/sci/ - Science & Math

[Anonymous No.12748131]

Is there something like this but for math? Also thoughts on this, I'm currently on classical mechanics

[Anonymous No.12748142]

>>12748131
If you’re not doing Landau start to finish you’re doing it wrong

[Anonymous No.12748148]

Hypothetically, suppose I'm taking a galois theory course and the textbook and professor are both ass, what textbook should I use to self teach?

[Anonymous No.12748152]

There's a few of them in the link below. Can't speak for the veracity of them though.
https://mega.nz/folder/kj5hWI6J#0cyw0-ZdvZKOJW3fPI6RfQ/folder/4rRQyITC

[Anonymous No.12748204]

>>12748142
No differential equations?

[Anonymous No.12748211]

>>12748204
I didn’t make it, just stole it from/sci/. Only thing I have matching OP’s request

[Anonymous No.12748234]

>>12748131
Haven't read Reif. I would go with Steane's Thermodynamics if you care about that, otherwise just read Bowley's Statistical mechanics after quantum mechanics. I would skip optics as well, and even solid state physics. Haven't read any book from blue box but those are standard textbooks, except for the qm one, which tends to be Sakurai. No idea about the rest.
Look for math sorcerer's and aleph zero's self study guide.

[Anonymous No.12748245]

>>12748142
This is probably going to sound dumb, but what exactly is number theory? Just studying numbers and how they interact with one another and their patterns? According to mathematician Carl Friedrich Gauss, its the queen of mathematics. Is it like the latin of mathematics in the sense that you can find number theory in just about every other branch in math? What is so great about it?

[Anonymous No.12748253]

>>12748245
>This is probably going to sound dumb, but what exactly is number theory
The theory of the integers.

[Anonymous No.12748263]

>>12748131
math is good because there isnt really a direct 100% set in stone order of what you must learn after calculus. after calculus you can choose to learn, with no more pre requisites

multivariable calculus
differential equations
real analysis
complex analysis
abstract algebra
linear algebra
differential geometry
set theory

Now obviously it isnt wise to go straight from calc 2 to differential geometry but it is possible. There is a pretty strict set in stone order that you learn math in if you choose to go to college for math
Calculus -> Linear Algebra & Differential Equations & Multivariable Calculus -> Abstract Algebra & Real Analysis -> whatever you want.

But there is nothing stopping you, in terms of required knowledge from learning damn near anything. Just pick up any book you think looks interesting and i guarantee there's at least something useful you can get out of it

[Anonymous No.12748269]

>>12748131

[Anonymous No.12748340]

>>12748131

[Anonymous No.12748350]

>>12748131
Replace Jackson 3rd edition with Jackson 2nd edition.
Advanced E&M should never be taught in SI units.

[Anonymous No.12748363]

>>12748131
Dont bother with gr. Take a differential geometry class/read a diff geo book instead. My physics gr class was trash and I learned way more reading an intro diffy geo book than I ever did from my reagan pole smoking "particle cosmologist" prof who didnt even do research.

[Anonymous No.12748379]

>>12748142
I second the landau books for the most part. Sometimes the notation is dated but translating to a more modern notation is useful. Also the paperback copies I got are of questionable print quality. Half the time dots over letters are not well separated. Really confusing for \dot{\psi} in quantum...

[Anonymous No.12748542]

>>12748131

[Anonymous No.12748624]

>>12748131
How much time will take to finish all of these?

[Anonymous No.12748683]

>>12748131
https://4chan-science.fandom.com/wiki/Physics_Textbook_Recommendations
https://4chan-science.fandom.com/wiki/Mathematics

[Anonymous No.12748690]

>>12748363
No. Wald's book is excellent. Schutz' book should be deleted from >>12748131, though

[Anonymous No.12748705]

>>12748340
>anime girl
An otherwise decent guide ruined

[Anonymous No.12748792]

>>12748131

Honestly classical mechanics is a good stopping point because the rest of the books veer off into bullshit territory pretty quickly. Just learn calculus, differential equations, and classical mechanics and you've mastered pretty much all physics has to offer.

[Anonymous No.12749258]

>>12748131
>no David Morin's Introduction to Classical Mechanics

[Anonymous No.12749272]

>>12749258
Taylor is shit
desu this whole thing should be remade to stop people becoming midwits

[Anonymous No.12749441]

>>12748690
Is there a better undergrad gr textbook than Schutz?

[Anonymous No.12749447]

>>12748624
Umderstanding them? Years

[Anonymous No.12749462]

>>12749441
I used Wald in undergrad.
Weinberg is also fine.

[Anonymous No.12749467]

>>12749462
I should add, in my opinion you should just look for a book that deemphasises lorentz transformations and meme shit. They're not physical, they obscure the theory, and the best way to understand relativity is to never introduce anything which isn't physical or work with the minimal number of concepts possible.

[Anonymous No.12749478]

Relativity and QM are bullshit. Once you read those books carefully with own thought, you realize they are the most bullshit money makers existent ever.

[Anonymous No.12749506]

How much proof-based maths should I know when I start a rigorous book in physics such as Landau or Arnold? Also, which one is better?

[Anonymous No.12749510]

>>12749506
arnold

[Anonymous No.12749518]

>>12749506
>rigorous book in physics such as Landau
Rigour is pointless in physics but even if it weren't Landau is far from rigorous

[Anonymous No.12749544]

>>12749510
Why is Arnold better?
>>12749518
I mean rigorous in a physics sense, not those dumbed down general physics books or literal baby-tier books like Taylor.

[Anonymous No.12749671]

>>12749441
We used Hartle in my undergrad. It is baby level GR but pretty good.

[Anonymous No.12749675]

>>12748269
best math chart on earth

[Anonymous No.12749688]

>>12749506
Physicists don’t often do proof-based math. I have only seen proofs in physics when doing background info in Fourier optics. Landau is rigorous in that he starts from first principles and derives everything from stationary action, which is what you want. To understand anything in physics, look for the stationary action principle for the subject. In mechanics it is simple. In E&M you move into 4 dimensions, add the Coulomb force, and stationary action gets you Maxwell’s equations in a relativistic setting. In QFT, use action density to describe the wave function. In GR, use Einstein-Hilbert action to derive field equations. It’s all about the principle of stationary action. Once you realize that, physics is pretty easy. As Euler said, “Every process in nature is either the maximization or minimization of something.”
That being said, a good primer on calculus of variations is nice if you haven’t seen it before. Landau does a pretty good job deriving Euler-Lagrange & showing basic calculus of variations. Be sure you understand his Mechanics book very well. Lagrangians, Hamiltonians, Canonical conjugates, &c... these don’t go away in any field in physics.

[Anonymous No.12749694]

>>12749272
What would your chart look like?

[Anonymous No.12749714]

>>12748269
Fuck that chart is based

[Anonymous No.12749731]

>>12748204
Laurence Evans for PDE

[Anonymous No.12749736]

>>12749731
Strauss for an intro to PDE

[Anonymous No.12749744]

>>12749731
absolutely terrible for a first book

[Anonymous No.12750143]

>>12749272
Yeah, Taylor isn't that good. Morin is abso-fucking-lutely amazing if you're not a brainlet but for some reason it never gets mentioned here.

[Anonymous No.12750250]

>>12749675
>>12749714
It's really not, most of the books are fine, but it suffers from the same problems all of these charts have, which is bloat and retarded prereqs. There is so much overlap and redundancies, why put 2 books that cover the same material? It just clutters the chart and makes it seem like they are both necessary. As for the prereqs, theoretically someone could go precalc-> proof book ->munkres, not to mention going to Lees book after that, but that is not realistically feasible. A good chart would be precise and leveled.

[Anonymous No.12750277]

>>12750250
and it's very obviously biased towards analysis and numerical math

[Anonymous No.12750300]

>>12749272
>>12750143
Taylor is fine, it just starts off slow.

[Anonymous No.12750337]

>>12750250
>theoretically someone could go precalc-> proof book ->munkres
They can. You don't need analysis for point-set topology.
>not to mention going to Lees book after that
The chart has second semester analysis and freshman level diffgeo as prerequisites.
>A good chart would be precise and leveled
What would your chart be?
>>12750277
>and it's very obviously biased towards analysis and numerical math
So it's biased to what other STEM major would want.

[Anonymous No.12750362]

I've been asked recently to tutor a few teenagers at my church that are far behind in math. They aren't literally retarded but they can hardly do arithmetic let alone algebra, geometry, calculus etc. Anyone familiar with textbooks or a curriculum I could use to teach them quickly.

[Anonymous No.12750401]

>>12748245
There are two number theories, analytic and algebraic. But it's basically >>12748253.

[Automatron No.12750431]

>>12750362
https://m.youtube.com/watch?v=5XHGbVnRkQc&t=71s

[Anonymous No.12750441]

>>12750300
Not really, it sucks. Morin is far better.

[Anonymous No.12750448]

>>12748148
What level? Galois Theory by Ian Stewart is pretty gentle.

[Anonymous No.12750465]

>>12750362
Euler's Elements of Algebra

[Anonymous No.12750501]

>>12750337
>They can. You don't need analysis for point-set topology
That's why I said theoretically, but it is not pedagogically sound. Without any analysis point set is unmotivated and boring (even more so than it already is).
>The chart has second semester analysis and freshman level diffgeo as prerequisites.
Then the arrows make no sense, sometimes they denote sufficient prereqs and sometimes they denote necessary prereqs, and sometimes they seem to be just recommendations. For instance, you don't need Hubbard and Hubbard for Strangs book, I wouldn't even recommend it. You need a a proof book for topology, if you are coming straight from precalc that is.

[Anonymous No.12750642]

>>12750250
If you self study any remotely complex subject then having multiple textbooks to reference is a huge asset imo. Different books have different strengths and accentuate different parts of the material, I don’t know why you would only read one, it seems like putting yourself at a disadvantage with no real advantage other than saving some neetbux

[Anonymous No.12751088]

>>12748131
kek, whose the guy that keeps adding the bible to these images?

[Anonymous No.12751106]

>>12748542
>wildeberger
One trick quack. Asking Wildeberger about math is like asking a communist what the answer to any social problem is.

[Anonymous No.12752004]

>>12751088
Weeds out the fedoras who would otherwise bitch at why they have to learn 'falsified' classical mechanics instead of going through the current string theory paradigm at an introductory level.

[Anonymous No.12752996]

>>12748705
no its not wtf. 6 books on proofs logic and set theory before you start learning arithmetic? are you retarded? By the time you get to "basic mathematics" you're gonna have picked up the rest of the chart by osmosis, but its very inefficient. A more proper intro would be

>>12748131
Intro:
Basic Mathematics
1 intro to proofs book. How to prove it/Book of proof are good

Intermediate:
Analysis 1 Tao
Linear Algebra by Strang
Vector Calc Hubbard & Hubbard
Analysis 2 Tao
Stats/probabillity book of your choice

Advanced:
Some easy Number theory book (might not be neccessary if you worked well in the early stages)
Artin Algebra
Measure Theory by Tao
Topology Munkres


In general though, whether a book is good comes down to idiosyncrasies of your own, like whether you like the writing style, how tenacious you are, and so you probably wanna look at the pdf of a couple books for each stage, just to see which book you like the best, and also maybe look at some reviews online.

[Anonymous No.12753956]

>>12752996
>no calculus
trash

[Anonymous No.12754245]

How do you even get the books for free if you are a poorfag?

[Anonymous No.12754305]

>>12748142
If I'm trying to refresh, relearn, and progress my math knowledge, is this a good start?
Specifically to aid my progress and prospects in learning drafting and help me with becoming a better welder/boilermaker.

[Anonymous No.12754310]

>>12754245
libgen

[Anonymous No.12754318]

>>12754310
Yeah but it doesn't have literally everything, and if there's books of a topic missing out then you'd be pretty much fucked and stuck?

[Anonymous No.12755214]

>>12754318
I'm sure it has everything in the op chart, and maybe even everything in any chart in this thread, meme books included

[Anonymous No.12755223]

>>12748131
Drop "The Arch-Wizard"!

[Anonymous No.12755239]

>>12755223
Dropping...

[Anonymous No.12755602]

>>12748148
Field Theory and It's Classical Problems

[Anonymous No.12755908]

>>12755239
Lol this is such a larp, I’m at a top Ivy and I can guarantee that nobody learns Galois theory in high school

[Anonymous No.12755970]

>>12755908
OH NONONO...

[Anonymous No.12755982]

>>12755970
18 or older to post

[Anonymous No.12756329]

>>12755982
ohoho
oohhhhhh--
kHhhHHHHHHGGGgGGGHHHHAHAHAHA

[Anonymous No.12757332]

[Anonymous No.12757356]

>>12754305
The 1st four books by Gelfand are good but beware that the problems are nonstandard and "puzzles" made for building understanding. Some of them will stump you so don't get discourage if you find it slow going. Lang's Basic Mathematics is more traditional but tight.

[Anonymous No.12757360]

>>12755908
>nobody learns Galois theory in high school
Crazy teachers have tried.

[Anonymous No.12757942]

>>12755908
This is probably based on a pretty famous russian blogpost, we have quite advanced math schools for gifted children. This has nothing to do with normal highschools though.

[Anonymous No.12757962]

>>12753956
literally vector calc by hubbard and hubbard, did you even read the list?

[Anonymous No.12758122]

>>12748263
For what purpose, and to what end?

Hoarding knowledge for the sake of it is fruitless. What's the end goal? There's no sense of pragmatism in just learning all random shit because you can.

[Anonymous No.12758170]

>>12750642
This is what I was thinking and I'm happy to see somebody else articulated it, because I wasn't going to put in the effort to try and explain.

Anons, multiple sources of literature on complex material like this is always good. Sometimes it takes a slightly different way of things being worded for a concept to click in one's head, so redundancy with subjects can be beneficial.

Also spaced repetition theory should remind you that you'll only further be ingraining the knowledge if you come across it in alternate texts.

Plus you have extra problem sets and examples to work from and reference.

It all depends on the scope of what your goals are - if you are going for something that requires mastery or you're looking to break new ground in some field, then it could be a huge boon.

Alternately if you learn this stuff just because you have tons of free time and don't plan on putting it to actual use then you can probably skip the saturated and redundant literature recommendations.

[Anonymous No.12759961]

>>12757962
>No single variable calculus

[Anonymous No.12759968]

>>12758122

[Anonymous No.12761669]

>>12758122
Why do anything at all then?

[Anonymous No.12762043]

>>12748142
What about Gelfand geometry?

[Anonymous No.12762050]

>>12759961
analysis 1 covers everything single variable calculus covers and more in depth. literally no reason to take a basic ass calc1 course, when you have the prerequisite knowledge to read a real analysis book

[Anonymous No.12763889]

>>12748340
I know this chart's extremely overkill but how many hours would it take to work through each of these books?

[Anonymous No.12763906]

>>12748245
It's notorious for being completely useless. I don't even think cryptography uses it much anymore since prime factorization has been broken.

[Anonymous No.12763955]

>>12755908
Literally the standard math curriculum in eastern Europe.

[Anonymous No.12765327]

>>12762043
Was released after the chart was made.

[Anonymous No.12765886]

>>12748142
Which of these proofs book is better? Book of proof or How to prove it?

[Anonymous No.12765908]

>>12755239
Sadly Kostrikin-Manin's introduction to algebra is not available on libgen, only his linear algebra book whose prerequisite is that algebra book.