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

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

#21

Post by zamalek »

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 wonder if it's even possible.

From a practical perspective it definitely is. I've picked up a fair amount of graph theory and with nothing but extreme persistence have grokked and used some fairly advanced stuff[1][2] (2nd-year dropout). It was, however, work-related. Just don't ask me to proof anything.

> the few lucrative jobs that make use of maths are in finance

There is also competency on the table here. Graph theory crops up day-to-day with the business software work I'm doing (three separate deliverables). Calculus is used to a point of absurdity in game development - e.g. the Fresnel term. Machine learning? Calculus, linear algebra, tensors. Profiling? A basic understanding of statistics. Compilers? Category theory, graph theory. Physics engines? ODE.

It's extremely valuable to know this stuff.

[1]: https://en.wikipedia.org/wiki/Tarjan%27s_strongly_connected_... [2]: https://eprint.iacr.org/2012/352.pdf

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

#23

Post by ryanmonroe »

zamalek wrote: post #21
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 wonder if it's even possible. From a practical perspective it definitely is. I've picked up a fair amount of graph theory and with nothing but extreme persistence have grokked and used some fairly advanced stuff[1][2] (2nd-year dropout). It was, however, work-related. Just don't ask me to proof anything. > the few lucrative jobs that make use of maths are in finance There is also competency on the table here. Gra…

>Just don't ask me to proof anything

I don't mean to offend, but being able to prove things is generally the main focus of advanced mathematics. If you can't prove what you know, or at least have a rough outline of a proof you could construct after referring to something, you haven't learned it in the same way those at a university have.

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

#24

Post by bitchy »

These books will kick your teeth in if you're not prepared. You either get a teacher who'll hold your hand or you need to gear up for fight(develop math maturity and learn all the tricks and tips). To the latter end, you can check out the Book of Proof by Richard Hammack[0] and Discrete Math by Susanna Epp[1].

[0] http://www.people.vcu.edu/~rhammack/BookOfProof/

[1] https://www.amazon.com/Discrete-Mathematics-Applications-Sus...

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

#25

Post by sotojuan »

elorant wrote: post #19
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…

You could learn math as a hobby, not because you're looking for a job. At least that's what I did. I like them for what they are and the immense satisfaction I get once I realize how a certain theory works. Other than that I don't expect any material reward from that knowledge.

This is a good point. Many of us learn a new language or tool as a hobby after work. Why not consider math like that?

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

#26

Post by zamalek »

ryanmonroe wrote: post #23
zamalek wrote: post #21

Earlier quoted context omitted.

> I wonder if it's even possible. From a practical perspective it definitely is. I've picked up a fair amount of graph theory and with nothing but extreme persistence have grokked and used some fairly advanced stuff[1][2] (2nd-year dropout). It was, however, work-related. Just don't ask me to proof anything. > the few lucrative jobs that make use of maths are in finance There is also competency on the table here. Gra…

>Just don't ask me to proof anything I don't mean to offend, but being able to prove things is generally the main focus of advanced mathematics. If you can't prove what you know, or at least have a rough outline of a proof you could construct after referring to something, you haven't learned it in the same way those at a university have.

No offense taken, you are completely correct. I can, however, still explain it and use it.

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

#27

Post by ryanmonroe »

mathgenius wrote: post #14

This stuff is brutally difficult to learn from books. Sigh. Maybe in the years since I studied this as an undergraduate things have changed with youtube and so-on. But there is nothing quite like talking to a real mathematician. One minute you are asking a question about some little thing you are stuck on, and the next minute the master is levitating and bending spoons! That's when you start to feel the real depth be…

I'd say the biggest benefit of being in the present year when learning math from a book is the availability of online resources like Stack Exchange where you can ask experts about the material you're learning if you get stuck. It's also nice that most books are available in pdf form so you can pick up multiple books on each subject you learn and easily switch back and forth between them.

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

#28

Post by ryanmonroe »

tgb wrote: post #15
biofox wrote: post #3

I have found the Chicago undergraduate mathematics bibliography useful for directing self-study: https://www.ocf.berkeley.edu/~abhishek/chicmath.htm Previously discussed on HN: https://news.ycombinator.com/item?id=9927909

As a math grad student, I can say that this Chicago list has primarily books that mathematicians know. The one posted here has primarily books that I am unfamiliar with. If one were to follow that one, other people trained in math would have a hard to judging what you've done (it's common to say things like "I've learned algebra at the level of Dummit and Foote" but this only works if people know the book you're refe…

An added benefit to learning from a book that's more popular is that if you hit a wall and have a specific question about the material as it's presented in your book, you're more likely to find your question answered online. You might even be able to find course material that follows the book, whether from an official online course or just because the professor at some university didn't bother to make the course page blocked off from non-students.

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

#29

Post by empath75 »

ryanmonroe wrote: post #23
zamalek wrote: post #21

Earlier quoted context omitted.

> I wonder if it's even possible. From a practical perspective it definitely is. I've picked up a fair amount of graph theory and with nothing but extreme persistence have grokked and used some fairly advanced stuff[1][2] (2nd-year dropout). It was, however, work-related. Just don't ask me to proof anything. > the few lucrative jobs that make use of maths are in finance There is also competency on the table here. Gra…

>Just don't ask me to proof anything I don't mean to offend, but being able to prove things is generally the main focus of advanced mathematics. If you can't prove what you know, or at least have a rough outline of a proof you could construct after referring to something, you haven't learned it in the same way those at a university have.

And? You can use advanced math without having a deep understanding of it.

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

#30

Post by chestervonwinch »

ryanmonroe wrote: post #28
tgb wrote: post #15

Earlier quoted context omitted.

As a math grad student, I can say that this Chicago list has primarily books that mathematicians know. The one posted here has primarily books that I am unfamiliar with. If one were to follow that one, other people trained in math would have a hard to judging what you've done (it's common to say things like "I've learned algebra at the level of Dummit and Foote" but this only works if people know the book you're refe…

An added benefit to learning from a book that's more popular is that if you hit a wall and have a specific question about the material as it's presented in your book, you're more likely to find your question answered online. You might even be able to find course material that follows the book, whether from an official online course or just because the professor at some university didn't bother to make the course page…

I've found this to be a big plus in my experience. Additionally, if you're question has not been answered, you at least have the benefit of widespread familiarity with the text you are using. This means friendly internet folk will have less mental overhead due to notation, etc., and less of a barrier to answering your question if you ask.
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