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So you want to study mathematics

susanrigetti.com

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Re: So you want to study mathematics

#31

Post by brimble »

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.

I've got Mathematics for the Nonmathematician by Kline and that's kinda heading the right way, but what about whole courses of study? More books? It's more of an introduction than a thorough resource or course, and feels like it needs another four or five volumes and a lot more exercises to be really useful.

I want a mathematics education designed for all those kids (likely a large majority?) who spent math from about junior high on wondering, aloud or to themselves, why the hell they were spending so much time learning all this. One that puts that question front and center and doesn't teach a single thing without answering it really well, first.

Re: So you want to study mathematics

#32

Post by elteto »

daxfohl wrote: post #8

I loved last year being able to take university courses online. I knocked out analysis, topology, and quantum mechanics as a non matriculated student. I'd had those books for years but never could get through them alone. (The main thing being, you really don't have anything to gague whether you know it well enough or not). I really wish there was more opportunity for that. I'd love to take a few more classes, mostly…

Where did you take your classes?

Re: So you want to study mathematics

#33

Post by pphysch »

susanrigetti wrote: post #27
pphysch wrote: post #25

IME (as a math-degree-haver) the value of mathematics is in improving one's ability to mentally model and reason about complicated real-world phenomena . A lot of folks lose sight of the reality and get lost in the mysticism, especially within the academic regime. > [Mathematics] is the purest and most beautiful of all the intellectual disciplines. It is the universal language, both of human beings and of the univers…

You cut out the middle of that paragraph, which says: "Sadly, there is all sorts of baggage around learning it (at least in the US educational system) that is completely unnecessary and awful and prevents many people from experiencing the pure joy of mathematics. One of the lies I have heard so many people repeat is that everyone is either a “math person” or a "language person” — such a profoundly ignorant and damagi…

I'm not sure what your point is. Are you implying that you are not contributing to the mystification and idealization of mathematics?

In other words, I do not see how you are dealing with the "baggage" of learning mathematics beyond name-dropping it. In my opinion, the mysticism is the baggage. And then the rest of the blogpost reads like a conventional curriculum within the conventional academic regime with which we associate that baggage.

Re: So you want to study mathematics

#34

Post by dekhn »

I'm still stuck at "wait, sets can contain other sets, and sets can contain themselves?" part of Russell's paradox, and I'm close to retirement!

I don't want to study math. I want to know enough of it to solve some well-understood problems I've wanted to solve for decades. Simply learning how to diagonalize a matrix (and how to use such a thing) meant more than understanding a bunch of complicated matrix theory.

Re: So you want to study mathematics

#35

Post by susanrigetti »

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.…

If you have a solid background in calculus, I'd recommend Zill's Advanced Engineering Mathematics, which is pretty much basic math for physicists and engineers (aka for people who need to "use it").

Re: So you want to study mathematics

#36

Post by adamsmith143 »

daxfohl wrote: post #8

I loved last year being able to take university courses online. I knocked out analysis, topology, and quantum mechanics as a non matriculated student. I'd had those books for years but never could get through them alone. (The main thing being, you really don't have anything to gague whether you know it well enough or not). I really wish there was more opportunity for that. I'd love to take a few more classes, mostly…

Texas AM has a program that gets somewhat close though it definitely has a computational focus. Here's a list of their recently offered courses: https://www.math.tamu.edu/graduate/distance/openletter.html

Re: So you want to study mathematics

#37

Post by jackallis »

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.…

i second this. there should clear distinction between academic math and "real world usage" math.

Re: So you want to study mathematics

#38

Post by brimble »

susanrigetti wrote: post #35
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.…

If you have a solid background in calculus, I'd recommend Zill's Advanced Engineering Mathematics, which is pretty much basic math for physicists and engineers (aka for people who need to "use it").

Heh, I have a long-forgotten-due-to-complete-lack-of-use-for-15-years-straight background in calculus. Solid, it is not. Thanks for the tip, though.

Re: So you want to study mathematics

#39

Post by tzs »

susanrigetti wrote: post #4
musgravepeter wrote: post #2

I've been on a Math journey since I retired a couple of years ago and I agree with all the books mentioned that I know and look forward to picking up some of the one I do not know. I agree baby Rudin is essential, but I find it tough going. Some books I liked for self study because they have answers: Introduction to Analysis, Mattock. Elementary Differential Geometry, Pressley. There is also recently Needham's Visual…

Agree that Baby Rudin is VERY difficult to study on its own. I recommend only studying it alongside the other two books I listed: Abbott's Understanding Analysis and Spivak's Calculus (which has a solutions manual). Abbott in particular is very straightforward (at least in comparison with baby Rudin haha)

Another point for Abbott is that it was one of the ~400 books Springer made available for free download near the start of the pandemic. I remember there were a few scripts here on HN back then to grab all those books, so many here probably already have a copy.

Re: So you want to study mathematics

#40

Post by susanrigetti »

brimble wrote: post #38
susanrigetti wrote: post #35

Earlier quoted context omitted.

If you have a solid background in calculus, I'd recommend Zill's Advanced Engineering Mathematics, which is pretty much basic math for physicists and engineers (aka for people who need to "use it").

Heh, I have a long-forgotten-due-to-complete-lack-of-use-for-15-years-straight background in calculus. Solid, it is not. Thanks for the tip, though.

In that case, I recommend starting out with Zill's Precalculus with Calculus Previews and then working through Stewart's Calculus: Early Transcendentals!
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