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Thread: Computer Science and Math and Stuff

  1. #161
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    Also, it should tell you how long it is, or if it will play forever. That way you know when to stop it.

  2. #162
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    I think my real analysis professor has it out for us. At least with this volume of homework, he wants us to really, really, really understand measure theory.

  3. #163
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  4. #164

  5. #165
    Is he still calling himself an astrophysicist? He hasn't published in over a decade.

    There is simply no way somebody can continue to be a scientist and spend as much time interacting with the media as he does. On the other hand, people like Brian Greene are still putting out about a paper a year despite taking the time to talk to the media.

    OTOH, maybe Tyson maybe simply thought astronomy was boring and wanted to pretend it wasn't by telling people so.

  6. #166
    "Kids, go into astronomy like me. Then you can spend the second half of your life pretending to others that you didn't quit because science is painstaking work compared to goofing around with the media."

  7. #167
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    RJ, you gotta like, occasionally rein in whatever part of you just wants to do successive riffs on whatever your first reaction to something is. You get so far off the map and jump to wild conclusions. I guess that's fine if you're just having a cheeky conversation or trying to be funny, but blerurughhh...

    What the hell do you know about this guy's intentions? Doesn't he see himself as a sort of popular educator? He certainly behaves like he sees himself as a popularizer of astronomy or the importance of science, not as a practicing, publishing astrophysicist. You can critique that if you want, but to go off into the weeds talking about him... quitting... doing real science... because it was too hard, and doing what he does now because he's lazy and wants to goof around with the media?

    Isn't there room for some goofy, relatable scientist guy to transition into a PR/public educator TV guy role without you ****ting all over him for not writing serious research papers anymore?

  8. #168
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    I don't really care one way or another about Neil Tyson, but I just don't get where you're coming from with this.

  9. #169
    You're right.

    I need to slow down a bit and stop with the perpetual low rent Jon`C schtick (see what I did there). Actually, I just read this article a few minutes ago.

    Are computers and the Internet making people a little bit autistic?
    Is technology making today's kids a bit autistic?
    Posted Nov 30, 2008

    One of the key components of Asperger's and autism is blindness to the nonverbal messages of other people. That blindness translates into a lack of emotional reciprocity, or responsiveness. After all, how can we respond if we don't receive the message?

    You smile, and I gaze back with a flat expression. You make a big frown, and my expression doesn't change. That's a sign of autism. Do the same thing with a neurotypical person - someone who isn't autistic - and they will instinctively mimic your expressions.

    Most of that ability to mimic others is innate - it's prewired in our brains and it emerges in early childhood. But what we do after the initial reaction is learned, and the way we integrate ourselves into society via nonverbal messages - that's almost all learned.

    Autistic people are set apart because we don't get the emotional signals from others to trigger the response and learning process. Therefore, even though we can learn many social interactions, they don't come naturally to us. And we're always awkward because we're blind to the triggers that are automatic in neurotypical people.

    I submit that something similar is happening with America's youth, for a different reason.

    Today's kids spend more and more time in front of computers, and more and more of their communication is electronic. For every minute spent in front of a computer, a minute interacting with other people face to face is lost. As a result, today's kids are not learning the fine points of nonverbal interaction. They don't interact in person enough to acquire the skills.

    They smile when someone smiles at them, because that's built in. However, they are not learning where to go from there. They are not learning the fine points of face to face interaction in our society. I say "our society" because the fine points of interpersonal interactions do differ between societies and cultures, and what's rude to you may be expected and normal behavior on the other side of the world. But without face-to-face contact, how can today's kids learn that?

    Instead, many of today's young people learn the subtleties of text messaging and email. They say, I can be connected to the whole world electronically, and that's true in a sense. The problem is, that electronic connectedness may come at the expense of learning how to act on a date, or in a group, or at a party. And those are vital skills every young person needs.

    I've spent much of my life trying to master face-to-face interaction with others. It's amazing to me, the idea that kids today may be casually disregarding a skill I've worked so hard to master. And it's such an insidious thing . . . they don't even see it happening. But it is. It's brain plasticity in action. Our brains build up the neural paths we use, and prune the ones we ignore. Yesterday's paths led to your friend next door, and the girl in Social Studies and maybe Uncle Bob. Tomorrow's paths lead to through the Xbox to some game enthusiast in China, and through the Blackberry to a like-minded person in Canada.

    The physical connection, and the skill to develop and maintain it, is vanishing. Is the tradeoff worth it?

    As a person with Asperger's, I have always had great success when communicating by writing, because my limited ability to respond to nonverbal cues does not matter in the written domain. You readers can't see my face . . . you only read my words. I'm grateful that I have the gift of writing in a clear and articulate manner. It's given me communication success that I could never have enjoyed otherwise.

    But to me, written interaction is not enough. In my last blog post, I wrote of my sense of aloneness, and my desire to join the community of mankind. To me, that is only done in person. I assumed (perhaps wrongly) that everyone felt that way, but now I'm not sure . . .


    Perhaps the integration of electronic communication into our lives has precipitated a new evolutionary step, and the way tomorrow's adults will engage one another is fundamentally different from the way I and everyone before did so.

    I wonder how it will work out.

    The idea of "computer enhanced evolution" makes me a little uneasy, and that's what we are experiencing today, as we integrate computer based communication into the very wiring of our brains.
    https://www.psychologytoday.com/blog...e-bit-autistic
    Last edited by Reverend Jones; 02-22-2018 at 11:10 PM.

  10. #170
    Quote Originally Posted by saberopus View Post
    I don't really care one way or another about Neil Tyson, but I just don't get where you're coming from with this.
    I had been wondering how badly I'd been rubbing the rest of you guys with some of my posts. Sorry for enticing the rant from you, but at least know the point isn't lost on me. I know I have a problem. Actually maybe my generation kind of does, if that guy's article makes sense.

  11. #171
    Shoulda been reading Marshall McLuhan rather than posting here

    <-- the medium is the moron
    Last edited by Reverend Jones; 02-22-2018 at 11:15 PM.

  12. #172
    That said, I still think it's slightly suspicious to listen too much to a man who tries to get people interested in science without actually being a scientist. (Edit: Not that he doesn't mean well, but who knows if we shouldn't simply be listening to other scientists instead? Although now that I think about it, a lot of what he seems to do is point people to the works of others scientists.) He might have other reasons for no longer practicing, and I suppose modern society sort of forces specialization, but I think it's not quite right for people to take Tyson as an authority on science to the exclusion of others who might be closer to the actual work at this point in his life (but see my edit).
    Last edited by Reverend Jones; 02-22-2018 at 11:30 PM.

  13. #173
    Quote Originally Posted by Reid View Post
    Maybe this is the point though. He's not a genius, and that's OK, even if he makes cringy tweets from time to time. Probably was wrong for me to tear into him like that.

  14. #174
    At the end of the day, the reason I post lots of plausible (or not-so-plausible) B.S. here is twofold:
    1. Take my mind off whatever potentially difficult / complicated thing I'm trying to get done IRL
    2. Entice others into saying something interesting (or be enticed myself by someone else)


    I should slow down though.

  15. #175
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    Quote Originally Posted by Reverend Jones View Post
    Maybe this is the point though. He's not a genius, and that's OK, even if he makes cringy tweets from time to time. Probably was wrong for me to tear into him like that.
    I guess the pattern to my linking people's twitters is: social media is toxic, and let's peoples minor dumbass thoughts become public proclamations.

  16. #176
    I hereby sentence you to 5 years in state prison for egregious crimes against apostrophes

  17. #177
    But yeah I agree with that.

  18. #178
    Quote Originally Posted by Reid View Post
    I guess the pattern to my linking people's twitters is: social media is toxic, and let's peoples minor dumbass thoughts become public proclamations.
    Marshall McLuhan

    tl;dr we're all ****ed

  19. #179
    Incidentally, Reid, I know I've treated you like trash on this topic, but since this is the "computer science and math stuff" thread, I would love to interest you in this post I made on somewhat the same matter at hand, in this very thread. I know that since I am not in a grad program, I am indeed a "pip squeak" before the collective intelligentsia of mathematics establishment as it exists today, but: from what I've gleaned from those greater than myself, I've come to appreciate what apparently is a minority view among mathematicians (although among the more problem solving oriented mathematicians I've interacted with, it is not quite as controversial a perspective to have as Cartier might seem to suggest). It's not necessarily in conflict with the majority view, either, but simply another angle to look at things, although I hope it might upset the degree of philosophical certainty through which you view the matter.

    Anyway, I've quoted the interesting passage from the beginning of this very interesting essay by Pierre Cartier. Of course I don't want to appear the insecure name dropper desperate for approval, a la Koobie, which you've tacitly taken me for once I had provoked you into doing so, but: I honestly think what Cartier has to say is quite convincing (and the remainder of the paper is quite fascinating in content as well). I've tried to more or less take inspiration from it, at least in spirit, in everything I work on (which is admittedly mostly outside of mathematics, per se). Finally, I will mention that just looking at who the paper is dedicated to is a big hint about the aesthetic being depicted here.

    Quote Originally Posted by Reverend Jones View Post
    If Vladimir's excellent (in my opinion) rant isn't your cup of tea, I could only suggest reading Pierre Cartier's take on this theme.
    (Emphasis in the original.)

    Quote Originally Posted by Pierre Cartier
    To the memory of Gian-Carlo Rota,
    modern master of mathematical magical tricks

    [...]

    The implicit philosophical belief of the working mathematician is today the
    Hilbert-Bourbaki formalism. Ideally, one works within a closed system:
    the basic principles are clearly enunciated once for all, including (that is an
    addition of twentieth century science) the formal rules of logical reasoning
    clothed in mathematical form. The basic principles include precise defini-
    tions of all mathematical objects, and the coherence between the various
    branches of mathematical sciences is achieved through reduction to basic
    models in the universe of sets. A very important feature of the system is its
    non-contradiction; after Godel, we have lost the initial hopes to establish
    this non-contradiction by a formal reasoning, but one can live with a corre-
    sponding belief in non-contradiction. The whole structure is certainly very
    appealing, but the illusion is that it is eternal, that it will function for ever
    according to the same principles. What history of mathematics teaches us is
    that the principles of mathematical deduction, and not simply the mathe-
    matical theories, have evolved over the centuries. In modern times, theories
    like General Topology or Lebesgue’s Integration Theory represent an almost
    perfect model of precision, flexibility and harmony, and their applications,
    for instance to probability theory, have been very successful.

    My thesis is:there is another way of doing mathematics, equally
    successful, and the two methods should supplement each other and
    not fight.


    This other way bears various names: symbolic method, operational calculus,
    operator theory... Euler was the first to use such methods in his extensive study
    of infinite series, convergent as well as divergent. The calculus of
    differences was developed by G. Boole around 1860 in a symbolic way, then
    Heaviside created his own symbolic calculus to deal with systems of differen-
    tial equations in electric circuitry. But the modern master was R. Feynman
    who used his diagrams, his disentangling of operators, his path integrals... The
    method consists in stretching the formulas to their extreme consequences,
    resorting to some internal feeling of coherence and harmony. There
    are obvious pitfalls in such methods, and only experience can tell you that
    for the Dirac δ-function an expression like xδ(x) or δ′(x) is lawful, but not
    δ(x)/x or δ(x)2. Very often, these so-called symbolic methods have been
    substantiated by later rigorous developments, for instance Schwartz distribution
    theory gives a rigorous meaning to δ(x), but physicists used sophisticated formulas
    in “momentum space” long before Schwartz codified the Fourier transformation
    for distributions. The Feynman “sums over histories” have been immensely
    successful in many problems, coming from physics as well from mathematics,
    despite the lack of a comprehensive rigorous theory.

    To conclude, I would like to offer some remarks about the word “formal”. For the
    mathematician, it usually means “according to the standard of formal rigor, of formal
    logic”. For the physicists, it is more or less synonymous with “heuristic” as opposed
    to “rigorous”. It is very often a source of misunderstanding between these two
    groups of scientists.

    [...]
    The point of view also summarizes much of the one I had been trying to convey in this thread as well, which I also think we (at least silently) were butting heads on. It's not just something I made up as an undergraduate as an "idea about how mathematics should be done" that I should "outgrow", but simply a minority report I've stolen from a venerable member of Bourbaki itself.

    (Originally, I came across this essay by reading it referenced in one of Doron Zeilberger's many infamous opinion essays).
    Last edited by Reverend Jones; 02-23-2018 at 12:50 AM.

  20. #180
    Finally, I would like to point you to this post as a summary of my point of view here, as it pertains to Cartier's essay. I don't care to argue the points I was trying to make about just how sound set theory might be, or how fruitless it might have been to try so hard to make it so. Instead, I would like to draw your attention to the quote I inserted, from Oliver Heaviside, which I will reproduce here:
    Quote Originally Posted by Oliver Heaviside
    In the preceding, I have purposely avoided giving any definition of 'equivalence.' Believing in example rather than precept, I have preferred to let the formulae, and the method of obtaining them, speak for themselves. Besides that, I could not give a satisfactory definition which I could feel sure would not require subsequent revision.
    And in particular:
    Mathematics is an experimental science, and definitions do not come first, but later on. They make themselves, when the nature of the subject has developed itself. It would be absurd to lay down the law beforehand.
    Last edited by Reverend Jones; 02-23-2018 at 01:14 AM.

  21. #181
    tl;dr: people who are secretly "mathematical physicists" at heart can contribute just as much to mathematics as the "snobbier", more logically inclined (rather than heuristically or formally inclined) variety of mathematician, and that actually, a great deal of interesting mathematics was pioneered by people who couldn't care less about mathematical logic.
    Last edited by Reverend Jones; 02-23-2018 at 01:15 AM.

  22. #182
    I don't mean to get hung up on the word axiom, but certainly, when physicists talk about the axioms of quantum mechanics, I very much doubt they understand the word in the same sense as modern mathematicians do when they speak of axioms of Euclidean geometry. Now, to be fair, when I brought up the possibility of the axioms being "wrong" (as Jon`C had suggested), I didn't necessarily qualify my use of the word axiom here, and indeed, perhaps I assumed the distinction didn't matter. But when Jon`C was talking about Euclidean space, and the choice of axioms that determined the fact that they might be working in Euclidean space (as they often do), well, certainly, those axioms are wrong, insofar as they lead to the wrong model of the universe. So really, what rubbed me the wrong way was that it seemed rather pedantic and condescending to hold onto this idea that it was wrong in any way to simply call axioms wrong in this narrow instance.
    Last edited by Reverend Jones; 02-23-2018 at 02:04 AM.

  23. #183
    Also, what is mathematics if not geometry, and aren't physicsts the geometers of the universe who simply pay more attention to experimental results than the pure mathematician only typically does indirectly (through the benefit of the pioneering work of the mathematical physicist, actually)? We should give them credit for that, and admit that mathematicians have learned a ton from the efforts of their work, long before logic typically enters the picture (again, see the second part of the Heaviside quote as an example of this sentiment).

  24. #184
    Also, I promise not to attack you for your views. And I don't even really care about the axiom stuff, that is just incidental. I am mostly just trying to get across my more general point of view, though this may help understand why I was adamant to the point of being uncivil before.

    Of course I accept the possibility that you might simply disregard all of this as simply wrong, and that's fine too. I think I've said enough on this topic that if you don't particularly care for this viewpoint, I am OK with that.

  25. #185
    Admiral of Awesome
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    Quote Originally Posted by Reverend Jones View Post
    "Kids, go into astronomy like me. Then you can spend the second half of your life pretending to others that you didn't quit because science is painstaking work compared to goofing around with the media."
    Science outreach and advocacy is a job that desperately needs doing, and very few scientists have both the personality and media savvy in order to achieve it. I can pretty much guarantee that NDT has had a greater effect on his field by focusing on his advocacy work than he would have ever had by focusing on research.

    And, also, noted non-scientist Bill Nye? Same thing.

  26. #186
    Yeah, I kind of came around to that opinion. I think I took Reid's initial remark way too far there, heh.

  27. #187
    The age of the polymath is long gone I guess. It is an inevitable fact of increasing specialization that the people who advocate for things may not actually do them all that much.

    Well, this has perhaps always been true anyway.

  28. #188
    Also, Reid, if you don't want to read all that egotistical non-sense I wrote about an hour ago, I would also be perfectly happy to accept a short "Jones, you're about 10 feet too far up your own ass for me to give you the time of day at this point".

  29. #189
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    Also, regarding the original Tweet:

    He’s not even wrong.

    An unhackable computer is absurd, but information security has a lot of low hanging fruit. Most companies are pretending that IS doesn’t even exist, let alone doing even the bare minimum about it. Improving that is where the money should be spent, not investigative work and international diplomacy to extradite foreign blah blah blah.

  30. #190
    air gaps considered harmful to convenience

  31. #191
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    Quote Originally Posted by Reverend Jones View Post
    I don't mean to get hung up on the word axiom, but certainly, when physicists talk about the axioms of quantum mechanics, I very much doubt they understand the word in the same sense as modern mathematicians do when they speak of axioms of Euclidean geometry. Now, to be fair, when I brought up the possibility of the axioms being "wrong" (as Jon`C had suggested), I didn't necessarily qualify my use of the word axiom here, and indeed, perhaps I assumed the distinction didn't matter. But when Jon`C was talking about Euclidean space, and the choice of axioms that determined the fact that they might be working in Euclidean space (as they often do), well, certainly, those axioms are wrong, insofar as they lead to the wrong model of the universe. So really, what rubbed me the wrong way was that it seemed rather pedantic and condescending to hold onto this idea that it was wrong in any way to simply call axioms wrong in this narrow instance.
    I don't doubt that the difference is in how we were using axiom, and I'm willing to accept that was the source of the whole debate.

    Allow me to explain why that sentence sounds so wrong to me by making a comparison. Euclidean geometry as Euclid formulated it, before any of the axioms, starts as a Q-vector space. The axioms give a bunch of restrictions on what kind of geometric objects can be permitted, which in turn construct other numbers and extend your Q-vector space into one much larger. But, can Euclidean geometry work in reality? Well, no, because spacetime is curved. Therefore the Euclidean geometry axioms are wrong.

    Now, let me compare that to the group axioms. The group axioms are a similar set of restrictions we apply to binary operations. We begin with a space of binary operations, and begin saying certain things are true a priori to begin cutting down the amount of objects that we permit. But, can groups exist in reality? Well, no, entropy is increasing, so inverse operations in the universe aren't possible. Therefore, the group axioms are wrong.

    Does it sound absurd to say the group axioms are wrong because entropy is increasing? It should, because it is absurd. But neither example above are any different from a mathematical perspective. Axioms from a mathematical perspective have zero relation to anything we deal with in physics, and if you took the consequence of calling a set of axioms "wrong" because one application you came up with has inaccuracies, then math becomes reduced to one big set of statements made about wrong axioms. I don't think anyone can seriously argue that all of mathematics is formulated incorrectly on this basis. But that's essentially what the argument is, or at least how it sounds.

    Also, as far as I'm aware, QM axioms are purely mathematical, as in bra-ket operator stuff. I'm not well versed in this so I won't speak on it, but I have a suspicion it would fall victim to the same problems if placed under the same scrutiny.

  32. #192
    Hah, well, for what it's worth, this conversation is making me think Foucault's characterization of Cartesian and Kantian subjectivity is actually pretty accurate (or at least reasonable as an interpretation).

  33. #193
    Quote Originally Posted by Reverend Jones View Post
    Is he still calling himself an astrophysicist? He hasn't published in over a decade.

    There is simply no way somebody can continue to be a scientist and spend as much time interacting with the media as he does. On the other hand, people like Brian Greene are still putting out about a paper a year despite taking the time to talk to the media.

    OTOH, maybe Tyson maybe simply thought astronomy was boring and wanted to pretend it wasn't by telling people so.
    Dude, attack NDT all you want, but you lay off Carl Sagan, y'hear? I don't think I could handle that.

  34. #194
    Quote Originally Posted by Eversor View Post
    Dude, attack NDT all you want, but you lay off Carl Sagan, y'hear? I don't think I could handle that.
    OK OK! I was wrong. Tell your sister, I was wrong.

  35. #195
    Quote Originally Posted by Reid View Post
    I don't doubt that the difference is in how we were using axiom, and I'm willing to accept that was the source of the whole debate.

    Allow me to explain why that sentence sounds so wrong to me by making a comparison. Euclidean geometry as Euclid formulated it, before any of the axioms, starts as a Q-vector space. The axioms give a bunch of restrictions on what kind of geometric objects can be permitted, which in turn construct other numbers and extend your Q-vector space into one much larger. But, can Euclidean geometry work in reality? Well, no, because spacetime is curved. Therefore the Euclidean geometry axioms are wrong.

    Now, let me compare that to the group axioms. The group axioms are a similar set of restrictions we apply to binary operations. We begin with a space of binary operations, and begin saying certain things are true a priori to begin cutting down the amount of objects that we permit. But, can groups exist in reality? Well, no, entropy is increasing, so inverse operations in the universe aren't possible. Therefore, the group axioms are wrong.

    Does it sound absurd to say the group axioms are wrong because entropy is increasing? It should, because it is absurd. But neither example above are any different from a mathematical perspective. Axioms from a mathematical perspective have zero relation to anything we deal with in physics, and if you took the consequence of calling a set of axioms "wrong" because one application you came up with has inaccuracies, then math becomes reduced to one big set of statements made about wrong axioms. I don't think anyone can seriously argue that all of mathematics is formulated incorrectly on this basis. But that's essentially what the argument is, or at least how it sounds.

    Also, as far as I'm aware, QM axioms are purely mathematical, as in bra-ket operator stuff. I'm not well versed in this so I won't speak on it, but I have a suspicion it would fall victim to the same problems if placed under the same scrutiny.
    I think you're mostly right here. Well, you're not wrong.

    Actually, I began to write a very lengthy post in order to explain where I am coming from here, but I really can't bring myself to finish it, because even if you were to fully appreciate it, you are close enough to the truth already that I can't bring myself to go through with writing it just to give myself cancer.

  36. #196
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    An important thing to note on that section by Cartier: France is and always has been the epicenter for Bourbakian style mathematics, and that style never penetrated as deeply in other traditions, so it strikes me that his complaints are more particular to France than globally.

  37. #197
    That's actually a really good point. In fact it also perhaps explains the highly polemical nature of the Vladimir Arnold essay I had linked to.

    [...]
    Unfortunately, it was an ugly twisted construction of mathematics like the one above which predominated in the teaching of mathematics for decades. Having originated in France, this pervertedness quickly spread to teaching of foundations of mathematics, first to university students, then to school pupils of all lines (first in France, then in other countries, including Russia).

    To the question "what is 2 + 3" a French primary school pupil replied: "3 + 2, since addition is commutative". He did not know what the sum was equal to and could not even understand what he was asked about!

    Another French pupil (quite rational, in my opinion) defined mathematics as follows: "there is a square, but that still has to be proved".

    Judging by my teaching experience in France, the university students' idea of mathematics (even of those taught mathematics at the École Normale Supérieure - I feel sorry most of all for these obviously intelligent but deformed kids) is as poor as that of this pupil.

    For example, these students have never seen a paraboloid and a question on the form of the surface given by the equation xy = z2 puts the mathematicians studying at ENS into a stupor. Drawing a curve given by parametric equations (like x = t3 - 3t, y = t4 - 2t2) on a plane is a totally impossible problem for students (and, probably, even for most French professors of mathematics).

    Beginning with l'Hospital's first textbook on calculus ("calculus for understanding of curved lines") and roughly until Goursat's textbook, the ability to solve such problems was considered to be (along with the knowledge of the times table) a necessary part of the craft of every mathematician.

    Mentally challenged zealots of "abstract mathematics" threw all the geometry (through which connection with physics and reality most often takes place in mathematics) out of teaching. Calculus textbooks by Goursat, Hermite, Picard were recently dumped by the student library of the Universities Paris 6 and 7 (Jussieu) as obsolete and, therefore, harmful (they were only rescued by my intervention).

    ENS students who have sat through courses on differential and algebraic geometry (read by respected mathematicians) turned out be acquainted neither with the Riemann surface of an elliptic curve y2 = x3 + ax + b nor, in fact, with the topological classification of surfaces (not even mentioning elliptic integrals of first kind and the group property of an elliptic curve, that is, the Euler-Abel addition theorem). They were only taught Hodge structures and Jacobi varieties!

    How could this happen in France, which gave the world Lagrange and Laplace, Cauchy and Poincaré, Leray and Thom? It seems to me that a reasonable explanation was given by I.G. Petrovskii, who taught me in 1966: genuine mathematicians do not gang up, but the weak need gangs in order to survive. They can unite on various grounds (it could be super-abstractness, anti-Semitism or "applied and industrial" problems), but the essence is always a solution of the social problem - survival in conditions of more literate surroundings.
    [...]

  38. #198
    Now since we are on the topic of polemical essays, I have a much better one, which I have just read with pleasure this evening. It is quite scathing.

    Turns out, sophmore differential equations course is hot garbage, and has been for at least a century.

    I've heard that Professor Pugh at UC Berkeley, who actually does research in something related to differential equations, well, he doesn't even teach the standard content, instead making it an intro to dynamical systems.
    Last edited by Reverend Jones; 02-24-2018 at 05:11 AM.

  39. #199
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    Quote Originally Posted by Reverend Jones View Post
    Now since we are on the topic of polemical essays, I have a much better one, which I have just read with pleasure this evening. It is quite scathing.

    Turns out, sophmore differential equations course is hot garbage, and has been for at least a century.

    I've heard that Professor Pugh at UC Berkeley, who actually does research in something related to differential equations, well, he doesn't even teach the standard content, instead making it an intro to dynamical systems.
    Starting to read this, and wanted to comment on one section:

    It is to be hoped that these new courses will be taught by mathematicians rather than by engineers: the budget of any mathematics department is entirely dependent on the number of engineering students enrolled in our elementary courses. Were it not for these courses, which engineers generously defer to mathematicians, our mathematics departments would be doomed to extinction.
    I think they're just trying to be funny, but.. this isn't true? At both my alma mater and the school I'm currently at, engineering math are sequestered off from "real math" which are pretty much reserved only for pure science majors.

  40. #200
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    Seemed like a fine text. I have never studied differential equations so I'm useless to give much commentary, but when I asked my mech engineer friend he said "we just solve them numerically", which as I understand it is how most people choose to do them.

    In any case, updating the curriculum to avoid trickfinding and promote understanding core concepts is a worthy goal. I try to get my calculus students to reason through problems instead of trying to memorize, but even then problems that should be reasonable for calc 2 are easy to memorize, often the problems they're capable of doing but are actually hard depend on noticing some trick, so talking about homework with them is ~****ing annoying~ because if I don't see the trick, I'll be stuck myself. I'd rather talk about the Riemann integral or why the arc length formulas make sense, but nah.

    Though, before the last exam, I really hammered into students that they should reason first about surfaces of revolution and think about why each part of the integral makes sense. I happened to grade that section on the exam, and my students did markedly better than the other prof's students. So I guess it works, which is nice to know.

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