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So you want to study mathematics
81–90 of 371 posts
Re: So you want to study mathematics
#82Are 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 think, the problem is, proofs are what makes math useful. This might sound a bit dense, but the alternative is what 90% of programmers do every day.
I think one can get far enough by applying known mathematical facts. (Proof: elementary school math is useful.)
Re: So you want to study mathematics
#83Calculus: I suggest just forget about "precalculus" and, instead, just get a good calculus book and dig in.
There are two main parts of calculus, and both can be well illustrated by driving a car. In the first part, we take the data on the odometer and from that construct the data on the speedometer. The speedometer values are called the (first) derivative of the odometer values. In the second part we take the speedometer values and construct the odometer values. The odometer values are the integral of the speedometer values. In notation, let t denote time measured in, say, seconds, and d(t) the distance, odometer value, at time t. Let s(t) be the speed at time t. Then in calculus
s(t) = d'(t) = d/dt d(t)
And d(t) is the integral of speed s(t) from time t = 0 to its present time.
Those are the basics.
Applications are all over physics, engineering, and the STEM fields.
Linear Algebra: The subject starts with a system of simultaneous linear equation. The property linearity is fundamental, a pillar of math and its applications. The STEM fields are awash in linearity. E.g., a concert hall performs a linear operation on the sound of the orchestra. E.g., in calculus, both differentiation and integration are linear. In the STEM fields, when a system is not linear, often our first step is to make an attack via a linear approximation. E.g., perpendicular projection onto a plane is a linear operator and the main idea in regression analysis curve fitting in statistics.
Most of math can be given simple intuitive explanations such as above.
Re: So you want to study mathematics
#84Are 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.…
> 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 the models a differential equation or integral can randomly appear usefully.
In retrospect I should have taken a stats class in high school when I had that 1 hour gap for 1 semester, just to build a better intuition around the basic concepts.
Re: So you want to study mathematics
#85As a math PhD I have to say the only way you're going to learn mathematics is if you actually have a pressing need to do so. i.e. You have a project at work that needs some math, you have a hobby that needs some math. In this case you just learn what you need. Just learning math for its own sake outside of a University STEM track is just too hard (I wouldn't be able to do it and I've tried).
Re: So you want to study mathematics
#86I read a Murakami novel in high school, 1Q84. The protagonist is a math teacher who talked about math in a way that I had never seen before. I'd been told I was "good at math" beforehand(for whatever that means, I'm not a fields medalist or anything), but for ~6 months after reading that book, I was _really good_. Like, suddenly I did not have to do any homework in my sr. year calculus class. I loved sitting in class and watching my teacher work through problems, and it seemingly imprinted directly into my brain, because while doing no homework I could still ace the exams while writing with a pen (no erasing and re-do'ing with a pencil). All because of the way this fictional teacher from 1Q84 talked about math.
Has anyone else had an experience like that? (With math or other things?)
Re: So you want to study mathematics
#87Are 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 just want a place I can go to weekly for 15min to practice math. It keeps track of what I know and gives me exercises of stuff so I can retain the skills.
I've forgotten 90% of the math stuff I learned
Re: So you want to study mathematics
#88I find it hard to believe that the author started to appreciate physics by reading The Feynman Lectures on Physics before any exposure to physics or even algebra, and in less than three years went from barely knowing high school math to enjoying advanced mathematical physics and graduate-level quantum physics. It looks this is one-in-a-million level brilliance as learning the sheer amount of requirement knowledge in…
I agree that this does not on its surface seem possible, but I can think of a few explanations.
1. I recently spent a week on one section of one chapter of a math book. I was able to follow it within an hour on the level of "these are the rules and this is the sequence of their application," but I have stuck with it since then because I wanted to understand it well enough that the proof they chose to use would seem obvious to me. If you saw "understanding math" like the peak of a mountain, you'd get there a lot more quickly, but if you want to try out every permutation of every device and condition anything can take forever.
2. Algebra seems simple in retrospect, and my teenage self was kind of dumb. Maybe with my complete adult brain I'd be able to finish highschool starting from scratch in a few months. Evidence to that point is the pacing of college remedial math classes. Maybe, to a certain extent, people have an innate math setpoint that they will snap to very quickly when given the chance.
3. Intelligence is equally distributed between genders, but most professional physicists are men, which means that for every professor there is almost exactly one corresponding woman who has equal potential but isn't in the system. If you heard that the department chair at a university sat down and read a book about topology without a lot of trouble you wouldn't be surprised at all. In other words, it's not surprising that someone can do this, it's surprising that someone who can do this is not in the social bucket for people that do it, but if you think about the other things you've heard about that, you realize you already knew.
I am inclined towards #3 out of all these explanations but all may be true at once.
Re: So you want to study mathematics
#89I 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?
University of Washington
Re: So you want to study mathematics
#90I am bit surprised there is nothing about graph theory in there. Also nothing about combinatorics or knot theory to mention two other subjects. If you want to make people dive into mathematics, it might be a good idea to show a broad range of subjects instead of focusing on the traditional subjects.
It’s amazing how different the subjects of mathematics are. It’s like the difference between a drum and flute. You listed some of my favorite stuff. Weirdly, when I was 11, my math tutor told me I’d probably really like finite mathematics. She turned out to be right.
> It’s amazing how different the subjects of mathematics are. It’s like the difference between a drum and flute.
I think it’s amazing how connected the fields are. It’s almost like “pick any two of analysis, algebra, geometry, number theory, topology, turn one into a adjective and you’ve got a new subject area”.
Topological algebra? Check (https://en.wikipedia.org/wiki/Topological_algebra)
Algebraic topology? Check (https://en.wikipedia.org/wiki/Algebraic_topology).
Geometric topology? Check (https://en.wikipedia.org/wiki/Geometric_topology).
Geometric algebra? Check (https://en.wikipedia.org/wiki/Geometric_algebra)
Algebraic geometry? Check (https://en.wikipedia.org/wiki/Algebraic_geometry)
Geometric number theory? Close (https://en.wikipedia.org/wiki/Geometry_of_numbers)
Mix algebra, number theory, and topology, and you may end up with arithmetic topology (https://en.wikipedia.org/wiki/Arithmetic_topology)
And don’t confuse that with arithmetic geometry (https://en.wikipedia.org/wiki/Arithmetic_geometry)