Looking for efficient ways on how to properly learn algebra, calculus, and more advanced math branches necessary in engineering and science. At the moment, I follow the instructions taught in class and repeat them as necessary. Perhaps not a good approach since there are many ways to tackle math exercises and I don't feel I'm developing problem-solving skills beyond what I'm taught. I feel like a drone following directions while the people around me understand the concepts and how to branch off of those concepts.
Do as many exercises as you can. That's the only way... When I first studied calculus, I didn't understood much of it.In fact, I felt like a robot. Don't feel worried if you haven't mastered all the concepts yet. You say you want this math for applications in science and engineering. I understood Calculus concepts better when I started seeing these applications. That was when I started enjoying it.
Thanks for the replies. Your advice generally falls in line with what my current math professor expressed to me. I can definitely vouch for doing as many exercises as one possibly can; that factor has helped me recognize patterns here and there in more difficult exercises. That should be good, no? Math seems to be all about patterns.
No, not really. Or at least I really want to believe that there is a better way for people. I see them droning away solving problem after problem and afterwards they still lacks any form of deeper understanding. I would say that the best way to learn it (Engineering maths) is something like this: Learn the intuitive explanations. Understand the intuitive explanations. Visualize them. Try to visualize the problem before you do it, when you do it think in your intuitive terms what you are actually doing, then you should understand that it is all actually trivial. When you get to that point you are done. Just hacking away at a lot of problems trying to get better at maths is like flapping around your arms randomly trying to get stronger arms.
I agree you should also get some intuition. But calculus is not that intuitive for the beginner, so don't worry too much about it now. You may even understand the concepts, but many of them will only become natural to you after you've seen the applications. Since most calculus books I've seen focus on getting the answer right (and many teachers too), I think now you should focus in the methods (even though some of the most obscure ones are rarely used) and a bit of intuition (like the relation between integrals and area, how to find the formula for the volume of a cone/sphere using integrals, the relation between position, velocity, acceleration and derivatives, intuition about epsilons and deltas (for limits)). That amount of intuition should be enough for getting good grades and passing the course (unless you are in a really demanding course). Believe me, when you see the applications of it, your intuition will naturally develop (and you'll have many A-HA! moments). This is also valid for other branches of mathematics: multivar calculus, linear algebra, differential equations... I've done that way, and it worked really nice.