Efficient Study Tips for Physics, Math, and Engineering Subjects

[nox]

Hi i been intressted in physics, along with math, computer science mostly ai, and electrical engineering for circuits and robotics.
thing is time is limited as we all know, and i wonder how to study most time efficient.
Right now i am reading through an electromagnetic physics book and i am after 2 weeks halfway through chapter 2, basically just learned how to calculate e fields from electric potentials. Thing is there are many many concepts and each one will take time, and i still don't know what i going to use this for. So i wonder if anyone would recommend another way to study.
Basically a few years ago i spent half a year going through 5 chapter of rudin and the payoff have not been that great.

My idea is this, take up the textbook and start flipping through it, read the summaries and big ideas, do not get bogged down in derivations, just read quickly through the chapter to learn what it contains. Then if a concept is intressting or i have a need for it, i will study it deeply, and try to reverse engineer what prerequsite topics are needed and study them deeply, so i can understand.
What i am purposing is a recursive way of study, so that i can spend time always learing something i actually use.
Is this recomended, or will i end up learning nothing cause of lack of fondation?
Thing is i studied so much on and off, and in math i did not get past real analysis or abstract algebra and physics i only can say i understand classical mechanics in lower division well. So i am now 30 wasting another 10 years with unstructured study will not do.
Thanks for all the advice.

Summary: I am looking for ways to study physics non linearly learning what i actually need and fill in the blanks as i need them.
Also how should i approach exercises, should i try them before reading the chapter, if i had 200 exercises how to pick ones i should focus on?

 

[mcastillo356]

Hi, nox, let's see if this link helps you:

https://en.wikipedia.org/wiki/SMART_criteria

Greetings!

 

[Choppy]

To build on the suggestion from @mcastillo356 above, something general like "learn the physics I need" is a very general goal. There's no clear end point, so you won't know if you've ever reached it, how much progress you've made toward it, and will be extremely challenging to prioritize it over just about anything else in your life that comes up with a deadline. And so what tends to happen is that you can wade deeply into a given textbook that seems interesting, but then get bogged down and never really get through the whole thing.

This is why most people need the structure of formal coursework to get through the fundamentals of a physics degree. Courses give you specific things to focus on, define your objectives, are realistic (in most cases) in what can be accomplished, and have deadlines that aren't easily avoided.

So then the question comes back to you. You can start from the broad context. What do you hope to accomplish? Do you want a formal education that will allow you to pursue a career doing research in physics or AI? Do you have a specific project in mind such as building a robot and you need to understand related background material?

 

[nox]

Thanks for the advice.
Ok so basically i got intressted in high school in mathematics, physics and computer science but i never got to the point where i knew why. I tried university for a few years but it did not work out, now about 10 years later i still find myself going in circles with the old same books.

The thing is i don't know why, i just want to be able to understand research papers, to write my own, to actually develop my own theories, contribute to the field. But i don't need to do it professionally. Its almost like i am afraid to do anything on my own if i haven't taken the course, like i am not allowed to try to tackle something that belongs to a subject i never learned well enough.

Today i tried a different approach and just jump in the textbook to concepts that seemed intressting, problem was i quickly zoom out to big and don't see the need for the book at all.

So maybe this is better to ask, what is the best way to expose myself to need to learn physics, basically learning by research, not just go linearly through what i am supposed to learn, but learning as i need? Is it best to do this by trying to read research papers, or are there websites with intressting problems that will force me to learn concepts from many fields in physics, or even stumble on a new field. To use textbooks as reference, and the real learning is by actually doing physics.

I know i have a very high ability to think of novel solutions, so maybe that is key to just spend my time solving difficult problems and learn that way. I would love any recomendations to sources of worth while problems to figure out, or papers etc, anything that motivates to actually learn the field.

I just don't think learning sequentually works for me, cause of my tendency of getting bored or loosing track. as pointed out earlier i need smart goals

 

[Mayhem]

1. Never skip a problem because it seems "too trivial" (if it actually is easy, just do it!)
2. Listen and learn from people smarter than you.
3. Be at complete peace with feeling and looking stupid.

 

[nox]

Really great advice.
So i decided that it will lead me nowhere to just study physics in a linear fashion like you do at university. Having both adhd and aspbergers i will just waste more time, and becoming demoralized. So i decided to stop trying prepare for some day where i can magically read and understand even develop my own field, and just do it. So Last night i started to read general relativity, jumped into chapter 4 about gravitation, looked at the first 2 exercises and did not understand them at all. But reading carefully to figure out what was asked, and what i need to learn to answer. It lead me to understand i need to learn differential geometry, and i started to lookup books on it. I then started to skim the first chapter of the GR book, and was surprised it was actually illuminating, i could grasp the concept of a light cone in flat spacetime, and understand Einsteins notation using superscript and subscript. Before this i spent a week learning the basics of machine learning, focusing on neural networks in keras, but get a broad overview of ai, the concept of an agent, problem solver to planner, and how it works with probabilities. Down to machine learning that is basically applied statistics, and to deep learning where the fun begins.

What i am learning is to read out of my depth, and be comfortable with reading and not understanding everything, but keeping at a certain layer of abstraction, and i suspect this is how graduate students learn, cause how else do you read 20 books each one taking years to master?
I am thinking of trying to contact a physicist anyone who will humor me, and ask for a problem or concept to work on to be a goal to be used as i learn. So the truth is i prob would not get more than a passing grade of Newton mechanics if i had a test today, and there are more holes than swish cheese in my fondation. But i feel reading the graduate stuff now is key for me, cause it shows me why i need certain concepts.

Lastly i do want to say that with my limited understanding i have an musing, i suspect that most models in physics are at a dead end, useful for technology but we have built it on assumptions that though they simplify they hold the field back. This is why i am very interested in developing new models, i don't seem to find much literatue on the subject of developing models from first principles tough. I could be dead wrong, but the quest of unifying all areas of physics is misplaced, every model is just a thought experiment, it is similar to the parameters of a neural network, it works but with no real insight in what the phenomena really is. I even believe mathematics is not sufficient to really model our reality, but how do we proceed then? What i want to have said in my rant is this, we prob will never be done with theory building, but maybe that's the point, that in order to understand something you have to look at it with fresh eyes often. So if we ever would invent a time machine, i suspect the physics involve would be be based on any known model.
Here is an idea what if time travel required a new model every timestep, that is based on separate kind of logic and thus different math frameworks. Imagine the gap between Newton and Einstein but that kind of development ever delta event.

Ok in my ramble i discovered something a concept, is this something physicists have thought about, that to traverse where the laws of physics seem to breakdown, you need a new framework/theory with its own sets of logic every new event? And this makes me wonder if there actually are several types of logic without them being isomorphic to each other. What about a field dealing with things that move cyclical between logic and chaos, that is can only be predicted half the time.
Ok sorry for the mega wall of text, i don't want to delete it, cause this have been my thoughts for like an hour, so maybe there is something interesting there.

Summary:
Recursive learning is best for me
I like to expose myself to novel problems that will for a basis for learning physics, my thesis so to say.
I believe only way to move the field forward is to create new models from first principle, and reconize how old assumptions hold us back. (ex linearity of cause and effect, is this a valid assumption?)
I realize without a degree i will never be taken seriously in academia, and that is ok, life is to short, and if i get lost on the way accomplishing nothing well at least i had fun
This respose was so long i wonder if i should create a new thread?