I have a decades-old math degree and ended up working in tech as an engineer. Are there options, like a "Math Camp for the Middle-aged" where I could get a chance to re-learn everything I've forgotten?
So you want to study mathematics
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Re: So you want to study mathematics
#62Are 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.…
Calculus and linear algebra seem to _totally_ dominate the curriculum in most (all?) countrie.
What about meta-mathematics? Topology? Logics? History of mathematics? Philosophy of mathematics? Combinatorics? Number theory? Discrete mathematics? Graph theory? In the post, the fieds under "electives" are by far the most interesting ones, IMHO.
And I fully agree, in-depth knowledge of probability theory as well as descriptive statistics and of course the application to systematic and sound decision making is absolute key, and ought to be taught to anyone from medic to policy makers (scary: Gigerenzer showed that medics tend to be confused about the difference between P(A|B) and P(B|A) - the very people whose job it is to diagnose whether you have cancer or not!).
Re: So you want to study mathematics
#63Are 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.
But the distinction is generally not as clear as you may think. (1) Much of the mathematics came from real world problems (so, in particular, one may get drawn into some kind of mathematical research and even end up discovering new mathematical facts). (2) Sometimes when applying mathematics one still needs to employ deduction (derive a formula, prove a statement one wants to rely on, etc.).
Re: So you want to study mathematics
#64Are 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.…
Or the math covered in finite math classes which is a mix of combinatorics, stats, probability and linear algebra. I remember doing my time in the math tutorial room during my grad school days and helping the kids from the business calc classes who were learning math they weren't going to use from books written by people who didn't understand the domain that they were trying to teach math for. Seriously, what business use is there for f(x) = x^1.3 or the indefinite integral thereof?
Re: So you want to study mathematics
#65Going from Strang to D&F seems like a steep jump. The former is an applied textbook for non-mathematicians and the latter is a proof-based text for advanced undergraduate / graduate-level math students. I would suggest working through a proof-based linear algebra book in between to ease the transition. Axler's is a good one. Alternatives include Hoffman and Kunze and the more modern Friedberg, Insel, and Spence.
I have been using Morris in my class.
Re: So you want to study mathematics
#66Earlier 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…
Proofs are indeed very practical. For example, I believe Leslie Lamport mentioned somewhere that he only came up with the final version of Paxos once he tried to prove it, and noticed that some condition he assumed wasn't necessary at all.
The reasoning behind having geometry be the standard high school sophomore math class is that that’s the age where kids would be ready to do proofs. Except that curriculum designers seem to have forgotten this and except in honors classes, most sophomores don’t get taught proofs in geometry and instead get a set of inert rules about shapes that they have no use for.
Re: So you want to study mathematics
#67Are 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 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.
The problem is that the answer will depend heavily from person to person and from field to field and often the most sensible answers require a mathematical maturity that creates a chicken-and-egg kind of difficulty.
Do you care about engineering? Well you'll need some calculus for that. Do you care about prediction modeling? Well there's some stats you'll need for that. Do you care about finding patterns in the world? Well there's abstract algebra for that. Do you care about reasoning itself? Have fun with mathematical logic. But because humans have different motivations, there's no one-size-fit-all motivation-based approach.
This is especially painful for mathematics because I think most people who have learned some amount of pure mathematics will relate heavily to what helpfulclippy says in a sibling comment: "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 everything from programming (will this algorithm work every time?) to executive decisions (why, specifically, should we believe X?)."
The skills of rigorous and abstract thinking that pure mathematics provides is both nearly-universally helpful, but also simultaneously as a result very difficult to motivate. "This will help you think better across everything you do" is lofty-sounding, but generally not a convincing sell unless someone is already curious. But it's true that being able to wrap one's mind around pure abstraction (after rattling off a rigorous definition for an abstract question: Question: "But what is X really?" Answer: "X is just that. No more, no less.") has ramifications for all that one does.
And the most painful part of all of this is if you try to start by teaching the wonders of pure mathematics instead of all the messy, boring rote stuff, students' eyes are liable to glaze over even more because of the aforementioned chicken-and-egg issue with mathematical maturity.
In this way it's similar to trying to motivate someone to read and write. The key that unlocks that interest for everyone is going to be different and it's very hard to explain the near-universal benefits that reading and writing bring to one's way of thinking (but I can always just have a computer transcribe it or read it aloud to me!) without some inherent curiosity in them.
Re: So you want to study mathematics
#68Where's statistics? You mean to tell me I could go through all that and come out not knowing statistics?
Agree, but I have a feeling that statistics is more like (theoretical) physics, in the sense that it is "not math."
Re: So you want to study mathematics
#69I'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…
Surprised Arnol'd isn't mentioned for ODEs.
Re: So you want to study mathematics
#70Going from Strang to D&F seems like a steep jump. The former is an applied textbook for non-mathematicians and the latter is a proof-based text for advanced undergraduate / graduate-level math students. I would suggest working through a proof-based linear algebra book in between to ease the transition. Axler's is a good one. Alternatives include Hoffman and Kunze and the more modern Friedberg, Insel, and Spence.
Strang's latest book DE&LA is disappointing, it is linear algebra and its applications with the abstraction taken out and mushed together with supplementary notes from ODE videolectures. Mattuck's ODE course is good.