No matter what the subject if you are feeding your brain some fuel its sure going to help you with programming or whatever.

So now has come the time that i need to know long division -- Binary Division -- I'm still not 100% sure on how to do it... but supprisingly, guess how i got to my current understanding of it? Abstract Algebra can help determine the cardinality of inputs and outputs of your program (the "surface area of testing"). the doubter: I think Wikipedia has vastly surpassed Mathworld in terms of usefulness and quantity of information.I mean: yeah, you're right, grown ups learn stuff the other way round (was that "breadth-first" you said?) and that's a fact I like someone else but me noticed. Thanks. But I'd stress this: don't let exercises put you off the math. If an exercise (or even a particular article or chapter) is starting to bore you, move on. Jump around as much as you need to. Let your intuition guide you. You'll learn much, much faster doing it that way, and your confidence will grow almost every day. I think the most important point (i.e. one of the ones I agree with, ha!) is that it is important to motivate students to learn something, and to engage their intuition. I remember learning vector calculus, and finding it difficult, and then learning the physics (electromagnetism) that gave birth to the math, and suddenly understanding it all (okay, sadly not all, but much more!).

Well Stevey, I'm happy for you that you're learning more math and enjoying it, but I think your article was rather weak.It really seems that in the past calculus and differential equations were at the heart of various engineering edeavors. Now, however, it seems that probability and discrete math are becoming more important, espeically given the new interdisciplinary mash-ups like 'genetic algorithms/genetic programming' (combining evolutionary biology with algorithm design), various social-insect based search methods (ACO, PSO - another biology meets engineering mashup), bioinformatics, etc. Probability and statistics play a big role in genetics and biology in general and now we're seeing biology and engineering combining. 5:59 PM, March 17, 2006 Anonymous said...

The right way to learn math is breadth-first, not depth-first. You need to survey the space, learn the names of things, figure out what's what. I think Knuth's "Concrete Mathematics" contains most of the math we'd need as programmers, and is also the most enjoyable math book I've come across. Now if only I can get around to studying it ... :) Mathematical Logic. I have a really cool totally unreadable book on the subject by Stephen Kleene, the inventor of the Kleene closure and, as far as I know, Kleenex. Don't read that one. I swear I've tried 20 times, and never made it past chapter 2. If anyone has a recommendation for a better introduction to this field, please post a comment. It's obviously important stuff, though. I think it was a divine act that led me to this blog. Recently I've had a huge urge to learn math (I'm very mathematically ignorant), but I've had no clue as to where I should even start. So thanks for the great blog. I'm adding it to my favorites. 8:05 PM, March 17, 2006 Anonymous said...

Course Catalog

I'm currently taking a Mathematical Logic course and we're using H.B. Enderton's A Mathematical Introduction to Logic. It's pretty good but nothing compared to the way the professor teaches it. The most fun stuff is the nonstandard analysis stuff. All those hyperreals and whatnot. In fact there's a good CC lisenced ebook on Calculus, shown using nonstandard analysis. It's available here http://www.math.wisc.edu/~keisler/calc.html 12:26 PM, March 17, 2006 Anonymous said...