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Comment by lunchladydoris | Hacker News Reader

I enjoy a mathematics textbook as much as the next person, but what annoys me is the lack of solutions to the problems in so many of the books I've skimmed outside of classes.

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That's why Khan Academy is awesome. I'm working through their calculus and differential equations curriculum right now to refresh my math and the amount and quality of autograded excercises is fantastic! The other nice thing is it periodically tests knowledge of previously studied material.

Oh, differential equations.

I'm doing ECE at university now and I have an exam in about 7 weeks. I've found that it's quite hard to identify what sort of differential equation a given problem is, and then how to solve it. However I've found that by looking around for other material I can understand it better.

For example web searching "type 4 differential equation" bought up this gem: https://www.math.ucdavis.edu/~thomases/W11_16C1_lec_1_7_11.p...

I think I'll try out Khan Academy because I've found that the lecturer's problem sheets probably aren't enough on their own.

I prefer solutions to some, but not all problems. Being able to independently and confidently verify your own solutions is an important skill to develop.

having the solutions does not stop you from developing that skill. however, the lack of solutions makes it difficult to make progress when you have time constraints, which is the common case.

This is absolutely a crucial skill. One of the most valuable exercises I had to do in college was during my introductory physics courses. Before solving any problem, we had to write what we expected the solution to look like, then after solving the problem, we had to write whether our solution seemed plausible. Did it fit our initial expectation? I not, could we explain the disparity? If we applied this value or equation to something else, would we get reasonable results (say, if the problem were estimating the gravitational force of the sun, what would this value give us for the length of the earth's year). Note that we'd get credit for this part even if our solution was wrong, as long as we recognized that it was in fact wrong.

It was a huuuge pain at the time and often took longer than the initial problem took to solve, but it did force me into the habit of critically evaluating my work, and its been one of the most valuable life skills I learned in college. It also helped develop my intuition, and significantly improved my teaching and presentation skills.

Sometimes the problem is more important than the solution.

Yes, but if you're cramming for an exam it is so much more productive to just read through a fully worked out solution instead of trying to figure out how to do it yourself.

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