1) Find a good source of information --- typically, this is either very good lectures (like on youtube), a good textbook, or good lecture notes.
2) Do problems. There is a fairly large gap between those that just watch the lectures and those that have sat down and try to go through each and every step of the logic, and that's what everyone here (on HN) is pointing out when they similarly mention doing problems.
2b) Have solutions to those problems. I make this a separate point because it's important to spend quality time on a problem yourself before looking at the solutions. At the end of the day, if you read the problems and then the solution right away, that's much closer to reading the textbook itself instead of the more rigorous learning one goes through when trying things themselves.
If you were to ask me what textbooks or lectures I recommend, I think that's a more personal question than many here might guess. What topics are you most interested in? Are you really just solely interested in a solid background? How patient are you when doing problems?
Regardless, I'll give my two cents for textbooks anyway. In no particular order:
1) Griffiths E&M: https://www.amazon.com/Introduction-Electrodynamics-David-J-...
2) Axler, Linear Algebra Done Right: https://www.amazon.com/Linear-Algebra-Right-Undergraduate-Ma...
* Second edition: https://www.amazon.com/dp/0387982582* Third edition: https://www.amazon.com/dp/3319307657I wonder whether widespread adoption of his book pushed editors to make it look flashier and watered down. The contents are the same though.
* Third edition: https://www.amazon.com/dp/3319307657I wonder whether widespread adoption of his book pushed editors to make it look flashier and watered down. The contents are the same though.
I wonder whether widespread adoption of his book pushed editors to make it look flashier and watered down. The contents are the same though.
By the way, some less applied materials include:
Liner Algebra Done Right (http://www.amazon.com/Linear-Algebra-Right-Undergraduate-Mat...)
Its breakthrough is its focus on the basic algebraic properties of vector spaces and linear maps between them. It de-emphasizes matrix computations and especially determinants (they are covered, but only insomuch as they are necessary).
In my experience, the result of a typical linear algebra course is most students don't fully understand the determinant and more importantly they don't understand the proofs of major theorems which involve long manipulations of the determinant. They also don't understand the more algebraic side of the subject because they aren't given a chance to--it's not covered in much detail. The result is they don't understand the subject overall much at all.
This book is based on the observation that the abstract algebra involved in linear algebra is actually remarkably easy, much more so than arcane determinant manipulations.