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These are replies submitted by DJKeenan

I cannot guarantee anything, but I have had no trouble running older worksheets—even from before Maple 9—with Maple 11. Also, I second JacquesC's comments about the reliability of the user interface in 11 (quite good, not flawless) and 9.5 (bordering on unacceptable). I had a related blog entry on this. More generally, there are many small (undocumented) improvements to reliability in Maple 11. I suggest upgrading.
… the name “martingale” derives from a French acronym for the gambling strategy of doubling one's bets until a win is secured. —Karlin S. & Taylor H.M., A First Course in Stochastic Processes (Academic Press, 1975), p.238.
Maple does significant theorem proving "under the hood". Also, have you looked at is? That can be invoked to prove some things. There are admittedly limitations; for example, not even Maple 11 can prove the Riemann Hypothesis. Could you give an example of what you would like to do?
I agree—that sounds good.
This discussion is interesting, but it is off-topic. I have set up a separate thread for documentation issues. Let's keep this thread for discussing whether/how Maple 11 changed the way you do mathematics.
I believe that Maple is now more than a tool. There is a post about this on my blog.
Note. In another thread, I raised the issue of document mode versus worksheet mode, and some respondents did not fully understand the distinction. To clarify, the following four things are different:
2D input in document mode;
2D input in worksheet mode;
1D input in document mode;
1D input in worksheet mode. (The Help system explains the differences.)
Maybe it would be good to be able to turn off implicit multiplication (in 2D input). I have been burned by implicit multiplication a few times. The issue likely arises from the desire to have copy/paste of 2D output (with its implicit multiplication) work. And that desire is understandable.
I support having a bug forum. It would be especially nice if there were a tag to indicate each bug's status (not-a-bug; documentation issue; to-be-fixed at priority k; fixed in release N; really a feature request; etc.). One potential problem might be antagonists, like V. Bondarenko, who do not seem to have Maple's best interests in mind. How would this be addressed?
I believe he means that the Help pages for apply, unapply, etc. should link to the Help page for curry. I agree with that, and have raised this general issue about Help pages before. The apparent unawareness of the curry function by other people with substantial Maple experience really supports the usefulness of such Help links.
I believe he means that the Help pages for apply, unapply, etc. should link to the Help page for curry. I agree with that, and have raised this general issue about Help pages before. The apparent unawareness of the curry function by other people with substantial Maple experience really supports the usefulness of such Help links.
Big J, I agree that an engineer should not usually have to develop his/her own tools in their professional work. Indeed, I would strongly advocate using Maple or similar, for example. I also think, though, that an engineer should have some understanding of how the tools work. In the weather forecasting analogy, the forecasters need not develop their own forecasting models, but they should roughly understand what data assimilation is. The main point is that all tools have strengths and weaknesses, and a good appreciation of those is important. Such an appreciation requires having some understanding of how the tools work. Otherwise, sooner or later, you will get burned. Another example is with numerical analysis: I think every software specialist should know something about the issues, even though only a few will actually write high-performance numerical routines. Yet most CS grads will complain that all this stuff that they learned in school is never used in their work. Does that sound familiar?! Mariner, both JacquesC and I have had substantial contact with engineering, even if we are not engineers. I was curious though—are you an engineer and if so, for how long?
If by "weatherman" you mean the person on television who reads the weather forecasts, then I agree. But such people are chosen in part because of their physical attractiveness and actually knowing much meteorology is not really necessary (even though it is often officially required—perhaps for promotional purposes). If, however, you mean a person who forecasts the weather, then you and I do not agree. It is true that many (most?) meteorologists are uncomfortable with the math in their discipline. But that does not imply that better mathematical understanding could not substantially improve their results. Let me give an example. In meteorology, "data assimilation" concerns the development and investigation of most techniques used to produce an estimate (termed an “analysis”) of the state of the atmosphere (its fields of temperature, winds, pressure, humidity and perhaps trace chemical constituents) at an instant in time given an incomplete, inaccurate, and diverse set of observations. Generally, a greatly-insufficient number of observations at any single time is augmented by extrapolating additional prior observations to that time by using a forecast model. (Some advanced techniques also consider observations at times in the near future, again using a model to connect times.) The observations are therefore considered as being “assimilated” by the model. Data assimilation is grounded in estimation, control theory, and inverse modeling. When, however, a colleague gave a seminar extolling the fact that data assimilation is a fundamentally statistical problem—because it attempts to blend diverse, but imperfect, information—the response that he received was “We are doing deterministic rather than statistical data assimilation”. This is a fantasy that illustrates an extreme lack of understanding of basic aspects of data assimilation. A fantasy, moreover, held by people who were far from novices in the field. My belief is that those people could improve their performances if they did not have such fantasies (there were presumably more than this one). And that means understanding more of the math.
I do not see how you could be a top engineer without being able to use advanced mathematics. More generally, the trend in most of the commercial world is increased use of mathematics. Have you ever used Amazon?—there is a lot of math and stats there (underlying how they choose what to recommend to you). Inventory management, or more generally, logistics? Finance? Insurance? Road/train/plane traffic? Automobile sales? Newspaper advertising space/rates? Economics? Pharmacology? Fisheries? Agriculture? Lumber (e.g. to avoid knots)? Home construction planning? Sports? …. The majority of activities are projected to become more mathematical. The reason is that the activity participants who become more mathematical will have an advantage over those who do not; so in a competitive environment, they will tend to win more.
If you ask Maple to calculate sum(a/x, x = 1 .. infinity) assuming a > 0 Maple correctly returns infinity. But if you ask Maple to calculate the sum given by Evan Stanley, Maple returns unevaluated. So Maple did not determine that Evan's sum diverges.
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