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So you want to study mathematics

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Re: So you want to study mathematics

#281

Post by eternityforest »

kjasdfj3 wrote: post #239
joatmon-snoo wrote: post #49

Earlier quoted context omitted.

My strong opinion as someone who majored in math is that, at least within the US, the standard calculus requirement should be replaced with statistics. So much more useful and so much more important as an adult. The analytical type of thinking that proof-writing is certainly useful, but you can make much the same argument of many other curricula, and besides, it's not like most intro calc courses even do any proofs.…

> My strong opinion as someone who majored in math is that, at least within the US, the standard calculus requirement should be replaced with statistics. So much more useful and so much more important as an adult. I'm questioning your math pedagogy. Calculus is the single most important math anyone, of any field, can learn as it's the first "practical math" you actually learn. Life behaves like calculus and in order…

Most people rarely seem to encounter anything well defined enough to use math or any kind of formal reasoning on, except stuff that has an app or a professional service for.

Maybe it would help them not get scammed by keto diets and unsafe drugs and such though.

Re: So you want to study mathematics

#282

Post by toto444 »

joatmon-snoo wrote: post #49
brimble wrote: post #31

Are there any "math for people who just want to use it" tracks in math pedagogy? I don't care a bit about proving any of it's true, or even reading others proofs of same. "Recognize which tool to apply, then apply tool", all focused on real-world use (so, yes, it wouldn't be "real" mathematics). That's the math education I'd like—try as I might, I just can't make myself care even a little about math for math's sake.…

My strong opinion as someone who majored in math is that, at least within the US, the standard calculus requirement should be replaced with statistics. So much more useful and so much more important as an adult. The analytical type of thinking that proof-writing is certainly useful, but you can make much the same argument of many other curricula, and besides, it's not like most intro calc courses even do any proofs.…

There is one problem that I have not seen mentioned. Statistics might be much more useful but except for the first chapter (discrete probability) they are much harder. As someone who wanted to work in data I have tried hard to understand probability distributions, I have watched 10s of videos by different professors, done exercises and sure I was able to pass but the truth is I never really understood it. The intuition behing statistics is non trivial. Sampling is very hard to understand. Even on HN during COVID there were mathematically literate people trying to make some back of the enveloppe probability calculation and all they were able to do was show their misunderstanding of how statistics work (to be fair I would not have been able to do the task myself but I could feel something in their reasoning was wrong).

Re: So you want to study mathematics

#283

Post by xzel »

mmmpop wrote: post #208
ghaff wrote: post #172

Earlier quoted context omitted.

For tests and the like, when I was an undergrad, it was fairly common to be able to bring in a one-page "cheat sheet." The idea was that you probably could derive a lot of the stuff given time and maybe references, but you almost certainly couldn't in a 1 hour exam in addition to solving the actual problems on the test.

>> 1 hour exam I'm trying to remember when I had one of those last! I actually don't love the idea of cheat-sheets but maaaybe if it's a cumulative final I could see it being helpful? If you're taking chapter exams on some material, I think you ought to have worked enough problems so that formulas/constants are drilled into your head. But I guess too, where do you draw the line at engineering appendices? I sure don't…

Generally for stem test for application of material not memorization (Medicine you need both, etc). My lower level undergrad math courses all allowed us to bring a crib sheet with equations. It helps you go back over and study/relearn. In the graduate math / physics courses a crib sheet was provided and standardized. Memorizing final PDE solutions or things like Laplace Transform tables is no bueno.

Re: So you want to study mathematics

#284

Post by eternityforest »

untake wrote: post #196

Wrong: math is neither hard nor difficult. It is this single belief that deters many people from learning it. Math is all about logic. It is nothing but how to go from A to B. Any person who can reason should be able to be good at math.

All over the world many people try to learn French. Almost any would tell you that learning a second language is hard. Nobody will fight you on this.

Math is a language to express entirely new concepts thar have nothing to do with everyday thinking and often include things like recursion that makes them impossible to reason about without more than just a few bytes of mental RAM.

There is no step by step algorithmic process to do it. If there were, a computer would be able to do it and far fewer people would want to learn.

Even at the level where there is an algorithm, it's far too big, nobody hand executes the source code of XCas by hand.

Math seems to require not just a skill that can be learned, but an inate ability to deal with multiple connected pieces of information at once, and to see abstract patterns in things.

In programming, if you have to understand more than one tiny bit at a time, you might consider tossing it and starting over. In math it's just normal for lots of ideas to connect.

Re: So you want to study mathematics

#285

Post by jldugger »

qumpis wrote: post #222
jldugger wrote: post #84

Earlier quoted context omitted.

> My strong opinion as someone who majored in math is that, at least within the US, the standard calculus requirement should be replaced with statistics. So much more useful and so much more important as an adult. Strong agree, but engineers probably need both. I'm currently watching a course on causal inference, and the tools are very much calculating gradients. And even if you just use someone else's MCMC, even in…

Which course, if I might ask? I only recall Brady Neal having his videos online

this one: https://xcelab.net/rm/statistical-rethinking/

Re: So you want to study mathematics

#286

Post by tshaddox »

brimble wrote: post #31

Are there any "math for people who just want to use it" tracks in math pedagogy? I don't care a bit about proving any of it's true, or even reading others proofs of same. "Recognize which tool to apply, then apply tool", all focused on real-world use (so, yes, it wouldn't be "real" mathematics). That's the math education I'd like—try as I might, I just can't make myself care even a little about math for math's sake.…

Proofs certainly aren’t the only aspect of what one might call “understanding mathematics.” Aren’t proofs generally limited to very specific mathematical courses (at least until you get to the cutting edge where new results inherently require proofs)?

Re: So you want to study mathematics

#287

Post by ghufran_syed »

criddell wrote: post #53
ghufran_syed wrote: post #16

I went from only having done high school math 10 years ago to completing an MS in math and statistics at my local state university while working in an unrelated field. I would recommend NOT starting with calculus if you haven’t done it, instead, just learn how to do proofs - I used Chartrand “Mathematical proofs” - You don’t need to know any math beyond algebra in order to do that most of this book. If you need to re…

I looked up the Chartrand Mathematical Proofs book and it's been a while since I had to buy a textbook, but $175 for hardcover and $75 for paperback or ebook? That's nuts. If I were a student today, I'd pirate that and feel absolutely no remorse for doing so.

you mean sites like libgen.rs and b-ok.cc ?

I should also have mentioned this completely free book by richard hammack as an alternative: https://www.people.vcu.edu/~rhammack/BookOfProof/

Re: So you want to study mathematics

#288

Post by FiberBundle »

timmg wrote: post #245
helpfulclippy wrote: post #47

Earlier quoted context omitted.

I did a degree in applied math. You’d think this would be “math you’ll use,” but the fact is that despite my program having a CS concentration, most of the stuff I did was not really applicable in practice. However, one thing that has been VERY applicable is proofwriting. Although math proofs are far more rigorous than most real world stuff, the discipline I learned in writing proofs has carried over into pretty much…

> However, one thing that has been VERY applicable is proofwriting. Dumb question: what’s the best way to learn proof writing — let’s say for “fun”?

Work through "How to prove it" by Velleman.

Re: So you want to study mathematics

#289

Post by torbTurret »

geebee wrote: post #151
joatmon-snoo wrote: post #49

Earlier quoted context omitted.

My strong opinion as someone who majored in math is that, at least within the US, the standard calculus requirement should be replaced with statistics. So much more useful and so much more important as an adult. The analytical type of thinking that proof-writing is certainly useful, but you can make much the same argument of many other curricula, and besides, it's not like most intro calc courses even do any proofs.…

I'm really wary of this. House wiring would be more useful than Shakespeare. That's not to knock house wiring, or statistics. I'd love to know more about both. But don't deny yourself an understanding of the meaning of limits. Almost all mathematics before calculus leaves you with a misimpression that neat formulas exist to solve problems. In reality, you've learned to draw straight lines with a ruler, and maybe a fe…

House wiring and Shakespeare are completely different subjects. (I’d expect someone professing Shakespeare to avoid such a straw man, but I see your point!)

Most people don’t need mathematical statistics, but far more will find meaning/interest in the immediate applications of lighter statistics than the another-math-class-full-of-equations that calculus feels like to many.

Anecdotally, most universities are scrambling to add lighter data science courses to their humanities majors. These all teach basic stats, and many ignore the low-level calculus required for those methods (again, speaking of the humanities versions here).

Re: So you want to study mathematics

#290

Post by PennRobotics »

brimble wrote: post #31

Are there any "math for people who just want to use it" tracks in math pedagogy? I don't care a bit about proving any of it's true, or even reading others proofs of same. "Recognize which tool to apply, then apply tool", all focused on real-world use (so, yes, it wouldn't be "real" mathematics). That's the math education I'd like—try as I might, I just can't make myself care even a little about math for math's sake.…

Street Fighting Mathematics.

It's still a bit much to absorb, but you can't really ever say the author didn't attempt to describe each lesson in real world terms. You memorize or learn to graphically/logically derive a few things, like how log(1+x)≈x for small x or how you can sorta guess for most quantities or plots. (One book example figures the data capacity of a CD if you know its music storage using informed guessing of each conversion factor from seconds of music to bits.)

As another example: powers of cos x from -pi/2 to pi/2... you can sketch cos x and then roughly sketch the second power, and then it's clear that the more times you do that, you get a bit more of a bell curve. One in the middle will always stay one in the middle, but you get less area with each iteration as the rest of the function approaches zero. If you wanted an integral, you eyeball where the plot is at 0.5, draw a full-height rectangle from the left 0.5 value and the right 0.5 value. Because the height is 1, the width is pretty close to the true area. You can decide at this point---if you want more precision---to visually guess if the tails or the main part of the function should have more area and adjust your answer.

There's an Open Access PDF at https://mitpress.mit.edu/books/street-fighting-mathematics

There were lecture videos on MIT's Open Learning Library (and somewhere else before that), but they're currently down.

The class site is https://ocw.mit.edu/courses/mathematics/18-098-street-fighti... as well as http://web.mit.edu/18.098/

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