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14867682 No.14867682 [Reply] [Original] [archived.moe]

what is a good book to learn about pic related?

>> No.14867685

>>14867682
Elementary Mathematics for Retardeds, Third Edition

>> No.14867719

>>14867685
begone esl

>> No.14867728

stokes gay theorem for trannys, 108th edition, author Larry Capija

>> No.14869360

Transitional Calculus: Intro to HRT

>> No.14869380

>>14869360
Ah yes, Homotopy Relation Theory, my favourite topic

>> No.14869405

>>14867682
Stoke my dick

>> No.14869426

>>14867682
Spivak manifolds.

>> No.14869438

amann escher bach analysis vol 3(the version that replace every he with a she)

>> No.14869477

Baby rudin

>> No.14869867

any of the books in the Wiki page for 'Tangent space'

>> No.14869891

>>14869426
only correct answer

>> No.14869903

>>14867682
>Stokes
I liked spivak's (calculus on manifolds) and folland's (real analysis) treatments of the subject. The former does a really good job of it.
The result you've posted is one where the actual method was elementary but setting everything up and realizing how it works was sort of nontrivial.

>> No.14869907

>>14869891
>Moreover, careful readers have noted a number of nontrivial oversights throughout the text, including missing hypotheses in theorems, inaccurately stated theorems, and proofs that fail to handle all cases.
I wonder what Addison-Wesley thinks of this
This criticism is new to me
If accurate, it would represent an academic gap in mathematics criticism
The philosophy department would have to explain their laxity

>> No.14869951

>>14867682
i admit that Stokes looks sexy as fuck, but it's a pretty trivial result by itself (basic application of Fundamental Theorem of Calculus), the difficulty is setting up all the machinery of manifolds, tangent spaces, forms and boundary. if you're not memeing and really want to learn all of this, go for Tu's Intro to Manifolds, it's a very good introduction that only requires basic topology and multivariable calculus. Lee's Intro to Smooth Manifolds is also very good, but a tougher, Lee's (different one) Differentiable Manifolds is even tougher

>> No.14869959

>>14869907
>>14869891
>>14869426
I like the book, but if you want to work through it you *have* to use one of the websites detailing all errata, because there are so many mistakes and typos.

>> No.14870547

>>14869438
>the version that replace every he with a she
unironically how did this happen?

>> No.14870589

>>14867682
Zorich

>> No.14870697

Munkres' Analysis on Manifolds

>> No.14870751
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14870751

>>14869951
>it's trivial but you have to do difficult things first
the issue with 'learning' is discharging material in an orderly way and going onto the next...the point of a test is that there is a complex reputation event that ties the honesty and integrity of the testing institution a.k.a. 'school' to its judgement of your mastery of the material, namely solving some exercises and problems making use of the new definitions, lemmas, theorems, and notational conventions you just learned and have become accustomed to
when you take the test, you're essentially saying that you're discharging the material you've learned up to this point according to the grading system of the school, and that means essentially
>well, I got a B+ or an A- in that class, and that's clearly good enough, so I can forget about what I learned
It should be a mindless & mechanical process where you practice writing the contents of your mind on every available surface in your own mind simply to flex your mathematical muscles and then at the end of the semester throw everything away
>it was all trivial
and clear your mind for the next semester, putting your new playthings, your new definitions and lemmas, your new notation, all of this away in the chest of toys in your nursery

>> No.14870880

>>14870751
bro wtf are you talking about

>> No.14872184

>>14867682
Aside from the trolling in this post, the best book that really got me to understand what was really going down with Stokes' theorem and differential forms was by far "A Visual Introduction to Differential Forms and Calculus on Manifolds" by [math]\textit{Jon Pierre Fortney}[/math]

>> No.14872262
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14872262

>>14867728
>Larry Capija

>>
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