/sci/ - Science & Math

>>15090487
>Linear algebra book
>Does not talk about matrices
>Does not talk about solving linear equations
What was he thinking?

>>15090487
Utter garbage.

unrigorous, outdated garbage

>>15090487
Is there a better LA book that is more concise, because I was going to buy this book.

>>15090560
I was about to pull the trigger on this one but i went with Apostol instead

>>15090487
Some of the proofs are wrong, lots of „hand-waviness", little to no applications, ...etc

>>15090565
Advanced Linear Algebra by Roman.

>>15090569
Apostol is still shit, Herbert Amann, Joachim Escher - Analysis I, II, III is the way to go.

>>15090575
this

>>15090565
Rao & Bhimasankaram is the most comprehensive first course Linear Algebra book I have found that cuts to the chase. Very terse though.

>>15090570
Its purpose is to be a short introduction, as short as possible.
If you want rigor you're supposed to read Munkres's Analysis on Manifolds.

Goodman & Gilman's: The Pharmacological Basis of Therapeutics: There is a lot of information that contrasts with medicine.

>>15090570
Which proof is wrong?

>>15090581
b-b-but anon i like it

>>15090488
is this true ? wtf

>>15090560
kek

>>15090610
it's wordy, at times even hand-wavy, though fairly comprehensive. Roman's book is better for someone with an abstract algebra background, he also says it's for advanced undergraduates in the preface so it's not all that advanced, contrary to what the title may suggest.

>>15090700
It does talk about matrices, but very lightly. It does not talk about solving linear equations at all.
>>15090714
>wordy
For a first course undergraduate book, I disagree, especially compared to every other UG Linear Algebra, except Hoffman.
>hand-wavy
When?
>better for someone with an abstract algebra background
Hence, not suitable for a first course. A common reason to learn Linear Algebra is its applications to much less advanced fields like Calculus or Statistics, where all that abstract algebra is just going to be unnecessary.

>>15090730
nta but learning about "muh applications" is retarded. The application comes from itself once you've mastered the theory. No mathematician should prioritize that over learning the theory.

>>15090920
Ah yes anon, you don't have to read about topological manifolds. Just read up about modules, and you are gonna develop the entire theory of multivariate analysis from it.

>>15090622
You can have a short introduction that is still rigorous enough and not hand-wavy, plus this doesn't explain why some proofs are completely wrong. I would still like it if those issues were fixed.

>>15090631
Proof of Theorem 5-1 for example: https://web.archive.org/web/20220817075746/http://www.petraaxolotl.com/mathematics/calculus-on-manifolds/ (But this one can be fixed)

There was another important one but I forgot about it.

>>15090581
you are so fucking stupid

Everything by Serge Lang

>>15091230
/thread

Rudin.

Stop recommending that garbage to undergrads.

Pugh is much better for its visual and intuitive approach. It is just as difficult.

>>15090488

It is meant for people who are used to the computational stuff.

I like Linear

>>15091387
I like Linear Algebra Done Wrong better because it has a good mix of abstract theory and computation.

>>15091384
>Pugh is much better for its visual and intuitive approach
>visual
>intuitive
Yuck

>>15091387
No one said anything about computational.

>>15090487
>wow, it's old
>wow, it's contrarian
>wow, it's le funny

>>15091144
>There was another important one but I forgot about it.

>>15091230
Siegel on Lang
>When I first saw [Lang's Diophantine geometry], about a year ago, I was disgusted with the way in which my own contributions to the subject had been disfigured and made unintelligible. My feeling is very well expressed when you mention Rip van Winkle!

>The whole style of the author contradicts the sense for simplicity and honesty which we admire in the works of the masters in number theory - Lagrange, Gauss, or on a smaller scale, Hardy, Landau. Just now Lang has published another book on algebraic numbers which, in my opinion, is still worse than the former one. I see a pig broken into a beautiful garden and rooting up all flowers and trees.

>Unfortunately there are many "fellow-travellers" who have already disgraced a large part of algebra and function theory; however, until now, number theory had not been touched. These people remind me of the impudent behaviour of the national socialists who sang: "Wir werden weiter marschieren, bis alles in Scherben zerfällt!"

>I am afraid that mathematics will perish before the end of this century if the present trend for senseless abstraction - as I call it: theory of the empty set - cannot be blocked up.

>>15091840
What's so bad about the book?

>>15092191
Lang presumes you're not a freshman and already know some stuff, old farts didn't like it because they didn't understand half of the prerequisites so it seemed like pointless abstraction to them

>>15090487

>>15094084
Care to elaborate?

>>15091158
Sounds like you got filtered by Amann & Escher.

>>15090581
How is Zorich compared to Amann & Escher?

>>15090487
Pedantic trash

>>15091230
Algebra is a classic
the other 50 books Lang shat out are ass

>>15090487
Guns, Germs, & Steel

>>15094337
No.

>>15090488
You only use those when you want to do it wrong. Hence the title.

>>15090487
learned lingebra from shilov, would have preferred axler

>>15091387
Professional computer scientist here
We need that shit too

Not overrated by people in general, but certainly overrated by the author.

>>15090581
Can someone post pdf of Herbert and Escher's analysis books

>>15099461
You can find them on annas-archive.org

>>15099461
Just get it on libgen

>>15099461
from libgen, decode from base64

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

>>15090487
This book is amazing, amazing I tell you.
It makes you understand linear algebra as what it is; functional analysis on finite dimensional vector spaces.

>T. Applied mathematician (pde chad)

>>15090487
Yeah it does suck. Just read the linear algebra section of your favorite analysis book.

>>15090570
Take that back you fucker. It's an exercise book and if you do them all its great.

>>15091599
Redditors love it.

>>15096052
Geographic determinism is such a weak hypothesis. He makes stronger arguments for racism while trying to defend against them.

>>15090487
Protip: read the books that /sci/ thinks are overrated, but don't read the ones they think are must read.

>>15091840
libtard cuck detected, engaging action t4

>>15100935
But anon, those are the exact same books.

>>15100355
>decode from base64
What kind of pleb do you take me for, that I can't instantly recognize it's base64?

>>15090487
setting aside his unfounded phobia of determinants for a moment, Axler is a fine LA textbook. problem is most seem to think that he was the first to write a "conceptual" LA book that focuses on vector spaces and transformations, instead of R^n and matrices, which is definitely not the case
>>15090565
don't listen to anyone else, picrel is the KING of linear algebra textbooks, only thing that's poorly explained is Jordal normal form. something in the same spirit, but simpler (and freely available online) is Linear Algebra Done Wrong (it's purposefully a play on LADR)

>>15101681
>KING of linear algebra textbooks
that would be kostrikin&manin

>>15101681
>problem is most seem to think that he was the first to write a "conceptual" LA book that focuses on vector spaces and transformations, instead of R^n and matrices, which is definitely not the case
No one believes that.

>>15101702
allow me to rephrase: most treat it as if he were the only one

>>15101681
No pure linear algebra books assumes R^n.

>>15100914
>It's an exercise book and if you do them all its great.
And that's an excuse for it containing some wrong proofs and unrigorous material?

>>15101698
>kostrikin&manin
heckin based

>>15101698
It's gotta be Kostrikin

>>15102075
It doesn't. In every version you buy there is a correction list in the back.

> Unrigorous

Unless your favorite book is by Rudin, I guarantee it's less rigorous.

Is this book worth it? I know some people who praise it but i am still not even sure what it is about

>>15102344
it's pretty based of the author to write this, but i think it's just too fucking long and bloated for what it purports to achieve, the time sink is simply not worth it. you'd be better off reading some standard real analysis textbook like Tao for the basics of multivariable differentiation (total/partial derivatives, Schwartz, etc.) and Tu or Lee for manifolds

>>15102468
Thanks anon. I'll get Taos books since they are just dirt cheap on amazon

>>15095762
I hated this shit SO much. why the fuck did i have to download his retarded package

any alternative to this?

>>15102907

>>15102344
It is non rigorous, and barely has any linear algebra as the name would suggest. Frankly I don't even know who it is written for. It has very little of the subjects in the title to be considered introductory, nor is it very advanced to be considered a second course. The only reason it is popular is because 3b1b recommended it.

>>15102907
Folland's modern real analysis

>>15103043
I didnt know 3b1b suggested it. That actually explains a lot.
The book is honestly not good, it just isnt good, a lot of masturbatory exposition and overlong and useless sections.

If you want an actually good book on multivariate analysis, read Munkre's Analysis on Manifolds (picrel)

>>15103347
i finished a maths degree years ago in mostly applied topics. did ok in complex analysis (which mostly felt like a bag of tricks rather than anything truly deep), but i was an absolute retard at real analysis. any decent books that approach it in an intuitive friendly way for retards like me? i took 2nd year real analysis but only just managed to pass.

>>15102907
Pugh is pretty good

>>15103380
Seems like understanding analysis by Abbott is a good choice for you.
It's very well written, really takes time to motivate and explain the concepts well, has a ton of well thought out exercises and even informs you on the history of what you're reading as you go along.

I always tell people that ask me, if you want enjoyment and learning, go for Abbott. If you actually want to get good at math go for Rudin.

>>15103442
Which specific book?

opinion on pic related?
it's one of the most recommened books for beginners to QM.
i tried reading it but on the first page it already has the wave function.
i admit that im a retard but isnt it too early to introduce wave function?
also please recommend an alternative.

>>15103562
To be Griffiths is a Memebook for American students and thats just it. He covers superficial everything you need to know to start with QM, you wont understand much about QM with that book. Why? Because he goes the Schroedinger Wavemechanics approach but doesn't go deep into it. Speaking of which, there are several different approaches of Quamntum mechanics, or lets say, formalism you could follow. The most known is the Wavemechanics by Schroedinger, the second is the Heisenbergian Matrixmechanics, the third is less of a formalism but involves Functional Analysis and therefore a bit of Matrix mechanics and its more of Mathematical Physics. One significant approach are Path Integrals by Feynman, also you shouldn't avoid Relativistic Quantum Mechanics, but i guess thats something that comes last. As for QM Books, have a quick List: "Principles of Quantum Mechanics" by Dirac. "Matrix mechanics" by H.S. Green (He was a student of Max Born), "Quantum Physics: A Functional Integral Point of View" by James Glimm and Arthur Jaffe. "Quantum Mechanics and Path Integrals" by Richard Feynman. Also Lev Landaus "Relativistic Quantum Mechanics" out of his "Course of Theoretical Physics" though, there is a newer one which fused with the Quantumelectrodynamic book so beware, keep your eyes open for the older one. Also if you are in the mood i totally recommend the Feynman lectures which also include a book on QM. All of those books are very basic and teach you the various different approaches and formalisms. What i can't recommend, but will include is W. Paulis "Wellenmechanik" and Schroedingers "Abhandlungen zur Wellenmechanik", "Mathematical Foundations of Quantum Mechanics" by Von Neumann. There are probably a few more, don't know, i am not at home, and those i don't recommend are gems but only useful if you know german and if you get your hands on them, but they are all rather Mathematical PHysics books so they'll teach the math behind. Good luck anon with QM

>>15102344
>i am still not even sure what it is about
Multivariable calculus in 2 to 3 dimensions, while emphasising differential forms. It's good in what it does, but it's written in a very lofty way. For some, that's good, but for others like I'd assume most on /sci/, it feels bloated and time-consuming.

>>15103622
I wouldn't mind getting it but i was really not sure if it would be a nice addition to my library and if it teaches anything new. Also its fucking expensive at least in europe, the only seller i found wants 180 bucks. Fuck that shit

>>15103630
>Also its fucking expensive at least in europe
Yeah, that's why only read some of the pdf through libgen. If you're interested in a first exposure to multivariable calculus, then I could recommend you, unironically, Lang's Calculus of Several Variables. It's much more brief and covers the material in a very intuitive approach with minimal formalities. /sci/ never shills it for that reason, but I think for people who are just getting into math, it's perfect.

>>15103636
I already covered multivariable calculus also working on real analysis right now, but i was just curious about that book because everyone keeps recommending it. Probably never gonna get it and just read some of the pdf now

>>15103562
inadequate, wouldn't be wrong to even call it malicious
easiest progression to QM would probably be Dirac, Shankar, Sakurai or Townsend, Shankar, Sakurai

>>15103801
Thanks for the suggestion anon.
im really liking this Shankar book. It starts off with the some math stuff before diving in. I really needed that cause I'm a retard.
It also helps that there's a solutions manual available.

>>15103448
thanks brother

>>15103347
Analysis on Manifolds is also not good, very sloppy in many parts.

>>15106012
What is your alternative?

>>15106012
>Analysis on Manifolds is also not good, very sloppy in many parts
I strongly disagree, its absolutely amazing as an introductory text.
I know about this book because the world class top of the line differential geometers at my uni recommend it for multivariate analysis.

>>15090488
>>Does not talk about matrices
>>Does not talk about solving linear equations
And that's unironically a good thing. Matrices are not linear algebra, they're just representations of linear maps in a particular basis. You should (and can) do linear algebra without matrices. Likewise solving equations is not linear algebra, its an application of linear algebra.

>>15091437
He's right and you didn't read the book

>>15102324
>>15106012
>>15102075
>>15108170
Just use read these before you start, the book is really great, we also used it for multi anal.
http://www.petraaxolotl.com/mathematics/calculus-on-manifolds/
https://www.jirka.org/spivak-errata.html

>>15108330
What is linear algebra?

>>15108343
Linear maps on finite dimensional vector spaces. Matrices are just a way to represent those mappings.

>>15108351
How can it be about only vector spaces when it's literally the last thing that happened in the development of linear algebra?

>>15108351
How can it be about only vector spaces when it's literally the last thing that happened in the development of linear algebra?

>>15108351
>Matrices are just a way to represent those mappings.
So you agree a Linear algebra book should talk extensively about matrices.

>>15108379
Because unifying ideas typically happen later in the development of subjects.

>>15108381
Nope. Like I said, you can do linear algebra without matrices, including matrices is just away of making abstract ideas more concrete. You can do linear algebra with matrices, but why would you?

>>15108382
So linear algebra is not about vector spaces but matrices, and vector spaces is just a way to generalise them?
>>15108384
>You can do linear algebra with matrices, but why would you?
Because matrices are ubiquitous in pure mathematics, and also in statistics, physics, computer science, etc.

>>15108408
>So linear algebra is not about vector spaces but matrices
No, where did you get that from? I told you what linear algebra was
>Because matrices are ubiquitous
So? Matrix computation isn't linear algebra... it's computation.

>>15108418
>it's computation
There. You outed yourself as an undergrad.

>>15108466
>t. undergrad
lmao.

>>15108330
>You should (and can) do linear algebra without matrices. Likewise solving equations is not linear algebra, its an application of linear algebra.
To add to this, the correct and general way to think about linear algebra is how its done in Axlers book.
Linear algebra is nothing but linear functional analysis in finite dimensional vector spaces, the fundamental ideas of linear algebra are those of functional analysis and the sooner you understand and reason about linear operators in this manner the better.
I'd like to emphazise that the situation of working with a linear operator in a finite dimensional vector space and not having a concrete matrix representation of said operator is very very common, for example when using FFTs or when doing polynomial interpolation.
Linear algebra isnt only matrix computations and the usefulness of its ideas far escape the confines of linear system solving.
This is why in my humble opinion Axler is not only a good book but probably the best out there as an introductory textbook for mathematicians.
If you must know, I am an applied mathematician working mostly on numerical simulations.