Re: [Edu-sig] Programming in High School
At 02:37 PM 12/8/2008 -0500, Vern Ceder wrote: ... here are the reasons I see that more schools don't offer programming: 1) Lack of qualified staff. Sadly a graduate with a teaching certificate (as required by the state) usually doesn't have anything like the background to teach programming, let alone do the sorts of things that Kirby has experimented with. What we need then, is not programming teachers, but teachers who are enthusiastic about technology, and use programming as a tool. I would think any teacher of math or science would have no difficulty using Python and integrating it into their teaching. Don't teach it as a separate subject, but introduce each new statement as it is needed. For-loops, as an example, could be introduced as a tool to plot functions. The, when the students are comfortable with that (and if there is time), show them a whole new and more general way of looking at for-loops (for item in collection). I remember taking a class in typing. There was a lot of stuff on proper etiquette and formatting of business letters, and emphasis on speed and accuracy, but it was one of the most valuable classes I ever took. Do they still have something like that, maybe a business skills class? Python has a special role here, in that it doesn't require a big, focused effort, as would Java. 2) Numbers - at my school, 6-10 kids in AP Programming is considered a good year. In the public schools around town, in a short-sighted drive for efficiency, (but see item 1 above also) administration routinely kills any elective that can't get 3 times that. 3) The whole integration trend in tech in education - 15 years ago it was assumed that as technology became ubiquitous we wouldn't have to teach it, any more than you need to know about electricity to turn on a light. Of course, that analogy was bogus on both ends, but schools have moved in that direction anyway, killing what little programming they did have. Only now (and only very slowly) are they realizing that their students are the poorer for it. This fits with Paul's theme that we don't need programmers because it will all be done for us, or Guido's that only the best students should study programming. I was once asked by a shop teacher why I am still doing programming. Aren't all the programs already written? We need lots of examples where programming is useful to non-programmers. I already mentioned the real estate agent needing to digest some data from the property appraisers office. For the shop teacher: How about a homeowner wanting to lay tiles, avoid wastage, and slivers that look bad along the edge. If you know Python, it is quicker to write a little program than find one, purchase and install it, read the manual, struggle with a bunch of stuff you don't really need, and maybe not get what you want in the end. I can think of lots of examples in engineering, but they are not ordinary problems that would seem relevant to high school students. What we need is a collection of relevant problems, easily solved with a quickie program. These factors (and others of course) combined with the many layers of bureaucracy create a negative feedback loop that is next to impossible for students, teachers or even parents to beat. In fact, I've talked to state education officials that nearly despair of making any headway in some of our schools. I would think the Federal government could play a positive role in encouraging modernization of our curricula. Are there any proposals for the new administration? I'm thinking of an effort similar to what the Internet Security Alliance is now making in the area of infrastructure for a more secure computing environment. There is a whole new enthusiasm replacing the despair of the last few years. ___ Edu-sig mailing list Edu-sig@python.org http://mail.python.org/mailman/listinfo/edu-sig
Re: [Edu-sig] Programming in High School
We need lots of examples where programming is useful to non-programmers. I already mentioned the real estate agent needing to digest some data from the property appraisers office. For the shop teacher: How about a homeowner wanting to lay tiles, avoid wastage, and slivers that look bad along the edge. If you know Python, it is quicker to write a little program than find one, purchase and install it, read the manual, struggle with a bunch of stuff you don't really need, and maybe not get what you want in the end. I can think of lots of examples in engineering, but they are not ordinary problems that would seem relevant to high school students. What we need is a collection of relevant problems, easily solved with a quickie program. Here is another suggestion: How about a program to predict stock prices? We'll need maybe 1000 traders, each responding to a dozen random external events. That will gives us a simple random walk around the mean. Now let's make it more interesting. Give each trader a herding tendency making it follow more closely what its nearest neighbors are doing. Turn up the herding coefficient and watch how it makes the market more erratic, ultimately turning random walk into boom and bust. ___ Edu-sig mailing list Edu-sig@python.org http://mail.python.org/mailman/listinfo/edu-sig
Re: [Edu-sig] Programming in High School
I agree that finding relevant problems that are easily solved with a quickie program is hard to find. One idea I've been toying with at Stratolab from our programming coures is having a programming game to artificially create interesting quickie programs. How about Robot Wars of the past, but you are writing your robot's logic in Python? Each student writes a little program, drops them into a folder on the network. The teacher's computer is running an Arena / Simulation. It checks the folder and loads any programs there and starts the simulation. Robots that die get deleted from the folder so students have to rewrite it and drop new copies in to see if they survive. -Winston On Dec 10, 2008, at 12:12 PM, Warren Sande wrote: David MacQuigg wrote: We need lots of examples where programming is useful to non- programmers. I already mentioned the real estate agent needing to digest some data from the property appraisers office. For the shop teacher: How about a homeowner wanting to lay tiles, avoid wastage, and slivers that look bad along the edge. If you know Python, it is quicker to write a little program than find one, purchase and install it, read the manual, struggle with a bunch of stuff you don't really need, and maybe not get what you want in the end. I can think of lots of examples in engineering, but they are not ordinary problems that would seem relevant to high school students. What we need is a collection of relevant problems, easily solved with a quickie program. These are not so easy to find. For many of these types of problems, creating a spreadsheet is more efficient that writing a program. (Why re-invent the wheel?) One could argue that having more people know how to use Excel is a good thing and goes part of the way to having a population that's more savvy at computers/math/problem- solving. That's another discussion. But the criteria of relevant problems, easily solved with a quickie program is tough to meet. Not much gets through that filter. Problems that are relevant and complicated enough to be interesting usually require a moderately complex program to solve them. The non- programmer has to make at least some investment in learning the basics (variables, loops, control structures, operators, lists, I/O) before taking on even the simplest problem-solving using a program. So we need to convince people that it's: a) not that hard and b) worth it. Warren Sande. ___ Edu-sig mailing list Edu-sig@python.org http://mail.python.org/mailman/listinfo/edu-sig Winston Wolff Stratolab - Computer Courses for Teens and Kids (646) 827-2242 - http://stratolab.com ___ Edu-sig mailing list Edu-sig@python.org http://mail.python.org/mailman/listinfo/edu-sig
Re: [Edu-sig] Programming in High School
I would think any teacher of math or science would have no difficulty using Python and integrating it into their teaching. Don't teach it as a separate subject, but introduce each new statement as it is needed. Right. That's the strategy I thought would be most practical working within the constraints of our math curriculum. I decided against doing something like a Python intro at the beginning of the semester, as student schedules are in flux for the first couple of weeks. The pace of a typical math course makes it quite possible to introduce little bits of Python here and there. The only problem has been resistance on the part of students who didn't see why they had to spend time on this when their friends in other classes didn't. That, or they were concerned that this would 'confuse' them, and they were worried about their grade. Silly stuff. And then this silly stuff would require my having to explain to various people about what this is all about. However, a lot of that has faded, and some students are even asking if we could do more Python. So that's encouraging. There is a big contrast between doing math the traditional way, solving equations by manipulating symbols in some boolean assertion to isolate a variable, vs. thinking computationally - creating sets of functions to model concepts. Introducing this stuff eventually requires rethinking the whole curriculum. But one step at a time. - Michel On Wed, Dec 10, 2008 at 7:35 AM, David MacQuigg [EMAIL PROTECTED]wrote: At 02:37 PM 12/8/2008 -0500, Vern Ceder wrote: ... here are the reasons I see that more schools don't offer programming: 1) Lack of qualified staff. Sadly a graduate with a teaching certificate (as required by the state) usually doesn't have anything like the background to teach programming, let alone do the sorts of things that Kirby has experimented with. What we need then, is not programming teachers, but teachers who are enthusiastic about technology, and use programming as a tool. I would think any teacher of math or science would have no difficulty using Python and integrating it into their teaching. Don't teach it as a separate subject, but introduce each new statement as it is needed. For-loops, as an example, could be introduced as a tool to plot functions. The, when the students are comfortable with that (and if there is time), show them a whole new and more general way of looking at for-loops (for item in collection). I remember taking a class in typing. There was a lot of stuff on proper etiquette and formatting of business letters, and emphasis on speed and accuracy, but it was one of the most valuable classes I ever took. Do they still have something like that, maybe a business skills class? Python has a special role here, in that it doesn't require a big, focused effort, as would Java. 2) Numbers - at my school, 6-10 kids in AP Programming is considered a good year. In the public schools around town, in a short-sighted drive for efficiency, (but see item 1 above also) administration routinely kills any elective that can't get 3 times that. 3) The whole integration trend in tech in education - 15 years ago it was assumed that as technology became ubiquitous we wouldn't have to teach it, any more than you need to know about electricity to turn on a light. Of course, that analogy was bogus on both ends, but schools have moved in that direction anyway, killing what little programming they did have. Only now (and only very slowly) are they realizing that their students are the poorer for it. This fits with Paul's theme that we don't need programmers because it will all be done for us, or Guido's that only the best students should study programming. I was once asked by a shop teacher why I am still doing programming. Aren't all the programs already written? We need lots of examples where programming is useful to non-programmers. I already mentioned the real estate agent needing to digest some data from the property appraisers office. For the shop teacher: How about a homeowner wanting to lay tiles, avoid wastage, and slivers that look bad along the edge. If you know Python, it is quicker to write a little program than find one, purchase and install it, read the manual, struggle with a bunch of stuff you don't really need, and maybe not get what you want in the end. I can think of lots of examples in engineering, but they are not ordinary problems that would seem relevant to high school students. What we need is a collection of relevant problems, easily solved with a quickie program. These factors (and others of course) combined with the many layers of bureaucracy create a negative feedback loop that is next to impossible for students, teachers or even parents to beat. In fact, I've talked to state education officials that nearly despair of making any headway in some of our schools. I would think the Federal government could play
Re: [Edu-sig] Programming in High School
2008/12/10 michel paul [EMAIL PROTECTED]: SNIP There is a big contrast between doing math the traditional way, solving equations by manipulating symbols in some boolean assertion to isolate a variable, vs. thinking computationally - creating sets of functions to model concepts. Introducing this stuff eventually requires rethinking the whole curriculum. But one step at a time. - Michel Yes Michel, but let's remember schoolish math isn't necessarily what the pros are doing to earn a living, with Mathematica, MathCad or whatever. Lots of degree holders in mathdom spend half their time talking to coders with humanities degrees like me, explaining what outputs from what inputs, in terms of algorithms per Knuth, i.e. the stuff you learn in K-12 isn't computer poor because of anything to do with real world mathematics in practice. The way I might do it in Portland (write ups in blogs) is take what we'd consider an advanced, college level theorem, such as Fermat's Little (not Last), and use Python to verify what it asserts, not the same thing as proving. What I say often @ Math Forum is something like: before you prove a theorem, you need to know what it means, i.e. you need to care. Having field applications helps motivate caring. We might not ever get to the proof in this class (heresy!) as these are underclassmen looking to understand RSA, haven't chosen to become mathematicians. What's so cool about Python is pow(2, 22, 23) is so easy to write and explain (no import required), whereas on a calculator you get digit overflow most the time, because of the overly small LCDs, hamster-brained programs (not open source). Per my Chicago talk, OSCONs before it, Texas Instruments is our only real competition in this picture in a business case sense, though fear of snakes (per 'Snakes on a Plane') is probably the biggest psychological barrier. North Americans are especially superstitious about snakes, owing to their making Eve do something bad in the Bible (what was it again?). Ruby has an edge in that sense (less charged) -- but then we have a Flying Circus, which helps a lot. We basically invite kids to fill in the form: pow(2, prime - 1, prime) and verify that they always get 1 for an answer. Then comes the tricky part: does that mean that if pow(2, n-1, n) returns 1, that n must be prime? Having verified it's true for like a gazillion primes, the overly casual thinker might say sure!. But of course this is a logical pitfall. if a then b does not support b therefore a. That's where we talk about Carmichael numbers, look them up on the web (OEIS). Fermat's Little is a special case of Euler's more general one about totients (lots of fun Python), in turn critical for getting RSA to work (per Knuth). All before college, looks good on your application (that you went to this cutting edge Quaker school or whatever). Kirby 4D ___ Edu-sig mailing list Edu-sig@python.org http://mail.python.org/mailman/listinfo/edu-sig
Re: [Edu-sig] Programming in High School
On Mon, Dec 8, 2008 at 6:57 AM, David MacQuigg [EMAIL PROTECTED] wrote: Kirby, This is very well written appeal, but in this mailing list, you may be preaching to the choir. What I would like to see is a discussion of *why* there is not more teaching of programming in high school. I can't seem to get an answer from the few high-school teachers and students I have asked. I suspect it has something to do with requiring all kids to have their own computers, not wanting the rich to have an advantage over the poor, etc. I've thought about teaching high school myself, but the bureaucracy seems overwhelming. It is a much more systemic problem than that. I put a lot of blame on the anti-intellectual forces in society that want education dumbed down so that they can lie to their own children, and then to the general public that grows up on this pablum. The fundamental problem is the insistence on factory-style efficiency in education, a trend started by Prussia in the 18th century. The result is that schools nearly always teach only material for which there is an official right answer, while in real life, whether business, government, the arts, or politics, all of the interesting questions have no right answer. The education of teachers was also radically dumbed-down in the Prussian system. Teachers were expected to know no more than was in the textbooks they would teach from, except at the highest levels in research universities. In this view of society, those who needed to deal with the unanswered questions on a daily basis (other than scientists and engineers) were to be children of the elite class who could afford to send them to private schools to receive an entirely different sort of education. The sort of exceedingly unpleasant system for generating leaders within an Empire that Kipling described in Stalky Co. http://www.geocities.com/Athens/Academy/6422/rev0882.html The Prussian system was put in place by a King who wanted a compliant public that would make no attempt to interfere in his planning of the next war, and by a right-wing Calvinist church movement that the King preferred over the more liberal-minded Lutherans. _All_ of the Imperial powers and the churches and business interests that supported them supported this system for public education at home and abroad. Japan and the State Shinto authorities particularly loved the German educational system. Plus ça change, plus ç'est la même chose. To come back to programming, what we have had since the introduction of personal computers in the 1970s has not been programming but so-called computer literacy, in which children might get as much as an hour or two a week in the computer lab. As an immediate consequence, nothing they learned about computers, or from using computers, could have any relevance to the curriculum. It is only now, with the advent of one-to-one computing, that we can even think of addressing this problem. If we compare the computer literacy approach to programming with the actual idea of literacy, we see that what we have been doing is pretending to think we are teaching reading and writing if we have one room in a school with 30 pencils and pads of paper, but no library, and we let kids practice handwriting for as much as an hour a week. But not at home, or in public, no of course not. But what would schools do with programming in a one-to-one computing environment? Well, I predict that if left to themselves, they would mess it up as badly as we mess up literacy, or math and science, or indeed any subject today. We only let students have access to an utterly boring and stultifying version. It is just like exposing children to killed or attenuated viruses in order to make them immune to those viral diseases. Our schoolbooks contain nothing like the versions of any of these fields that made the practitioners fall in love with the possibilities enough to put forth the effort to master some part of it, and our schools make far too many children immune to learning anything ever again. Earth Treasury has just recently, actually just yesterday, come to the conclusion that we are ready to rethink the notion of a textbook, and to rework the curriculum from top to bottom, in order to integrate Free Software into every aspect of every subject. Some things in education actually take place in the material world, of course, including gym, manual training, art, and music. Even there, the computer is an important tool. Think of all of the computerized athletic training and analysis systems of Olympic athletes and the pros; or of CAD/CAM; or digital art and electronic music. The occasion yesterday was the Program for the Future conference at the Tech Museum (San Jose CA), Adobe Systems, and Stanford, and the celebration of the 40th anniversary of Doug Engelbart's Mother of All Demos (look it up and watch the video), which laid the foundations for all modern user interfaces, and much else in software engineering, innovation
Re: [Edu-sig] Programming in High School
On Wed, Dec 10, 2008 at 1:57 PM, Edward Cherlin [EMAIL PROTECTED] wrote: SNIP The occasion yesterday was the Program for the Future conference at the Tech Museum (San Jose CA), Adobe Systems, and Stanford, and the celebration of the 40th anniversary of Doug Engelbart's Mother of All Demos (look it up and watch the video), which laid the foundations for all modern user interfaces, and much else in software engineering, innovation support, and more. We have come nowhere near realizing it all. I talked with Doug, with Alan Kay (of Dynabook, Smalltalk and GUI fame) of Viewpoints Research Institute and with Mike Linksvayer from Creative Commons (look up their cc:Learn project) yesterday, and with Sugar Labs, FLOSS Manuals, and Open Learning Exchange before that, and they are all ready to talk about how we can do all this. So let me know about any subject and age range you want to work on. This seemed an eloquent essay Edward, love poking fun at those Prussians, aka control freaks par excellance. Makes me start humming bars from Pink Floyd (hey, teacher...) just thinking about it. Safe to say, much time has elapsed and for all the whining we hear from constructivists, as if their way had never been tried, it has been, with mixed results, which is to say we've had many success stories, generations of geek reared on Dr. Spock, Vulcan Spock and beyond, given microscopes, computers, free reign, lots of adulation in school, quite the opposite of the Prussian philosophy. Result: Apple Computer, Silicon Valley, Silicon Forest i.e., thanks to the long-ago demise of top-down authoritarian thinking in some circles, we have some thriving subcultures on planet Earth where the mind runs free, bringing good things to life (GE slogan), making the world a better place etc. etc. The question is: how to spread the love? My approach is to leverage local strengths, Portland's good ats, and that's a pretty long list, including cartoon-making, music, comedy and, yes, teaching Python at a level most cities can't match, thanks to me, but also thanks to a lot of people, many unsung (so far). Tim Bauman comes to mind (one of my proteges, aka Ki Master George). Jason certainly (a fine teacher of SQL Alchemy and like that). Allison Randall, Damien Conway, R0ml, Ravencroft... a lot of us, right here on this list. I'm not saying all of these celebs live in PDX, just that there's reason to hope that we're not just now, at long last, emerging from the dark ages, as if Prussia had just folded yesterday. No, we've been enjoying the fresh air for a few generations now, and are ready to bring it on as one recent president put it (meaning something else maybe, always hard to decipher that guy, study Dan Quayle as a primer maybe?). Guido's CP4E was a continuation of a noble tradition, Alan Kay in the lineage, or Kenneth Iverson in my case (I encountered Alan much later, long after I'd fallen in love with APL at Princeton, Alan then in his kill Smalltalk slayer chapter (more in this archive)) I think the right approach is to think in terms of an svn tree, i.e. a trunk with many branches. We're *not* all converging to the same page (this won't be Prussia again, don't worry). Some of us, like me, will probably use J quite a bit, because of the APL heritage. Others will use Scheme / LISP, that Big Lambda family (Python's is little lambda). It's not about finding the one right way to do it (Prussian fallacy) but rather one of encouraging local faculties to seize control of their own destinies and not wait for big publishers to show them how it's done. We already have Cut the Knot, Mathworld, gazillions of math-oriented YouTubes. We're awash in relevant curriculum materials. The last time I said anything about Kusasa (which was quite awhile ago), it was to suggest there was no need for any new curriculum writing whatsoever, just people need time to catch up, process what's already out there. Of course that's a pretty stupid thing to say to a bevy of curriculum writers rarin' to go, but I think you see my point anyway. There's a documentary on Britney Spears on my TV at the moment, gotta run. She's one of those music millennium geeks I really appreciate these days, love how she figures into our circus, no dummy that gl. http://mybizmo.blogspot.com/2008/10/pythonic-math.html Kirby ___ Edu-sig mailing list Edu-sig@python.org http://mail.python.org/mailman/listinfo/edu-sig
Re: [Edu-sig] Programming in High School
Daniel Ajoy schrieb: But the criteria of relevant problems, easily solved with a quickie program is tough to meet. ... And another point is that some problems cannot be solved using algebra or trig. I believe this is one: http://neoparaiso.com/logo/problema-triangulos.html It asks the student to determine the values of the segments a and b. This is a nice problem, which could also find an easy solution in Python, not only in Logo, of course ;-) Like the on attached one, for instance. I'd only like to add a few remarks to the problem discussed in this thread - which I also know very well as a high school teacher in Vienna, Austria. (1) One root of the problem seems to be that whatever relevant problem we pose, there are *a lot* of different adequate tools to approach it in these modern times and it is by no means clear that programming is the 'natural' approach. See for instance http://www.rg16.at/~glingl/triangle/ for a different solution to Daniel's problem. (2) To profit from beeing able to program needs continuous practice. So as a teacher of a math class you had to convince *all* of your students to do it continually. (3) This - at least here in Austria - seems to be impossible as long as programming is not part of the official math curriculum (like for instance the appropriate use of a pocket calculator). Even core math is not done by *all* students on their own free will, because they enjoy it, or they are interested in it, but by some of them often only because they *need* it for their gradutation. And I suppose that programming will never be part of the standard curriculum, even if only because only a small part of the maths teachers are proficient in programming. So they naturally would oppose such a change. (4) Moreover it seems to me, that even in the area of computer science or computer technology the part which is occupied by programming is getting smaller. 25 years ago, if you wanted to do some interesting things with a computer, you *had* to be able to program, while nowadays there are so many interesting things you can do without programming. For instance what do you think, which part of the people working in the comuter game industry are programmers? I suppose, this trend also diminishes the young people's interest in programming (as well as the school authorities interest in putting programming into the mainstream curricula.) (5) Despite all of this I'd also like to contribute a problem, I stumbled over yersterday, incidentally. It might not be 'relevant' but it's also one that most probably couldn't be solved without computers and which without doubt has the potential to stimulate the student's interest in math as well as computing: Christian Goldbach (1690-1783), stated several number theoretical conjectures, among them the famous Goldbach conjecture, concerning the set of even numbers 2. An other (similar) one is the following: every odd positive integer could be written in the form p + 2*a**2, where p is a prime (or 1, then considered a prime) and a =0 is an integer. Example: 23 = 5 + 2*3**2 (to use Python notation). Euler checked this conjecture for odd numbers up to 2500 and he didn't find a counter example. Only a century later two counter examples were found in the range below 1. What are these two numbers? The curious thing is, that to this day these two numbers remain the only ones found. Regards Gregor Daniel ___ Edu-sig mailing list Edu-sig@python.org http://mail.python.org/mailman/listinfo/edu-sig # Daniel Ajoys triangle problem # from Edusig, 10. 12. 2008 from turtle import * def triangle(wx): penup(); home(); pendown() forward(130) left(180-38) forward(wx) setheading(180 + towards(0,0)) forward(70) right(180-101) forward(88) #stamp() return ycor() setup(500,250) mode(world) reset() fd(250) triangle(80) triangle(50) # no-frills graphical solution # of course one could play around with colors etc... wx1 = 80 wx2 = 50 epsilon = 0.1 while True: wx = (wx1 + wx2)/2.0 y = triangle(wx) if abs(y) epsilon: print Solution:, wx break if y 0: wx1 = wx else: wx2 = wx setworldcoordinates(190, -2.5, 200, 2.5) write(str(pos())+ for wx = + str(wx)) ___ Edu-sig mailing list Edu-sig@python.org http://mail.python.org/mailman/listinfo/edu-sig
[Edu-sig] computer algebra
So I've been yakking with Ian (tizard.stanford.edu) re the new fractions.py, installed in Standard Library per 2.6, saw it demoed at a recent user group meeting (PPUG). Python's __div__ is similar to Mathematica's computer algebra notion of division in that you're free to divide any type by any type, providing this makes any algebraic sense, using a kind of liberal duck typing. What I mean by that is __div__ by itself doesn't pre-specify anything, so if there's a meaningful way to deploy the division operator between arguments A, B, then go ahead and do it, write you code accordingly. In Java, we could write __div__ in all different ways depending on valid type permutations (not that Java has operator overloading, just stricter typing at write time means you've gotta post guards at the gate in your methods). Python, with late binding, duck typing, won't post guards, but you'll still need to write algorithms capable of sorting out the possibilities. Maybe the user throws you a matrix? Has an inverse. OK, so __div__ makes some sense... fractions.py in contrast, implements the narrow Q type, the rational number, defined as p / q where p, q are members of the set integers. One could imagine a Fraction class that eats two complex numbers, or two Decimals. Computer algebra attaches meaning here, as in both sets we're able to define a multiplicative identity such that A / B means A * B**(-1) i.e. A * pow(B, -1) i.e. A * (1/B). So the results of this operation, Fraction(A, B), might be some object holding the Decimal or Complex result. In generic algebra, everything's a duck, although conversion between types is possible (yes, that sounds nonsensical). fractions.Fraction, on the other hand, barfs on anything but integers, isn't trying to be all divisions to all possible types, isn't pretending this is Mathematica or a generic CAS. Note that I'm not criticizing fractions.py in any way, am so far quite happy with it. I'm simply drawing attention to some fine points. Related: When I went to all the trouble to compose two functions, f and g, using __mul__, I'd get comments like: but the open oh (another symbol) is the composition operator i.e. you're only using * because ASCII doesn't include the 'open oh'. However, I was making a different point: that in group theory math texts, we're proud to use regular multiplication and division operators for such operations as compositions of functions because we're thinking __mul__ and __div__ have that generic meaning -- we neither need, nor want, the proliferation of symbols the open oh people think we must need. Note that by open oh I'm not talking about big oh, a different notation that I don't think is redundant, agree with Knuth that if your calculus book doesn't include it, you're probably in one of those computer illiterate schools (ETS slave, whatever). Kirby ___ Edu-sig mailing list Edu-sig@python.org http://mail.python.org/mailman/listinfo/edu-sig
Re: [Edu-sig] computer algebra
On Wed, Dec 10, 2008 at 6:47 PM, kirby urner [EMAIL PROTECTED] wrote: So I've been yakking with Ian (tizard.stanford.edu) re the new fractions.py, installed in Standard Library per 2.6, saw it demoed at a recent user group meeting (PPUG). Python's __div__ is similar to Mathematica's computer algebra notion of division in that you're free to divide any type by any type, providing this makes any algebraic sense, using a kind of liberal duck typing. What I mean by that is __div__ by itself doesn't pre-specify anything, so if there's a meaningful way to deploy the division operator between arguments A, B, then go ahead and do it, write you code accordingly. Or unmeaningful! Unlike (I presume) Mathematica, Python doesn't mind if you define a/b as multiplication. Your users might mind though. :-) In Java, we could write __div__ in all different ways depending on valid type permutations (not that Java has operator overloading, just stricter typing at write time means you've gotta post guards at the gate in your methods). Python, with late binding, duck typing, won't post guards, but you'll still need to write algorithms capable of sorting out the possibilities. Maybe the user throws you a matrix? Has an inverse. OK, so __div__ makes some sense... fractions.py in contrast, implements the narrow Q type, the rational number, defined as p / q where p, q are members of the set integers. One could imagine a Fraction class that eats two complex numbers, or two Decimals. Computer algebra attaches meaning here, as in both sets we're able to define a multiplicative identity such that A / B means A * B**(-1) i.e. A * pow(B, -1) i.e. A * (1/B). It's not so easy though. The specific purpose of the Fraction class is to always reduce the fraction to a canonical representation using the GCD algorithm (e.g. 15/12 becomes 5/4), which only applies to integers. So the results of this operation, Fraction(A, B), might be some object holding the Decimal or Complex result. In generic algebra, everything's a duck, although conversion between types is possible (yes, that sounds nonsensical). fractions.Fraction, on the other hand, barfs on anything but integers, isn't trying to be all divisions to all possible types, isn't pretending this is Mathematica or a generic CAS. Fortunately Python supports a way of overloading binary operators where it is sufficient if *one* of the operands knows how to deal with the other. So Fraction(3, 4) * 2j happily returns 1.5j. You don't have to teach Fraction about Matrix if you can teach Matrix about Fraction. Note that I'm not criticizing fractions.py in any way, am so far quite happy with it. I'm simply drawing attention to some fine points. Related: When I went to all the trouble to compose two functions, f and g, using __mul__, I'd get comments like: but the open oh (another symbol) is the composition operator i.e. you're only using * because ASCII doesn't include the 'open oh'. However, I was making a different point: that in group theory math texts, we're proud to use regular multiplication and division operators for such operations as compositions of functions because we're thinking __mul__ and __div__ have that generic meaning -- we neither need, nor want, the proliferation of symbols the open oh people think we must need. There are different schools of thought about this actually. I don't think pride comes into it. Inventing and using specialized symbols is often useful in math because it provides more context. If you write f * g the reader would need to know in advance that f and g are functions or else they wouldn't know what was meant. But if you write f o g then the reader can *infer* that f and g are functions. Python happens to use the former (overloading based on argument types); Python's predecessor ABC used the latter (type inferencing based on operators). Neither is necessarily better than the other. There are also fields of mathematics where both are used, with a different meaning; e.g. f o g would mean functional composition while f * g could mean the function you get by multiplying f(x) and g(x). In Python: def open_oh(f, g): return lambda x: f(g(x)) def star(f, g): return lambda x: f(x) * g(x) Note that by open oh I'm not talking about big oh, a different notation that I don't think is redundant, agree with Knuth that if your calculus book doesn't include it, you're probably in one of those computer illiterate schools (ETS slave, whatever). I think that comment is a little out of line. BTW big Oh is not part of calculus, it's part of complexity theory, a totally different field (more relevant to computers than calculus though). -- --Guido van Rossum (home page: http://www.python.org/~guido/) ___ Edu-sig mailing list Edu-sig@python.org http://mail.python.org/mailman/listinfo/edu-sig
Re: [Edu-sig] computer algebra
On Wed, Dec 10, 2008 at 8:27 PM, Guido van Rossum [EMAIL PROTECTED] wrote: SNIP There are different schools of thought about this actually. I don't think pride comes into it. Well, *my* school is quite pompous about it. We think open oh is for sissies. But that's just us (quirky). Others more sobering. GOOD STUFF Note that by open oh I'm not talking about big oh, a different notation that I don't think is redundant, agree with Knuth that if your calculus book doesn't include it, you're probably in one of those computer illiterate schools (ETS slave, whatever). I think that comment is a little out of line. BTW big Oh is not part of calculus, it's part of complexity theory, a totally different field (more relevant to computers than calculus though). Not part of calculus as commonly taught today, but *would* be if Donald Knuth had his way: http://micromath.wordpress.com/2008/04/14/donald-knuth-calculus-via-o-notation/ Kirby -- --Guido van Rossum (home page: http://www.python.org/~guido/) ___ Edu-sig mailing list Edu-sig@python.org http://mail.python.org/mailman/listinfo/edu-sig
Re: [Edu-sig] computer algebra
The problem is that calculus tends to deal with the concept of infinitesimally
small and O(eps) is used for small eps. Computer Science tends to deal with
complexity and O(n) is used for large n. The Big-Oh definitions are different:
i) In calculus f(x) in O(g(x)) iff lim_{x\rightarrow 0} f(x)/g(x) \infty
ii) In CS f(x) in O(g(x)) iff lim_{x\rightarrow\infty} f(x)/g(x) \infty
It is common to use (i) to teach calculus (I was thought that way) but it is
not common to use (ii) to teach algorithms. I do so in my notes for Design and
Analysis of Algorithms [1]
and students like it but many computer scientists believe that using limits is
just an extra step.
Massimo
[1]http://bazaar.launchpad.net/%7Emdipierro/algorithms-animator/devel/download/3/csc321notes.pdf-20080914191632-ofooevmsoqqnkrpz-6/csc321notes.pdf?file_id=csc321notes.pdf-20080914191632-ofooevmsoqqnkrpz-6
From: [EMAIL PROTECTED] [EMAIL PROTECTED] On Behalf Of kirby urner [EMAIL
PROTECTED]
Sent: Wednesday, December 10, 2008 10:39 PM
To: edu-sig@python.org
Subject: Re: [Edu-sig] computer algebra
On Wed, Dec 10, 2008 at 8:27 PM, Guido van Rossum [EMAIL PROTECTED] wrote:
SNIP
There are different schools of thought about this actually. I don't
think pride comes into it.
Well, *my* school is quite pompous about it. We think open oh is for sissies.
But that's just us (quirky). Others more sobering.
GOOD STUFF
Note that by open oh I'm not talking about big oh, a different
notation that I don't think is redundant, agree with Knuth that if
your calculus book doesn't include it, you're probably in one of those
computer illiterate schools (ETS slave, whatever).
I think that comment is a little out of line. BTW big Oh is not part
of calculus, it's part of complexity theory, a totally different field
(more relevant to computers than calculus though).
Not part of calculus as commonly taught today, but *would* be if
Donald Knuth had his way:
http://micromath.wordpress.com/2008/04/14/donald-knuth-calculus-via-o-notation/
Kirby
--
--Guido van Rossum (home page: http://www.python.org/~guido/)
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