Reading plan for self-studying parallel to classes

[buchholz]

Hi,

I'm currently in "gymnasiet" in Denmark, which I understand is similar to high school in the US. It's what gives you access to universities, so to speak. After "gymnasiet", which I'm done with summer 2019, I'm planning on going to university for a physics degree.

I'm currently taking physics B and math B (A levels next year) and while I like it a lot, it can feel a bit slow sometimes and a bit far from some of the topics I find so extremely interesting like quantum mechanics, black holes, relativity and so on. Of course, I understand that I need the foundation before I can get to the other stuff.

Now to my actual question...

I'd like to advance more than what I will if I simply follow the course I am on in school and I would like to not have to wait years before I get to stuff like black holes in university (if that is even something it touches on) in years time, so I'd like to put together a self-study plan I can work at while I go to school. Something that will let me advance as much as possible, at the rate I am able to go through the stuff while also doing school stuff.

My first thought was to dive into Susskinds three books of The Theoretical Minimum series, but I've read from a couple of places on the internet that it's more a kind of "laymans physics", so I'm thinking it might not be worth it to put my time into if it doesn't actually teach me the stuff properly. I've also thought about some of the Griffiths books, but I'm not sure if they are too advanced for me yet.

So basically, would anybody help me with advice for putting together a personal reading plan to achieve my goal of getting a ton of knowledge of physics?

I should add that for math (for itself and to support the physics) I already have plan that I have been at for some time now:

- Algebra – Gelfand
- Trigonometry – Gelfand
- Functions and Graphs – Gelfand
- Method of Coordinates – Gelfand
- A First Course in Calculus – Lang
- Calculus – Spivak
- Vector Calculus, Linear Algebra, and Differential Forms: A Unified Approach – Hubbard
- Linear Algebra – Friedberg or Linear Algebra – Lang
- Elementary Differential Equations – Boyce and DiPrima

Thanks in advance.

 

[The Bill]

I recommend you watch Ramamurti Shankar's lecture series "Fundamentals of Physics" on YouTube. He has a good pair of books to go with it, too, but I recommend watching the lectures first to see if you like his style.

 

[buchholz]

I recommend you watch Ramamurti Shankar's lecture series "Fundamentals of Physics" on YouTube. He has a good pair of books to go with it, too, but I recommend watching the lectures first to see if you like his style.

Thanks, I'll definitely check it out. Do you recommend watching the lectures first and then reading the books, or doing it simultaneously or not bothering with the books if I watch the lectures?

 

[The Bill]

Thanks, I'll definitely check it out. Do you recommend watching the lectures first and then read the books, or doing it simultaneously or not bothering with the books if I watch the lectures?

I recommend you watch at least a few of the lectures before deciding. The books complement the lectures well, so if you want to use the books, I'd recommend you use them simultaneously.

You can, however, get a lot out of just the lectures and the exercises, which are available free on Yale's website for the courses in the "course materials" downloads:

http://oyc.yale.edu/physics/phys-200
http://oyc.yale.edu/physics/phys-201

I do recommend the books if you like his style and you appreciate having a book to work through.

 

[buchholz]

I recommend you watch at least a few of the lectures before deciding. The books complement the lectures well, so if you want to use the books, I'd recommend you use them simultaneously.

You can, however, get a lot out of just the lectures and the exercises, which are available free on Yale's website for the courses in the "course materials" downloads:

http://oyc.yale.edu/physics/phys-200
http://oyc.yale.edu/physics/phys-201

I do recommend the books if you like his style and you appreciate having a book to work through.

That's awesome! Thanks a ton. I'll definite watch a couple of the lectures and do the exercises, and then decide what to do from there. I'm mostly a "book on my own time" kinda guy, but that sounds like pure gold that fits right into my plan.

 

[vanhees71]

Your math-reading plan looks very ambitious. On the other hand the serious physicist cannot learn enough math (most important to get started is linear algebra, calculus/analysis (including vector analysis at least for 3D Euclidean space with div, grad, curl and the integral theorems), and function theory (analytic functions of one complex variable, theorem of residues etc).

Then, before going to advanced topics of modern physics, I strongly recommend to learn classical physics first. There's no chance to really understand at least quantum theory (partially also General Relativity, which however is a classical theory after all) before having a good grasp of the concepts of classical physics. What you need for sure is classical mechanics, including analytical mechanics in its formulation as the principle of least action in the Hamiltonian formalism on phase space. The aim must be to understand Poisson brackets. This should also include space-time symmetries (Galilei-Newton and special relativity, i.e., Einstein-Minkowski spacetime). Then you should go on with classical electrodynamics, including it's formulation in the manifestly covariant relativistic way, which reveals the true structure of Maxwell's equations. Some classical statistical mechanics and hydrodynamics doesn't hurt, but that's not so important.

Then you can attack quantum theory (first non-relativistic quantum theory, then relativistic QFT) or General relativity (in the order of your choice).

Susskind's theoretial minimum books are great. They are not of the typical popular-physics books, which tend to be more confusing than helping but provide the real thing with mathematics on a minimal level.

I don't know, whether you can read a German physics book, but if so, I highly recommend

M. Bartelmann et al, Theoretische Physik, Springer-Verlag (2015)

It covers all the BSc-level physics (classical mechanics, electrodynamics (including SRT), non-relativistic quantum mechanics, and statistical physics (both classical and quantum)). It's a marvelous book, which covers all these subjects in a very coherent way and provides both the mathematical methodology and physics intuition any theoretical physicist should achieve during his or her studies in the first (in Germany six) semesters. I only wish the same author team would also write a book for the MSc level (relativistic QFT, GR) :-))).

In English, I'd recommend, to look at the Feynman Lectures. They are available online for free (although to really study a book you need a printed copy ;-)):

http://feynmanlectures.info/

 

[buchholz]

Your math-reading plan looks very ambitious. On the other hand the serious physicist cannot learn enough math (most important to get started is linear algebra, calculus/analysis (including vector analysis at least for 3D Euclidean space with div, grad, curl and the integral theorems), and function theory (analytic functions of one complex variable, theorem of residues etc).

Then, before going to advanced topics of modern physics, I strongly recommend to learn classical physics first. There's no chance to really understand at least quantum theory (partially also General Relativity, which however is a classical theory after all) before having a good grasp of the concepts of classical physics. What you need for sure is classical mechanics, including analytical mechanics in its formulation as the principle of least action in the Hamiltonian formalism on phase space. The aim must be to understand Poisson brackets. This should also include space-time symmetries (Galilei-Newton and special relativity, i.e., Einstein-Minkowski spacetime). Then you should go on with classical electrodynamics, including it's formulation in the manifestly covariant relativistic way, which reveals the true structure of Maxwell's equations. Some classical statistical mechanics and hydrodynamics doesn't hurt, but that's not so important.

Then you can attack quantum theory (first non-relativistic quantum theory, then relativistic QFT) or General relativity (in the order of your choice).

Susskind's theoretial minimum books are great. They are not of the typical popular-physics books, which tend to be more confusing than helping but provide the real thing with mathematics on a minimal level.

I don't know, whether you can read a German physics book, but if so, I highly recommend

M. Bartelmann et al, Theoretische Physik, Springer-Verlag (2015)

It covers all the BSc-level physics (classical mechanics, electrodynamics (including SRT), non-relativistic quantum mechanics, and statistical physics (both classical and quantum)). It's a marvelous book, which covers all these subjects in a very coherent way and provides both the mathematical methodology and physics intuition any theoretical physicist should achieve during his or her studies in the first (in Germany six) semesters. I only wish the same author team would also write a book for the MSc level (relativistic QFT, GR) :-))).

In English, I'd recommend, to look at the Feynman Lectures. They are available online for free (although to really study a book you need a printed copy ;-)):

http://feynmanlectures.info/

Thanks a ton, and indeed, I also think my math reading plan looks ambitious, but as you mention yourself, you only limit yourself in physics if you don't know enough math. At least, that is what I've come to understand.

Thanks to The Bill and micromass, I have a current study plan I feel is quite good, and I'd love to hear what you think about it. Here it comes:

My math plan have been changed a bit to this:

• Algebra – Gelfand
• Trigonometry – Gelfand
• Functions and Graphs – Gelfand
• Method of Coordinates – Gelfand
• Elementary Calculus – Keisler
• Calculus – Spivak
• Vector Calculus, Linear Algebra, and Differential Forms: A Unified Approach – Hubbard
• Linear Algebra – Friedberg
• Elementary Differential Equations – Boyce and DiPrima

and while I'm going through that list, I will also be going through Velleman on a parallel track to learn proofs properly.

I will be waiting with physics (except for school, of course) until I'm done with Keisler. At that point, I will continue with the math track as well as starting up a two track physics plan which consist of reading Kleppner and supplementing that with the lectures and exercises from Yale PHYS 200 and 201 by R. Shankar.

What do you think?

 

[vanhees71]

Sounds good. I don't know the book by Kleppner, but usually people recommend it frequently here on the forums.

 

[Buffu]

Functions and Graphs – Gelfand

No need for this book if you will use Keisler.

• Method of Coordinates – Gelfand

This one is for analytical geometry ?

• Vector Calculus, Linear Algebra, and Differential Forms: A Unified Approach – Hubbard

• Linear Algebra – Friedberg

• Elementary Differential Equations – Boyce and DiPrima

The order is not correct with these three. Linear algebra should be on the top.

Since your are using Calculus by Spivak, I think Linear Algebra : Done Wrong is a better option than Friedberg.

 

[buchholz]

No need for this book if you will use Keisler.

So Keisler covers the material of Functions and Graphs by Gelfand?

This one is for analytical geometry ?

I'm not very versed in the branches of maths ... the reason I put it on the list is because I read it suggested on similar threads for stuff you should know to better handle physics.

The order is not correct with these three. Linear algebra should be on the top.

Noted.

Since your are using Calculus by Spivak, I think Linear Algebra : Done Wrong is a better option than Friedberg.

Thank you for the advice. Any specific reason Linear Algebra: Done Wrong is better than Friedberg?

 

[Buffu]

Keisler covers the material of Functions and Graphs by Gelfand?

Yes however it does not cover things like fractional part and floor function but those things are not very important.

I'm not very versed in the branches of maths ... the reason I put it on the list is because I read it suggested on similar threads for stuff you should know to better handle physics.

Can you link those threads ?

Thank you for the advice. Any specific reason Linear Algebra: Done Wrong is better than Friedberg?

Friedberg is rather basic compared to Linear Algebra : Done Wrong. The whole of Friedberg's book is covered in first 4 chapters of Linear Algebra : Done Wrong. However if you can read Spivak then you should have no problem in reading Linear Algebra : Done Wrong.

I suggest you try Linear algebra : Done Wrong after reading Spivak, if you find it too difficult then you can always move to a more basic book like Friedberg.

Linear algebra done wrong is free, you can download it from http://www.math.brown.edu/~treil/papers/LADW/LADW.html.

 

[smodak]

For an all around modern treatment of classical physics, you could look at Modern Classical Physics by Thorne. It might be at a higer level than you are looking for though.

Another book worth looking is The Physical World by Manton and Mee

 

[Amrator]

Your math-reading plan looks very ambitious. On the other hand the serious physicist cannot learn enough math (most important to get started is linear algebra, calculus/analysis (including vector analysis at least for 3D Euclidean space with div, grad, curl and the integral theorems), and function theory (analytic functions of one complex variable, theorem of residues etc).

Then, before going to advanced topics of modern physics, I strongly recommend to learn classical physics first. There's no chance to really understand at least quantum theory (partially also General Relativity, which however is a classical theory after all) before having a good grasp of the concepts of classical physics. What you need for sure is classical mechanics, including analytical mechanics in its formulation as the principle of least action in the Hamiltonian formalism on phase space. The aim must be to understand Poisson brackets. This should also include space-time symmetries (Galilei-Newton and special relativity, i.e., Einstein-Minkowski spacetime). Then you should go on with classical electrodynamics, including it's formulation in the manifestly covariant relativistic way, which reveals the true structure of Maxwell's equations. Some classical statistical mechanics and hydrodynamics doesn't hurt, but that's not so important.

Then you can attack quantum theory (first non-relativistic quantum theory, then relativistic QFT) or General relativity (in the order of your choice).

Susskind's theoretial minimum books are great. They are not of the typical popular-physics books, which tend to be more confusing than helping but provide the real thing with mathematics on a minimal level.

I don't know, whether you can read a German physics book, but if so, I highly recommend

M. Bartelmann et al, Theoretische Physik, Springer-Verlag (2015)

It covers all the BSc-level physics (classical mechanics, electrodynamics (including SRT), non-relativistic quantum mechanics, and statistical physics (both classical and quantum)). It's a marvelous book, which covers all these subjects in a very coherent way and provides both the mathematical methodology and physics intuition any theoretical physicist should achieve during his or her studies in the first (in Germany six) semesters. I only wish the same author team would also write a book for the MSc level (relativistic QFT, GR) :-))).

In English, I'd recommend, to look at the Feynman Lectures. They are available online for free (although to really study a book you need a printed copy ;-)):

http://feynmanlectures.info/

How is statistical mechanics not important? It's very important for condensed matter physics and cosmology.

 

[buchholz]

Yes however it does not cover things like fractional part and floor function but those things are not very important.

Looking at the content of Functions and Graphs, it's not very big, and I've heard it's great so I'm probably going to go through because I do have the time even though it's perhaps not necessary.

Can you link those threads ?

Not really. I just looked at a lot of threads on this forums, reddit and all other places where google searches led me to and dissolved all that into my initial plan and have afterwards gotten help from others, like you. Especially a lot by micromass, and it all leads me to believe that it is actually a good book to read for physics.

Friedberg is rather basic compared to Linear Algebra : Done Wrong. The whole of Friedberg's book is covered in first 4 chapters of Linear Algebra : Done Wrong. However if you can read Spivak then you should have no problem in reading Linear Algebra : Done Wrong.

I suggest you try Linear algebra : Done Wrong after reading Spivak, if you find it too difficult then you can always move to a more basic book like Friedberg.

Linear algebra done wrong is free, you can download it from http://www.math.brown.edu/~treil/papers/LADW/LADW.html.

The reason I've been recommended Friedberg over Linear Algebra: Done Wrong is because Friedberg is much better when it comes to exercises and problems, is what I'm told, which is important when it comes to learning stuff in my experience. From what I've gathered, there is no doubt that Linear Algebra: Done Wrong is awesome, but perhaps for me learning stuff, I should rather read Friedberg as the plan suggest and Linear Algebra: Done Wrong at a later point.

 

[buchholz]

For an all around modern treatment of classical physics, you could look at Modern Classical Physics by Thorne. It might be at a higer level than you are looking for though.

Another book worth looking is The Physical World by Manton and Mee

Thanks, I'll definitely keep that in mind for when I get to that point after a whole lot of math books.

 

[vanhees71]

How is statistical mechanics not important? It's very important for condensed matter physics and cosmology.

I've not said that statistical mechanics is not important. I'm using it all the time in my research work (including transport theory applied in heavy-ion physics), but when I learned physics I came to the conclusion that one should not learn statistical mechanics (or better statistical physics) within the realm of classical physics since it's so complicated. Already the ideal gas, treated as a classical system of non-interacting point particles, is quite incomprehensible. It already starts with the problem to define a natural measure of phase-space volume. In QT it's a no-brainer, having the natural constant $\hbar$, and you can derive that the correct measure for the phase-space element is $\propto \mathrm{d}^{3N} q \mathrm{d}^{3N} p/\hbar^{3N}$. Then there is the problem with counting microstates without having a clear picture about indinstinguishability of particles leading to the Gibbs paradox. This is gone with quantum many-body theory leading quite naturally to the notion of fermions and bosons (in 3 or more spatial dimensions), which solves the Gibbs-paradox problem by just not even introduce it.

So in this sense quantum statistical physics is easier to learn than classical statistical physics, and you need it anyway to clarify, why macroscopic bodies surrounding us behave classically.