Mr. F
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 Jan9 comment Pedagogy: How to cure students of the “law of universal linearity”? Another point is that Greek symbols still "feel" "mathy" and are seen as "expected math symbols" even by young students. So using Greek symbols might actually be counter-productive: to the extent that a student has anxiety about what a symbol is allowed to mean and whether it has some special meaning, using Greek letters over more "regular" things like x and y might only make the anxiety worse. But using a symbol like a tree, fire hydrant, tulip, pineapple, or anything that's totally not at all possibly confusable with "official mathy type stuff" could have a better chance of working. Jan9 awarded Good Answer Jan7 awarded Nice Answer Jan7 answered Pedagogy: How to cure students of the “law of universal linearity”? Dec3 revised Random variables tending to 0 a.s. but with $\mathbb{E}(sup_n|X_n|) = \infty$ added 580 characters in body Dec3 revised Random variables tending to 0 a.s. but with $\mathbb{E}(sup_n|X_n|) = \infty$ deleted 2 characters in body Dec3 revised Random variables tending to 0 a.s. but with $\mathbb{E}(sup_n|X_n|) = \infty$ added 1 characters in body Dec3 revised Random variables tending to 0 a.s. but with $\mathbb{E}(sup_n|X_n|) = \infty$ added 1 characters in body Dec3 answered Random variables tending to 0 a.s. but with $\mathbb{E}(sup_n|X_n|) = \infty$ Nov21 comment How to study math to really understand it and have a healthy lifestyle with free time? Can you elaborate? Nov5 comment Is it worth pursuing a statistics minor? I want to go to pure math grad school. Also, all else equal, extra time to absolutely destroy the Math GRE subject test is worth much more than the minor. So if classes for the minor would prevent you from utterly crushing the Math GRE, don't downweight that -- it could be and important consideration. (This is conditional on the desire to go to math grad school. The stats minor is probably more valuable unconditionally). Check this link for some other considerations. Nov5 comment Is it worth pursuing a statistics minor? I want to go to pure math grad school. Another question: do you attend an undergraduate school where you feel the school's reputation for math majors is good enough to propel you into the pure math grad schools of your choice? If your undergrad school is extremely strong, then it's probably fine to spend extra classes on more well-roundedness (such as in stats). If the best PhD programs will cast any amount of skepticism on your undergrad math program's rigor, you'll be better served just cramming in as many advanced math classes as you can to prove you're good enough at it to be admitted. Nov5 revised Is it worth pursuing a statistics minor? I want to go to pure math grad school. added 1196 characters in body Nov5 answered Is it worth pursuing a statistics minor? I want to go to pure math grad school. Oct24 awarded Citizen Patrol Oct9 comment Best applications-oriented introductory calculus textbooks? I am more saying that there is some base rate of curiosity which is a required pre-req for understanding how a physical problem motivates a mathematical model. And most students who find they want or need to take calculus do not have that base rate of curiosity. Oct9 comment Best applications-oriented introductory calculus textbooks? I understand. I guess I said it poorly. What I more mean is: a student who passes through calculus once is not equipped to understand the motivations for using calculus. Sure, they can recite platitudes about how it's used in some field, but that's about all they are in any position to appreciate. Which is probably why most "applications" sections (as you point out) just contain platitudes like "This can be used in fluid dynamics..." I'm not saying my point here is right. Just that my prior is that you can't motivate calculus from scratch with applications; it doesn't work well. Oct9 comment Best applications-oriented introductory calculus textbooks? Maybe the book you're looking for is hard to find because it's just not very useful. In my own lectures, which admittedly focus more on probability, I've never seen students take to problems because of physical motivations. But after mastering a technique, like e.g. moment generating functions, then they are eager to see how it applied. I might just have outlier experiences, but both in my undergrad and grad school, and as a lecturer, it just never worked this way even for bright students. Is there evidence that it worked this way for bright students in the past? Oct9 comment Best applications-oriented introductory calculus textbooks? The scope of the question is also hard to understand. For instance, in my own education I had to plod through two courses in advanced calculus, just doing lots of problems, mastering limits, beating all algebra mistakes out of my hand over and over. After that I read "Div Grad Curl and All That" and it was wonderful. If I had read such a book before doing all that gross rote algebra, it wouldn't have meant anything. Similarly, I had to slog through differential equations before coming across some useful boundary values problems books that motivated things with physics. Oct9 comment Best applications-oriented introductory calculus textbooks? "justifying its inclusion in a liberal education for purposes other than contemptible ones like using it as a weeder for medical school or business school applicants." This kind of normative statement seems unnecessary in the question. I, for one, am glad these things help weed out such applicants, even though there are many better reasons to study the calculus.