How to Learn Advanced Mathematics Without Heading to University

Re: How to Learn Advanced Mathematics Without Heading to University – Part 3

#151

Post by ska » Tue, Sep 06, 2016, 1:35 PM UTC

Chris2048 wrote: post #42

ploika wrote: post #40

Earlier quoted context omitted.

You won't do a calculus class for mathematicians without also heaps of real analysis and/or measure theory. It's a different story for a field like engineering, but that's not what the blog post is about. If you haven't studied the proofs, you haven't studied advanced mathematics. As for Bayesian vs. Frequentist, it's another vim vs. emacs style debate most of the time - which is most appropriate to use, as opposed t…

Isn't there a very small demand for actual, proof-writing mathematicians, versus "mathematicians" in the sense that they can use advanced math. I'd say being able to use advanced math, even for engineering, is a suitable definition for "having studied advanced mathematics".

   'versus "mathematicians" in the sense that they can use advanced math.'

Those people are not "mathematicians", they have other useful names (most physicists, bio-statisticians, some engineers, etc.)

Mathematicians are people who create new mathematics, not people who use mathematics.

Re: How to Learn Advanced Mathematics Without Heading to University – Part 3

#152

Post by optimuspaul » Tue, Sep 06, 2016, 1:59 PM UTC

nextos wrote: post #122

fromMars wrote: post #107

Earlier quoted context omitted.

I have studied a lot of mathematics on my own. I did study physics as an undergrad. But, I went back and studied Real Analysis, Measure Theory, Combinatorics, Topology, and Stochastic Calculus. I have found, though, that while I have a decent grasp of the concepts my understanding and ability to solve problems isn't as strong as the math grad students who studied these topics deeply. I have found the knowledge useful…

I don't see anything stupid about learning advanced mathematics on your own if you have previously followed a rigorous undergrad in physics or compsci. Lots of mathematicians switch to a different subfield within their careers. And they do so by self studying, obviously. If your compsci or physics undergrad provided you with a decent degree of mathematical maturity, it should be doable. The problem here is that comps…

I disagree. I've been studying advanced math on my own for years with some success. I didn't have any rigorous undergrad experience, I don't even have a degree. But I also don't learn the same way most would, classrooms were never my forte, and I've found the way that advanced math is taught even just in textbooks lacks creativity.

Humans are capable of great things, don't discourage someone from trying.

Re: How to Learn Advanced Mathematics Without Heading to University – Part 3

#153

Post by Chris2048 » Tue, Sep 06, 2016, 2:02 PM UTC

ska wrote: post #151

Chris2048 wrote: post #42

Earlier quoted context omitted.

Isn't there a very small demand for actual, proof-writing mathematicians, versus "mathematicians" in the sense that they can use advanced math. I'd say being able to use advanced math, even for engineering, is a suitable definition for "having studied advanced mathematics".

'versus "mathematicians" in the sense that they can use advanced math.' Those people are not "mathematicians", they have other useful names (most physicists, bio-statisticians, some engineers, etc.) Mathematicians are people who create new mathematics, not people who use mathematics.

Where does that definition come from?

I feel the term is often used more broadly.

http://c2.com/cgi/wiki?MathematicianDefinition

In any case, the point stands - The need for persons who can construct mathematical proofs, versus those who simply need to derive the correct numerical result, is very different.

As such, most classes that teach calculus are for practical, applied purposes - who don't need to "prove what they know" beyond demonstration procedural competence.

Re: How to Learn Advanced Mathematics Without Heading to University – Part 3

#154

Post by Roodgorf » Tue, Sep 06, 2016, 2:24 PM UTC

whorleater wrote: post #110

svanderbleek wrote: post #101

Earlier quoted context omitted.

I hope it is not stupid. I won't fit inside the university system at this point. They would make me take courses on subjects I already know which is a waste. I have about 20 hours on the weekend I can use towards accomplishing a class and I will have minimal waste since my curriculum is tailored directly for me. Of course it is only because I already wasted a decade learning math poorly that I know what I want to kno…

Prerequisites for classes are oftentimes a suggestion, you can easily get into a class you don't meet the prerequisites for by simply signing up for the class (most class registration systems don't bar this), or by emailing the professor and getting an override. Furthermore, if you're a non-degree seeking student, the university cares very little about you, so you can skate by with a lot more freedom with classes.

> most class registration systems don't bar this

Interesting, anecdotally, I went to three different universities and they all barred this from happening without an explicit override from a professor or occasionally an adviser. Just curious what experience you have that makes you say this?

Re: How to Learn Advanced Mathematics Without Heading to University – Part 3

#155

Post by chris_wot » Tue, Sep 06, 2016, 2:25 PM UTC

Retra wrote: post #138

chris_wot wrote: post #117

Earlier quoted context omitted.

Its it stupid at all. I taught myself Triginometry from a book for fun . Sure, not everyone's idea of a good time but I don't see the need to take a University or College course for lots of money when in fact I only spent about AU$34.95 on a good book and I didn't need to feel rushed in getting to grips with the concepts. I learn different things at different speeds, a course makes me go at a speed I don't enjoy. Thi…

I'm not sure there are many places where Trigonometry is considered advanced mathematics.

Rather missing the point I fear.

Re: How to Learn Advanced Mathematics Without Heading to University – Part 3

#156

Post by fsloth » Tue, Sep 06, 2016, 2:29 PM UTC

kragen wrote: post #105

p1esk wrote: post #98

Earlier quoted context omitted.

* the most advanced math I had was Algebra 2* How could you get a BS in CS without taking calculus courses? Which school did you go to?

It's kind of a shame that so many schools push you to study calculus in order to study CS; digital computers are algebraic machines, not analytical ones, pace Babbage. Combinatorics and graph theory would be far more useful. (Although maybe this will change with machine learning.)

Computers would be darn boring without calculus. Graphics, games, audio, animation - basically anything enabling creativity on a computer needs calculus tools. The interesting bits start to happen once one has built sufficient substrate out of the discrete parts. This is my personal opinion only, of course.

Re: How to Learn Advanced Mathematics Without Heading to University – Part 3

#157

Post by clarry » Tue, Sep 06, 2016, 2:31 PM UTC

throwaway729 wrote: post #109

bpchaps wrote: post #89

Earlier quoted context omitted.

Sometimes the issue isn't time - it's money and access to schooling. Just because you've had the access, doesn't mean others do - and there are many, many who don't.

> Just because you've had the access, doesn't mean others do... I don't think that the author of the post you're responding to is making any sort of normative claim. > Sometimes the issue isn't time - it's money and access to schooling I think the author is suggesting that if you have that kind of free time, then you either a) must be independently wealthy, or else that b) trading some of that free time for cash you…

I don't think it's a decent assumption for "almost everyone" in the west. I'd say it often is the case that you won't have enough free time for such studies unless you trade cash (income) for the free time. At which point you may not have much after paying the bills. Or you're unemployed and, well, don't have the cash. You suggest trading some of that free time for cash, as if unemployment were something people solve by snapping their fingers and choosing to make a trade. That sounds a bit insulting towards all the people (who are many) that struggle with unemployment in western countries.

Re: How to Learn Advanced Mathematics Without Heading to University – Part 3

#158

Post by clarry » Tue, Sep 06, 2016, 2:35 PM UTC

yodsanklai wrote: post #17

> How to Learn Advanced Mathematics Without Heading to University I wonder if it's even possible. Learning maths requires much work, time and dedication. Doing so alone must be very difficult. There are several things universities provide that are hard to replicate alone: a degree, which gives you access to a job, motivation, learning environment, and "peace of mind". What I mean by peace of mind is that, when you're…

I find that educational institutions are incredibly good at killing motivation. And I can't have peace of mind knowing that only the constantly accumulating debt helps me pay the bills during a five or six-year session that I might not be able to endure due to the said killing of motivation. And that even if I graduated with a degree, it wouldn't automatically secure a job I like or a happy life.

Re: How to Learn Advanced Mathematics Without Heading to University – Part 3

#159

Post by whorleater » Tue, Sep 06, 2016, 2:39 PM UTC

Roodgorf wrote: post #154

whorleater wrote: post #110

Earlier quoted context omitted.

Prerequisites for classes are oftentimes a suggestion, you can easily get into a class you don't meet the prerequisites for by simply signing up for the class (most class registration systems don't bar this), or by emailing the professor and getting an override. Furthermore, if you're a non-degree seeking student, the university cares very little about you, so you can skate by with a lot more freedom with classes.

> most class registration systems don't bar this Interesting, anecdotally, I went to three different universities and they all barred this from happening without an explicit override from a professor or occasionally an adviser. Just curious what experience you have that makes you say this?

Huh, I've attended classes at two universities: one for my undergraduate and one while I was in HS, and neither had a system in place to explicitly bar you from registering for a class whose pre-reqs you didn't fulfill. At best you'd get a scary message confirmation message telling asking you "You don't meet the pre-reqs, you may be dropped from the class, are you sure?".

Also, at least when I was an undergrad, the Banner student system (from ellucian company) had no system in place for barring you from registering from classes. This was frequently the point of discussion between the professors that I TA'd for.

Re: How to Learn Advanced Mathematics Without Heading to University – Part 3

#160

Post by atondwal » Tue, Sep 06, 2016, 2:42 PM UTC

lumberjack wrote: post #83

This is stupid. The hard part about a Math degree is the number of hours you have to put in. If you cannot go to university full time, go part time. If you cannot go part time, you don't have enough time to actually learn any of these topics on your own. I've done these classes. It's typically 150 hours per class and it's not something you do after coming exhausted home from work either. After those 150 hours you'll…

This course of study seems to take just as much, if not more, time than a math ugrad+master's at a typical uni. The people who could really benefit from having a path of textbooks like this fall into two categories: those who don't have access a university (due to poverty, rural location, and/or being a shift worker, for example), and high school students.

And I think the latter category is more important than people realize. When I was a high school student, I benefitted greatly from t'Hooft's theorist.html (like this, but for physics, and put together by one of the Greats of the field). It's part of what got me really interested in physics, it was a whole lot of fun, and it actually did a pretty good job of preparing me for graduate-level coursework. Eventually I left physics and math for CS (I'm in PL, so this is even less drastic of career change than one might think), but I still have warm memories of working along t'Hooft's guide and checking off topics as I finished the problems in each textbook.