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

quantstart.com

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

#11

Post by shogunmike »

Chris2048 wrote: post #7
Hnrobert42 wrote: post #2

Am I missing something? This just appears to be a link to buy some guy's ebooks.

He lists ebooks on his blog, but this is a blog post. That said, I'm not sure of the value of linking to part 3, unless the idea is it is the latest and already links back to parts 1 & 2.

Indeed, this is the latest article and it does link back to parts 1 & 2.

Each part of the series is designed to cover the "typical" modules on a UK four-year undergraduate Masters of Mathematics degree.

However, it can be challenging in the latter two years to include a broad enough set of modules to cover all interests, so I have had to stick to those "core" modules likely to be found in many degrees, as well as those more specifically related to quant finance and machine learning.

However, it is my hope that individuals will be motivated to look at other areas as well, even if they're not directly related to career paths!

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

#12

Post by shogunmike »

mathgeek wrote: post #6
Hnrobert42 wrote: post #2

Am I missing something? This just appears to be a link to buy some guy's ebooks.

There are about a half dozen ads (and a fade-in popover) above the actually content. It's a terrible site design from the perspective of someone wanting to read the content on mobile, but the article is there. I also just left without reading it, due to the ads.

Thankyou for the necessary feedback!

I'm actually in the process of overhauling the design of the site, particularly with regards to mobile, as the current Bootstrap-derived design pushes all sidebar content to the top on mobile/table.

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

#14

Post by mathgenius »

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 behind the concepts. It doesn't come from books.

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

#15

Post by tgb »

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 referring to).

On the other hand, books written for mainstream math majors and graduate students are not necessarily the ones best suited for an autodidact. Perhaps the author of this post has selected those that are more appropriate, but I can't judge. Also, Springer is a great name in math books and you generally don't go too far wrong by sticking with them, but I've never seen their undergraduate series before. Perhaps they're more common in the UK than the US?

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

#16

Post by Chris2048 »

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…

You want an amazing, 21st century math tutorial?

I was astounded by this: https://acko.net/blog/how-to-fold-a-julia-fractal/

Amazing intro to complex numbers.

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

#17

Post by yodsanklai »

> 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 a student, your job is to study, that's what you're expected to do and normally your degree will give you access to a job (esp. if your university is reputable).

Now suppose someone learns advanced maths on their own. There's a huge opportunity cost. Not only it takes a lot of time, and the few lucrative jobs that make use of maths are in finance. I suspect financial institutions are very conservative and rarely recruit someone without a proper academic background.

An other thing when learning things alone, is that your job is twofold. You must be teacher and student at the same time. You need to find the material, impose yourself some pacing, decide when it's ok to move on etc... It may be ok when you want to learn a new technique in a field you already know, but something as broad as "learning advanced mathematics" seems impossible.

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

#18

Post by Chris2048 »

Chris2048 wrote: post #16
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…

You want an amazing, 21st century math tutorial? I was astounded by this: https://acko.net/blog/how-to-fold-a-julia-fractal/ Amazing intro to complex numbers.

also: https://acko.net/files/gltalks/toolsforthought/

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

#19

Post by elorant »

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.

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

#20

Post by Chris2048 »

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…

What I actually need is "learning math in a short time",

With a few, minimal yet illustrative examples (ala katas), plenty diagrams/illustrations and other mental aids, an no rigour - not a single bit of set-theory!

The proofs and rigor can come later...

Incidentally, I'm a dev in finance, looking to move into quant dev. I have a math degree (completed 2007) and I'm doing a "CQF" to catch up with the relevant quant knowledge. I think cyptography, and stats/data analytics might also be a good area for mathy-dev.

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