Mathematical Methods for Physics [pdf]
ma.imperial.ac.uk
ma.imperial.ac.uk
My professor for the courses always said it was about putting more mathematical tools in your tool box. Which is a perspective I've since carried.
There will always be major knowledge gaps or roadblocks/impasses of understanding, like notation or clarification needed. This is not to say it cannot be done but I have to see anyone do it.
The way I do it is to create exercise where I am required to fill as much of details as possible in the must explicit way. Sometimes, this is in the form of lecturing my friends for several hours. Or reproducing some computational results from computational physics (writing software and getting results correctly requires alot of details getting right). Similarly, when I studied such notes (for some of which I did not have accompanying course), I tried to fill as much of details as possible in the notes and do the exercises.
The ultimate state you want to reach is one where you can derive some results topic with enough details from scratch (without looking at the notes), like the way one can remember movie plot or something.
If you can take this process of understanding (and getting details right) very seriously + feynman technique, these can be helpful. But, you need to be really serious about learning and applying them (e.g. reproducing some results)
In theory one can do that also with self-study. Most people don't, they just watch some youtube video or read a Wikipedia page, and then they think they have understood something. But the deeper understanding that comes from applying this new knowledge is missing. That step is forced when you take a university course that has some form of examination in-built. Doing it yourself is possible but non-obvious, hard, perhaps even unpleasant, and it's rare people do it. Some do though, and their understanding isn't inferior to a university graduate.
Nevertheless, some brains lack even that ability, gravitating instead toward echo chambers where everyone shares the same views, so no mutual checks are possible.
This is a strange take. Why or how would you ever see someone do it? It is very unlikely you would be aware of them.
I do concur most ppl I’ve seen lacking formal education in physics - no matter how smart - do have some gaps in their knowledge. There seems to be something of a tacit knowledge transfer involved - but I have no clue what it is. Maybe physicists radiate physics particles or something. I’m kidding. But I have no clear mechanistic model what makes physicists physicists. It’s not smarts (some required I guess, but does not suffice).
Maybe it’s just going through a specific set of rote calculations and lab work needed.
This is a strange take.
How is it strange? What you meant to say is you disagree.
Well, when you learn something, do you remember everything that contributed to your learning it, and go back and acknowledge it? I try very hard to acknowledge those from whose instruction I have benefited, and I doubt I come anywhere near that ideal.
Come to that, one measure of real expertise is knowing you're never done learning, so, even for someone who does acknowledge every single source along the way, the more they know the more presumptuous it'll seem to say they are done learning it, so they probably won't.
No, I meant what I wrote.
In general there are 8+ billion people on the planet, of which some number are trying to autodidact through MSc physics equivalent. It’s possible you are in a circumstances where you engage with lot of autodidacts, but I personally have no model how you could do that (unless you are a tutor which ofc you may be!).
I’m also guessing most autodidacts arent observable through the internet.
I may be totally wrong of course!
I suspect people who learn physics via the textbooks end up learning some paralllel reality which is closed-form and models engineered trinkets.
Physics isnt mathematics, and it isnt engineering. I think this is communicated in how its performed, in the emotional tensor of its practice. A good physicist has a healthy contempt of both.
A typo for "tenor," I presume, but a funny one!
You would see someone be proficient at math or physics and then get surprised they had no degree, just like anything else. You can find such programmers everywhere, even algorithms are very easy to self study compared to math and physics, but people proficient in math or physics without a corresponding degree is almost non existent.
> Maybe it’s just going through a specific set of rote calculations and lab work needed.
I think the biggest problem is error correction. Everyone who learns math and physics accumulates errors as they learn, and if nobody is there to correct the wrong assumptions they will just continue to accumulate. To do that you need an instructor grading your tests, or at least almost everyone needs that since they can't grade their own answers fairly, their incorrect understanding leads to incorrect grading of their own answers.
This is why programming and algorithms is so easy to learn in comparison, since there its easy to grade yourself. If the program works you did it right, otherwise not. For algorithms there are plenty of sites you can practice implementing algorithms for problems and they tell you if you did it right. There are no such sites for math or physics, so there unless you are a genius at self correcting you need an instructor to just get proficient.
Edit: In short, if you can write code that works the first time you run it without testing etc, and you can do that over and over and never be wrong, then you can self learn math and physics without an instructor.
But if you need to execute your code and test to get it right, then you need an instructor to learn math and physics correctly as well.
openstax.org has a lot of good books. [1]
[0] https://www.youtube.com/playlist?list=PL49CF3715CB9EF31D [1] https://openstax.org/subjects/math
edit: i am an autodidact who loves to learn.
On the other hand, I easily taught myself programming and electronics, after an "intro" course in both subjects.
One problem is that both classroom and self learning of physics are almost entirely confined to theory, but physics is an experimental discipline. In fact most laypeople are unaware that experimental physicists outnumber theoreticians. In grad school, there was a noticeable distinction, that the students who went into theory were scary smart. With a few exceptions, the experimental students including myself were considered to be the lesser intellects. I barely survived the coursework, and owe my degree to my work in the lab.
In physics, we do have tests. Mother nature provides them.
Yes! All the endings are happy and the unfinished stories are utterly fascinating. And there are already so many stories with happy endings!
Mathematics is our best bildungsroman
I'm not sure the practice of mathematical research supports that all the endings are happy, but definitely all the journeys are interesting.
https://archive.org/details/concrete-mathematics/page/n11/mo...
True, they're not hard to make on a computer, but who is spending time to do that? And is the result more clear? More educational? Or simply more beautiful?