Mathematics Stack Exchange
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Questions tagged [reference-request]

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.

This tag is for questions seeking external references (books, articles, websites, etc.) about a particular subject. It is intended for use along with other, more "mathematical" tags. Please do not use this as the only tag for your questions. See this discussion on Meta.

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Fun but serious mathematics books to gift advanced undergraduates.

I am looking for fun, interesting mathematics textbooks which would make good studious holiday gifts for advanced mathematics undergraduates or beginning graduate students. They should be serious but also readable. In particular, I am looking for…
Samuel Handwich
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The Integral that Stumped Feynman?

In "Surely You're Joking, Mr. Feynman!," Nobel-prize winning Physicist Richard Feynman said that he challenged his colleagues to give him an integral that they could evaluate with only complex methods that he could not do with real…
Argon
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What books must every math undergraduate read?

I'm still a student, but the same books keep getting named by my tutors (Rudin, Royden). I've read Baby Rudin and begun Royden though I'm unsure if there are other books that I "should" be working on if I want to study beyond Masters. I'm not there…
Adam
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Eigenvectors of real symmetric matrices are orthogonal

Can someone point me to a paper, or show here, why symmetric matrices have orthogonal eigenvectors? In particular, I'd like to see proof that for a symmetric matrix $A$ there exists decomposition $A = Q\Lambda Q^{-1} = Q\Lambda Q^{T}$ where…
Phonon
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Good books and lecture notes about category theory.

What are the best books and lecture notes on category theory?
Hendrik Brummermann
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10 answers

Exterior Derivative vs. Covariant Derivative vs. Lie Derivative

In differential geometry, there are several notions of differentiation, namely: Exterior Derivative, $d$ Covariant Derivative/Connection, $\nabla$ Lie Derivative, $\mathcal{L}$. I have listed them in order of appearance in my education/in…
Michael Albanese
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Is computer science a branch of mathematics?

I have been wondering, is computer science a branch of mathematics? No one has ever adequately described it to me. It all seems very math-like to me. My second question is, are there any books about computer science/programming that are very…
user107952
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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. Unfortunately I cannot attend a course right…
Harddaysknight
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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)
Prasoon Saurav
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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 points if the text has a section on the Riemann…
MBP
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Overview of basic results about images and preimages

Are there some good overviews of basic facts about images and inverse images of sets under functions?
Martin Sleziak
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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 to Analysis" by Gaughan. While it's a good book,…
CritChamp
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Examples of mathematical discoveries which were kept as a secret

There could be several personal, social, philosophical and even political reasons to keep a mathematical discovery as a secret. For example it is completely expected that if some mathematician find a proof of $P=NP$, he is not allowed by the…
user180918
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11 answers

What is the best book to learn probability?

Question is quite straight... I'm not very good in this subject but need to understand at a good level.
Eduardo Xavier
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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 are not: For example, while something like…
Three
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