Ask HN: how do you learn Math?
10 comments
Knowledge passes from the paper, to the pencil, to the hand, up the body, and to the brain. My point: do lots of problems. Schaum's has some good material. Mathematics is just like anything else. If you want to be good at it, you have to practice it. It doesn't matter what level you are at, whether it be arithmetic or writing complex proofs.
I've never used Schaum's outline series before, but I shall look that up. Thank you.
Hi Chocobean,
I can sympathize. Completely.
I had a horrible math education in high school (more detail is provided elsewhere on YC.) I hate the plug-and-chug rules approach, and I'm fairly math-phobic. I completely avoided math during my first college experience, even taking a class in C++ once just to avoid taking Calculus for an analytics requirement. I had no interest in programming at the time, and the C++ class was probably worse than any math I could have been subjected to. The instructor was just learning English, so we practiced (inflicted?) our developing skills on each other. Anyway, I taught myself math before going to college the second time. I have no idea how I did it, other than tons of practice problems and a tutor. Youthful ambition, I guess. All of the math related to econ and finance examples, so I think that made it easier for me. I needed to have a conceptual understanding of why you were doing something in order to understand the 'rules.'
Then I 'lost' what math I had learned on my own after a mini-stroke around age 30 (or maybe it was lost from the brain lesions, who knows.) I work mostly in software and finance now, so math is kind of important. Attempting to cram again, I found that the same learning techniques no longer worked for me. Nothing stuck. I bought about $15,000 worth of self-instruction materials, in part because I hate streaming video or reading lengthy books online, and also because there was less material available online at the time. Most of what I bought sucks and was wasted money. I stopped reading any books that lost me in the first few minutes, or that had many obvious errors. I procrastinated quite a bit. I eventually rebuilt my basic math foundation (up through basic Calc), but I've never advanced to the level I want to be. Someday.
If you're a visual learner and willing to spend some dough: Thinkwell, Chalkdust, and MathTutorDVD were pretty good and were better values than the rest of the 'courses' I bought. Thinkwell was easily the most entertaining, and their courses covered a good bit of material, but their interface is kind of a pain. MathTutorDVD was good, but it has less of a conceptual overview or explanation component. It's just a dude working out problems on a whiteboard. Chalkdust, like many multimedia math courses, is spendy - but the guy speaks clear English if that's important to you. [If you can, watch a sample of any training before you buy it. I spent $300 on a course from a professor in NY, and I wanted to stab my eardrums out from his voice and accent (mostly his specific voice, the accent just made it worse.) I had a similar problem with a course from an Indian professor... I couldn't understand about every other word. It was like the C++ class all over again.] Now, of course, there are tons of FREE online video courses at MIT OCW, UC-Berk, FreeVideoLectures.com, etc. etc. Try those first. If something doesn't click or you don't like the presenter, move on. I'd definitely try to find materials that balance concepts (why, how) with completed practice problems. Just keep trying...eventually something will stick. I'm pretty much hopeless, and some stuff eventually seeped into even my melon. I'm sure you'll do well...the fact that you're worried about it at all is a good sign. Good luck.
I can sympathize. Completely.
I had a horrible math education in high school (more detail is provided elsewhere on YC.) I hate the plug-and-chug rules approach, and I'm fairly math-phobic. I completely avoided math during my first college experience, even taking a class in C++ once just to avoid taking Calculus for an analytics requirement. I had no interest in programming at the time, and the C++ class was probably worse than any math I could have been subjected to. The instructor was just learning English, so we practiced (inflicted?) our developing skills on each other. Anyway, I taught myself math before going to college the second time. I have no idea how I did it, other than tons of practice problems and a tutor. Youthful ambition, I guess. All of the math related to econ and finance examples, so I think that made it easier for me. I needed to have a conceptual understanding of why you were doing something in order to understand the 'rules.'
Then I 'lost' what math I had learned on my own after a mini-stroke around age 30 (or maybe it was lost from the brain lesions, who knows.) I work mostly in software and finance now, so math is kind of important. Attempting to cram again, I found that the same learning techniques no longer worked for me. Nothing stuck. I bought about $15,000 worth of self-instruction materials, in part because I hate streaming video or reading lengthy books online, and also because there was less material available online at the time. Most of what I bought sucks and was wasted money. I stopped reading any books that lost me in the first few minutes, or that had many obvious errors. I procrastinated quite a bit. I eventually rebuilt my basic math foundation (up through basic Calc), but I've never advanced to the level I want to be. Someday.
If you're a visual learner and willing to spend some dough: Thinkwell, Chalkdust, and MathTutorDVD were pretty good and were better values than the rest of the 'courses' I bought. Thinkwell was easily the most entertaining, and their courses covered a good bit of material, but their interface is kind of a pain. MathTutorDVD was good, but it has less of a conceptual overview or explanation component. It's just a dude working out problems on a whiteboard. Chalkdust, like many multimedia math courses, is spendy - but the guy speaks clear English if that's important to you. [If you can, watch a sample of any training before you buy it. I spent $300 on a course from a professor in NY, and I wanted to stab my eardrums out from his voice and accent (mostly his specific voice, the accent just made it worse.) I had a similar problem with a course from an Indian professor... I couldn't understand about every other word. It was like the C++ class all over again.] Now, of course, there are tons of FREE online video courses at MIT OCW, UC-Berk, FreeVideoLectures.com, etc. etc. Try those first. If something doesn't click or you don't like the presenter, move on. I'd definitely try to find materials that balance concepts (why, how) with completed practice problems. Just keep trying...eventually something will stick. I'm pretty much hopeless, and some stuff eventually seeped into even my melon. I'm sure you'll do well...the fact that you're worried about it at all is a good sign. Good luck.
" I needed to have a conceptual understanding of why you were doing something in order to understand the 'rules.' "
That's exactly it. I frequently got frustrated in high school Calc class because I couldn't understand why we were doing certain things. THe problem is that so much material needed to be just groked at once, and then and only then can they explain and prove anything....this time around I'm a lot more proactive in spotting when I'm only "faking" understanding, and working it out.
Another poster commented that with Algebra for example it all boils down to applications of axioms. So for that I am doing tonnes of practice.
amazing story =) I too believe that there is life beyond Math, but for now, rumours has it that doing some math will make me a better hacker(at least for bureaucratic reasons). So I shall persist.
That's exactly it. I frequently got frustrated in high school Calc class because I couldn't understand why we were doing certain things. THe problem is that so much material needed to be just groked at once, and then and only then can they explain and prove anything....this time around I'm a lot more proactive in spotting when I'm only "faking" understanding, and working it out.
Another poster commented that with Algebra for example it all boils down to applications of axioms. So for that I am doing tonnes of practice.
amazing story =) I too believe that there is life beyond Math, but for now, rumours has it that doing some math will make me a better hacker(at least for bureaucratic reasons). So I shall persist.
My oldest son has dyscalculia -- the numbers simply don't compute for him -- and he is a visual-spatial type, so needs the big picture (context) to understand anything. Here is a list of stuff we used while homeschooling him:
http://kidslikemine.com/mathlist.shtml
HTH.
HTH.
http://news.ycombinator.com/item?id=733369
Riemann for Anti-dummies: Introduction and Critique
I think there is less math in undergraduate computer science programs than you might think.
If they require you to take calculus or a discreet mathematics course then you might have to re-learn some things, but exponents and logs aren't that common in pure CS classes.
I know this doesn't really answer your question, but good advice might just be: don't freak out.
If they require you to take calculus or a discreet mathematics course then you might have to re-learn some things, but exponents and logs aren't that common in pure CS classes.
I know this doesn't really answer your question, but good advice might just be: don't freak out.
thanks. =)
my particular university has first and second year calc and then other maths and stats all the way up to 4th year level, unfortunately. I was always an A/B student back in highschool, but that was when I did this stuff day in day out. Plus I don't have the teenage angst to fuel me anymore. The comsci courses are making me so happy though, that I think I should manage to pull through.
my particular university has first and second year calc and then other maths and stats all the way up to 4th year level, unfortunately. I was always an A/B student back in highschool, but that was when I did this stuff day in day out. Plus I don't have the teenage angst to fuel me anymore. The comsci courses are making me so happy though, that I think I should manage to pull through.
I go the rules route. I don't know that you can learn algebra any other way, can you? I mean, if you don't know the rules, how are you going to do the problem? I hated proofs, though that is more applicable to geometry.
I don't know that I agree with this. If you don't like just following rules, then you want to try to understand why the rules work and make sense. E.g. why are you allowed to add "x" both sides of the equation or divide both sides by 2?
The rest of it is like what BrentRitterbeck says. You just need to do enough problems to be able to look at a problem and say to yourself "I think this technique will work."
Proofs in algebra aren't usually very enlightening with respect to the theorem they are trying to prove, but they can teach you a new technique (e.g. proving the quadratic equation can teach you how to "complete the square").
The rest of it is like what BrentRitterbeck says. You just need to do enough problems to be able to look at a problem and say to yourself "I think this technique will work."
Proofs in algebra aren't usually very enlightening with respect to the theorem they are trying to prove, but they can teach you a new technique (e.g. proving the quadratic equation can teach you how to "complete the square").
How did you learn math? Any recommendation of sites to pick up this stuff easily again?
Seriously I'm having trouble doing some simple algebra...it's scaring the heck out of me.