Questions tagged [book-recommendation]
This tag is for questions about recommendation of books for some particular area, topic, problem. Use this tag together with (reference-request) tag.
3,581 questions
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Book Recommendation for Vector Bundles
I am interested in learning more about general vector bundle theory. More specifically, vector bundles of class $C^k$ for $k\in\mathbb{N}$ or $C^\infty$ or real-analytic whose fibers can be given the ...
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Function spaces, uniformities, and k-spaces
I'm looking for a resource that covers the interplay between function and uniform spaces and k-spaces. All the texts I've seen so far cover one or two of the three, but never the full combination in ...
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many example of rings [closed]
I'm studying commutative ring theory from Hideyuki Matsumura's book, but it's so abstract that I try to come up with lots of concrete examples on my own---for instance, classifying commutative ...
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1
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Recommendation on books/notes that treat Summations rigorously [closed]
I am an undergraduate in Mathematics, almost finishing the degree. Treatment of summations (sigma notation) has always bothered me, since in most cases we can convince ourselves that their ...
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Cauchy integral formula for derivatives — general proof [duplicate]
The Cauchy Integral Formula for Derivatives states that if $f$ is analytic inside and on a simple closed contour $C$, and $z_0$ is a point inside $C$, then for any integer $n \ge 0$,
$$
f^{(n)}(z_0) = ...
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Books on Abstract Algebra [duplicate]
I am looking for a book covering topics in algebra, specifically in rings and modules. I am a graduate student, so I do not want a very basic book. I have taken a look at the book by Dummit and Foote, ...
- 1,478
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Textbook for self study of Graduate Level Linear algebra [duplicate]
Having just finished my masters, with my dissertation being heavily applied, but more than half of my credits in various abstract algebra courses(Modules, Semigroups, Number Theory etc.), I was ...
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References on algebraic structure of free groups
I’m studying the algebraic properties of free groups and would like to learn more about results such as:
Structure of abelian subgroup of the free group.
Let $F$ be a finitely generated free group ...
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Recommended book or note for methods of mathematical proof [duplicate]
I asking about good book for undergraduate student to learn methods of mathematical proofs in more details and has lot of examples. I found "book of proof by richard hammack" but I want more....
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Textbooks on multilinear algebra and contractions
A friend of mine is currently writing his Bachelor's thesis on the topic of elastic materials. In particular, this involves higher-order derivatives. These are naturally expressed in the language of ...
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More rigorous alternatives to Ahlfors' "Complex Analysis"
I am currently reading Ahlfors' Complex Analysis and am still in the early chapters. My impression so far is that the exposition is not particularly rigorous, though I may be mistaken. I prefer the ...
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Look for books for maths competition [duplicate]
I'am a high schooler who's looking to participate at competitions like HMMT PUMAC or CMIMC, and i want something to work one apart from the original archive of the cited competitions especially Number ...
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Books about algebra in style of category theory
The philosophy of category theory is that we focus on relations between objects, but not on inner structure of objects. So, are there any algebra books that develop some area of algebra (for ex. ...
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116
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Book recommendations for rigorous multivariable calculus with emphasis on differential forms
I'm looking to study the analysis of differential and integral calculus for functions of several variables from a rigorous perspective, with a particular emphasis on differential forms.
My background ...
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Looking for introductory book on Fourier Series and Analysis [duplicate]
It should start from the very beginning deriving the Fourier series. I have tried a book by Elias M. Stein & Rami Shakarchi. It's a good book but they assume that reader has already been ...
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Book Recommendation On Analytic Number Theory
I am planning to study number theory, and as preparation I have studied high school–level differential and integral calculus (primarily single-variable), high school algebra, and a little abstract ...
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Where can I find material about the algebra of the Cauchy Product?
I'm trying to figure out the algebraic properties of the Cauchy product ($c_n=\sum_{k=0}^na_kb_{n-k}$). I'm doing it by myself and I feel like there should be some literature on it. I didn't find it ...
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Rigorous and geometric definition of curl of a video
I have always know that the curl of a vector field $\mathbf{F}$ is given from this definition:
Let $\mathbf{F} : D \to \mathbb{R}^3$, with $D \subseteq \mathbb{R}^3$ open, be a vector field of class $...
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Are there any recommended resources on profinite groups, particularly regarding arithmetic applications?
I'm currently reading Fourier Analysis on Number Fields but unsatisfied with its treatment of profinite groups, since I'm not fond of excessive point-set topology techniques.
Many number-theoretic ...
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75
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Looking for a 3D geometry textbook.
Looking for a textbook on 3D synthetic geometry that concerns points, lines, planes, spheres, and their intersections, tangency relations, and incidence relations. Importantly, it should NOT focus on ...
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What math subjects are relevant for someone wanting to learn how and why plane and solid geometry, projective geometry work in the context of art?
everyone! I am hoping to get some direction and book recommendations. I am an artist and have been learning from an art teacher a little about the role that geometry played for the Old Masters and the ...
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I wonder whether there exists a book of "Formal power series" and "Formal infinite products"?
Recently, I have read some books related to analytic number theory, and many problems of manipulating power series or infinite products without caring about convergence have puzzled me. I find that ...
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Linear optimisation resources
I am trying to learn linear optimisation using the book introduction to linear optimisation by bertsimas. I am having trouble understanding the concepts of polyhedral representation and polyhedrally ...
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Modern References to Fourier series in PDEs
I've been looking for reference about solving PDE with Fourier Series. I have a lot of references about Harmonic Analysis like "Fourier Analysis" by Javier Duoandikoetxea and Classical ...
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2
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Categorical 'frameworks' that attach 'simpler' dynamical systems to more complex systems
In the 'obvious' matter of a 'framework of attaching anonymous dynamical systems to other [specified] dynamical systems [...] in accordance with general categorical principles' as answered by Alp ...
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A self-contained, modern book on complex analysis? [duplicate]
As the title says, I'm looking for a modern, rigorous book on complex analysis to restudy the subject from scratch, hoping to study after Riemann surfaces and their connection with algebraic curves ...
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101
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Reference request: Book listing all known convergence tests for series.
In studying calculus and introductory real analysis, I’ve come across many different tests for determining the convergence of series—such as ratio tests, comparison tests, integral tests, and others.
...
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97
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Minimal transitive model of ZF
I've heard that the following is a theorem of Shepherdson and was rediscovered by Cohen:
If there is a transitive model of ZF, then there is a minimal transitive model M in the sense that for
all ...
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930
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Is there a book that covers interesting ideas in contour integration?
I recently took a complex analysis class and obviously studied a lot about contour integration, but I wonder if there's more to it. I mean, usually taking the integral comes down to choosing a branch ...
3
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1
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63
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Jet bundles with structure group?
In most references for jet bundles that I have seen (like Saunders), the authors only study jet bundles $J^k E$ of fibre bundles $\pi: E \to M$ without a specified structure group. What differences ...
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Modern books on Number Theory [closed]
Are there modern books on Number Theory?
Previous questions asking for same books was answered by suggestion following books :
1 . William J. LeVeque
Fundamentals of Number Theory
2 . Kenneth ...
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0
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119
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Math-heavy book on analytic continuation.
I'm looking for a comprehensive and rigorous textbook on analytic continuation that emphasizes mathematical formalism over plain exposition. Ideally, the book should contain a large number of worked ...
8
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313
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Second/Advanced Course in Complex Analysis
I took an undergrad class in complex analysis, and I would like to learn more complex analysis (as I have heard the field is very useful/inspiration for other things).
My class did everything in open ...
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Good Graph Theory book for self-learning that satisfies the requirements: "... any course that contains Turan's theorem"
Any recommendations for a good self-learning book, ideally suitable for an undergrad, that satisfies the requirements that it is "not just a catalogue of definitions. For example, any course that ...
- 1,995
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Looking for a book or youtube video with great visuals for equations of lines and planes in space
One of my worst areas of math, where I have really struggled to improve, is understanding and working with equations of lines and planes in (3D) space, especially when it comes to the intuition behind ...
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Algebra is my challenge [closed]
I want to learn more about algebra and matrices. I just turned 52 and mathematics is one of the subjects that it makes me feel that I can challenge and maintain my brain healthy. Could you recommend ...
3
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Please suggest a book that explains this theorem. We can use this theorem when we prove $e^{iz}=\cos z+i \sin z$. (Sin Hitotumatu's analysis book.)
I am reading "Introduction to Analysis 1" (in Japanese) by Sin Hitotumatu.
This book contains the following theorem.
I found this theorem interesting.
For example we can use this theorem ...
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"Calculus on Manifolds" by Michael Spivak vs "Introduction to Smooth Manifolds" by John M. Lee (Edited)
The prerequisites that Lee lists for his book that are also part of Spivak's book are: differentiation of functions $A\subseteq\mathbb{R}^m\to\mathbb{R}^n$, the inverse function theorem, the implicit ...
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Book recommendation : Variation of shape functionals on a surface
As someone with working knowledge of basics of surfaces, curvature, tensors, differential operators, I am looking for a good textbook which can help me learn calculus of variation on surfaces.
My main ...
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159
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Computational Complexity - Rudich/Wigderson vs. Arora/Barak
I am planning to self-study Computational Complexity Theory. After some research, I have narrowed down the following two books:
Rudich/Wigderson—Computational Complexity Theory
Arora/Barak—...
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Spectral theory for Frechet algebra?
In most textbooks discussing spectral theory of operators, they focus on a Banach algebra of operators due to the power that completeness provides. Frechet spaces are complete metric spaces too, so is ...
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There are two approaches to defining $\int_{\gamma}f$. Could you recommend a complex analysis book that takes the first approach?
There are two approaches to defining $\int_{\gamma}f$.
The first is to build up the theory of complex Riemann sums by mimicking the real case.
The second is to define $\int_{\gamma}f(z)dz:=\int_{a}^{b}...
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Is there a text that approaches Calculus of Variations as a special case of results on Banach Spaces?
It seems to me (correct me if I'm wrong) that Calculus of Variation is a subset of Analysis in Banach Spaces (see this post for an example).
Is there any text that approaches more general results on ...
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Sobolev functions on torus
I am looking for a well-written book (preferably lecture notes) that covers Parseval's formula and the embedding theorem $H^{m+n/2}(\mathbb{T}^n)\hookrightarrow C^m(\mathbb{T}^n)$ for Sobolev ...
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Reference request: ring and geometry of mixed characteristics
It seems that to study p-adic numbers or ring of mixed characteristics, one has to start from a number theory perspective. I wonder if there is a good textbook about ring or geometry of mixed ...
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Recommended reading on jet bundles
I am currently starting my PhD, and one of the topics it deals with is Jet Bundles. To get started I am studying D. J. Saunders, "The Geometry of Jet Bundles", but I was wondering if there ...
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Book recommendation for Markov chains on $\mathbb{R}^n$
I'm looking for book recommendations on Markov chains specifically defined on $\mathbb{R}^n$. I need resources that avoid excessive measure theory and focus on concrete definitions of transition ...
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How Can I Truly Understand Mathematics Instead of Just Following Rules?"
I want to ask a somewhat philosophical question. I’m a 10th-grade student currently studying systems of linear equations. I’ve learned to solve both simple and relatively complex equations. However, I’...
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Some good books for noncommutative ring theory [closed]
I am teaching myself noncommutative ring theory and have started reading T.Y. Lam's A First Course in Noncommutative Rings, but I find it quite difficult. What are the prerequisites for this book? I ...
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Book recommendations for self learning algebraic topology. [duplicate]
I'm an undergraduate physics major currently taking a point-set topology class, and honestly I'm enjoying it a bit more than I'd expect to. It kind of feels like... analysis but slightly less nitpicky?...
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