gaffa: A heavy obstacle for me is that I have a hard time thinking in terms of math, numbers and logic. I can understand concepts on the superficial level and kind of intuitively “feel” their meaning in the back of my mind, but I have a hard time bringing the concepts into the frond of my mind and visualize them in detail using mathematical reasoning. I tend to end up in a sort of “I know that you can calculate X with this information, and knowing this is good enough for me”-state, but I’d like to be in the state where I am using the information to actually calculate the value of X in my head.
I’ve found that the only to get past this is to practice solving problems a whole bunch. If your brain doesn’t already have the skill of looking at a problem and slicing it up into all the right pieces with the right labels so that a solution falls out, then the only way to get it to do that is to practice a lot.
I recommend getting an introductory undergraduate text in whatever field you want to understand mathematically, one with lots of exercises and a solutions manual. Read a chapter and then just start grinding through one exercise after another. On each exercise, give yourself a certain allotted time to try to solve it on your own, maybe 20 or 30 minutes or so. If you haven’t solved it before the clock runs out, read the solutions manual and then work through it yourself. Then move on to the next problem, again trying to solve it within an allotted time.
Don’t worry too much if the solutions manual whips out some crazy trick that seems totally unmotivated to you. Just make sure that you understand why the trick works, and then move on. Once you see the “trick” enough times, it will start to seem like the obvious thing to try, not a trick at all.
I’ve found that the only to get past this is to practice solving problems a whole bunch. If your brain doesn’t already have the skill of looking at a problem and slicing it up into all the right pieces with the right labels so that a solution falls out, then the only way to get it to do that is to practice a lot.
I recommend getting an introductory undergraduate text in whatever field you want to understand mathematically, one with lots of exercises and a solutions manual. Read a chapter and then just start grinding through one exercise after another. On each exercise, give yourself a certain allotted time to try to solve it on your own, maybe 20 or 30 minutes or so. If you haven’t solved it before the clock runs out, read the solutions manual and then work through it yourself. Then move on to the next problem, again trying to solve it within an allotted time.
Don’t worry too much if the solutions manual whips out some crazy trick that seems totally unmotivated to you. Just make sure that you understand why the trick works, and then move on. Once you see the “trick” enough times, it will start to seem like the obvious thing to try, not a trick at all.