/sci/ - Science & Math

[Anonymous No.11201263]

Kino books thread

[Anonymous No.11201266]

[Anonymous No.11201268]

[Anonymous No.11201275]

>I studied algebra in middle school

[Anonymous No.11201279]

[Anonymous No.11201315]

[Anonymous No.11201317]

[Anonymous No.11201325]

>>11201263

[Anonymous No.11201509]

>>11201325

/thread

[Anonymous No.11201511]

[Anonymous No.11201536]

>>11201317
very nice

[Anonymous No.11201538]

>>11201511
lol

[Anonymous No.11201542]

>>11201538
what's so funny?

[Anonymous No.11201564]

[Anonymous No.11201593]

>>11201564
post your ugly fat fucking hairy face. I know you

[Anonymous No.11201726]

>>11201593

[Anonymous No.11201746]

>>11201317
jesus that is really super. how'd a nitwit like you get so tasteful?

[Anonymous No.11201751]

[Anonymous No.11201785]

yellow book bad

[Anonymous No.11201871]

>>11201263

[Anonymous No.11201881]

>>11201263
The ending was a bit weak but Chapters 5 and 10 are GOAT.

[Anonymous No.11201967]

>>11201275
200+IQ book right here

[Anonymous No.11202227]

>>11201881
cringe

[Anonymous No.11202249]

>>11201263
>kino book thread
>not a single one is by Milnor

Neck yourselves fucking illiterate philistines, maybe you’ll have a sense of taste when you choke

[Anonymous No.11203557]

>>11201266
>>11201751
>>11202249
yes

[Anonymous No.11203827]

[Anonymous No.11204084]

>>11201263
what's a good book for smooth brains who can barely do multiplication or division but want to get to a point were you can grasp astrodynamics?

[Anonymous No.11204128]

My favourite book while studying at university by far, really good pacing, great characters, develops concepts at the perfect pace.

[Anonymous No.11204358]

>>11204128
Pitch it to me.
I always found solitons to be niche solutions that strangely get seemly unwarranted attention. Am I wrong? Are they the base for anything?

[Anonymous No.11204697]

[Anonymous No.11204700]

>>11204084
dontbwaste your time sweatie

[Anonymous No.11204745]

>>11201317
>>11201746
>>11204697
how much differential geometry did you know before this book started to make sense ?

[Anonymous No.11204750]

>>11204745

[Anonymous No.11204765]

>>11204750
that's not really what I'm asking. even though the material is developed from scratch, this book is definitely not for a first read in diff geo.

[Anonymous No.11204782]

>>11204765
> this book is definitely not for a first read in diff geo.
why not?

[Anonymous No.11204787]

>>11201263
I really like this one

[Anonymous No.11204963]

>>11201542
stop.

[Anonymous No.11204969]

>>11204782
very non-standard point of view

[Anonymous No.11205105]

>>11204745
I read it (read the first 100 pages or so) in 2010 before finishing my masters and got a lot out of it. Today it's a much nicer read. It's a pretty text. Not too many texts are pretty in that way.

[Anonymous No.11205186]

>>11202249
For you, my king

[Anonymous No.11205377]

>>11204787
Why? What's so special about it? How's it compared to Rudin, Pugh and Tao?

[Anonymous No.11205410]

[Anonymous No.11205555]

>>11204700
I have time in spades HUN

[Anonymous No.11206289]

>>11204969
You should probably know what submanifolds in [math]\mathbb{R}^n[/math] are.

[Anonymous No.11206326]

>>11201263
I drive a lot while I wage slave. Is there any kino books I could listen to in audio book form?

[Anonymous No.11206365]

[Anonymous No.11206399]

>>11206289
?

[Anonymous No.11206564]

What's people's view on this book?
(I guess opinions might depend on your field of study)

[Anonymous No.11206647]

>>11206564
started reading last week, it's great

[Anonymous No.11206650]

>>11206564
Kino. Belongs to this thread.

[Anonymous No.11206652]

>>11206564
>>11206647
I mean it's definitely kino if that's what you're asking

[Anonymous No.11206771]

>>11206647
>>11206650
Went to the library to scan through the mechanics books in physics, engineering and math to compare presentations of the rigid rotor chapters in various books and over time, for the recommendation section of a small video and text on theorems about the moment of inertia tensor.
I had consulted Arnold's book half a decade ago when I had uneasy feelings about the axiomatic treatment of Newtonian mechanics. Not the mathematical axioms, but the physical postulates - in particular the question of how to properly introduce the notion of "force", "reference frame" and "force-free" without circularity. (And I was interested in the historical reception on grounding your physics on point sized actions was, and how the status of Newton played into that. Afaik Boltzmann's >>11201726 atom model was attacked brutally just over 100 years ago and he ended up hanging himself.) That was at the same time as >>11205105 and I took a mathematical turn and dropped the question.
To my surprise, Arnold himself held (for me) surprising views that were (or are?) highly debated, as evidenced e.g. by this late 90's text of his
>This is an extended text of the address at the discussion on teaching of mathematics in Palais de Découverte in Paris on 7 March 1997.
>Mathematics is a part of physics. Physics is an experimental science, a part of natural science. Mathematics is the part of physics where experiments are cheap.
>The Jacobi identity (which forces the heights of a triangle to cross at one point) is an experimental fact in the same way as that the Earth is round
(you can find the essay by googling those lines)

I only know Arnold as wrinkly old man, but here I see he was quite the Chad, pic related.
Just saw it as I came across this text "Foundations of Mechanics"
https://www.amazon.com/Foundations-Mechanics-Ralph-Abraham/dp/0201408406
by an an author called Abraham (his colleague Marsden is more known), which goes full on commutative diagrams, and that in 1967.

[Anonymous No.11206774]

Here's a working link to that essay

https://dsweb.siam.org/The-Magazine/All-Issues/vi-arnold-on-teaching-mathematics

[Anonymous No.11206788]

Here's a working link to that essay

https://dsweb.siam.org/The-Magazine/All-Issues/vi-arnold-on-teaching-mathematics

[Anonymous No.11206825]

>>11206788
thanks

[Anonymous No.11206828]

>>11206788
>drawing a curve given by the parametric equations
I'd honestly have problems drawing that properly.
Sure, picking out t=-1, 0, 1 and a couple more and filling it in is easy, but I'd probably fuck concavities and convexities up if I didn't take some time.

[Anonymous No.11206835]

>>11206828
I think the point is that the students who learned New Math (which was hot at the time), getting at things from a pure algebraic perspective, didn't identify X's and Y's there with Decart'ian coordinate functions in the first place

[Anonymous No.11206974]

>>11205186
Not the guy you responded to but god damn. Perfection.

[Anonymous No.11206978]

>>11205377
Its actually well written

[Anonymous No.11207130]

>>11206564
Every book by Arnold is nice. This one is very nice.

[Anonymous No.11207935]

the last chapter is probably a bit too hard, same for a few paragraphs in scattering and solid movements, but the rest is really, really good.

[Anonymous No.11207937]

>>11206564
Same content as Landau's, more rigorous (of course), but less physical insight and actual phenomenons described.

[Anonymous No.11207970]

>>11207937
Although if I recall correctly, Landau goes with Lagrangian functions from page 1 and is more vocal about the physics of it.

And of course it's not as coordinate free as Arnold. Since the nice coordinate free reformulations of all things differential geometry in mathematics, there's the general attitude of distain for coordinate expression and indices, but I think this attitude goes a little bit too far. I tend to like my differential operators emphasized (and all natural operations/transformations, for that matter), but afaik (although I've never verified this), there's cases of expressions that have exponential notational blowup (I think this is even a formal result) if you don't use indices. The issue is when you have a term with various indexed arguments and functions at the same time, where not going with overall outer sums over everything is sheer impossible. Something like [math] \sum_i G_i(\sum_j F_i^j(I(x^j, y_i(t_j))), z^i) [/math].

Also I just made the rigid body clip

https://youtu.be/ccsldiiJH7k

[Anonymous No.11207997]

>>11207970
Yes, Landau's book is a physics book ; emphasis is on invariants given by the Lagrangian and how we solve equations with them.
Arnold's book on ODE was my first introduction to differential geometry and I'm dying to know more about them, but I can't find a good book about it. (I'm a physics student.)

[Anonymous No.11208012]

[Anonymous No.11208021]

>>11207970
O MY FIDDLING AROUND WITH UPPER AND LOWER INDICES AND DOING EINSTEIN SUMMATION
Man, fuck physicist notation, why do you negroes do this stuff.
>>11207997
Differential Geometry as Riemannian Geometry?
Chavel is honestly the better text, but a physicist should enjoy Petersen more.
Neither text is actually good, tho. Chavel is somewhat schizophrenic for reasons I can't explain and Petersen goes way too hard on the physishittery. Supply is scarce in this field.

[Anonymous No.11208025]

>>11208021
Not really, Differential Geometry as the study of manifolds and other shit
Lee's series looks promising, but I'm too uneducated to know if there's actually something more to differential geometry than studying manifolds (because that's all Lee's books are about)

[Anonymous No.11208076]

>>11208025
>more to differential geometry than studying manifolds
Sort of? Differential geometry doesn't study manifolds or differential manifolds, those would be topology (specifically either low or high dimension, but specific dimensions have their own specific theories) and differential topology. It really only becomes differential geometry once you add more structure, such as:
A symplectic structure, a contact structure, a metric tensor, a Finsler norm, a Cartan, Affine or Ehresman connection, a complex structure, a C.R. structure, etc.
Rather than just going for Lee, I'd recommend picking up the classical theory of curves and surfaces first. Toponogov seems good.

[Anonymous No.11208079]

>>11208021
Hey I didn't even do implicit summation in that example.

>>11208021
I remember reading into Peterson Peterson at one point, but it didn't feel very much like physics, actually.
The General Relativity book by Wald
(https://www.amazon.com/General-Relativity-Robert-M-Wald/dp/0226870332))
is a lot of Riemannian geometry next to the physics of it. I think by Peterson being physics you may mean dwelling around on various tensors for too long? And Laplacians in many explicit metrics?

>>11208025
>if there's actually something more to differential geometry than studying manifolds
I'm not sure that that's what you really mean to say. Yes it's about manifolds, but there's lots of aspects to it.
I think for a physicist, or let's say without any ring theory at hand, it's initially tough to appreciate deRham cohomology. People like to present coordinate free Stokes, but without the whole algebra of the operators, looking back, this strikes me of a bit as a gimmick.
I don't know what topics you've seen or liked being tackled by an explicit differential geometric approach. There's this book by Waldmann (not sure if it has an English translation) which has 200-300 pages on the Poisson bracket for classical mechanics, and then uses it to do deformation quantization (related to Wigner approaches). So you consider a classical manifold and search for a non-commutative bilinear "star-operation" * on it's functional algebras so that f(X,P)*g(X,P)-g(X,P)*f(X,P) is isomorphic to the operator algebra [f, g](X,Y) you have in a Hilber space.
Apart from even-dimensional forms being defined on a manifold, there's also structures for odd-dimensional ones.
There's e.g. contact geometry
https://en.wikipedia.org/wiki/Contact_geometry
which has been used to formulate phenomenological thermodynamics (which tends to be super awkward in the classical presentation, because there's often extensive quantities deltas "delta X:=..." defined without there being a potential "X" for them)

[Anonymous No.11208143]

>>11201542
I've read a different edition of this text, it sucks shit

[Anonymous No.11208486]

>>11203827
ha. this does not exist!

[Anonymous No.11208617]

>>11208079
I took riemannian geometry from Peter Peterson and he didn't even use his own text. Good class