i don't recall the lessons in school when i was told how to do long division, or which trigonometric functions to apply to which triangles, or which combinatorial functions to apply to which problems. but if i had to do any of this right now, i could easily figure it out, because it's nothing more complicated than middle school math. It may not be a Computer Science degree(Actually its Bach of Information Technology -- but no-one comment on that) But still requires abit of knowledge.. I write teribly bad in english but i try to think in math (when i think at all )and it is not a very great problem for me 3:48 PM, March 19, 2006 Abhinav said...

but it's much more important to explain why and how the algorithm works. firstly, because there are other "learning types"; people who can't remember a list of seemingly arbitrary computational steps easily, but will be able to perform the calculation effortlessly once they 'get' it. and secondly, and that's the important part, because this provides you with actual insight into the subject matter and builds problem solving skills that you can make good use of every single day in your life. Let's take geometry as an example of a common language. In a strict sense, geometry is almost useless as vocational training - except to mathematics students who go on to teach the subject. But in a broader sense, the construct of geometry is deductive reasoning. And the sort of reasoning used here is crucial in a host of disciplines. It may be courtroom law that draws on the mental disciplines and processes inculcated by geometry. About that then, maybe at a certain point it the future it will; and with everybody programming (lawyers and medics alike) old CS graduates will end up being underspecialized. 6:37 PM, March 17, 2006 mfwic said... 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...

about the book

But before that there were a lot of tears. And I don't use much of what I learned in my daily life as a programmewr/tech writer. (Then again, MOST of what is taught in high school, and college for that matter, has no bearing on Real Life After School) One reservation though: It seems to me that your approach to mathematics ( the just-in-time method?) leads to only surface understanding that can be dangerous--literally deadly. Probability and statistics, is an area, for example, where these errors can be especially egregious since for some it seems deceptively simple to some. Subtleties that come from deeper knowledge are lost.

You could figure it out because you know that division is just repeated subtraction. The intuitive notion of division is deeply ingrained now. last word on logic Kleene is one of the best and most original in field but well his view is specific and ... i prefer to be Feynman's slave than Kleene's ... there is good handbook of logic editet by Jon Barwise tooThe 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 ... :) Forgive me for what might seem like a double post but I felt compelled to correct (and add to) the initial post; it was was written in haste before I had to go out. Perhaps it's the mathematician in me. I couldn't agree more. Please write a book. I was one of those CS majors who did enough to get by and now that i'm in the industry I'm actually really enjoying it and find myself reading up a lot of math/CS type of stuff. I think universities should tailor an applied-math-for software engineers type of class and teach it using the methods/content you suggest. 11:21 AM, March 17, 2006 Anonymous said...

I am an engineering, and i must say that even though i use, discrete math to model functions for digital logic, by far and wide i use trig and differential calculus much more, as modeling changing systems is much more important to me, also the trig identities i would stress are very important, how else would i be able to use fouriers series etc etc.Linear Algebra is the single most important math subject in undergraduate education. You begin to do real math, serious abstraction, and it is applicable to everything under the sun. pen and paper for doing my math-any math, mostly discrete though. Pen and paper gets me the feel which I find

Math is... ummm, please don't tell anyone I said this; I'll never get invited to another party as long as I live. But math, well... I'd better whisper this, so listen up: (it's actually kinda fun.) It all depends on the type of programming you are doing. If you like to do encryption programming or game programming, you NEED math.. and lots of it. However, many algorithms already exist for the in-astute 12:25 PM, March 17, 2006 Anonymous said... All that are old books and citizens of richer places in the world can and should try to find shorter and better way but this is part of my own way long time ago and it is what you can find if you are an ex-communist citizen (in russian too) any way all these autors are extremely good and if not pressed to much for time (if you can find for reading Kleene you have enough ;-)Some of what you are experiencing is mathematical readiness. You are ready, and you weren't earlier. But, I, too would change the learning of mathematics. I would eliminate calculators so that the experience of "how things go" is being learned all along. Students who learn without calculators "get it" in a way that those who use them just don't. Here is some of the information that I discuss and demonstrate in the book. I don't claim these to be original discoveries However, by surveying math, trying to figure out what problems people have been trying to solve (and which of these might actually prove useful to you someday), you'll start seeing patterns in the notation, and it'll stop being so alien-looking. For instance, a summation sign (capital-sigma) or product sign (capital-pi) will look scary at first, even if you know the basics. But if you're a programmer, you'll soon realize it's just a loop: one that sums values, one that multiplies them. Integration is just a summation over a continuous section of a curve, so that won't stay scary for very long, either.