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!
For the love of God, don't use Feynman lectures to learn physics. That's something you read after you know physics, for relaxation and conceptual stuff. Resnick & Halliday is a much better freshman/sophomore book.
Susskind's "theoretical minimum" is actually pretty good.
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.
context: former theoretical physics grad student, dropped out ABD to start a company.
this comment is right on the money on several fronts:
- the Feynman lectures are great after you already understand some of the mechanics of "doing" physics and have some other exposure to the topics, Halliday & Resnick is a better place to start on any one topic
- with infinite time, i'd always follow the approach of learning the math first and then the physics, the book by Boas is pretty good for self study of the minimum necessary math
- there's no real reason to follow a traditional grad school curriculum ala Fowler unless you need to pass quals in a traditional grad school setting
- simulating physical systems on computers is a pretty good exercise, but very time-consuming, avoid if you already spend a lot of time in front of computers
and some thoughts of my own:
- "get a strong foundation in Physics" is a bit too vague to be a useful goal, some examples of potentially better goals: "be able to pass a classical mechanics qual in the allotted time", "be able to write down the standard model and explain it", "be able to grok N papers from the X section of arxiv per week", "be able to write down toy classical field theories and calculate their predictions", ...
- if you are looking to avoid computers, try supplementing your reading with simple experiments either by buying educational kits or by hacking together things
- the books by David Griffiths (esp the E&M one) are awesome
- try to follow curiosity instead of a program: trying to answer "how do superconducting materials work?" for yourself is better than "follow the grad intro to condensed matter that's available online"
- use the physics stackexchange and other forums: asking and answering questions can be very helpful
I'll second Griffiths for E&M, Quantum, and Particle. I think everyone that has gone through a physics undergrad will swear by Griffiths. He is just such a delight.
But I'll suggest Marion and Thornton  for Classical. With Griffiths for E&M and Thornton for Classical you should be able to get a really good grasp on most of "physics". I'll also say that these series are upper division for undergrads. Given OP's background I think these would be fine starting points. If not, start with Halliday.
For grad level, the gold standard is Goldstein for Classical  and Jackson for Electrodynamics.
These types of books will give you a very strong base in physics and should enable you to branch out. Given your ML background you may be very interested in thermodynamics and statistical mechanics.
I'll also add an "out there" idea. Sign up for physics classes at your local community college if they offer labs. I say this as someone who went Physics -> CS and is doing HPC + ML. Labs really stress and force you to do analysis. Lower division labs won't ask too much, but if you go in with this intent I think you can get a lot out of it. I'm sure that if you did these lower div labs and talked to a professor at your local uni they would allow you to sit in on upper division labs (you would NEED to show that you are serious first, because these labs can be dangerous! Happy to help you learn doesn't mean happy to babysit and make sure you don't electrocute yourself or making sure you don't take a laser to the eye. TAing undergrad labs I saw enough people get electrocuted, including myself... more than once).
Second Griffiths books, I used both his E&M and QM books in undergrad. His voice is excellent.
I can't believe I am reading a recommendation that someone with little background in E&M self-studies with Jackson. That book is incredibly difficult even with a great graduate-level professor.
The problems from undergrad (I think we used Purcell) were virtually identical. Jackson's book had problems which were more algebraically/computationally difficult, but otherwise; it was basically the same thing. It's a well written classic; no reason to use the book with slightly wimpier problems.
He asked me how to learn physics; not how to learn some wimpy undergrad physics which doesn't give you the big picture. Hindsight my undergrad E&M book was a waste of time, and we should have just used Jackson. I still have Jackson (and Eyges) on my shelf; the undergrad book was recycled years ago.
My graduate E&M course was actually taught out of Schwinger, which I thought was quite nice. I would never recommend it as a first run through E&M.
Jackson's problems are more technically difficult than, say, Purcell's, but how much of that difficulty actually helps with understanding E&M?
+1. The Jackson book is notoriously difficult. I think Griffith's book might be better for a self-learner but, iirc, and I haven't read the book in more than 10 years now, he expects a pretty good understanding of applied calculus before you open the book, so read up on that! Best of luck with the studies OP.
Also, the look into the Feynman book QED once you have a little bit under your belt. Its a fun and pretty short read and there isn't much math at all. I also think its a fun thing to read while learning EM since it opens you mind up to the next subject down the line, QED.
academic virtue signaling. like people recommending TAOCP to people that don't know how to program or rudin (either one!) to people that don't know any math.
To me that’s just a subjective list the author likes.
The replies seem a bit on the level of “...but everyone knows really.”
I always took notions like “expert” virtue signaling to mean experts seem convinced we should all learn via the timelines they did.
Uni students versed in textbook physics, linear timelines for learning cause that’s how society taught them, are also experts in working cognitive theories. Incredible.
>To me that’s just a subjective list the author likes.
but the prompt isn't "list some books you like" but "how should I learn" so there's obviously intent in picking those books.
“Likes for learning” is not an unreasonable acquiescence for the reader to consider.
English is a terrible language and taking how we use it so literally is as bad as the language itself.
It all depends on your background in PDEs. I think the undergrad physics curriculum is pretty weak relative to some engineering disciplines here and Jackson is what really exposes this.
Coming from Nuclear Engineering I thought it was fine.
I think PDEs are just weak in all undergrad curriculum. Most engineers I know could only do very basic PDEs. Physicists could do a little more because they learned it from Griffiths E&M. PDEs are typically more a grad school thing. The idea is to form a strong understanding first.
This piece of advice is wrong on so many levels, from the general context. I cannot believe it got 1st place here.
(I got a Ph.D. in theoretical quantum optics, and I do have over a decade of experience teaching gifted high-school students. There is a lot of experience that works, and doesn't work, on people without prior background.)
Feynman Lectures are much a more lively, insightful, overview of physics (I started reading when I was 14 or 15 y.o.; jumped there after reading one advanced high-school textbook). While I do know people who preferred Halliday & Resnick, these were people who liked a more straightforward, even if less insightful or colorful, approach.
> learn the math tools first.
Nope. You can spend 2 years (not a joke) to get mathematics to prove Stokes theorem, in one of the more general versions. Or draw a few cubes and squares, and get there is 15 mins or so. For regular 1 dim integrals, it is a one year course of mathematical analysis, if you want to do it rigorously.
For many tools (e.g. Fenman Path Integrals) there is no rigorous math approach that is in use (at all). While, sure, you need to continuously improve your mathematical skills, my strong suggestion is first physics, then maths. Same Dirac Delta first as a trick, only later (and if you wish for math's sake) learn about distributions, Radon measures, etc.
For E&M: for introduction, totally start with Griffiths. It is much more approachable as the introduction.
> There's very little difference in undergraduate vs graduate quantum mechanics.
I don't know where to get started, but it is nor true. For quantum information - yes, you can start with undergraduate maths. For anything going into quantum field theory, you would need to know much more about Lagrangian mechanics, group representations, symmetries, differential geometry, etc.
> You can spend 2 years (not a joke) to get mathematics to prove Stokes theorem, in one of the more general versions.
You're out of your mind. You don't need to prove Gauss-Stokes in the general version to understand Maxwell's equations; you just need 3-d calculus, and you're done. Bike shedding the process further is silly: I could claim you don't really understand GR (or for that matter, E&M) without Hatcher-level understanding of Algebraic topology. All you need is the simple calculus theorem, such as is presented in Jackson.
> For anything going into quantum field theory....
This is a rubbish argument: yes, you need more math to do quantum field theory. You also need basic quantum mechanics first, which is what I'm talking about for a self study program. If you want to go on to fiddle with QED, you can fool around with Itzykson and Zuber (and Griffiths book) later, when you actually know how non-relativistic QM works, and how relativity works. First learn basic Schroedinger stuff and something like S-matrix theory. Don't learn the shitty undergrad training wheels crapola; do the real thing. That's my advice in general. If you work your way through a differential equations book; there is no point in doing the intermediate stuff and a great argument (it's a waste of time; a make work program for physics professors, and a weeder for people with low dedication to the subject) for skipping it.
FWIIW I was not a theorist, though I had some theory papers queued up on quantum dynamics. I think what everyone knows after first year of grad school is a pretty good basket of knowledge, which is why the 1st year grad school program is virtually identical everywhere in the world. It's like a gentleman learning Latin in the old days. There is a direct line from advanced calculus to completed first years of grad school physics; one which I outlined above. The imbecile make-work program of doing a bunch of intermediate problems in junior and senior year; it's really not worth it if you're an adult with a functioning cerebral cortex. Or if you're trying to pass prelims/GREs which test you on these subjects. Otherwise; skip it -do the important bits, and revisit the training wheels versions later when you need them. That's all.
To be frank, I don't get what you are up to. I sense a lot of anger, mixed with somehow chaotic notes.
> why the 1st year grad school program is virtually identical everywhere in the world
Certainly, it isn't. In the US usually starts with heavy regular coursework. In many European, there is some coursework. Unlike undergraduate physics, which is less varied, the subjects vary heavily on the place (specialization, the focus of concrete groups). In my case, it was purely research, no classes or teaching (it is less common, though).
Source: quite a lot of my friends did graduate-level physics in various places worldwide.
"For the love of God, don't use Feynman lectures to learn physics. That's something you read after you know physics, for relaxation and conceptual stuff..."
Agree with this 100%. To learn math or physics you have to do it, experiment, and all that.
Feynman lectures are fine as a supplement to more standard text.
HRK is for learning physics, feynman is for feeling like you're learning physics when you aren't, and ll is for feeling like you're understanding nothing.
LL and Feynman are definitely nice to look back upon though.
L&L assumes a particular set of steps and shared reading culture. I had the good fortune to have a professor take me through volume 1 in a classical mechanics class. Thereafter other volumes became very straightforward to read and taught me a lot of physics.
Yeah I think that's right. LL is now something I look back upon frequently for reference... but you have to have been introduced properly.
We all learn differently. Please don't deal in pedagogical certainties that may close doors unventured. Feynman's lectures were crucially eye-opening for me and many others.
It's pretty well established now that Feynman is not a good general approach for introductory physics. Plenty of talented teachers have tried it, and moved on to something more effective.
This doesn't contradict your point. A particular individual may find them very helpful in learning and understanding the foundational stuff. By all means try, and if it works for you, great.
However, it shouldn't be at the top of anyone's list of things to try first. And if you have tried, and it didn't work well for you - it's not you.
> It's pretty well established now that Feynman is not a good general approach for introductory physics.
For people at the Physics Olympiad level, it is hard to find something as eye-opening and insightful as Feynman Lectures on Physics.
For more "general audience", I guess that a more step-by-step is preferred. I know many people (usually not the Olympiad tribe) who preferred Halliday & Resnick.
I don't see how your contention really fits - physics Olympiad types are by definition not general.
For what it's worth, when I was in that position I found some of the Landau and Lifshitz stuff at least as insightful. I'm all for Feynman as a supplement, by the way.
I'm a logician and the Feynman lectures were incomprehensible when I tried to work through them. I for one am glad to see people pushing students toward more approachable texts.
> Plenty of talented teachers have tried it, and moved on to something more effective.
Including, you know, Richard Feynman.
Exactly. I ask that the applicability of Feynman’s lectures is not presented in absolutes - not always, not for everyone, not never.
But definitely sometimes for some. Including to start with.
They’re quite beautiful.
I disagree with you. I teach physics. Everyone interested in physics should read the Feynman lectures, but they are neither sufficient or necessary to understand physics. They are merely oomph on top of already good understanding.
Let's imagine physics=boxing. No amount of reading boxing books, or watching boxing videos is going to teach you any boxing. To learn boxing you have to throw 10,000 punches. To learn physics, you need to solve 1000s of questions. That is the necessary and sufficient condition for understanding physics.
Same way one learns software engineering after writing 100s/1000s of programs, not by watching videos of smart people coding (though that can help make you better).
Let's imagine physics=boxing. No amount of reading boxing books, or watching boxing videos is going to teach you any boxing. To learn boxing you have to throw 10,000 punches. To learn physics, you need to solve 1000s of questions.
I'm not sure that this is a very good analogy. You can buy a heavy bag, and go out in your garage and throw 10000 punches - with no instruction - and still not know how to throw a proper punch. OTOH, you can watch a few videos, learn some technique, and then go refine it by throwing the 10000 punches in the gym, and be a lot better off. Of course, it still won't be as good as hands-on training from a proper trainer, but my point is that you need both in the boxing case.
For physics... eh, I dunno. My original plan for college was to major in physics, and then I discovered computers, and physics went (mostly) out the door and in the rear-view mirror.
> learn some technique,
Exactly. Feynman lectures tell you what the laws are, and why they make intuitive sense. They don't tell you how to apply the laws to a wide variety of scenarios, even those not discussed in the book. Physics textbooks like Haliday & Resnick do exactly this; briefly state the law and then teach you how to apply the law.
But merely reading those textbooks won't help you either. You still have to turn to the exercises and solve a bunch of questions correctly to actually learn.
> Everyone interested in physics should read the Feynman lectures, but they are neither sufficient or necessary to understand physics
We actually agree, almost perfectly.
I contend that for some, including myself, they are an incredibly powerful tool for building an intuition. Not only after other studies, but during and before as well.
You say your part as someone who teaches, and that's important. Conversely, I say my part as someone who has learned and is learning.
But we are in almost perfect agreement.
I found the "no-nonsense" series of books on elementary theoretical physics by Jakob Schwichtenberg to be pretty good as a complement to Susskind's.
So far, they seem like a good way of reconnecting odd pieces of university program scattered around in my head. Maybe from scratch, they do not have enough math and overexplain some stuff. What are the usual arguments against this though?
"I'd suggest not actually trying to simulate physical systems on a computer" I cannot disagree enough with this statement. I am double major in Physics and CS.
There are two kinds of physics, Math and Physics. Most of what you learn in uni physics is Math. But the Math is only one (outdated) description of the nature of physical law.
Leonard Susskind himself has said on multiple occasions that the equations of physics are at most highschool math however the solutions are sometimes phd+ level.
To me Physics is the study of the relationship between state. Mostly this state is finite and the laws governing its evolution are simple and local. A computer is the best tool to discover the solutions to this evolving state.
And I cannot disagree enough with your comment.
>There are two kinds of physics, Math and Physics. Most of what you learn in uni physics is Math. But the Math is only one (outdated) description of the nature of physical law.
Lord knows what you mean by this. By "math physics" do you mean theoretical, and by "physics physics" the experimental part? Even then, this doesn't make any sense. Every physics course teaches theory and experiment. Particularly, what do you mean by "Math is only one outdated description of the nature of physical law"? I'm very curious, maybe I'm missing something.
>Leonard Susskind himself has said on multiple occasions that the equations of physics are at most highschool math however the solutions are sometimes phd+ level.
So? Again, I don't see what you're trying to imply with this. Seems a perfectly correct observation.
>To me Physics is the study of the relationship between state. Mostly this state is finite and the laws governing its evolution are simple and local. A computer is the best tool to discover the solutions to this evolving state.
This to my opinion is, for a lack of a better word, "hipsterism". Physics is the science that studies the universe at the most fundamental level/low level. That's it. "State"? "This state is finite"? What do you mean by "this state is finite"? I struggle to see what this is trying to describe (there are infinite degrees of freedom in many theories throughout physics).
Faraday did a lot of "self studying of Physics". He was a book binder who didn't know any Math (had to drop out of school at 13). The reason he got into it was not because he read a Physics or Math textbook or worked out math problems, but because some one liked the way he bound books and gave him a ticket to a Humphrey Davy talk at the Royal Institution. Thats all it took to get into Physics.
Without him dreaming up his experiments and tinkering away, god knows when Maxwell's equations would have been discovered.
Why did we have to wait for a Faraday to show up to do his simple experiments? How come all the natural philosophers and mathematicians of the age, around the whole planet, had not thought to do them?
If Faraday had asked that bunch how do I self-study physics the answers wouldn't have been too different to what we see today.
Today's version of Faraday could very well be some kid hacking away at some computer game, dreaming up scenarios, exercising imagination and cooking up experiments in the same way Faraday did.
Let me see if I can do a defense that doesnt merely look like an obvious backpedal.
If you want to do a standard study in physics you are probably going to go through a significant amount of mathematics. This is because the laws "universe at the most fundamental level/low level" are expressed as math equations. If OP wants to go that route then there are tons of resources available to them.
But since OP already has a CS degree I think a possible entry point is exploring these laws through computers and in some way deriving them from simulation (here is one such simulation https://www.falstad.com/gas/)
lets leave the more outlandish claims alone for now. Perhaps I went to far.
> Most of what you learn in uni physics is Math. But the Math is only one (outdated) description of the nature of physical law.
Is this the lack of additional parameters for the equations? All of my physics problems (only took a couple courses) were like "what if this spherical horse rolled down a hill at 34 degree decline" but failed to include friction, atmosphere. Just gravity. It always felt fake to me. Perhaps this is what you were alluding to by the "outdated" description?
By outdated what I more mean is that I think if the greats of the ~1800 had modern computers they would probably not use mathematics in its current form to study physics. There already has been on transition of this kind. Newton used Geometry to study physics whereas today we use Math which more has its roots in symbolic logic.
If people in 1800s had modern computers we'd be sitting now on ruins of the global nuclear war of 1850 all watching TikTok.
I am to really glad to hear commentary like this coming from physicists. (read: glad to see others siding with my biases).
Ceteris paribus there is one significant distinction between Mathematics and Computer Science: state.
The Mathematical Universe is immutable/stateless/timeless. The Computational Universe is mutable/stateful/time-bound.
The observer effect in physics can be trivially expressed and evaluated as a mutating getter in any programming language.
It cannot be expressed in any Mathematical grammar.
It seems likely that anything that can be expressed in "any programming language" is isomorphic to something that exists in math and can be expressed in that language (automata theory, type theory, category theory, pick your poison).
That is probably because you think expression end evaluation are isomorphic. They aren't.
Not all functions are referentially transparent. All Mathematical functions are assumed to be.
> Computational Universe is mutable/stateful/time-bound
A bunch of functional programmers would like to have a word with you.
A bunch of functional programmers continue to insist that the Turing Machine has no ticker tape which stores state?
Yeah. I know ;)
Yeah! So you know that read:T call that you have implemented in Scala?
You know that it could produce a different result on consecutive calls, right? Because the notion of a mutex/lock doesn’t exist in Math.
Mathematics doesn’t allow that, because it is not a “pure function”.
Non-determinism is the norm in distributed systems.
e.g any networked Turing machine.
You seem to imply that there's no mathematical model/theory of non-deterministic/distributed systems. Surely you don't believe that?
I am implying that Mathematical semantics are broken/incomplete.
Mathematics uses denotational semantics. It implies pass by-value and pass-by-reference are equivalent. They are in theory, they aren't in practice. That is why Haskell's lazy evaluation leaks time.
Engineers/physicists intuitively rely at least on operational semantics. It's a higher order logic, and since Linear Logic time is localized.
> That is why Haskell's lazy evaluation leaks time.
Could you maybe illustrate this with an example?
So as a brief summary: laziness leaks time. Whether that's a good or a bad thing depends on what you want/need. It may be a bad thing if you are doing cryptography because time leaks allow side-channel attacks ( https://en.wikipedia.org/wiki/Timing_attack ).
As with all philosophical squabbles - there are arguments for each side. It's up to you to make up your mind based on your particular use-case.
And so in context of crypto + Haskell, have a look at these two posts:
I was more wondering how time leaks and laziness relates to denotational vs operational semantics? I couldn't find anything about either in the links (they seem to be general descriptions of haskell and laziness..?).
Trivially. For any given system 'safety' is an operational concept, not a denotational one.
You can't formalize the notion of 'safety' let alone prove (in the Mathematical sense) that your code has it without examining its runtime behaviour.
In the words of Donald Knuth: Beware of bugs in the above code; I have only proved it correct, not tried it.
In one context lazy evaluation may be 'safe' - it another it may be 'dangerous' - the context in which this assertion is made is always about human needs and expectations, not mathematics.
With particular example being that lazy evaluation allows for side-channel attacks in cryptographic systems. That's undesirable - hence operationally 'unsafe'.
>The observer effect in physics can be trivially expressed and evaluated as a mutating getter in any programming language.
>It cannot be expressed in any Mathematical grammar.
What on earth are you trying to say...? There is a whole mathematical treatment of quantum mechanics, measurement effect included (several treatments). More to the point, any algorithm can be formalised in e.g. a Turing machine, or any other equivalent universal model of computation. So there's literally nothing in "computer science" that you cannot express in mathematics.
This reeks of Dunning-Kruger: you don't even know enough about what you're talking about to realise how badly little sense you're making. I strongly suggest you familiarise yourself with a topic before opining about it. I'll be hard-pressed to believe you ever opened a physics textbook in your life after high school. Why then do you feel the need to talk blindly about it? I never opened a book about aeronautics in my life, therefore I would never presume to lecture anybody about plane-building... That would just be arrogance.
it's like... kinda true that the observer effect can be expressed as a mutating getter... but that isn't useful. The idea that it can't be expressed is really ignorant.
>This reeks of Dunning-Kruger: you don't even know enough about what you're talking about to realise how badly little sense you're making. I strongly suggest you familiarise yourself with a topic before opining about it. I'll be hard-pressed to believe you ever opened a physics textbook in your life after high school. Why then do you feel the need to talk blindly about it?
You can just address their ideas, this extra stuff isn't helpful.
>Any algorithm can be formalised in e.g. a Turing machine, or any other equivalent universal model of computation
>>The lesson is for those “experts” who “know” that all reasonable models of computation are equivalent to Turing machines. This is true if one looks just at functions from N toN. However, at higher types, such as the type of our function m, questions of representation become important, and it does matter which model of computation is used.
Mathematics only proves things up to isomorphism. Two things that are theoretically equivalent are not necessarily empirically equivalent.
Or, just the good ol' adage: in theory there is no difference between theory and practice, but in practice there is.
>So there's literally nothing in "computer science" that you cannot express in mathematics.
In addition to the examples in the blog post linked above, you cannot express a mutating getter in Mathematics.
Go ahead. I'll wait.
The link you has its fallacy in the premise. It's defining "function" as "computable function", then complaining that many results that follow do not agree with the former definition! Either I'm really missing something or this is some poor attempt at trolling / bait-and-switch. Of course you have problems with that "computable function" definition when dealing with functions from Real -> Real, since many (in fact, almost all) real numbers are not computable!
Re mutating getter:
Monads for example are a standard way of formalising state in a pure-function universe. You seem to have some fundamental misconception about what "mathematics" is, since you keep repeating something about purity. Mathematics is merely the rigorous study of formal systems, of which your mystical "mutating getter" is one such system.
You have some deeply flawed (or entirely absent) philosophical upbringing. There are no "foundations" to anything - all definitions are arbitrary.
To assert that a premise is fallacious mandates that you have some prior notion of "fallaciousness".
You don't have an objective criterion for asserting whether one definition is better than another because you don't have a notion of "betterness" - it's all conventional.
It's precisely because I am an over-zealous formalist is why I see Mathematics for what it is - grammar, syntax and semantics.
It's just language.
Mutating getter? Sounds like a generator function that yields. Or a pseudo random number generator implemented with a monad (WorldState, Value). Or any tail-recursive non-void function that carry state without loss?
I'm definitely not an expert but aren't irrational numbers are the best examples to show that these types of constructs already exist in math? You can't calculate them in finite amount of time. You use an analytical formula or series expansions to get the nth term instead.
Assume that it is a black box to you, even though it is a white box to me.
Every time you call read() on it - you get a different result. It has side-effects.
This violates the “purity” of Mathematics.
I just explained three different models to represent side-effects without leaving the purity. I'm not sure if you are trolling, throwing random big words or simply have a really misguided impression about how computer science connects with math.
Your monad(WorldState, Value) example assumes shared global state. So not a networked system then?
That's not a train-smash for your argument if you can show me a Mathematical model for a global mutex.
When the discussion turns to control-flow you are inevitably in the land of well-ordered imperatives, not Mathematical, lazy-evaluated declaratives.
What is special about a mutating getter? It operates on the state of the object S and outputs a new state S' and some value x. Some programming languages allow you to write 'functions' without explicitly passing all input state into the function, but does that imply anything fundamental or interesting about mathematics or computation? Is that anything more than a type of syntactic sugar?
What is "special" is that the system has a peculiar property: f(x) != f(x).
If we claim to be subscribed to denotational (Mathematical) semantics then the above contradicts the identity axiom.
And it's not any deep and world-changing insight either - it's obvious to anybody who sees that the LHS and RHS are only evaluated at runtime - they don't have any inherent (denotational) meaning, which is why I keep harping on: programmers use different semantics to mathematicians. We care about things like interaction and control flow structures as first class citizens - those are precisely the things that have no mathematical equivalents. Timeouts, exceptions, retry loops.
It's not "syntactic sugar" - it's necessity for reifying control flow. In the words of the (late) Ed Nelson: The dwelling place of meaning is syntax; semantics is the home of illusion.
Of course it isn't. OP seems to have some kind of misconception about what "mathematics" means, since they keep fixating on a vague concept of purity of notation.
> In addition to the examples in the blog post linked above, you cannot express a mutating getter in Mathematics.
Neither can you express foobarish bamboozles...
I can express a mutating getter in any modern programming language much like you just expressed “foobarish bambozles” in English.
Please don't use that style of quotation for non-code. It is awful on mobile.
I thought I would also add my two cents, though there have been many excellent responses already. I recently defended my PhD in Physics (MIT '18).
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.
> (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.
This is something our education system does a poor job at.
My observation from watching a 3.5-year-old all the time is that bootstrapping most skills (e.g. riding a 2-wheeled scooter, solving simple logic puzzles, drawing, cutting with scissors, building structures out of construction toys) does not require frequent or extensive practice per se, but only practice spaced out in time, combined with a positive emotional outlook. The student can try something with limited success for a little while (maybe 15–30 minutes), go away for a few weeks, come try again and fail again, go away for another few weeks, etc., and after a few months there are sudden leaps in ability as the brain has apparently been churning away at the problem in the background without any obvious deliberate effort in between.
I think we should be organizing education to expose concepts and tools early before people are “ready”, but not putting any particular pressure on repeated failure/struggle, and then trying again intermittently.
Instead we try to organize instruction so that each idea, tool, or method is taught once, with students encountering something new for the first time and being expected to understand it through short-term brute effort and punished if they fail, and then often a concept or idea is subsequently left aside and not revisited.
> being expected to understand it through short-term brute effort
Very true, very true. But I have to give grades.
Sure there are things you can do, like quizzes they take as many times as they want and where you only take the final value. But then people don't complete the work. I can't pass them along to Calc II without knowing 70% of Calc I.
It's a tough question in psychology. I had hoped tech would help with it, but I've not had luck in that direction.
>as the brain has apparently been churning away at the problem in the background without any obvious deliberate effort in between.
This is so fundamental. I picked up a similar concept from a passionate english teacher in 7th grade. He said, after a certain point you've done all that you can do, so let your subconscious work on it, sleep on it and the next day or week you'll find your idea coming together. Paraphrased of course.
Sleep is a very important component of this IMO. It doesn't work as well if you are in poor health and sleep-deprived.
It's like some kind of garbage collection and backend processing happens that we just don't fully understand yet as part of the learning process.
Similarly, I found back in college that concepts processed and stored in short-term memory needed to be "slept on" to fully and solidly store into long-term memory and "stick".
Control the input, carefully imagine and focus on the desired output and your brain will take care of much of the rest. Let it.
An excellent list. Pretty much hits the nail on the head. The only thing I would is this:
Often times, well known phenomena and concepts are NOT explained well specifically because they are well known. Whether it's a lecturer or a YouTube video, lots of sources tend to skimp out on the fundamentals. Having said that, don't let it discourage you. It took me forever to discover what the Uncertainty Principle actually means and how it manifests itself in real life. This is related to point 5) I guess.
A lot of good pieces of advice (especially on problem-solving, timescale, and moving on).
However, some points are IMHO superfluous, for example:
> Not all topics are equally important. Focus on the important parts.
These statements are correct and general, and most people would agree with (even having no idea the topic), but are rarely actionable (or even: make sense for a newcomer). Vide most of the motivational quotations.
In short: hard to disagree. But how the heck a newcomer knows what is important and what is not?
The introduction or author's foreword usually covers that in my experience. They'll say which chapters you can skip, and sometimes lay out a map of the key milestone chapters.
In addition to said here:
There are plenty of textbooks and lecture notes available online and that article links to most of the popular choices. Make sure to choose correct order of topics to avoid getting stuck!
Wow, thanks for the link! What an incredible resource! It’s really a shame that she had to become famous for being mistreated, rather than for writing such a helpful post as this.
I think it's essential to have a strong grasp of high school mathematics, not just high marks, but actually understand it. Gaps here are very serious. What do you think?
(not parent) Agreed. But I would also say that physics can actually help you a lot with understanding math. I learned both physics and math very organically at high school, going way ahead the curriculum, and to me it was more like a single subject. For a physicist, math is just such an essential tool. I cannot imagine having the understanding of calculus that I have without physics. (But then again that's why I'm not a mathematician.)
Isn't an important aspect of learning Physics is being able to conduct experiments in a lab?
I'm not the original commenter but here's my thoughts.
For reference, I studied theoretical physics up to a bachelor level in university. Despite the "theory" focus I still had to do the same amount of lab work as everyone else. I did not enjoy it. I didn't learn much about the concepts from it.
I did however learn about the importance of visualising and representing data, statistics and so on.
We all learn differently I guess - for me lab work was a chore and that mental barrier probably didn't help me learn what the experiments were designed to teach.
Absolutely. How can you claim to model something if you haven't at least looked at the thing with your own eyes, played with it with your (metaphoric) hands?
Experiments teach you, that reality is complicated and models have to be simple, but with judicious choices of assumptions, one can still get accurate and precise prediction out of simple models. I am a theoretical physicist, but I would say the experimental courses I have taken were the most important courses in understanding the limitation of theory.
I disagree. Perhaps in some areas, like electromagnetism or optics, but there are large fields in physics where it's not necessary (statistical mechanics, quantum mechanics, gravity, high-energy physics)
I am not saying that you should to do experiments in every area. Just that experiments in a few areas (usually mechanics/EM/optics/basic QM targeted by undergrad labs) is sufficient to give you the necessary intuition about the limitations of theory in all areas.
Short answer: not every physicist works in a lab. Theoretical & mathematical physics are entirely about working with mathematical models of phenomena that other people observed in a lab. It's enough to understand that any theory is rooted in the experimental, and should be falsifiable by it.
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 for Resnick Halliday or Fowler. Don't start with Freyman. I made that mistake, wasted a lot of time.
How does Halliday + Resnick compare to Young + Freedman?
I personally really like the old (1960's) editions of Halliday and Resnick. I feel they are superior to the editions published today, and are available for very cheap.
At that level, the textbooks are more or less the same. So neither is superior than the other.
I found in my undergrad I used both. Sometimes one would explain a specific topic better. Sometimes I just needed to hear the topic explained from a different voice. With the number of old editions and online copies floating around, I don't think it is bad to recommend both.
Good question. I'm not personally familiar with Young + Freedman so I can't compare.
There are a few themes that physics revolves around:
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).
I think points 1-6 apply best to someone with an undergrad degree (and maybe even an undergrad degree in physics), since it's hard to grasp ie the action principle and Noether's theorem without having seen at least a bit of Newtonian and classical mechanics and E&M. Certainly my high school self would have struggled here.
I really like the idea of "depth first and work backwards" though. I finished undergrad with a degree in physics about a year ago, focused mostly on AMO, but since then I've seen all these headlines about AdS-CFT correspondence and cool quantum gravity papers and trying to read them is wayyy over my head. What I realized was that to read these papers, I needed to backtrack. I kinda needed to be familiar with some of the toy models for black holes in a quantum setting, which requires quantum field theory, which requires classical field theory, which I never got around to in school.
So now I'm reading a set of classical field theory notes and loving it! Plus I get to look forward to the eventual dig all the way back down to AdS-CFT.
"A lot of problems in mechanics can be boiled down to writing down the correct Lagrangian."
There's something that intuitively sounds very right about that...
This list seems very interesting...
I will have to explore all of these areas in greater detail... I'm not a physicist by profession, but I find most of your list's topics fascinating...
I think this is a good list. I think if you are interested in physics just for intellectual breadth, and not to become a physicist, it makes sense to focus on "big picture" ideas. Analytical mechanics and Noether's theorem are appealing big picture ideas.
If you were writing a good guide on how to scare off a beginner from physics, congratulations.
I self-studied physics when I was a high-school student. I read The Feynman Lectures of Physics, and it was a great introduction (especially Vol 1 and 2; Vol 3 gives interesting insights but I wouldn't treat is like a canon of quantum physics). It is accessible online, https://www.feynmanlectures.caltech.edu/, so go there and read chapter by chapter the pace you like. AFTER there are plenty of ways to go, but for an overview, it is a masterpiece.
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...
Second this. Vol 1 was the most influential physics book at high school for me. Though be prepared to go through it repeatedly. At least as a teenager with still developing abstract thinking, I had to think things through over and over again.
I was a physicist for a time and I learned physics via numerical simulation: I would find problems I could solve by hand and code them up---solving integrals, derivatives, systems of equations all numerically and comparing the results. Only a handful of physics problems have closed-form solutions, and being able to turn an interesting problem into code and "play around with it" was enormous fun for me and helped me build intuition as well. This advice strongly depends on your mathematics background, but with some basic calculus you can already start playing around.
Just to add my own two cents here: while I absolutely agree that numerical simulation is a great approach for understanding physics, the canonical closed-form solutions really are a necessary step for building an intuitive understanding of principles like symmetry and the importance of choosing useful reference frames. These are things that are very well complemented by building numerical models (and I think it would be tough to build those models without that understanding of concepts like that in the first place), but it's important to recognize that it's very difficult to skip directly to the numerical models stage.
As I said, I think the parent covered that, but just wanted to try to make it a little more explicit.
I've been taking a similar approach and pursuing this topic by getting into Computational Fluid Dynamics and understanding physics in code first, then trying to bridge the code to the more rigorous mathematical representation.
This is after I tried reading a bunch of physics books and, while interesting, I couldn't really get my head around "Ok, so how would I program something like that?"
But then there's this, you might find it interesting, it helped me understand how everything fits together a lot more: https://github.com/barbagroup/CFDPython
Also, physics is a big area, so this is just one part, specifically the physics of fluid simulation. But there's a big market behind CFD too, so you could do worse in picking something with some directly practical application.
This sounds interesting! Could you talk a bit more about what sources you used to find problems and learn from that translated well to this approach?
The Applications chapter in the "Introduction to High Performance Scientific Computing" book  (it's freely available as a PDF) has some chapters dedicated to relevant computational physics problems, i.e., Molecular Dynamics, N-body problems, and Monte Carlo methods (e.g., for approximating integrals).
The book has been posted on HN in the past 
Math for Game Programmers - Jorge Rodriguez. There is a playlist on youtube.
Game programming is an underrated/underused tool to teach math, physics and programming.
Game engine implements only a tiny slice of physics science, and even that in very distorted smoke-and-mirrors way in order to make it run in realtime. You learn more about computational optimizations, numerical methods and linear algebra, while physics is mostly elementary level. For example, all of optics is stuffed into highly optimized and simplified rendering pipeline and "physically based rendering" is anything but.
I'd recommend starting here: https://ocw.mit.edu/courses/audio-video-courses/#physics
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.
Hi, I'm a physicist and former IPhO contestant from Hungary. Unfortunately most of the books I could suggest are Hungarian, but there are some resources in English for hard physics problems.
KoMaL  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  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.
 and  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.
 https://www.komal.hu/verseny/feladatok.e.shtml  https://ortvay.elte.hu/main.html  https://www.cambridge.org/gb/academic/subjects/physics/gener...  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.
Read the Feynman Lectures https://www.feynmanlectures.caltech.edu/
It's perhaps worth being aware that when Feynman initially gave his course at Caltech, most of the students either did extremely well or completely bombed the exam. The middle ground kinda disappeared. So if you read the Feynman lectures and struggle to understand his perspective from the first few chapters, it may be best to give up sooner than later (and move onto other sources).
Fantastic material! That being said I'd recommend to have several alternative textbooks for every subject at hand. Whenever stuck - one should switch to another and try a different take.
I second Feynman lectures! It is a delightful introduction to physics. Susskind's theoretical minimum series is also a good starting point: http://theoreticalminimum.com/courses
The Feynman lextures are must if someone wants to develop intuitions in physics. Volume 3 (quantum mechanics) is a bit difficult for new learners or undergraduates, but I absolutely recommend reading vol.1 & 2.
I've also been self-studying physics recently. Here are the books that I settled on as providing a good introduction to classical mechanics:
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
Structure and Interpretation of Classical Mechanics is so cool - I highly recommend it, especially to someone with a programming background. It's one of the main reasons I switched from CS to physics in college.
Back in the day I self-studied through MIT OCW, and found it remarkably complete. It's better in quality than what you would get at almost all universities, including MIT itself (!), because only the best lecturers tend to get immortalized on OCW.
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  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 .
It would help to know what background you have and what interests you/what you hope to get out of it. Did you have basic physics in undergrad?
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.
1) Richard Wolfson's _Essential University Physics_ is excellent! It doesn't get lost in math, but also doesn't oversimplify. It's thinner than Halliday & Resnick, e.g. I've read a lot of Classical Mechanics books, and this is my favourite for a solid foundation for university-level physics. The first half (volume) is Mechanics, and the second volume is on electricity and magnetism.
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?
> Purcell for Electricity & Magnetism
This once came out as part of Berkeley Physics Course  which I think would be a great complement to Feynman's Lectures.
Regarding simulating mechanics, and combining physics + CS:
1) Have a read through Witkin & Baraff's Physically Based Modelling SIGGRAPH 2001 course notes. Short, sweet, and packed with real-world expertise/tricks.
2) Look up stuff by Chris Hecker from the '90s and early aughts.
3) Ian Millington's _Game Physics Engine Development_ is very good.
You might try Feynman's Lectures on Physics. They're available free online  or you can get a nicely bound boxed set.
I was interested in this too as someone who's worked in web apps the last 8-10 years and was super inspired by the SpaceX Falcon Heavy landing (science fiction is now science fact!) I looked into graduate programs, especially those online, and found the JHU Space Systems Engineering program. The prerequisites for THAT program are a year of college Calculus and a year of college Physics. I'm currently taking that, "year", which is really just Physics I and II and Calculus I and II at Thomas Edison State University. They've been doing distance learning for decades.
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'm a current PhD student in physics. Here's a bit of an oddball idea, that might be complementary. Read, sit with, and understand this paper: https://journals.aps.org/pr/abstract/10.1103/PhysRev.106.620
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.
I think the guide is ok, but I actually believe some of the things that are in the graduate section should be in the undergraduate section.
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.
Hyperphysics is nice if you haven't seen it: http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html
I would like to add one of my favorite mathematical "cookbooks" -- "Mathematical Methods in the Physical Sciences" by Mary Boas.
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.
This is the book we started to use in my Mathematical Methods in Physics course. It was good, but the professor decided (rightly, in my opinion) to focus more on working from linear algebra/differential equations textbooks so I never went through it. Might pull it back out and do that.
I have a bunch of letters before my name that have something to do with physics and what you're asking is far to open.
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.
I discovered the post by Susan Fowler a few years ago and really liked it.
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 ) again, just to stay up-to-date :)
Other ressources: brilliant.org, quanta magazine,youtube channels (Veritasium/Vsauce/Physics Girl/PBS Spacetime...), ...
 e.g. Leonard Susskind's "The theoretical minimum" series.
The other comments are great! Great resources and points.
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!).
If you can find Walter Lewin's courses online, they can get you through the first years of physics.
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).
For a 'strong foundation', you'll want to look at a first-year textbook and make sure your math skills are up to it. Use something with an eraser on it.
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 see a lot of people recommending Halliday and Resnick, but I used Serway- Physics for Scientists and Engineers in college and that textbook was one of the best I felt I ever read. Its been quite some time since I was in college though, maybe its fallen out of favor?
No, Serway's totally fine! But Halliday, Resnick, and Krane was written for honors freshman physics courses, so it's just kicked up a notch relative to the other intro books.
Is a great starting point. There are also free online courses for that.
There are some general concepts that make frequent appearances, it's worth looking out for them because they can help form connections between different areas. Some examples: 1. the harmonic oscillator and associated quadratic potential. 2. Wave-like phenomena and the wave equation. This comes up in all kinds of mechanical and em systems, plus the schroedinger equation itself. 3. Decomposition of functions into orthogonal sets of other functions, its not just a mathematical trick, but a powerful way of reconceptualizing things. 4. Approximations and expansions are everywhere. Always keep in mind what it is youre solving for and look at its sensitivity to other properties of the system.
If you have the freshman/junior Halliday-Resnick stuff down I'd suggest jumping right in. Susskind's Theoretical Minimum (https://theoreticalminimum.com) is excellent, he has a lot of videos online. I'm using the book version (https://www.amazon.com/Theoretical-Minimum-Start-Doing-Physi...) for self study.
MIT Open Courseware is the best I've found. https://ocw.mit.edu/courses/physics/
Mostly what other people have said here, I’ll recap:
— 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!
After decades of successful and unsuccessful self study, the thing I have found for myself is that I have to have an end goal in mind of what I want to do with the knowledge. Then it's usually pretty obvious how to work backwards and figure out how to get there. I've been tremendously unsuccessful when trying to learn just with the goal of learning. It's much harder then to quantify what is good enough, and just end up with a very surface level understanding even after putting in a lot of work.
I have a list of resources  I found to be helpful when I was doing my physics undergrad. I can highly recommend MIT's courses.
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).
This is amazing, thank you! I will most definitely take you up on your offer!
That is a good list. I also suggest looking into Newton's Principa, there is so much cleaverness in that book.
I would suggest S Chandrashekhar's Principia For the Common Reader.
This is an extremely good site (especially the physics part). I go back to this page quite often, whenever I want to start learning something new.
Here is a guide by G. 't Hooft to learn physics.
Looks incredibly comprehensive. Has anyone done similar work for other topics ? (biology springs to mind as something I would have no idea where to start from.)
Something somewhat similar is How to Become a Pure Mathematician (or Statistician)
Start by brushing up on your math, there’s not much you can really get into without first getting into the calculus of variations, which you probably haven’t covered. From that you can get into Hamiltonian mechanics and from there you can start to really grapple with quantum mechanics.
After dealing with the more technical side, you should read Paul Dirac’s book “the principles of quantum mechanics”
The most difficult thing will be getting your math up to speed so you really need to dual track the physics and math.
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.
Get Young and Freedman- university Physics and start working on problems. You can find help with those problems online. Make a study guide with timeline. Make flash cards and learn the equations. Find exams online and take those just like you were in school and have a friend grade it.
You need to chose a subfield, find the classic academic books or moocs on them until you reach a level that enables you to read research articles. Then you read the research articles..
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
I dunno but I think I once came across a reddit post about a user who asked how they can understand the bits and bites of electronics and they were reffered to a book which I don't really know its title and its what I currently looking for.
I need some help to remember this book.
It was probably "The Art of Electronics". It's a fantastic book and absolutely worth buying.
I highly recommend Road to Reality by Roger Penrose. Takes you all the way from classical through modern physics, and introduces all the necessary math. Gives you a good overview of the territory, but you might want to supplement with some extra literature/lectures to go more in-depth certain places.
Penrose's is a terrible book for a beginner to try to learn from. It's a weird mix of relatively simple stuff and one you can't possibly appreciate if you do not have a degree in math or physics. It has a tendency to dwell on simple and familiar things and then rush through rather involved topics that are no doubt something a beginner would not have a chance to be prepared for.
I don't know of anybody who's ever learned new stuff from that book. It literally zooms from addition and subtraction to fiber bundles in a few hundred pages. That's simply not enough to pick up anything but the bare intuition, and certainly not enough to do any nontrivial calculations. The only people I know who enjoyed the book at all were those who already knew the stuff in it, but in that case the book was pointless!
Isaac Asimov (non-fiction/essays)
All have written numerous excellent books on various physics topics, and each explains the concepts they wish to convey clearly, with as much or as little mathematics as you like.
Before I went to university to read physics, I devoured their (and others) popular science books, and had a pretty good understanding of the majority of the material on my degree course before I started it - the degree filled in the blanks, annealed the maths in my mind - but there’s little as good as a book written by an expert on a topic to imbue knowledge.
In general I think actual textbooks or course materials (the OP mentioned MIT Open Courseware, which I think is a good set of course materials--full disclosure: I'm an MIT alum) are better for learning physics, or any scientific field, than pop science books, however high quality.
That said, if you are going to read pop science books, I don't think Michio Kaku is a good choice. He is much too prone to treat way-out speculations as though they were established physics.
Find the source outline for an undergraduate physics program at a university you like. Find equivalent offerings of those courses for free (YouTube, etc). Watch a couple lectures per day, taking notes, doing the homeworks. 4-5 years later, you're done. : ^ )
It take more than a few months to learn.
The second time I learned physics or other subjects is through history science and physicist biography books. This is not as efficient as physics textbooks, but fleshes out the how and why many of these ideas came about.
May I suggest Susskind's lectures:
Probably first you should get a rough idea what you want to learn. When I studied Physics the standard track was Mathematics, Experimental Physics (Mechanics, Electrodynamics), Theoretical Physics (Mechanics), and then other topics, Wave Physics, Thermodynamics, Solid state Physics and Particle Physics. Normally first the experimental course comes and then usually with some delay the theoretical.
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
Anyone knows of a good reference for numerical methods for quantum mechanics ?
start with http://www.brilliant.org
Ummm, open a physics text book?
Your link is already a great resource, thanks for that! I didn't know Susan Fowler was a physics major at UPenn.
The tl;dr; seems to be get "University Physics with Modern Physics" and go from there?
My personal recommendations for an undergraduate course in physics (based in large part off of my own undergrad curriculum):
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!
I was going to say I thought I recognized these books! Just a note that the first edition of Kittel (part of the Berkeley physics series too) is arguably _better_ than K&K. The latter has one or two slightly more zeitgeisty problems.
step 1. study math
The answer is not mine, it's from Quora. But I think the info, which is presented in it, will be useful to you.
In a nut shell, information-wise, Physics entails primarily:
- principles and laws;
- definitions, terminologies and nomenclatures;
- process flows;
- causes and consequences;
notwithstanding a slew of lab experiments in problem solving;
So, it's good to know a good number of diagramming techniques, e.g. idea maps, concept maps, Venn or matrix diagrams, flow charts, fish-bone diagrams, etc. to help you to flesh out important information, as part of your note-taking/note-making;
First thing first:
Learn to segregate the "core material" from "elaborative material", with the help of your subject/exam syllabi."
- Core material" = key concepts; principles; laws; definitions; terminologies; nomenclatures; diagrams and drawings, etc.;"
- Elaborative material" = examples, illustrations, anecdotes, etc.;
That's to say, your focus is on "core material", and using Pareto's Law, generally about 80% of exam questions are more likely to come from "core material".
This is not to say "elaborative material" is not important.
Tactically speaking, once you have the full grasp of "core material", "elaborative material" is more likely to fall in automatically.
You may even want to explore the use of the following study tools:
i) SQ5R reading/studying strategy:
It's a structured system [SQ5R is an acronym for SURVEY, QUESTIONS, READ, RECORD, RECITE, REVIEW, REFLECT], but it equips you with efficient and effective ways to navigate academic materials, especially the intellectually-intense ones, with ease and expediency.
I append herewith a nice document for you to read:
ii) Cornell Notes:
It's a far more superior system that the conventional outline method, known to most students in schools, college and universities.
It's latent power comes from its simple and yet elegant three-column spatial configuration for taking notes and making notes.
The "cue" column is the most powerful system I have ever known, as it facilitates - and expedites - your memory retention/recall via self-testing.
You may want to read this nice write-up on Cornell Notes method of note-taking and note-making, in conjunction with SQ5R reading strategy:
Guide to Effective Note Taking - SQ3R and Cornell - The Student Power
If you think you have an artistic streak in you, you may even want to explore the multitudinous graphical methods of note-taking and note-making, like idea mapping, cluster diagramming, and other graphic organisers and visual tools.
As a supplementary routine to SQ5R and Cornell Notes, you may even want to explore the use of the proven Index Card Strategy to deal with your "core material", particularly the definitions, terminologies and nomenclatures, for quick and convenient "learning-on-the-go": commuting and waiting in queue.
For your final test/exam preparation, you can even expand the foregoing "Divide and Conquer Strategy" as follows:
Grab a large sheet of blank paper, butcher roll or news print roll, say 8 ft by 4 ft or so, and paste it on the wall, and a box of colour markers, both fat-tip and fine-tip.
Some assorted colour sticky notes, too!
Now, pick up your subject textbook.
With the fat-tip marker, write the subject title on the centre of the paper on the wall.
You may want to draw a simple image of your choice to represent this title.
Using your knowledge of "core" ideas and "elaborative" details you have developed earlier, write them all down, using your fine-tip markers, on the wall paper, all along the periphery.
You can transcribe "elaborative" details on to your sticky notes, and place them alongside the "core" ideas.
Upon completion, stand back, do a gallery walk and quickly review just to make sure that you have not missed out any important data from your notes and/or subject textbook.
This single sheet of completed wall paper for the chosen subject will be your consolidated and summarised study sheet for your subject test/exam.
The beauty of this elaborate process is that you have at your complete disposal all the "core" ideas and "elaborative" details all nicely laid out on one single sheet of paper, at a visual glance.
You can then use each large consolidated/summarised sheet for self-testing or reciprocal questioning with a study buddy.
For the fun of it, you may even want to paste the completed wall paper on to the bedroom ceiling hovering over your bed, so that you can do what I often like to call the 3 R's (recap/review/reinforce) prior to hitting the sack.
I just realize, I could just paste you the lik. Sorry. https://www.quora.com/How-do-I-study-physics-by-myself/answe...
You can take your Nordic feminist radical views and shove them up your ass. Do well to remember that.
Everybody recommending Feynman would do well to remember his attitude towards women. Instead, here's a few hours of Susskind on general relativity , string theory , and quantum mechanics .
Please stop demanding dead people to be absolute saints and please cherish their good qualities.
Most of the top scientists I can name were very failed humans in other ways. If you demand absolute totalitarian compliance with modern ethical dogma you will not find many people, I'm afraid.
Feynman was also obviously socially very insecure given his double jeopardy background (blue collar parents and a jew). Rampant antisemitism was very much a thing in Feynmans day. I think this affected his obvious need to pose as the cool rebel and the alpha intellectual. But he was also ruthlessly honest. And loved physics and loved explaining things.
Please remember him for the things he loved. Not for his failures.
Poppycock! A person's art is separable from their other beliefs and actions, and Feynman was among the best both in individual contributions and communication to laymen. In any case, I'm unaware of any attitude he had about women aside from wanting to have sex with most of them.
I wouldn't recommend either because i find it to be impossible to learn physics or other complex ideas from an audio stream. But i don't think feynmann was at his core disrespectful towards women, regardless of his intermittent usage of swear words. Not from the accounts I read anyways. so that kind of criticism is ultimately more of the old social conservative critique against the bachelor lifestyle.
People can have different opinion on whether Feynman needs to be condemned or not
BUT I can stand behind recommending Susskind!