
Re: Structured Programming
Posted:
Mar 7, 2014 7:25 AM



On Thu, Mar 6, 2014 at 11:57 PM, Robert Hansen <bob@rsccore.com> wrote:
> On Mar 6, 2014, at 11:22 PM, kirby urner <kirby.urner@gmail.com> wrote: > > > > > Yet here you are back to teaching students that f(x) means something > like... > > > > int factorial(int n) { > > if (n == 1) return n; > > return n * factorial(n  1); > > } > > > > Isn't it a lot easier, in math class, to get the point across by saying > n! = 1 * 2 * 3 * ... * n? > > > > > > They'll probably use a calculator rather than something they wrote > > in code. They won't use pencil and paper much. > > > > Factorial is used in probabilities / combinatorics, so we would be > > adding more functions to this one soon, making use of factorial(). > > I don't think you understood what I meant. The factorial *function* falls > out of and intertwines with all the mathematics of combinatorics and > probability. How did you reduce that to *the factorial* is used in > probabilities and combinatorics? Is used? I just hope your book is like > Litvin's in that it treats the mathematics behind the application, before > the application. > > http://www.skylit.com/python/text/Chapter05.pdf > http://www.skylit.com/python/text/Chapter10.pdf >
I was using "the factorial" as shorthand for "the factorial function". "The sine and cosine are used in trig a lot" would be a similar tautology.
I have not written a book, though I have enough web pages with graphics (which I made, so they're mine to use as I wish) and postings to amount to several books. But my goal is not to be the big textbook writer in this picture.
My goal is to change the law to where math credit is available to students who take courses such as those using the Litvins' text and a gazillion other texts that will materialize in response to the opening floodgates to this "new kind of math course".
Speaking of which, I'm anticipating Wolfram getting a slice of this market, and Wolfram Language continuing to make inroads.
The Python stuff is laying some of the groundwork, somewhat inadvertently, for Wolfram. IPython and IPython Notebooks look quite a bit like Mathematica in terms of providing numbered prompts, executable cells and so on. And SAGE.
Raspberry Pi (a $35 computer with USB x2 and HD out), which features Python a lot, now includes the proprietary Wolfram stuff for free as well  without sacrificing profit as one develops a hunger to run it faster on other platforms.
These tools are so much better than spreadsheets, which bury the algebra in formulae tied to cell numbers. But we can use those too. Lots of jobrelevant tools to start mastering.
> That is all I am saying. You seem to want to begin these topics with > programming while Litvin begins them with mathematics and then moves on to > the programming. > > If your approach is different from Litvin's, how is it be different? What > do you add and what do your remove? > > Bob Hansen >
For the sake of our continuing agreement, wherein students have already had algebra before taking these this new kind of math course, lets just say we'll use the Litvins book for now, adding to the syllabus as various faculties edit / recombine more open source materials, in a mix with more proprietary stuff.
I'll be contributing (am already) with my input, but it's not important for everyone to teach "Kirby's way" or "Wolfram's way" or any one particular way  we should separate content from legality as different issues.
Kirby just wants a new kind of math courses to be street legal, then we can depend on the usual competition, "market forces" etc. for winnowing and culling. I want teachers themselves, individual schools, to have a lot more curriculum design responsibilities than we give them today  again, another issue.
Such "market forces" talk makes the politicians happy, as we're sounding like good capitalists here, developing interesting work for people (jobs!). But it's not what big publishers want to hear, as their plan is to standardize and continue capturing lucratively vast markets.
The optional nature of these courses is also to our advantage: we're letting 'em vote with their feet while not tearing up the preexisting traditional late 1900s precalc / calc track, so those wanting to stick purely to "the old way of doing things" (older teachers mostly) will have that option, at least for a couple more decades (a generation at least).
Kirby

