I'm a CS graduate student, and I do a lot of Deep Learning Research. I've always wanted to get a strong foundation in Physics, and while on lockdown because of COVID, I thought it would be a great opportunity.
I've run across this incredible guide https://www.susanjfowler.com/blog/2016/8/13/so-you-want-to-l... and I was also thinking about going through MIT Open Courseware following their bachelor's curriculum.
Do you all have any suggestions or tips? I really appreciate it!
First of all - great idea! It is never too late to learn math and physics! In fact, with hard work and commitment, anybody can muster them to a high level.
(1) Reading =/= understanding in math and physics. You understand a topic only if you can solve the problems.
(2) Work through the solved problems you encounter in textbooks carefully.
(3) Most people around me have never read any physics textbook cover to cover. E.g. reading Halliday, Resnick & Walker completely might take you years! Not all topics are equally important. Focus on the important parts.
(4) You need guidance on what is important and what is not. Online courses, college material (especially problem sets!), teaching webpages could be a helpful guide. MIT OCW is an excellent resource, once you are ready for it.
(5) Finding someone to talk to is really useful. You will likely have questions. Cultivating some relationship that allows you to ask questions is invaluable.
(4) College courses in math and physics have a very definitive order. It is really difficult to skip any step along the way. E.g. to understand special relativity, you must first understand classical physics and electrodynamics.
(5) Be prepared that the timescales in physics are long. Often, what turns people off is that they do not get things quickly (e.g. in 15-30 minutes). If you find yourself thinking hours about seemingly simple problems, do not despair! That is normal in physics.
(6) You have to 'soak in' physics. It takes time. Initially, you might feel like you do not make a lot of progress, but the more you know, the quicker it will get. Give yourself time and be patient and persistent.
(7) Often, just writing things down helps a lot with making things stick. It is a way of developing 'muscle memory'. So try and take notes while reading. Copying out solved problems from textbooks is also a good technique.
(8) Counterintuitive: If you get completely stuck, move on! Learning often happens in non-linear ways. If you hit an insurmountable roadblock, just keep going. When you return in a few days/weeks, things will almost certainly be clearer.
Are you a PhD student? And if so, are you aiming at a career in academic research? I'll offer my advice as a math professor, and as someone who supervises students.
If you want to get a strong foundation in physics, then reading Halliday + Resnick, and doing a large number of the exercises, would be one good way to go about it. (Look for used copies of previous editions on Amazon -- they'll be cheap.) There are plenty of other good suggestions in the blog post you linked, and also in this thread.
However, and I hate to throw water on such a noble aspiration, are you sure that this is what you want to do? Getting a "strong foundation" takes a lot of effort. If you want to invest this effort, then great! But you might consider investing that effort into learning something closer to your field, which would both be interesting and directly help in your research.
In my observation, it is common for graduate students and professors to learn about areas outside their research area, but they don't always worry so much about getting a "strong foundation". For example, when I was a PhD student, one of my fellow students enrolled in a graduate course in physics, without worrying too much about whether he satisfied the prerequisites. It was a great experience for him, and it's one that apparently helped him a great deal in his mathematics research career.
Myself, I have invested a fair amount of time learning algebraic geometry, which is a difficult area of mathematics, different from my specialty. The results have been ambiguous -- I still don't know the field nearly as well as I wish I did. In particular, I still have only a sketchy understanding of the foundations. But, happily, I know enough to talk to algebraic geometers. Indeed, I'm currently writing a paper with a colleague in the subject, which involves both his specialty and mine -- it's not one that either of us could have written on our own.
In any case, good luck and best wishes to you!
1. Action Principle: A lot of problems in mechanics can be boiled down to writing down the correct Lagrangian.
2. Statistical physics, this teaches you about to think in terms of "Zustandssummen" and is the starting point for deriving lots of interesting laws like black body radiation.
3. Field (Gauge) Theory, turns out you can write down and derive interesting Lagrangians for Electrodynamics, Fluid Dynamics and General Relativity as well.
3.1. Noethers Theorem and Symmetries allow you to get a unified view of conserved quantities.
4. Spinors, they are fundamental for understanding the quantum behaviour of matter
5. Path Integrals necessary to understand Feynman diagrams and Calculations in Quantum Field Theory.
6. Do the harmonic oscillator in as many different ways as possible, a lot of physics can be understood by solving the harmonic oscillator or coupled oscillators. Once you've understood why this is the case and the situations in which it isn't true, you will have understood a lot of physics.
I would recommend a depth first instead of breadth first approach. Pick something advanced that really interests you and work backwards what prerequisites you need to understand it. There are parts of classical physics that are super interesting but barely anyone learns about them anymore (I skimmed through Sommerfeld's lectures on theoretical physics once, they contain all kinds of super interesting problems with spinning billiard balls, tops and so on, this was at a time when Quantum Mechanics was in its infancy).
However, make sure you practice your skills. It is very easy to get the impression that one understands something, yet not being able to solve a basic exercise (no matter if it is programming or physics).
For an intro to quantum physics, I gathered some materials "Quantum mechanics for high-school students": https://p.migdal.pl/2016/08/15/quantum-mechanics-for-high-sc...
As you come from a programming background, I really encourage you to write small simulations of some pieces. For problems, it is easy to find books with problems for Olympiad preparation (I have a long list of them but in Polish). Or something like: https://physics.stackexchange.com/questions/20832/is-there-a...
In my experience these are some of the best online courses you can watch to learn physics. Personally, I would look into the trying to watch the lectures from Walter Lewin--Walter is a fantastic orator and has a really great mad-scientist persona that is really captivating. Some additional archived lectures can be found here: http://dspace.mit.edu/handle/1721.1/34001 and here: https://ocw.mit.edu/courses/physics/archived-physics-courses...
I got my minor in physics from NYU many many moons ago (yes I'm getting old), but I found that the MIT lectures and OCW materials went way beyond the NYU coursework in both breadth and depth. I watched these lectures and worked through the lecture notes & assignments for Physics I, II, III, Quantum I, II, and several others in addition to digging into the Mathematics lectures / content. I found this material to be the most helpful out there. I'll also point out that I emailed the professors (Lewin, and others) and was pleased to receive a warm and helpful response on several occasions. I hope these are as helpful for your learning as they were for mine.
Once, you are able to complete the video lectures here, OCW has a massive amount of content for some of the more advanced courses that aren't in video format. In my experience, going through these video lectures and some of the mathematics lectures should set you up well to be able to comprehend even the most advanced content across field theory and string theory.
Cheers!
Going through the series 8.012, 8.022, 8.03, 8.033, 8.04, 8.044, 8.05, 8.06 will give you the core theoretical knowledge of a physics major. (I assume you already know all the relevant math background.) If you prefer lecture notes, I imagine the best thing is to go through David Tong's lecture notes [0] from start to finish, as these cover almost the entire Cambridge undergraduate curriculum very clearly. If you want textbooks, at least in America, the books one uses for these courses are pretty standardized, and Fowler's blog post lays out these standard choices. For more advanced books, I have a pretty extensive bibliography in the front matter of my personal lecture notes [1].
0: http://www.damtp.cam.ac.uk/user/tong/teaching.html 1: https://knzhou.github.io/#lectures
KoMaL [1] is a high school competition, students have one month to solve five physics problems (they can solve more, but only the five best is counted each month). Unfortunately older archives are only in Hungarian, but this is an endless resource, you can come back for new problems each month.
Ortvay [2] is a yearly take-home, one week long problem solving competition for University students. These problems are _very_ hard, so don't be discouraged by not being able to solve them right away.
[3] and [4] are some of my favorite books with Physics problems from Hungarian authors. The problems have varying difficulty, but they are clearly marked in this regard. There are separate hints and full solutions.
[1] https://www.komal.hu/verseny/feladatok.e.shtml [2] https://ortvay.elte.hu/main.html [3] https://www.cambridge.org/gb/academic/subjects/physics/gener... [4] https://www.cambridge.org/gb/academic/subjects/physics/gener...
* Don't get discouraged. Physics is hard!
* Work on problems, and don't let yourself look at the solutions too soon. Sometimes it takes a few days of thinking to solve a problem.
* When reading through equations, go really slow. Make sure you fully understand each step and don't let yourself skim.
Edit: +1 for the guide you linked, it looks excellent.
Classical Mechanics - John R Taylor
Structure and Interpretation of Classical Mechanics - Sussman & Wisdom https://mitpress.mit.edu/books/structure-and-interpretation-...
The Theoretical Minimum - Susskind https://theoreticalminimum.com/
Introduction to Classical Mechanics - David J Morin
So, that's a typical first-year (two term) course in physics.
After that, do Purcell for Electricity & Magnetism
You'll often get advice, like "you need to learn XYZ math first". Don't listen to this! Just learn the math as you go along -- it's much more efficient. The have to learn X first puts up unnecessary roadblocks and chances to get discouraged. You can always circle back for more elegant treatments once you math up. E.g. learning 4-vectors makes special relativity a lot less ad-hoc and weird seeming. It becomes obvious.
P.S. I was prototyping a subscription app to teach E&M, but started to think of just teaching physics in general. Would you pay something like $15/mo to have a adaptive-learning app/game/personal AL tutor to teach you first & 2nd year physics?
Foundation can mean a lot of things. It can mean having a really solid grasp of how Newtonian mechanics is put together. It can mean having a solid grasp of doing experimental physics on classical systems. It can mean having a mathematical understanding of symplectic manifolds and quantization. It can mean replacing your naive physical model of motion in your hind brain with a learned, Newtonian model.
If you've never done any lab work, actually getting a stopwatch and conducting experiments with balls rolling down inclined planes and the like can be...eye opening.
You will need problems to work, otherwise anything you do is superficial. For example, here's a collection of elementary physics problems: https://archive.org/details/BukhovtsevEtAlProblemsInElementa... (The Russians were great about building this kind of collection.)
If you can give some more detail, it will help us direct you better.
The courses aren't super cheap, they're around $2,000 each, but having classmates, a mentor, deadlines, and a legit program to structure my learning around has been so helpful. Not to mention that my grades are legit for pre-reqs if I do want to go the full grad school route. I'm almost done with the I level courses and started the II level courses 2/3 of the way through the I.
I think a lot of people on here might say my approach is kind of basic (I see people recommending working differential equations or something to start), but I've found it really enlightening to start from the very beginning and things are starting to get challenging as I get into the second level, especially with Calculus. Maybe if you just looked up Physics I and II and Calc I and II curriculums, and got the textbooks (Conceptual Physics by Paul G Hewitt and Calculus: Early Transcendentals by Robert Smith) you could do a lot of the same exercises.
Hope that's helpful!
I say this because -- It motivates and sketches statistical mechanics, which I expect is the most interesting topic to you given your specialty. -- It elegantly makes a point that I think is very important about physics: that physics is _almost entirely_ mathematical. The remainder is just about constraining the math to reflect the possibilities that seem to be actually realizable in nature.
Of course there's a lot more to physics than is described here, and you'll want to study the particular phenomena that emerge -- that's the whole point. But I think that given your background, setting this perspective will allow you to ask the right questions when you approach a new topic, and allow you to go out of the normal order.
One more note about the nature of doing/understanding physics: a huge part of it is taking the right limit. Reasonably complicated systems described in the language of some theory are generally intractable to analyze exactly, or to draw general conclusions from, so you need to throw something away to make progress. Figuring out the right limit is the same as figuring out what details you can throw away while preserving the core phenomenon you're interested in.
One thing that is important: Everything starts with classical mechanics. Newtownian phsyics is the base for everything and you will never advance without knowing this really well. That said, in my undergrad mechanics class in my first term as a physics student, we started out with classical Newtonian mechanics and then quickly moved on to the Lagrangian and Hamiltonian formulations of classical mechanics. I don't see why that should be something reserved for graduate classes.
Further, since you're not a math or physics student, I assume you will quickly reach the limits of your math education. Things that are required for properly understanding the theoretical foundations even just mechanics are:
- n-dimensional calculus (think Tensors, Gradients, divergences, Laplacians, etc.)
- complex numbers and functions
- basic knowledge of differential equations and ways to solve them
- things like Fourier transforms and things like Vector spaces, groups and symmetries
- basic statistics knowledge of course
- linear algebra
Second, like some people have already mentioned: Just reading a book will not teach you physics. Actually solving the problem in whatever resources you're using will, though. They take much, much longer than just reading a book, however.
I studied physics (2001-2006) and teach physics (and math) at a high school and am working through the list of proposed books (and others [1]) again, just to stay up-to-date :)
Other ressources: brilliant.org, quanta magazine,youtube channels (Veritasium/Vsauce/Physics Girl/PBS Spacetime...), ...
[1] e.g. Leonard Susskind's "The theoretical minimum" series.
Bad Integrals? Tensor Analysis? Fancy functions and special polynomials? PDE tricks?
Boas has solutions!
Methods are practically explained and succinct. It's my favorite book to brush up on a old technique or learn some new methods.
Wolfram's Mathworld is also a good reference, but not as much of a learning tool.
Old joke from Anonymous: "Theoretical physicists aren't very expensive -- they only need a blackboard and an eraser. Compare that to a philosopher -- much the same but without the eraser."
I think what is crucially important is to have someone to talk to. To engage with another human being in a discussion, at every step of the learning curve.
I studied physics in Germany 2005-2010, an then did my PhD 2010-2015.
In hindsight, I must conclude that being forced to discuss things with other people at every step was what taught me the most, was long-term the most rewarding.
About my own level of understanding, about judging my abilities, about how to actually solve problems.
Examples from my time studying:
- discussion among two people: trying to grasp and crack the same exercise
- discussion in the larger study group (5 people): when helping each other out, having to admit not having understood a certain thing, and specifically trying to address the "wait, I don't get this yet"s everyone has.
- discussion in exercise class (20 people): presenting "your" solution in a concise way, seeing other solutions, discussing caveats, pros, cons, elegance, deficiencies
- discussion in seminars: presenting "old" concepts to each other, discussing them and their historical relevance
... and so on.
In hindsight these countless discussions in smaller and larger study groups were _priceless_ towards understanding what physics is about. I mean it! After all, physics is science, and in science you can only contribute in a meaningful way when you understand the mental model of your fellow scientists reasonably well, when you "speak the same language".
I understand that this might be in conflict with "self-studying physics". If it is then it's important to be aware of it, possibly to try really hard to compensate for it (to find someone to do this together with, maybe!).
The main way to learn physics though, on your own or in a program, is by doing problems and labs. You can start by doing the coursework you find for an established class. Another is by working through problems in a text book. As for labs, hacking together what you can is both valuable and rewarding. A few examples are estimating absolute zero, measuring the coefficient of friction, exploring momentum with ball bearings.
A few other things that I have found work for me. First, work towards a goal. Whether that be to calculate the orbit of a planet, understand quantum tunneling, or estimate a dynamic process. The second is to take the time follow thoughts as far as you can, using the social communities and resources available on the web (quora, reddit, etc).
Is a great starting point. There are also free online courses for that.
— Solve exercises
— Learn the fundamentals (action principle, conservation laws, symmetries, statistical physics)
— With that, work on generalized coordinates, Lagrangian and Hamiltonian mechanics
— Brush up your calculus, vector calculus and linear algebra kung-fu
— Have a personal project to aim your efforts. For me, it was understanding precisely how nuclear weapons work (so I have to run many geometrical and hydrodynamic calculations). For you it might be something else.
— If you stuck with some textbook, grab another one, you will be able to return later with the new knowledge. Physics is fractal.
Best of luck!
Learning physics can be tough at times if you're doing it alone as it's common to get stuck on a hard problem and need to talk it through with someone else. If you ever want to discuss any problems feel free to reach out to me (see the contact page on my website).
I would suggest S Chandrashekhar's Principia For the Common Reader.
After dealing with the more technical side, you should read Paul Dirac’s book “the principles of quantum mechanics”
The Landau books are good but assume probably more math than typical college text in mechanics, em, qm, etc.
Probably a bit down the road for you if following typical curriculums (perhaps not others) the MIT 80X series by Zwiebach were good.
I need some help to remember this book.
Since you probably have a good background in optimization, work through problems in:
- Taylor for Classical Mechanics or Goldstein (a bit more advanced) - Griffiths for E/M and Quantum.
For stat. mech. I find the chemists have more intuitive textbooks.
- Introduction to Modern Statistical Mechanics by Chandler
Still, you can decide if you want more Mathematics, more Theory or less. (Probably the CS Maths should get you covered pretty well for the start) I'd do a research on popular recommendations of books and then see which ones you like and interest - the styles and contents are often so different. While going through the books you can try to find nice YouTube videos and other stuff.
Of course you get a deeper understanding when doing some exercises, although this can be tough. I'd highly recommend finding a book that has a solution section/solution book or maybe some online course that offers that. The exercises for Experimental Physics are usually not long but can be surprising. ;) Also it might be surprising that depending on your interest a strong foundation in Mathematics is not critical, although you'll still need to wrap your head around the common math problems.
One motivating thing is that while you go through the topics (Mechanics, Electrodynamics, Wave theory, QM, ...) the frameworks and approaches are somewhat repetitive and just get more sophisticated over time.
TL;DR: pick a curriculum and combine it with your favorite material
Foundations:
1. Newtonian Mechanics by A.P. French (https://archive.org/details/NewtonianMechanics/mode/2up). This will give you a good foundation for what is to come.
2. Spacetime Physics by Taylor & Wheeler --- first edition if you can find it! It is much, much better than the second! Special relativity is conceptually strange, but mathematically pretty easy, so you can jump right into it after learning Newtonian mechanics. Have a little fun!
3. Electricity & Magnetism by Purcell. This book is a little unusual in that it derives magnetism from the laws of special relativity. This is the more natural approach than just asserting the laws of magnetism since magnetism is fundamentally a relativistic phenomenon.
4. Waves by Crawford. (https://archive.org/details/Waves_371/mode/2up) A bit hard to find in print, but a really excellent textbook. Waves are a fascinating topic because they come up in every area of physics, so a course focused around them has a huge number of applications.
5. Introduction to Quantum Mechanics by Griffiths. The best introduction to the topic you will find!
6. Thermal Physics by Kittel & Kroemer. I haven't actually found an introductory book on statistical physics that I'm crazy about, but this one isn't too bad.
That should last you some time. But once you're through with those and are looking for more, then here are some advanced topics:
7. Analytical Mechanics by Hand & Finch. This will teach you advanced Newtonian mechanics --- in particular Lagrangian and Hamiltonian dynamics. There is a chapter on chaotic dynamics towards the end, too. Another option here is Classical Mechanics by Goldstein.
8. Introduction to Electrodynamics by Griffiths. More advanced E&M than Purcell. If you want to go further, then there's always Classical Electrodynamics by Jackson.
9. Principles of Quantum Mechanics by Shankar. This spends more time on the mathematical foundations of QM than Griffiths does and goes into the path integral formalism and touches on relativistic QM towards the end of the book.
10. A First Course in General Relativity by Schutz. There are arbitrarily advanced texts on GR, but I'd recommend starting off with something friendly like Schutz.
11. An Introduction to Elementary Particles by Griffiths. Not super advanced mathematically, but it's a good thing to read over to prepare you for more advanced QFT texts. The first chapter is especially good as a history of the development of particle physics.
12. Quantum Field Theory in a Nutshell by Zee.
13. Modern Classical Physics by Thorne & Blandford. This is a tour de force. It's an enormous book but it really touches on everything that is left out by the above books. It covers optics, fluid dynamics, statistical physics, plasma physics, and more. (I'm currently reading through it and have only gotten through 6 chapters, but it's really an incredible textbook.)
14. Statistical Mechanics: Entropy, Order Parameters, and Complexity by Sethna. This is a really fun book, but almost all the material is in the problems.
Finally, and most importantly --- remember that physics is not a spectator sport! You must do problems. A lot of them --- and hard ones, too!
The tl;dr; seems to be get "University Physics with Modern Physics" and go from there?
Susskind's "theoretical minimum" is actually pretty good.
http://theoreticalminimum.com/courses
Fowler gives a pretty conventional undergraduate physics curriculum (adding Feynman in there somehow). If it were me: learn the math tools first. I assume you know linear algebra; learn differential equations. From there, go straight to higher level books. There's very little difference in undergraduate vs graduate quantum mechanics and E&M other than the math is slightly more sophisticated in grad school. Might as well do it right. Messiah for QM and Jackson for E&M. Classical mechanics, the tradition is to learn Lagrangian mechanics in high level undergrad and Hamiltonian in grad school. There's no real reason to do it in this order, and a decent reason (understanding Quantum) to do it in reverse order. Amusingly, the math is cleaner in Hamiltonian mechanics, but you may find yourself unable to do some simple problems you can do with Newtonian physics; so this will be a weird working backward thing. Stat Mech, I think you should just read Reif; skip Ma or whatever they use in grad school now.
FWIIW I know/knew people who did this: started grad school without having done any undergrad courses in physics. I think skipping a lot of the introductory stuff, and visiting it later is actually better.
The rest of it can be done with the same machinery you learned in QM, E&M, Mechanics and Stat Mech. Max leverage if you had to pick one: probably classical mechanics for a DL guy, E&M for general knowledge of tools.
I'd suggest not actually trying to simulate physical systems on a computer: you probably stare at computers too much anyway.
If you want a general grounding have a look at Fundamentals of Physics any addition and work through some of the problems.
You will need calculus, which CS doesn't use at all.
If you want something better: http://www.goodtheorist.science/ It will take you 10 years or so.
http://www.staff.science.uu.nl/~hooft101/theorist.html
It take more than a few months to learn.
[0] https://www.youtube.com/playlist?list=PLD9DDFBDC338226CA
[1] https://www.youtube.com/playlist?list=PLA2FDCCBC7956448F
[2] https://www.youtube.com/playlist?list=PLA27CEA1B8B27EB67