The program offers college and career preparatory intensives for high school and middle school students, as well as exploratory arts and learning camps for elementary school students in collaboration with the Arts & Learning Conservatory. But if you have weaker ones, than it might make sense.and it's not crazy off the beaten path (see point 1).The Summer Academies in the Arts are part of a movement by UC Irvine's Claire Trevor School of the Arts to provide meaningful opportunities for the community to engage in Arts, Dance, Drama, Music, and Technology on campus and to contribute to youth development. If you have strong CS students, would not bother, teach 'em new stuff. Note: That this is not a strong rationale, is a marginal one. And this is a part of that course that has some special relevance (more than partial fractions or the like). I'd say the rationale for giving them to CS AGAIN is that in general (IN GENERAL), CS are a bit math weak compared to other STEMS, so perhaps they need a bit more exposure to stuff they should have learned in standard second semester calculus (or even high school AP BC). but at the end of the second semester and usually a little harder, more "off the path" of just learning antidifferentiation tricks. Not even some "advanced calc" or "engine math" or God Help Us (real analysis) thingie. Are a normal part of the calculus sequence (even the AP BC) in the US. Rationale for (re)covering with CS students. Rationale for ever learning: They are related to numerical methods and algorithms. So many problems which may come up in modelling natural phenomena through computers can be treated quite easily be consider Taylor expansions. What does this mean? Suppose that I am a computer scientist and I wish to figure out how many terms of the series of $e$ I should take such that the difference between the series evaluation and actual value of $e$ below some error, then naturally the method of answering this systematically would be same as knowing what convergence is.Īnd more, the series convergence tests tells us what sequences it is worth to try search for bounds and which are not.Īnd to my understanding, Taylor series is like the swiss knife of modelling. Let make take for example convergent sequences, what does it mean to converge? If we have a sequence $(a_n)$ that means, for any possible $\epsilon$, there is some $N$ such that for any $m>N$, we have: Is there a textbook that has been used by previous instructors when teaching this class? If so, then you should be able to see how the text integrates these topics into the narrative, and where these topics get used to support other topics.īecause every single one of those concepts naturally come up when you want to "do" things with computers! One thing I don't quite understand about your list of topics is that you're supposed to be teaching them concepts taught in second-semester calculus (in the US), but the sub-topics include the integral test, and that makes it sound like they've already had a year of calculus. Whether one of your students will use Taylor series is probably luck of the draw, but they're a basic tool of literacy in STEM. Big O notation is a staple of computer science. Although it is also possible to define them without using limits, the style of those definitions is essentially the same as the style of definition used to define a limit: inequalities and several levels of quantifiers. Big O and related notations relate closely to these notions.
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