Now there are two ways in which you can increase your understanding of these issues. One way is to remember the general ideas and then go home and try to figure out what commands you need and make sure you don't leave one out. Make the set shorter or longer for convidence and try to understand the tradeoffs by trying to do problems with your choice. This is the way I would do it because I have that kind of personality! It's the way I study -- to understand somethingby trying to work it out or, in other words, to understand something by creating it. Not creating it one hundred percent, of course; but taking a hint as to which direction to go but not remembering the details. These you work out for yourself.
The other way, which is also valuable, is to read carefully how someone else did it. I find the first method best for me, once I have understood the basic idea. If I get stuck I look at a book that tells me how someone else did it. I turn the pages and then I say "Oh, I forgot that bit", then close the book and carry on. Finally, after you've figured out how to do it you read how they did it and find out how dum your solution is and how much more clever and efficient theirs is! But this way you can understand the cleverness of their ideas and have a framework in which to think about the problem. When I start straight off to read someone else's solution I find it boring and uninteresting, with no way of putting the whole picture together. AT least, thats the way it works for me!
Throughout the book, I will suggest some problems for you to play with. You might feel tempted to skip them. If they're too hard, fine. Some of them are pretty difficult! But you might skip them thinking that, well, they've probably been done by somebody else; so what's the point? Well, of course they've been done! But so what? Do them for the fun of it. That's how to learn the knack of doing things when you have to do them. Let me give you an example. Suppose I wanted to add up a series of numbers,
1 + 2 + 3 + 4 + 5 + 6 + 7 ...
up to say, 62. No doubt you know how to do it; but when you play with this sort of problem as a kid, and you haven't been shown the answer ... it's fun trying to figure out how to do it. Then, as you go into adulthood, you develop a certain confidence that you can discover things' but if they've already been discovered, that shouldn't bother you at all. What one fool can do, so can another, and the fact that some other fool beat you to it shouldn't disturb you: you should get a kick out of having discovered something. Most of the problems I give you in this book have been worked over many times, and many ingenious solutions have been devised for them. But if you keep proving stuff that other s have done, getting confidence, increasing the complexities of your solution for the fun of it -- then one day you'll turn around and discover that nobody actually did that one! And that's the way to become a scientist.
The quote is from none other than Richard Feynman in his Lectures on Computation (a great read by the way). [reproduced without permission]
Honestly I think that's one of the biggest problems with science and math education in this country. They have taken something which is fun and challenging, a path of discovery, and reduced it to memorizing a list of dogmatic equations handed down from high. Students are all but taught that the men and women that discovered these laws are somehow above the rest of us.
One of the best kept secrets of science is that scientists are in fact mere mortals. They have their faults, and deficiencies just like the rest of us. You don't need anything special to do science, all you need is a sense of curiosity and wonder, and the resolve to spend some time working at it. The more time you work at it, the better you get.
Science is not a list of facts. It is not plugging numbers into equations. It is neither history nor accounting. It is, in its purest form, the recognition that as human beings we are each endowed with the power to come to understand the world around us.
I firmly believe that anyone of a sane mind is capable of becoming a physicist. I'm not saying that everyone should be; people should follow their passions, but I worry that too many students are turned away thinking they aren't cut out to be scientists, and that's rubbish.
And that's my two cents.