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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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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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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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, ...
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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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0
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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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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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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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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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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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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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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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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 ...
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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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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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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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"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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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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2
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142
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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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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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Good books and lecture notes about category theory.
What are the best books and lecture notes on category theory?
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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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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 ...
217
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29
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What is a good complex analysis textbook, barring Ahlfors's?
I'm out of college, and trying to self-learn complex analysis. I'm finding Ahlfors' text difficult. Any recommendations? I'm probably at an intermediate sophistication level for an undergrad. (Bonus ...
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0
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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 ...
1
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0
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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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0
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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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Calculus book with extremely hard questions
So, I'm taking Calculus BC in school as a 11th grader currently. My teacher tends to put extremely hard problems on the test. Most of these questions require a lot of work or thinking out of the box. ...
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Good book for self study of a First Course in Real Analysis
Does anyone have a recommendation for a book to use for the self study of real analysis? Several years ago when I completed about half a semester of Real Analysis I, the instructor used "Introduction ...
211
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32
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123k
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Books on Number Theory for Layman
Books on Number Theory for anyone who loves Mathematics?
(Beginner to Advanced & just for someone who has a basic grasp of math)
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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 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 ...
0
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3
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192
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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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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.
...
148
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23
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The Best of Dover Books (a.k.a the best cheap mathematical texts)
Perhaps this is a repeat question -- let me know if it is -- but I am interested in knowing the best of Dover mathematics books. The reason is because Dover books are very cheap and most other books ...
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Book Recommendations for Learning Python for Mathematics.
Lately, I've been finding that I often need to compute various things and graph some pretty complicated functions. I've realized that learning to program, especially in Python, could be really helpful ...
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1
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227
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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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0
answers
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 ...
3
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0
answers
224
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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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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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What is a good textbook to learn about infinite-dimensional manifolds?
The goal of this question is to serve as an "abstract duplicate target", as there are currently many different questions on this site about this exact topic.
Which textbooks are there to ...
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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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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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Good Book On Combinatorics
What is your recommendation for an in-depth introductory combinatoric book? A book that doesn't just tell you about the multiplication principle, but rather shows the whole logic behind the questions ...
248
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Teaching myself differential topology and differential geometry
I have a hazy notion of some stuff in differential geometry and a better, but still not quite rigorous understanding of basics of differential topology.
I have decided to fix this lacuna once for all....
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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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31
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Non-textbook Math book recommendation to read to my kids
I'm looking for a book to read to my kids.
NOT a kids book, but not too mature for a kid. My youngest kid that reads with me is 6 and the eldest is 10.
I'm looking for a book that is good literature, ...
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