I'm looking for purely theoretical books which include all important theorems.

"Oh, Apostol."

The books should include many illustrations/visualizations of those theorems/proofs/problems/etc., in order to understand those concepts intuitively.

"Definitely not Apostol then."

​

I really liked the Pearson Common Core series when I was teaching high school. And the Stewart and Larson calculus texts are both great. They cover all of the major topics and give clear explanations and examples. These are textbooks that include a lot of (good!) exercises, but working through exercises is the best way learn this material, so I'm recommending them anyway.

by asianinvasians 2019-11-17

Book is
Calculus: Early Transcendentals by James Stewart, 8th edition I’m pretty sure. Blue cover with guitar https://www.amazon.com/Calculus-Early-Transcendentals-James-Stewart/dp/1285741552

You could rent for 20 dollars and you can find it cheaper at other textbook stores.

by godelski 2018-05-18

The best route is a community college. You can get most of this through a CC. Some offer discrete math, not many offer graph theory, and you probably won't get much astro (but you can get astronomy) or string theory from them. But it is good to get academic contacts who can give you direction. Someone who personally understands your drive and work ethic will have a better ability to give you suggestions. So this is my number one suggestion.

If you want to self learn, well let's go through some books and then youtube channels.

Books: Missing Discrete and Graph Theory

(You can get previous versions to save money. The content of these is mostly the same). Mostly in order of level (math then physics)

Calculus: Stewart's Calculus[1] (this is pretty much the standard) This has calc 1,2, and 3 (multi variable)

Linear Algebra: David Lay [2]. Start sometime after calc 2 (series problems). This will start you on some optimization and constraint solving. Stress learning eigen values/vectors and least squares. I don't have a good level 2 book, but that would mean looking into coordinate transformations, QR decomposition, and some more stuff.

Differential Equations: Blanchard Differential equations [3]. You will need diff eq to gain a true appreciation for physics. You will also gain a lot of the pre-req's for optimization and constraint solving.

Physics: Halliday and Resnik[4] is one of my favorites. But this is the lower college level (3 courses: Classical, E&M, Rel/quant). If you are relearning you can skip to below (though you might struggle a little more) Req: Taken or taking Calc 1 (differentiation and integration required later)

Classical Dynamics: Thornton[5] You will learn A LOT about constraint, optimization, and simple harmonic motion (necessary!!). You will also learn about Hamiltonian Systems. (1.5 courses) Req: Diff Eq, Calc 3

Electrodynamics: Griffiths [6]. Another standard. You won't find a better book than this for E&M. (1.5 courses) Req: Diff Eq, Calc 3

Quantum Mechanics: Griffiths [7] (He's the man, seriously) (1.5 courses) Req: Diff Eq, Calc 3 (lin algebra is nice, same with a tad of group theory)

Astrophysics: BOB [8] Lovingly called the "Big Orange Book" you will see this on every astrophysicists' shelves. (2+ courses) Req: Calc 1

Particle Physics: That's right! You guessed it! Griffiths![9] Take after QM.

Youtube:

BlackPenRedPen[10]: Fantastic teacher. He will help you with calc and help you understand a lot of tricks that you might not see in the above books. I can't stress enough that you should watch him.

Go find MIT OCWs, I'm not going to list them.

Honorable mentions: 3Blue1Brown[11], Numberphile[12], Veritasium[13], StandUpMaths[14], SmarterEveryDay[15]. All these people talk about some neat concepts that will help you gain more interest and think about things to pursue. But they are not course channels, they are much more casual (somewhere between what you'd see on the Discovery Channel and a classroom, more towards the latter).

Addendum:

> I follow a bunch of folks on the internet and idolize them for their multifaceted personalities

Don't stress too much about being like those people you idolize. I guarantee that you see them as much more intelligent people than they are or think of (not dissing on them, but we tend to put these people on pedestals and this is a big contributor to Imposter Syndrome. Which WILL have, probably already does, an effect on your learning process). Don't compare yourself. You can get to most of these peoples' levels by just doing an hour or two a day for a few years.

> I can totally see that these are the folks who have high IQs and they can easily learn a new domain in a few months if they were put in one.

This is a skill. A trainable skill. Just remember that. Some people are much more proficient at it, but I be you'll see that they have much more experience. In music you sight read. Doing the same thing with math, physics, engineering, etc will result in the same increase in talent.

My first reaction to this was:

I'm looking for purely theoretical books which include all important theorems."Oh, Apostol."

The books should include many illustrations/visualizations of those theorems/proofs/problems/etc., in order to understand those concepts intuitively."Definitely not Apostol then."

​

I really liked the Pearson Common Core series when I was teaching high school. And the Stewart and Larson calculus texts are both great. They cover all of the major topics and give clear explanations and examples. These

aretextbooks that include a lot of (good!) exercises, but working through exercises is the best way learn this material, so I'm recommending them anyway.Book is Calculus: Early Transcendentals by James Stewart, 8th edition I’m pretty sure. Blue cover with guitar https://www.amazon.com/Calculus-Early-Transcendentals-James-Stewart/dp/1285741552

https://www.amazon.com/Calculus-Early-Transcendentals-James-Stewart/dp/1285741552

You could rent for 20 dollars and you can find it cheaper at other textbook stores.

If you want to self learn, well let's go through some books and then youtube channels.

Books:Missing Discrete and Graph Theory(You can get previous versions to save money. The content of these is mostly the same). Mostly in order of level (math then physics)

Calculus: Stewart's Calculus[1] (this is pretty much the standard) This has calc 1,2, and 3 (multi variable)Linear Algebra: David Lay [2]. Start sometime after calc 2 (series problems). This will start you on some optimization and constraint solving. Stress learning eigen values/vectors and least squares. I don't have a good level 2 book, but that would mean looking into coordinate transformations, QR decomposition, and some more stuff.Differential Equations: Blanchard Differential equations [3]. You will need diff eq to gain a true appreciation for physics. You will also gain a lot of the pre-req's for optimization and constraint solving.Physics: Halliday and Resnik[4] is one of my favorites. But this is the lower college level (3 courses: Classical, E&M, Rel/quant). If you are relearning you can skip to below (though you might struggle a little more) Req: Taken or taking Calc 1 (differentiation and integration required later)Classical Dynamics: Thornton[5] You will learn A LOT about constraint, optimization, and simple harmonic motion (necessary!!). You will also learn about Hamiltonian Systems. (1.5 courses) Req: Diff Eq, Calc 3Electrodynamics: Griffiths [6]. Another standard. You won't find a better book than this for E&M. (1.5 courses) Req: Diff Eq, Calc 3Quantum Mechanics: Griffiths [7] (He's the man, seriously) (1.5 courses) Req: Diff Eq, Calc 3 (lin algebra is nice, same with a tad of group theory)Astrophysics: BOB [8] Lovingly called the "Big Orange Book" you will see this on every astrophysicists' shelves. (2+ courses) Req: Calc 1Particle Physics: That's right! You guessed it! Griffiths![9] Take after QM.Youtube:BlackPenRedPen[10]: Fantastic teacher. He will help you with calc and help you understand a lot of tricks that you might not see in the above books. I can't stress enough that you should watch him.Go find MIT OCWs, I'm not going to list them.

Honorable mentions: 3Blue1Brown[11], Numberphile[12], Veritasium[13], StandUpMaths[14], SmarterEveryDay[15]. All these people talk about some neat concepts that will help you gain more interest and think about things to pursue. But they are not course channels, they are much more casual (somewhere between what you'd see on the Discovery Channel and a classroom, more towards the latter).Addendum:

> I follow a bunch of folks on the internet and idolize them for their multifaceted personalities

Don't stress too much about being like those people you idolize. I guarantee that you see them as much more intelligent people than they are or think of (not dissing on them, but we tend to put these people on pedestals and this is a big contributor to Imposter Syndrome. Which WILL have, probably already does, an effect on your learning process). Don't compare yourself. You can get to most of these peoples' levels by just doing an hour or two a day for a few years.

> I can totally see that these are the folks who have high IQs and they can easily learn a new domain in a few months if they were put in one.

This is a skill. A trainable skill. Just remember that. Some people are much more proficient at it, but I be you'll see that they have much more experience. In music you sight read. Doing the same thing with math, physics, engineering, etc will result in the same increase in talent.

[1] https://smile.amazon.com/Calculus-Early-Transcendentals-Jame...

[2] https://smile.amazon.com/Linear-Algebra-Its-Applications-3rd...

[3] https://smile.amazon.com/Differential-Equations-Tools-Printe...

[4] https://smile.amazon.com/Fundamentals-Physics-David-Halliday...

[5] https://smile.amazon.com/Classical-Dynamics-Particles-System...

[6] https://smile.amazon.com/Introduction-Electrodynamics-David-...

[7] https://smile.amazon.com/Introduction-Quantum-Mechanics-Davi...

[8] https://smile.amazon.com/Introduction-Modern-Astrophysics-Br...

[9] https://smile.amazon.com/Introduction-Elementary-Particles-D...

[10] https://www.youtube.com/channel/UC_SvYP0k05UKiJ_2ndB02IA

[11] https://www.youtube.com/channel/UCYO_jab_esuFRV4b17AJtAw

[12]https://www.youtube.com/channel/UCoxcjq-8xIDTYp3uz647V5A

[13] https://www.youtube.com/channel/UCHnyfMqiRRG1u-2MsSQLbXA

[14] https://www.youtube.com/user/standupmaths

[15] https://www.youtube.com/channel/UC6107grRI4m0o2-emgoDnAA

[0]https://www.amazon.com/Calculus-Early-Transcendentals-James-...