I still remember how dumbfounded I was as a physics undergrad the first time I worked through the derivation of the wave equation of light from Maxwell's Laws. There are so many beautiful, awe-inspiring and existentially important ideas in physics that I wish more people could appreciate. Happy to see someone (especially someone so accomplished as prof t'Hooft) attempting to make them accessible for anyone with sufficient motivation and an internet connection.
For those curious but with less ambition (t'Hooft's syllabus is pretty wild for people who don't actually want to work in the field) I'd recommend Leonard Susskind's Theoretical Minimum series. It's a lecture series recorded at Stanford, available for free on Youtube. There's even one or two books by now I believe that cover classical and quantum mechanics. The video lectures go all the way to the standard model, general relativity, cosmology and even some string theory - all of it presented in a way that people with upper high-school or lower undergrad level math knowledge should be able to follow.
Three books (classical mechanics, quantum mech., and special relativity + classical field theory) and a 4th one on general relativity coming next year.
I remember the very moment in my first year of phys undergrad when it clicked for me that what I was learning in my ODE, lin-alg, and classical mechanics were all related. It was like this 'holy shit it all makes sense' moment.
This a good resource with lots of nice links but while I can see something like a syllabus helping beginners see an overall direction, I don't think this site encourages the right approach to learning physics.
I not keen on telling everyone to learn every topic presented or else they 'fail'. He's telling people they have to reproduce his entire physics education exactly as he did which I don't think is suitable for people learning on their own.
If you're a self taught programmer you probably didn't learn by finding a university's syllabus and trying to replicate it. Trying to reproduce a university's syllabus seems to me an unreasonable goal and I worry that Hooft's list encourages people to gain a shallow understanding with little understanding.
My main take aways from my university education was that most modules truly wished to teach a new way of seeing things or teach skills in manipulating new objects. Analysis is a good example: simply going through theorems and proofs isn't the goal, it's to learn the skills needed to write them, understand the mathematical logic and gain intuition.
Another important thing is that science is both broad and deep, despite having common topics, and this list simply doesn't convey this. A learner is much better off using what they find interesting and needed as a guide. It's fine if you don't learn one particular topic or approach something in one particular way because all studying will teach transferable skills. I'd expect someone who's said taught to have more limited time compared to an undergraduate, so I think focusing is fine and potentially necessary.
> If you're a self taught programmer you probably didn't learn by finding a university's syllabus and trying to replicate it.
I actually did this. A cs degree has like 6 or 8 dedicated computer classes when you break it down. Everything else is like Gen eds and math. It's pretty much algorithms and ds, maybe assembly and operating systems. Then some elective classes.
I get where you’re coming from, but the website intro quite literally clarified its audience as being the group of people that want to replicate his education.
This website isn’t about Jesus teaching a man to fish, it’s Captain Ahab advertising for Ishmael-types mental enough to join his crew for Moby Dick’s skull.
Still, an important thing for a physics undergrad student to realise is that they can't learn everything. Properly learning what Hooft listed would be the equivalent of a good education but I don't like the combination of being biased towards his interests while also demanding that this is the only correct way.
My science background didn't follow the exact same route and, after comparing notes with a friend at a different university and looking at modules of other universities, while they both follow the same general pattern, the order is different and the module selection available expresses different focuses of the department.
Personally, I think his list doesn't contain enough core mathematics and is too broad. Major areas that professional theoretical physicists specialise in are not mentioned at all (atomic physics, quantum information, condensed matter physics, density functional theory, mathematical physics, fluid dynamics).
I guess my complaint is that the list fails to highlight the core topics and fundamentals as well as failing to demonstrate how one can specialise. A vital skill needed to be a good theoretical physicist is the ability to think for yourself and learn without a syllabus.
> Note that this site NOT meant to be very pedagogical. I avoid texts with lots of colorful but distracting pictures from authors who try hard to be funny. Also, the subjects included are somewhat focused towards my own interests.
LIST OF SUBJECTS, IN LOGICAL ORDER ARE ON THE SIDE. (Not everything has to be done in this order, but this approximately indicates the logical coherence of the various subjects. Some notes are at a higher level than others).
> Still, an important thing for a physics undergrad student to realise is that they can't learn everything.
I mean I “get” what you’re saying, but it’s such a vague notion in this context. You can learn precisely as much as you are willing to. I’m not even a physics major (CprE undergrad, SE by trade), yet I have a working understanding of Schrödinger equation mathematics. This was not born out of elective or required study, I taught myself QM post-graduation with a textbook & MIT-OCW. I worked through the textbook up to TISE. I went back and relearned Frobenius method to understand how the 3D hydrogen atom results in these wild ass wave equations. My point is I’m in an adjacent field (that I’m already continually extending my knowledge in) and I can still find time to climb the modern phys ladder if/when I feel like it.
And then on top of that, like I said this website is a shopping list for “would-be crewmen”, so I think it’s reasonable to assume the man is listing everything he has studied, so you can “study everything”. Now maybe what you mean to say is you can’t go deep in everything. But you can become conversationally proficient across subjects, so that you can be able to ask the right questions.
In general, “you can’t study everything” seems vague or off-topic.
Also, sorry for sounding like a prick, I know I do, it’s not my intention. It certainly seems like you know more about the field than I do and your opinions are probably grounded in more relevant information than mine.
Don't worry about, you're not coming across as rude at all.
I guess my point is that you were able to understand the Schrödinger equation without covering a whole bunch of other stuff first: it's fine to not cover everything. The other conversely is that it's not as simple as checking topics off a checklist: the basics of quantum mechanics can be approached from various perspectives, for example. Personally, I'm keen on gaining a very good intuition of linear algebra — in particular, the idea of writing linear operators as a matrix WRT a given basis and eigenvectors — in order to be confident with the quantum mechanics. I guess you've noticed this though since you've spent time learning something else (the Frobenius method). My overall point is that each topic is very deep and everyone plots their own path through all the different areas.
I don't think we're disagreeing. I think really that this is a good list. I suppose that the main thing every beginner wants is a jumping off point which is probably something I've taken for granted. I find university module listing useful myself for computer science despite not having studies it formally.
> I guess my point is that you were able to understand the Schrödinger equation without covering a whole bunch of other stuff first
I did cover a bunch of other stuff though: 3 semesters of calc, linear algebra, diffeq, classical mechanics & electromagnetism, all before I even studied any of Rayleigh’s experiments. Granted my understanding of Schrödinger wasn’t prereq’d by my understanding of, say, 5/2R solution for the classics ball rolling down a plane and up through a loop no slipping (one of those things you never forget, unfortunately), but like the original derivation Schrödinger did for the wave equation in constant potential field (at least the ones from the textbook I read) goes straight back to Netwon’s F=ma & dp/dt = F for its basis. So you can absolutely bet that my understanding of Newton’s formulation of force was crucial to my understanding of Schrödinger. It was the interplay of linear algebra, complex mathematics, differential equations, and Newtonian intuitions. That is a huge foundation to be building on top of. Furthermore I have done exercises with bras & kets that let you treat the whole thing like a great big matrix, but my experience in building my education has been that if I try to skip a chapter it invariably is a building block that I need to go back and reread. It’s like executing code: eventually, you have to step down inside the function call and execute all its lines before proceeding.
And to tie things back around this is precisely why the guy with the website is saying “look, if you want to talk directly to Nobel prize winning physicists, pay your dues, there are no shortcuts.”
We’re in a world of climate disaster because we’ve allowed too many shortcutters to drive the boat for too long.
>>> I had the extreme luck of having excellent teachers around me. That helps one from running astray.
>>> More than rudimentary intelligence is assumed to be present, because ordinary students can master this material only when assisted by patient teachers.
I can't comment on my intelligence per se without being either self promoting or self deprecating. ;-) But I'm indebted to having good teachers for getting me through college math and physics, and for a professor to teach me how to do research. Working against whatever intelligence I possessed, was my lack of organization and focus, and the structure of the academic environment was vital for me.
Oddly enough, there were other things that I learned easily on my own such as electronics and programming. So I can't say that all things need to be taught by teachers, or even that a single person can follow a single heuristic.
> But I'm indebted to having good teachers for getting me through college math and physics
As a visual learner, I didn’t really understand linear algebra or differential equations until 3Blue1Brown came along through my YouTube. I got through that advanced college maths, but it was all just a pattern matching game back then. Seeing these equations move with life flipped the switch.
I'm trying to give myself an undergraduate education in math and/or physics this way. When I study a subject, here's what I'd ideally need:
1. Explanation of the subject. Could be videos or textbook.
2. Problems to work on. Much like learning guitar, you have to learn math and physics by doing.
3. Feedback on my solutions. Did I solve it right, or did I have some fundamental misunderstanding? Also, when I'm stuck, it can be useful for someone to look at it and say "here's where you went wrong."
4. Community and deadlines. It's easy to put off the next lesson/chapter without those. We talk about students with "sufficient motivation," but motivation isn't a fixed thing, and having a community and deadlines can really push up motivation.
A web page or video can explain a subject. A textbook will have problems to work on. But feedback, community and deadlines are something you get from a University class or a MOOC. And there are precious few MOOCs for even 3rd or 4th year undergraduate topics.
“Read everything” is not really a game plan for anything. Most of the suggested topic lists to anemic to be useful. And I have looked at the suggested books before and find them uninspiring. For example, there are ton of special relativity and general relativity books missing from the relevant lists that I’d recommend. (I know because I’ve collected them in hopes of finally learning the material well. I like differential geometry, and it’s a life goal to fully understand general relativity.)
This is interesting, but all of the links I tried were broken or led to broken pages. Unfortunately, with the widespread use of LMSs a lot of useful material is now behind University firewalls.
Thank you for sharing this post! At first glance I was surprised the page was so short and had so few concrete suggestions. Then…I found the “Next” button and saw how much content there was!
