Questions tagged [textbook-recommendation]
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 used to indicate the subject. For other questions on books, please use the tag books. Also, see reference-request for a related tag.
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Best algebraic geometry textbook? (other than Hartshorne)
I think (almost) everyone agrees that Hartshorne's Algebraic Geometry is still the best.
Then what might be the 2nd best?
It can be a book, preprint, online lecture note, webpage, etc.
One suggestion ...
148
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26
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Good "casual" advanced math books
I'm curious if there are any good math books out there that take a "casual approach" to higher level topics. I'm very interested in advanced math, but have lost the time as of late to study textbooks ...
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Statistics for mathematicians
I'm looking for an overview of statistics suitable for the mathematically mature reader: someone familiar with measure theoretic probability at say Billingsley level, but almost completely ignorant of ...
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Books that teach other subjects, written for a mathematician
Say I am a mathematician who doesn't know any chemistry but would like to learn it. What books should I read?
Or say I want to learn about Einstein's theory of relativity, but I don't even know much ...
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Is Mac Lane still the best place to learn category theory?
For a student embarking on a study of algebraic topology, requiring a knowledge of basic category theory, with a long-term view toward higher/stable/derived category theory, ...
Is Mac Lane still ...
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8
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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 ...
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Wanted: a "Coq for the working mathematician"
Sorry for a possibly off-topic question -- there are four StackExchange subs each of which could be construed as the proper place for this question, and I've just picked the one I'm most familiar with....
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Algebraic topology beyond the basics: any texts bridging the gap?
Peter May said famously that algebraic topology is a subject poorly served by its textbooks. Sadly, I have to agree. Although we have a freightcar full of excellent first-year algebraic topology texts ...
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Suggestions for a good Measure Theory book
I have taken analysis and have looked at different measures, but I am currently looking at realizing a certain problem in a different light and feel that I need a better background in various measures ...
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12
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Advanced Differential Geometry Textbook
I tried this post on StackExchange with no luck. Hopefully the experts at MathOverflow can help.
In algebraic topology there are two canonical "advanced" textbooks that go quite far beyond the usual ...
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Linear Algebra Texts?
Can anyone suggest a relatively gentle linear algebra text that integrates vector spaces and matrix algebra right from the start? I've found in the past that students react in very negative ways to ...
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If I want to study Jacob Lurie's books "Higher Topoi Theory", "Derived AG", what prerequisites should I have?
I've been told that it's important to know modern physics, Differential Geometry and Algebraic Topology for understanding higher structures. Is there any other prerequisite for understanding Lurie's ...
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Natural transformations as categorical homotopies
Every text book I've ever read about Category Theory gives the definition of natural transformation as a collection of morphisms which make the well known diagrams commute.
There is another possible ...
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A good book of functional analysis [closed]
I'm a student (I've been studying mathematics 4 years at the university) and I like functional analysis and topology, but I only studied 6 credits of functional analysis and 7 in topology (the basics)....
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12
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Homological Algebra texts
I would like to hear the communities' ideas on good Homological Algebra textbooks / references. The standard example is of course Weibel (which I'll leave for someone else to describe).
As usual, ...
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Computer science for mathematicians
This is a big-list community question, so I'm sorry in advance if it is deemed too soft but I haven't seen anything similar yet.
I've seen computer scientists post questions looking to learn things ...
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Good differential equations text for undergraduates who want to become pure mathematicians
Alright, so I have been taking a while to soak in as much advanced mathematics as an undergraduate as possible, taking courses in algebra, topology, complex analysis (a less rigorous undergraduate ...
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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 ...
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Introductory text on geometric group theory?
Can someone indicate me a good introductory text on geometric group theory?
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Good lattice theory books?
A recent answer motivated me to post about this. I've always had a vague, unpleasant feeling that somehow lattice theory has been completely robbed of the important place it deserves in mathematics - ...
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8
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Roadmap for studying arithmetic geometry
I have read Hartshorne's Algebraic Geometry from chapter 1 to chapter 4, so I'd like to find some suggestions about the next step to study arithmetic geometry.
I want to know how to use scheme ...
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7
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Classification of (compact) Lie groups
I would like to study/understand the (complete) classification of compact lie groups. I know there are a lot of books on this subject, but I'd like to hear what's the best route I can follow (in your ...
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Good algebraic number theory books
I have just finished a master's degree in mathematics and want to learn everything possible about algebraic number fields and especially applications to the generalized Pell equation (my thesis topic),...
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8
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An "advanced beginner's" book on algebraic topology?
It has so happened that I have come this far knowing nothing on the subject of algebraic topology (as in homology theories of topological spaces and their applications). I've decided to finally read ...
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introductory book on spectral sequences
I have studied some basic homological algebra. But I can't send to get started on spectral sequences. I find Weibel and McCleary hard to understand.
Are there books or web resources that serve as ...
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Resources for learning practical category theory
I've been doing functional programming, primarily in OCaml, for a couple years now, and have recently ventured into the land of monads. I'm able to work them now, and understand how to use them, but ...
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How to start game theory?
I recently got interested in game theory but I don't know where should I start.
Can anyone recommend any references and textbooks?
And what are the prerequisites of game theory?
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Book on mathematical "rigorous" String Theory?
I've been looking high and low for a mathematical book on String Theory. The only book I could find was "A Mathematical Introduction to String Theory" by Albeverio, Jost, Paycha and ...
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Real algebraic geometry vs. algebraic geometry
This question is predicated on my understanding that real algebraic geometry (henceforth RAG) is the version of algebraic geometry (AG) one gets when replacing (esp. algebraically closed) fields with ...
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12
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Introductory text on Riemannian geometry
I have studied differential geometry, and am looking for basic introductory texts on Riemannian geometry. My target is eventually Kähler geometry, but certain topics like geodesics, curvature, ...
41
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2
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Introductory text on Galois representations
Could someone please recommend a good introductory text on Galois representations? In particular, something that might help with reading Serre's "Abelian l-Adic Representations and Elliptic Curves" ...
41
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4
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Elementary number theory text from a categorical perspective
My question is somewhat similar to this previous question, but from a slightly different perspective. Is there any textbook on elementary number theory that develops the properties of $\mathbb{Z}$ as, ...
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Why not a Roadmap for Homotopy Theory and Spectra?
MO has seen plenty of roadmap questions but oddly enough I haven't seen one for homotopy theory. As an algebraic geometer who's fond of derived categories I would like some guidance on how to build up ...
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26
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Text for an introductory Real Analysis course.
Any suggestions on a good text to use for teaching an introductory Real Analysis course? Specifically what have you found to be useful about the approach taken in specific texts?
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Insightful books about elementary mathematics
What are some books that discuss elementary mathematical topics ('school mathematics'), like arithmetic, basic non-abstract algebra, plane & solid geometry, trigonometry, etc, in an insightful way?...
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What are some good group theory references?
I'm curious about what books people use for a group theory reference. I don't currently own a dedicated group theory book, and I think I'd find such a book very helpful in my research. What is your ...
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Exposition of Grothendieck's mathematics
As Wikipedia says:
In Grothendieck's retrospective Récoltes et Semailles, he identified twelve of his contributions which he believed qualified as "great ideas". In chronological order, ...
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Good introductory book to type theory?
I don't know anything about type theory and I would like to learn it.
I'm interested to know how we can found mathematics on it.
So, I would be interested by any text about type theory whose angle ...
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5
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A reference for geometric class field theory?
The classic reference of this topic is Serre's Algebraic Groups and Class Fields. However, many parts of this book use Weil's language, which I find quite hard to follow. Is there another reference ...
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Textbook for Etale Cohomology
What is the best textbook (or book) for studying Etale cohomology?
user16974
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Matsumura: "Commutative Algebra" versus "Commutative Ring Theory"
There are two books by Matsumura on commutative algebra. The earlier one is called Commutative Algebra and is frequently cited in Hartshorne. The more recent version is called Commutative Ring ...
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Textbook recommendations for undergraduate proof-writing class
I am teaching the proof-writing class (for the 3rd time) in the Fall and plan to buck the party line and use a different text than the default Bond and Keane. My parameters are as follows:
Logic, ...
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Lecture notes on representations of finite groups
Next term I am supposed to teach a course on representation of finite groups. This is a third year course for undegrads. I was thinking to use the book of Grodon James and Martin Liebeck "...
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11
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A book for problems in Functional Analysis
I want to know if there's any book that categorizes problems by subjects of Functional Analysis.
I'm studying Functional Analysis now a days and I really need to solve some problems in order to ...
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Book recommendation for cobordism theory
I am planning to organize a seminar on cobordism theory and I'm looking for a reference. Such a reference is preferably a book, but I'm open to other ideas.
The audience is familiar with ...
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Euclid with Birkhoff
I'm looking for a short and elementary book which does Euclidean geometry with Birkhoff's axioms.
It would be best if it would also include some topics in projective (and/or) hyperbolic geometry.
...
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Good books on problem solving / math olympiad [closed]
I would want all book tips you could think of regarding problem solving and books in general, in elementary mathematics, with a certain flavour for "advanced problem solving". An example ...
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Suggestions for good books on class field theory
Recently I tried to learn class field theory, but I find it is difficult. I have read the book "Algebraic Number Theory" by J. W. S. Cassels and A. Frohlich. In the book, the approach to class field ...
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Book on symplectic geometry
Can someone please tell me some introductory book on symplectic geometry? I have no prior idea of the subject but I do know about Lagrangian and Hamiltonian dynamics (at the level of Landau-Lifshitz ...
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Modern source for spectra (including ring spectra)
I am looking for a modern introduction to spectra that improves on the treatment by Adams in his "Stable Homotopy and Generalized Homology" notes (by improves I mean taking into account what ...