tag:blogger.com,1999:blog-7691251033406320222.post645049051951135438..comments2024-03-26T04:19:38.862-07:00Comments on kitchen table math, the sequel: Richard on Physics FirstCatherine Johnsonhttp://www.blogger.com/profile/03347093496361370174noreply@blogger.comBlogger11125tag:blogger.com,1999:blog-7691251033406320222.post-42098761875088099322009-06-16T22:17:54.012-07:002009-06-16T22:17:54.012-07:00I'd agree with Barry and Vlorbik also.
I stud...I'd agree with Barry and Vlorbik also.<br /><br />I studied my Math in the UK where the idea of using limits as a substantive introduction to calculus is almost unheard of. The common approach can be found <a href="http://www.mathsrevision.net/alevel/pages.php?page=23" rel="nofollow"> here. </a><br /><br /><br />The usual approach would be differentiation from first priciples leading onto optimisation and integrating to find area under curves in grade 11.<br /><br />In Grade 12, we'd stretch calculus methods (chain rule, integration by parts, etc ....) .... a rigorous approach to limits is saved for undergraduate level work.<br /><br />Using limits as an introduction to calculus would be akin to using Peano's axioms as an introduction to consecutive numbers.Richard Inoreply@blogger.comtag:blogger.com,1999:blog-7691251033406320222.post-72289157278507836972009-06-16T13:21:54.074-07:002009-06-16T13:21:54.074-07:00It varies. I know that at my school, they spend n...It varies. I know that at my school, they spend nearly half of Calc I on limits, which is overkill. The order Barry Garelick describes makes a lot more sense to me.ChemProfnoreply@blogger.comtag:blogger.com,1999:blog-7691251033406320222.post-54460060318932868422009-06-16T13:15:24.577-07:002009-06-16T13:15:24.577-07:00I recall that limits were introduced in order to d...I recall that limits were introduced in order to define what a derivative is. There wasn't extensive work done with limits--just general operations and some derivations, but not a whole bunch. After Calc III, there was a "bridge course" that I had to take which was fundamentals of real analysis which then gets into sequences, limits thereof, Caucy sequences, continuity, epsilon delta, etc. We had a smattering of epsilon delta in freshman calc, but I was not up to it at that point.Barry Garelickhttps://www.blogger.com/profile/01281266848110087415noreply@blogger.comtag:blogger.com,1999:blog-7691251033406320222.post-23895213226430446532009-06-16T12:01:11.057-07:002009-06-16T12:01:11.057-07:00Yeah, I'd agree with vlorbik here. When I fir...Yeah, I'd agree with vlorbik here. When I first hit calculus, I didn't see the point of limits (just like I didn't see the point of logarithms when I hit Algebra II). The mathematicians love limits, but I wonder if students would get more out of them if they started with series, derivatives, and integration, and then talked about the underlying theory and "epsilon-delta."ChemProfnoreply@blogger.comtag:blogger.com,1999:blog-7691251033406320222.post-49617058676773982872009-06-16T04:08:06.158-07:002009-06-16T04:08:06.158-07:00"Formulas are important, certainly, but the c..."Formulas are important, certainly, but the course takes the approach that every equation is in fact also a sentence that can be understood, and solved, in English."<br /><br />so why do these folks<br />think they call it "calculus"?<br />--i.e., collection of techniques<br />for *performing calculations*.<br /><br />careful study of limits<br />(and of continuity; much the same)<br />was historically much *later*<br />than derivatives and integrals.<br />and probably for most students<br />it'd be easier to *delay*<br />limits rather than (as in almost<br />every calculus *book*)<br />putting 'em first.<br />"handwaving" was good enough<br />for newton, leibniz, and euler.<br />"epsilon-delta" is a 19th century<br />thing; calculus got started<br />in the 17th. this was no accident.<br /><br /><br />i've long felt that the "natural"<br />intro to calculus is *series*.<br />something along the lines of<br /><a href="http://books.google.com/books?id=Pv_Aa9d6ovsC&dq=Konrad+Knopp&printsec=frontcover&source=an&hl=en&ei=NXs3SuRSlIy2B5HrodUM&sa=X&oi=book_result&ct=result&resnum=4" rel="nofollow">konrad knopp's classic</a>.r. r. vlorbikhttps://www.blogger.com/profile/02746118913980983815noreply@blogger.comtag:blogger.com,1999:blog-7691251033406320222.post-42663616903717067212009-06-15T10:51:12.589-07:002009-06-15T10:51:12.589-07:00Incidentally, there really is a rigorous, mathemat...Incidentally, there really is a rigorous, mathematically correct class on Calculus without Calculus: Limits. <br /><br />Calculus was the natural end product of studying limits; it's an elegant unification of all the different methods used in limit problems, and generalizable well beyond the original, uh, limits of Limits. In HS, we had to take a year of Precalculus before Calc; arrogant schmuck that I was, I was insulted by the notion at the time, but, in retrospect, I think it saved my mathematical future. I think we spent close to half of the year picking apart limits and continuity in seemingly every way imaginable. <br /><br />Unfortunately, I'm pretty sure that's not what this book is about.Independent Georgehttps://www.blogger.com/profile/14559237565237736636noreply@blogger.comtag:blogger.com,1999:blog-7691251033406320222.post-66106631711203920082009-06-15T08:30:39.633-07:002009-06-15T08:30:39.633-07:00When I was an undergraduate there was a course ent...When I was an undergraduate there was a course entitled (informally) "Physics for Poets." It was not a course for the lazy but apparently it required much less math expertise than "regular" Physics 100 or whatever it was called then, and it didn't qualify you for more advanced courses in physics. At that time you needed 2 or 3 lab science credits to graduate, even if you were in the humanities. I took zoology, geology and I think botany. Really loved geology and had I taken it before junior year might have decided to change fields.<br /><br />High school physics was fascinating (and well-taught in my case; I loved it) but for some reason I didn't get seriously interested in sciences until much later. Too many competing interests.<br /><br />Do many colleges still require a cross section of courses -- some math, some science, etc even if you are in sociology or comparative literature?palisadeskhttps://www.blogger.com/profile/13700503881038569921noreply@blogger.comtag:blogger.com,1999:blog-7691251033406320222.post-52772097516598497852009-06-15T06:15:09.989-07:002009-06-15T06:15:09.989-07:00I'm planning to teach myself calculus using Sa...I'm planning to teach myself calculus using Saxon Calculus.<br /><br />Of course, first I have to get through Saxon Advanced Math.<br /><br />BUT: first I have to get proficient in logarithms.<br /><br />AND: this summer, it's ALEKS geometry.<br /><br />As soon as I finish ALEKS Algebra 1.<br /><br />(Does that sound like a lot?)Catherine Johnsonhttps://www.blogger.com/profile/03347093496361370174noreply@blogger.comtag:blogger.com,1999:blog-7691251033406320222.post-345031652488516692009-06-15T06:13:38.251-07:002009-06-15T06:13:38.251-07:00It's definitely calculus appreciation -- but t...It's definitely calculus appreciation -- but there are a couple of engineering & math major types who say the course was useful to them as an adjunct to a real course.Catherine Johnsonhttps://www.blogger.com/profile/03347093496361370174noreply@blogger.comtag:blogger.com,1999:blog-7691251033406320222.post-59836100089947760902009-06-15T05:30:07.833-07:002009-06-15T05:30:07.833-07:00The calculus text you linked to appears to be calc...The calculus text you linked to appears to be calculus appreciation. Content free calculus and physics for the 21st century!Barry Garelickhttps://www.blogger.com/profile/01281266848110087415noreply@blogger.comtag:blogger.com,1999:blog-7691251033406320222.post-70321945745394469202009-06-14T18:26:57.540-07:002009-06-14T18:26:57.540-07:00Hey! I just bought that!
Having received "C...Hey! I just bought that!<br /><br />Having received "Chicago Calculus" in college (All Modeling Deer Populations on TI-81s All the Time!), it should be right up my alley.<br /><br /><br />(Have I told the story yet about the physics prof who team taught the course with the calc guy getting utterly steamed in January when we couldn't integrate yet? We'd only done derivatives to that point, but yeah, we kinda needed to know a little more to move ahead in physics. So he stopped the physics lecture and started an impromptu calculus one.)TerriWhttps://www.blogger.com/profile/18200629750466604443noreply@blogger.com