Start with the basics and spend a ton of time with them. Try not to move on until you're very solid on the fundamentals of a particular topic. Moving on too early is by far the most common root cause of the problems math and physics students have learning.
Do as many problems as you can. Assume you don't understand something until you've done lots and lots of practice problems. "Math is not a spectator sport." I think that's from "How to Solve It". It holds true for physics.
If there's a specific level or topic in math/physics you're looking to learn, post it and people will probably be able to give you a good recommendation for a book.
Also, if you're not extraordinarily comfortable with algebra (manipulating equations, basic trig identities, log and exponent identities), go back and start there. Everything is so much easier with that skill under your belt.
The best method is to find a teacher or teachers who can provide you guidance and feedback. Short that, engage with experts (directly, or indirectly by finding their writings and talks) to find out what they think is an appropriate way to learn their areas of expertise (that doesn't involve them directly teaching you) and the background areas.
I wouldn't just take his word for the recommended background reading, but take that set of resources and see what others have to say about them. Maybe they have alternative suggestions ("X is a good book, but has a poor set of exercises. Consider Y as an alternative or supplement. Z is a poorly written book because... consider ..."). Find multiple sources like this and build out a study list.
Go to things like MIT's OpenCourseWare which offer a more complete set of information on the college course curricula (versus the relatively incomplete set of information on most actual university course websites). Work through the courses in, generally, the same order the students would be expected to (as most later courses are founded on the earlier ones, jumping ahead isn't terribly easy).
Khan Academy (http://khanacademy.org) is commonly recommended here, I've never gone through it though so can't comment beyond that. They started off with just math material but have branched out since then. Mostly at the K-12 level and pushing into undergraduate level material.
You'd think that the best method has changed because of internet. Despite many excellent videos, say, on Youtube, the best method, by far, I think is still books. (Of course, if you want to become a professional, then you have to go to school.)
If it's a big enough school, you can probably sit in on the year 1 or year 2 lectures without anyone asking for an ID, too. If you aren't interested in credentials, this would get you up to "novice" level in math and physics without much trouble. Year 3 and 4 lectures would be too small for you to reliably go unnoticed. Smaller institutions will also catch you earlier.
Of course, you won't get feedback with this approach. At least not easily, as you won't have an assigned TA and they'll notice if you start showing up to office hours.
You should learn physics and math by solving problems in text books.
Don't expect to read the text and learn, as if you were digesting a short story or a news article, you have to learn by doing.
There are physics books that a famous because they teach you how to think in physics or in mathematics, but have abridged or non-existent problem sections, I would defocus these books from your curriculum.
In fact, you probably shouldn't even read the books or even watch any youtube lectures, just try and solve problems and if you don't understand the material only then consult the text/youtube.
I think key to be good at math/physics is good memory, try improving that the best you can. And then a lot of practice, also you need to base that with fundamental logical thinking. philosophy is good for that
I wholeheartedly disagree. I have a PhD in math and a terrible memory. I pick up methods, not facts. I'd say that I got good because I learned to re-derive everything from scratch, and practiced enough to do that in the heat and pressure of an exam.
I'm currently getting a high school advanced math certificate (in Dutch). It's a good platform and it gives me the opportunity to ask teachers much more advanced questions that relate to the material.
I supplement my theory by watching 3Blue1Brown. Remembering double angle formula's is easy because of it :)
So for me, I've learned a few things. I need:
- Fellow students in a WhatsApp group
- Teachers giving an answer in about a day on questions I have
- Good exercises that give immediate feedback
- 3Blue1Brown + Khan Academy giving better explanations
I'm simply describing the nature of the course that I'm going through :P But I've also noticed that these things help.
14 comments
[ 2.9 ms ] story [ 47.5 ms ] threadDo as many problems as you can. Assume you don't understand something until you've done lots and lots of practice problems. "Math is not a spectator sport." I think that's from "How to Solve It". It holds true for physics.
If there's a specific level or topic in math/physics you're looking to learn, post it and people will probably be able to give you a good recommendation for a book.
Also, if you're not extraordinarily comfortable with algebra (manipulating equations, basic trig identities, log and exponent identities), go back and start there. Everything is so much easier with that skill under your belt.
I cannot emphasize this enough. Hour a day on each chapter until the problems are boringly easy.
For instance, John Baez has this: https://math.ucr.edu/home/baez/books.html
I wouldn't just take his word for the recommended background reading, but take that set of resources and see what others have to say about them. Maybe they have alternative suggestions ("X is a good book, but has a poor set of exercises. Consider Y as an alternative or supplement. Z is a poorly written book because... consider ..."). Find multiple sources like this and build out a study list.
Go to things like MIT's OpenCourseWare which offer a more complete set of information on the college course curricula (versus the relatively incomplete set of information on most actual university course websites). Work through the courses in, generally, the same order the students would be expected to (as most later courses are founded on the earlier ones, jumping ahead isn't terribly easy).
Khan Academy (http://khanacademy.org) is commonly recommended here, I've never gone through it though so can't comment beyond that. They started off with just math material but have branched out since then. Mostly at the K-12 level and pushing into undergraduate level material.
Consider signing up at a local academic institution, many will accept payment by modules rather than for an entire degree.
Of course, you won't get feedback with this approach. At least not easily, as you won't have an assigned TA and they'll notice if you start showing up to office hours.
Don't expect to read the text and learn, as if you were digesting a short story or a news article, you have to learn by doing.
There are physics books that a famous because they teach you how to think in physics or in mathematics, but have abridged or non-existent problem sections, I would defocus these books from your curriculum.
In fact, you probably shouldn't even read the books or even watch any youtube lectures, just try and solve problems and if you don't understand the material only then consult the text/youtube.
It's highly interactive and engaging, which helps it feel less dry!
I supplement my theory by watching 3Blue1Brown. Remembering double angle formula's is easy because of it :)
So for me, I've learned a few things. I need:
- Fellow students in a WhatsApp group
- Teachers giving an answer in about a day on questions I have
- Good exercises that give immediate feedback
- 3Blue1Brown + Khan Academy giving better explanations
I'm simply describing the nature of the course that I'm going through :P But I've also noticed that these things help.