curves. I found some books ...
3
votes
1answer
136 views

Colombeau generalized functions

I'm currently reading some aspects of Colombeau generalized functions, and in almost all of his examples he discuss aspects of Quantum Field Theory, but then I go to some "standard" texts on QFT and I ...
7
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1answer
1k views

Review paper/book on Finite Difference Methods for PDEs

I am looking for a good, relatively modern, review paper/book on Finite Difference Methods for PDEs with a theoretical emphasis in mind. By theoretical emphasis I mean that I care about theorems (i.e. ...
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1answer
641 views

What are the differences between The Princeton Companion to Applied Mathematics and Mathematics for Physics by Michael Stone and Paul Goldbart?

Both of them are applied mathematics books. What are the main differences between them? Which is more mathematical i.e. mathematically advanced, mathematically rigorous?
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0answers
208 views

Reference for PDE problem book

What I need is a source of solved exercises, problems in Partial Differential Equations; to be hard enough (olympiad style) and in areas like Calderon-Zygmund theory and applications, Paley-Littlewood ...
3
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1answer
186 views

Introduction to geometric discrepancy theory?

Recently in search of tests for uniformity of multidimensional distributions I luckily stumbled upon something called 'geometric discrepancy theory'. It seems to be a very powerful and elegant ...
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1answer
528 views

Introductory text to Sobolev spaces and PDE's [closed]

I'm looking for a good introductory to Sobolev, preferably with an emphasis to their relationship to PDE's analysis. I have only seen thus far Giovanni Leoni's "First Course in Sobolev Spaces" which ...
9
votes
3answers
598 views

Text for studying group representations in the context of (abstract) harmonic analysis

I would like to study elements of representation theory as I often encounter it when reading texts on harmonic analysis. I was therefore curious if someone could recommend a book for this. When ...
2
votes
2answers
482 views

Generalizations of the Euler-Maclaurin Summation Formula

I'm using the Euler-Maclaurin formula in a research I'm working on. However brilliant is the elementary proof found here, I need and want to know more about it. Namely Specifically, I would like to ...
3
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1answer
1k views

How to learn concepts of Functional Analysis which are common in PDE

I am a master student and working in PDE area. I am trying to gain deep understanding of some of the concepts in functional analysis which are common tools in PDE research, such as weak*-topology, ...
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6answers
2k views

Undergraduate ODE textbook following Rota

I imagine many people are familiar with the extremely entertaining article "Ten Lessons I Wish I Had Learned Before I Started Teaching Differential Equations" by Gian-Carlo Rota. (If you're not, do ...
2
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1answer
55 views

Specific discrete system $x_n = A(n,u)\cdot x_{n-1}$ control papers

Basic discrete control theory mostly studies systems which can be represented as $x_n=A(n)x_{n-1}+B(n)u_n$. I wonder if optimal control of specific discrete systems of the type $x_n = A(n,u)\cdot x_{...
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4answers
921 views

Braided Hopf algebras and Quantum Field Theories

It is well-known, that there are a lot of applications of classical Hopf algebras in QFT, e.g. Connes-Kreimer renormalization, Birkhoff decomposition, Zimmermann formula, properties of Rota-Baxter ...
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3answers
394 views

Combinatorial aspects of continued fractions

Recently, I got interested in the study of the combinatorial aspects of continued fractions. Precisely, I read of the following lemma of Flajolet (see here): Lemma. It holds $$\sum_{\omega} \nu(\...