Here is the best mathematics course on YouTube:
Introduction to Higher Mathematics (Bill Shillito) - https://youtube.com/playlist?list=PLZzHxk_TPOStgPtqRZ6KzmkUQ...
So you want to study mathematics
241–250 of 371 posts
Re: So you want to study mathematics
#242The curriculum guides Susan Rigetti provides are an amazing resource for self-study. And the fact that she worked through all of this is truly inspiring. Not to be greedy, but do any of you know of other thorough curriculum guides like this? I know about https://teachyourselfcs.com already -- another amazing guide. Are there others? I would love to find one for statistics especially, but really any subject would be i…
I posted recently asking for exactly this... but for medicine.
I have a body, everyone I know has a body.
The operate pretty much the same everywhere in the world.
I would like to know how it works.
Re: So you want to study mathematics
#243This felt like it was written by a physicist or engineer. Too much emphasis on differential equations and not enough on things like topology, functional analysis and/or non-introductory parts of algebra like say representation theory.
As someone studying teaching math, I found it interesting to compare her suggestions:
- Calc I-IV
- Intro to proofs
- Linear algebra
- (Abstract) algebra I-II
- Real analysis
- Complex analysis
- Ordinary differential equations
- Partial differential equations
- (Others)
- A couple teaching courses (including one for roughly grades 5-8)
- Calc I-IV
- Statistics (one without calc, one with)
- Linear algebra
- Discrete
- Geometry
- Number theory
- History of math (apparently not just a history class, I haven't taken it yet)
- Abstract algebra and into to topologyRe: So you want to study mathematics
#244Earlier quoted context omitted.
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 descr…
Anything besides a cursory layperson's outlook on a lot of these topics (besides basic logic and history/philosophy of math -- although not sure how you would teach the last two/what you have in mind as curriculum) requires calculus and/or linear algebra. There is a reason they say you can never learn too much linear algebra. And yes probability and statistics are fundamental. I was shocked a bit when I learned it wa…
A decade+ ago when I was in school, the policy was to push honors and AP classes for "college-bound" students. Stats (not offered as honors or AP in my school) was one of the fun courses that co-op kids got to take while we were stuck in pre-calc.
Re: So you want to study mathematics
#245Are 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 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”?
Re: So you want to study mathematics
#246Are 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.…
It depends on which department you take math course in. Any course offered in a math department, even statistics and probability will be treated formally there because that's what mathematics is. What you probably need is to take math courses from an applied mathematics department like physics or engineering.
But math is a broad field so you're going to have to pick specific courses. For example, partial differential equations are quite common. But if you learn it in a math department it'll have proofs and full rigour just like a course in set theory. While some techniques for solving them will be covered, we mostly study the underlying mathematical structures, why certain techniques work, etc. If you take it in a physics department they'll teach you techniques and numerical methods to solve a certain class of problems like heat equations or fluid dynamics. But learning through direct applications will inevitably limit you to those techniques while learning things in full generality tends to make it easier to pick up specific techniques when needed.
Re: So you want to study mathematics
#247Are 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 dunno, at that point, are you really doing math? Math is proof. Now, granted, nobody expects you to know exactly how everything is proved. But there is an expectation that you can prove most of the stuff. Otherwise, it's very easy to stray from the truth into the plausible-sounding, but incorrect. That said, you're absolutely correct that more justification and motivation is important. So much of math can be taught…
We're now at a point where college math departments have to offer an "introduction to proofs" for students who have never seen one. Even high school geometry is now taught with few or no proofs.
Re: So you want to study mathematics
#248[deleted]
Re: So you want to study mathematics
#249If doing math is essential to conceptual understanding and application, could the interface of math and physics be made more human-centered? For instance, the shift from Roman numerals to Arabic numerals made doing math easier. Based on your experience, might it be possible to increase accessibility by revising some of the arcane conventions of math and physics? See Brett Victor’s 2011 proposal: http://worrydream.com…
Sure, an introductory notation could be created to bridge the gap, and that could be more human friendly.
That said, as someone who uses notation for math regularly, I want to keep using notation. It’s a helpful tool, and it is an efficient and precise language.
Re: So you want to study mathematics
#250Earlier 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…
I think calculus and trigonometry shouldn't be taught to non-math majors. You have the perspective of someone who is passionate about calculus, which is great, but considering many people aren't as passionate, what you're suggesting (status quo) doesn't work. Or maybe you have ideas on teaching calculus better than how it's currently done? Calculus is obviously extremely important, but I don't think it's useful to drill a few things that most people will quickly forget after the test.
I do think logic is important, and teaching that instead of focusing on math proofs might be a good alternative.