First, I would like to thank everyone who has written with expressions of support for our project and wishes for its success. It is still a very early stage and obviously success is not guaranteed. However, I think that if the results do not turn out as we expect we will have only ourselves to blame, for the starting conditions are almost ideal. Essentially we have got now everything that I have ever wanted and could expect to get for this sort of purpose and I think we have a very good plan so I think it is now a question of whether we still have enough energy for the implementation and how much our other commitments interfere with this. Fortunately my main partner in this enterprise is a young female mathematician (about the same age as my daughter) who is quite knowledgable about Mathematica, has been using it for a few years for really serious research work and (unlike me) is full of energy and not so easily distracted.
The idea of this project has been maturing in my mind for many years, most of which I spent teaching at universities in Japan. In my last Japanese university Mathematica was used quite extensively but basically only for teaching calculus. That worked about as well as described by others in many posts recently and in more distant past. There were the usual problems: the competition for time between mathematics and Mathematica, the fact that a Mathematica based course had to be taught by a Mathematica enthusiast or it would not be taught at all, and, perhaps the most serious, that, since Mathematica could not be used in the examinations, students had little incentive to devote enough time to it to get to the point where they could do things that were non trivial enough to be enjoyable. Already then I had some ideas of how one could attempt to overcome these difficulties but being a "gaijin" I was a little too isolated even to get an opportunity to test them. The situation changed quite radically in this respect when I moved over here.
The main idea, not particularly original but, it seems to me, rather rarely tried, is that students should be the main "driving force" of this kind of project. The problems with faculty driven projects have already been discussed many times and they seem to be the same everywhere. The situation here is similar to other places: in the mathematics department we have a few mathematica users, a few users of other mathematical programs and a lot more people who use computers mainly for e-mail and perhaps Latex (there are also some who still prefer pen and paper). But almost everybody I have talked to, is in favour of the idea of students being able to use math software for the purpose of illustrating geometrically the concepts taught in lectures (almost everyone likes this aspect and most people with they had more skill in this area, but of course are not willing to spend any time on acquiring them). Using software for computations, as have been noted, is more controversial. Generally most mathematicians are indeed opposed to computers being used for computations in the "normal course" but are quite happy about additional "computation centred" courses in the same are being available, so this is another thing we are attempting to realise.
Returning to "conceptual illustrations" (rather than straight "computations"): although as has been noted, there is an enormous number of all kinds of mathematical illustrations on the Internet, including Java animations and the Wolfram Demonstrations site, yet what is available is very often not quite what is wanted. One reason for that is probably that the maths department at Warsaw University sees itself as a rather elite institution. One result of that is that many of our courses are "monographical" and lecturers try to avoid "standard" examples or "cliche" problems. We do not, in fact, teach calculus in the sense that this term is used in the US - instead we have analysis courses with detailed proofs even for computer science students. Topics such as "integration techniques" are dealt with in one lecture, and we never have exam problems in which students are simply asked to compute some integral. It is assumed that many of these techniques they had already learned in high school or, if not, can learn by themselves from textbooks. So the issue of using (or not using) Mathematica to do this sort of calculations hardly arises. Instead one needs to find, what I would say are, more subtle ways of using Mathematica. One such "technique" that I try to stress to students is in connection with proofs of and counterexamples to mathematical statements.
Problems here are rarely formulated in the form "prove the following statement". Instead, the usual form is "prove the following statement, if it is true, and if not, find a counter-example." Now, in this sort of situation, which resembles real research in mathematics, often the hardest thing is to decide whether one should attempt to prove a result or to look for a counter-example. It is in this sort of situation that looking at sophisticated graphic illustrations, or computing special cases, and generally experimenting with Mathematica can very often (particularly in problems in real and complex analysis) be very helpful. In fact this is how I myself almost always approach any problem that is susceptible to this sort of treatment (unfortunately a lot of my own research, being concerned with infinite dimensional objects, is not).
One important element in this idea of "making students the driving force" is that we have many rather good students, which means they are capable of taking an additional work-load and that (and this is based on experience) the majority of them enjoy Mathematica. It will probably be incomprehensible to RJF, but this seems particularly true of many of our computer science students. One reason is that quite a few of them are naturally inclined to mathematics as well as computer science. In fact, every year, some of them decide that they would rather be mathematicians (which is perhaps why we teach them all this abstract mathematics, a lot of which is probably irrelevant to computer science) and some end up with two degrees - in math and in computer science. Often for these students, probably for reasons that are very similar to those described by David Bailey in his very insightful post) find an approach to mathematics via Mathematica more congenial to their way of thinking than the traditional somewhat "Bourbakist" approaches which still prevail among mathematicians. Another reason why computer science students are natural audience of Mathematica based mathematics courses is that none of them suffer from "computer allergy" that is still quite common among older mathematicians and is sometimes found among younger ones, and that, of course, they find programming very easy, which is not necessarily true of all mathematics students. In fact, I have noticed that computer science students, who often are already familiar with quite many different languages (they often start programming long before entering university) find programming in Mathematica intriguing and fun and quickly learn to do (for me) quite amazing things.
Of course, another important thing was making sure that students can actually get credit for doing work in Mathematica. The fact that they also enjoy it helps, but students are human and like other humans are not likely to do much serious work for nothing.
Well, there is plenty more I could still say on this topic, but I have to get back to other things. So I just wanted to make a final comment on one other matter. It's nothing new, I have written this before and it is something that I differ about with some of the persons who have posted in this thread. Briefly, I am not an enthusiast of using Mathematica for "simple" symbolic manipulation. I am sure that may view of this is the same as that of the great majority of mathematicians and that the reason for this is not "conservatism". Generally we believe that in mathematics computers should be used to do things that are too hard or too time consuming for humans and human beings should do the things that humans find easy. The reasons for this are practical (this is the only way to really remain "in control" of your work - which is essential to avoid producing nonsense) and educational (doing symbolic and even numerical computations by hand is an essential activity that is needed to acquire understanding of concepts). Of course I do not object to Mathematica having capabilities I do not need or intend to use or teach. If other people find them useful, they could be a selling point for Mathematica and help to pay for the development of more features that I want (of course, as long as the issue of excessive complexity of interface is kept under control).
On 27 May 2013, at 10:24, Ingolf Dahl <email@example.com> wrote:
> Andrzej, > I think this really sounds interesting, and hope to hear more about your > experiences later here. Of course there are questions and problems with it, > all new projects are "impossible" in one or another way. The really > interesting thing is to know if these impossibilities can be handled in some > good way. Good luck! > > Ingolf Dahl > Sweden > >> -----Original Message----- >> From: Andrzej Kozlowski [mailto:firstname.lastname@example.org] >> Sent: den 25 maj 2013 11:42 >> To: email@example.com >> Subject: Re: Work on Basic Mathematica Stephen! >> >> Well, to disappoint everyone I have to confess that here, at Warsaw > University, we are >> going to have a university wide course in Mathematica, open to all > students of mathematics, >> natural sciences, economics and finance and even (oh horror!) computer > science (in fact, I >> am not in the process of trying to "sell" this course to my the students > in my analysis for >> computer science class). We have actually received a grant, quite > substantial by Polish >> standards, to implement such a course, and, of course, since everyone > likes extra money, this >> has meant that there has been no opposition or grumbling about it from any > "old fogies" >> (except perhaps one guy who complained that Mathematica was not open > source but we >> quickly stifled him). >> >> An even greater heresy: the course also is going to involve some knowledge > of Wolfram >> Alpha: in fact it is entitled "Mathematics with Mathematica and Wolfram > Alpha". (To RJF - >> no, we are not going to teach anything about any other CAS. If anyone > likes to use >> something other than Mathematica they can learn it itself, but won't get > any credit for it). >> Actually, our course is going to be a "supervised, self-study and Internet > based course". In >> other words, we (the project authors, who are getting paid for designing > and realising it) will >> prepare study materials (scripts, videos, problems in different > disciplines that can be solved >> with the help of Mathematica or Wolfram|Alpha, tests, etc. but there won't > be any lectures. >> There will however be tests and students will be able to get credit for > passing them - >> otherwise, of course, it would be hard to get them interested. >> >> A large part of the grant is for buying a fairly large number of copies of > Mathematica (in >> addition to the ones that are already here). >> >> Our motives for designing this project are quite selfish (and I don't only > mean the fact that >> we are going to be paid for this). There are several of us who want to use > Mathematica in >> our courses and it is a pain to have to waste time on teaching students > the basics of >> Mathematica. Soon there will be several new courses available to math and > science students >> in which Mathematica will be used. One of them is a new course on the > differential >> geometry of curves and surfaces, which will be offered in addition to the > already existing >> one which does not use any computer software. (Students will be able to > take both >> sequentially - they are going to be sufficiently different for this to > make sense). There is also >> a course that I have taught in the past, for which there has been a big > demand among >> students of finance - on modelling jump processes. Contrary to the strange > ideas RJF got >> from my earlier post, this is not something that statistics packages have > been doing for years, >> actually it involves things that are pretty new (so much that there are > still unresolved >> problems with some of the >> algorithms) and, in fact, I am proud to admit to having played a certain > role in this >> implementation in Mathematica. >> >> We actually have quite a few people here who although they themselves > don't use >> Mathematica or CAS systems at all, have shown a lot of interest in having > students learn >> such things. The main interest is, in fact, not so much in symbolic > computation but in >> graphics used to illustrate various phenomena in topology, complex > analysis etc. Although >> one might expect that there should already be lots of such illustrations > available on the >> Internet (or even on Wolfram's Demonstrations Site" >> this does not seem to be actually the case. >> >> Of course, all of this is at this time only in its infancy. About a year > from now I should be >> able to say something about the success or failure of this project. At > this time the thing that >> worries me the most is the amount of work I foresee in trying to realise > all we have promised >> in the proposal. >> >> Andrzej Kozlowski >> >> >> >> On 24 May 2013, at 12:27, mathgroup <firstname.lastname@example.org> wrote: >> >>> I had to chuckle at your use of the word 'conceal'.....unfortunately, >>> I agree with your comment....mentioning Mathematica seems akin to >>> treason.....that was the reaction I felt... >>> >>> >>> jb >>> >>> >>> -----Original Message----- >>> From: Murray Eisenberg >>> Sent: Thursday, May 23, 2013 10:00 AM >>> To: mathgroup >>> Subject: Re: Work on Basic Mathematica Stephen! >>> >>> This is not an uncommon situation at colleges and universities. >>> >>> Too many of the old fogies -- and, more dangerously, the "young >>> fogies" -- know about Ma. . t. .b and cannot imagine why anybody who >>> needs to do computing would use anything else. After all, it was good > enough for them. >>> (Exception: Canadians who thing the same about M . . . e.) >>> >>> Similarly, too many mathematicians cannot see why their students >>> should not learn how to carry out long and complex symbolic >>> calculations, e.g., symbolic integration, with paper and pencil; after > all, they had to do it. >>> Oddly enough, some of these same mathematicians use powerful symbolic >>> programs to do their own research in number theory, algebraic geometry, > etc. >>> >>> But I'm sympathetic to the view that there shouldn't be a course in a >>> mathematics department on Mathematica per se. Just as there shouldn't >>> be a course there in LaTeX per se. Just as Computer Science >>> departments say they don't have a course in any programming language. >>> >>> So if one is to make any headway, then one has to almost conceal the >>> Mathematica within a mathematics course whose subject is some >>> mathematical topics, or an engineering course whose subject is some >>> engineering topic, etc. Just as, e.g., in some "junior year writing" >>> courses taught by math departments, LaTeX is introduced and students >>> have to do some or all of their papers in LaTeX. Or a mathematics >>> department course in complex analysis where small teams of students do >>> projects presenting some topic via a Mathematica notebook (where a >>> couple of the projects might be teaching some Mathematica basics). >>> >>> Perhaps this "sneaky" way is not the most efficient way for teaching >>> and learning Mathematica, but it can work. In fact, Stephen Wolfram >>> wrote in "The Mathematica Book" some years ago that, after learning a >>> few basics and trying some simple examples from the book (today, the >>> Documentation Center), "You will probably find it best to start by >>> picking a specific problem to work on. Pick a problem that you >>> understand well. . . Then go through each step in solving the problem, >>> learning what you need to know about Mathematica to do it." >>> >>> >>> On May 23, 2013, at 4:10 AM, mathgroup <email@example.com> wrote: >>> >>>> David... >>>> >>>> But that was exactly my point...I tried so hard with our Community >>>> College and University to get Mathematica into the curriculum....or, >>>> as I said, to give some lectures and examples on the use of >>>> Mathematica....and ALL of them, Engineering, Math and Physics Depts >>>> said 'Thanks but No Thanks', as if they have something against >>>> Mathematica....It seemed that the idea that students would not use >>>> pencil and paper in as laborious a manner as possible really bothered >>>> them....Not once did they think perhaps this might lead to a real >>>> enjoyment of technical subjects and perhaps to much better >>>> understanding of their course work......even when I was working I was >>>> affectionately known as 'The Mathematica Nut'...although, I'm >>>> reminded of something that Nietzsche said.... >>>> >>>> "Overzealousness on the part of one person can lead the others to >>>> Apostasy"..... >>>> >>>> jerry blimbaum >>>> >>>> -----Original Message----- >>>> From: djmpark >>>> Sent: Wednesday, May 22, 2013 9:28 AM >>>> To: 'mathgroup ' ; firstname.lastname@example.org >>>> Subject: Re: Work on Basic Mathematica Stephen! >>>> >>>> It will be done by example. Several people will work together, >>>> exchanging Mathematica notebooks or working on a common notebook. The >>>> notebooks will be what I call "literate"; they will look something >>>> like a technical paper or report, but they will take advantage of all >>>> the active and dynamic features of Mathematica, and contain generated >>>> knowledge in the form of active and immediately accessible routines >>>> and definitions developed in the course of the effort. >>>> >>>> The notebooks will be of higher integrity than paper and pencil work, >>>> or using Mathematica as a programmed calculator and copying out >>>> because of all the self-proofing and additional checks that can be >>>> performed. (Of course, one can still make errors but they should be >>>> rarer and not the common >>>> variety.) >>>> >>>> That all this can be done in a single application is a tremendous >>>> advantage. >>>> >>>> Someday other people will see what they are doing and the advantages >>>> are so great they will want to do the same thing. The task is getting >>>> more people to write and use good examples. >>>> >>>> >>>> David Park >>>> email@example.com >>>> http://home.comcast.net/~djmpark/index.html >>>> >>>> >>>> >>>> >>>> From: mathgroup [mailto:firstname.lastname@example.org] >>>> >>>> I want to comment on my experience , limited of course, with >>>> students of Engineering, Engineers and Professors of >>>> Engineering.....my background is Physics... >>>> >>>> First, I get the impression that , in the main, Symbolic >>>> Computation, etc. >>>> is not something they are really interested in......After I retired, >>>> I took several courses in Electromagnetics, one Graduate and the >>>> other Undergraduate......No one suggested the use of or taught the >>>> potential applications of Mathematica....Even in the Graduate course, >>>> I was the only student using Symbolic software ......in fact, the >>>> students did everything by hand and whenever something required >>>> software, such as Antenna patterns, out came M-------b with some code >>>> , etc....and that was the end of it....So, the students knew no >>>> better....and the Professors didn't care or weren't interested >>>> themselves in the benefits of learning and solving problems >>>> Symbolically....I asked one Professor if I could give a class lecture >>>> on the >>>> use of Mathematica for Electromagnetics...He agreed but than said 'I > can >>>> only give you about ten minutes'....I respectfully declined the > offer.... >>>> >>>> So, how does WRI expand its market?....IMO, there have to be >>>> dedicated Teachers on how to use Mathematica in what I'll call the >>>> Research Mode not just define given functions from the text and plot >>>> it.......from what I have seen of the attitude of Instructors and >>>> Professors I'm anything but Optimistic....I went to our local >>>> Colleges and suggested a sequence of courses in Mathematica ending >>>> with Animation and Simulation....That got me nowhere especially with >>>> the Math Depts...so, in part, I see people who are stuck in pencil >>>> and paper and refuse to get out of it.... >>>> >>>> Again, of course, this is my limited experience...Perhaps others have >>>> had different and better ones... >>>> >>>> Jerry Blimbaum >>>> >>>> >>>> >>>> -----Original Message----- >>>> From: email@example.com >>>> Sent: Sunday, May 19, 2013 4:50 AM >>>> To: firstname.lastname@example.org >>>> Subject: Re: Work on Basic Mathematica Stephen! >>>> >>>> I have (maybe) a minority perspective on Mathematica being an >>>> engineer. I used it long ago at university at version 1. The next >>>> time I would use it would be a wolfram approved ebay purchase of >>>> version 4. I have used it ever since, but am still rookie in some >>>> ways. >>>> >>>> I believe WRI is attempting to broaden the user base rather than >>>> deepen the product. They are doing this by adding (from our >>>> perspective) non-value add features to lure people in. The argument >>>> is the learning curve is less which should lead to greater sales. >>>> This is not how it works at any place I have been. >>>> >>>> The only engineering sales force that matters is engineers. If they >>>> can't argue for the product, it will not happen. Engineers can't >>>> argue for something they are unable use until after purchase and >>>> additional training. >>>> If you want engineers to demonstrate something or argue for it, you >>>> have to do more than offer wizards and connections to WolframAlpha >>>> which only apply after the sale. Engineers need to show >>>> understanding and capability. >>>> Managers have to show accounting they are saving money by buying >>>> Mathematica. Improvements in quality of OUR products or ability to >>>> address greater problems is not quantifiable to the brigade of MBAs >>>> who run modern businesses. There has to be quantifiable savings. >>>> This has to be demonstrated by engineering staff before purchase and >>>> framed in terms of reduced need for time (salary expense). >>>> >>>> I think this can only be achieved by making the online education >>>> material targeted to a specific audience. This material must solve >>>> real problems in a way that conveys the underlying capability. >>>> >>>> I have been told by WRI that most users will only use 5% (at most) of >>>> Mathematicas total ability. LoL, if only everyone would use the same > 5%. >>>> >>>> If you want us to be able to sell it, you have to provide training >>>> for free so we can get started solving engineering problems prior to >>>> purchase. >>>> Combine this with a 60 day trial and you could save a lot of WRI >>>> development dollars on bells and whistles that won't increase sales. >>>> Help us help you! >>>> Stop trying to treat sales tools as a profit center! >>>> >>> >>> --- >>> Murray Eisenberg > email@example.com >>> Mathematics & Statistics Dept. >>> Lederle Graduate Research Tower phone 413 549-1020 (H) >>> University of Massachusetts 413 45-2838 > (W) >>> 710 North Pleasant Street fax 413 545-1801 >>> Amherst, MA 01003-9305 >>> >>> >>> >>> >>> >> > > >